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# Excel 2010 Data Analysis ### Introduction The popularity of Excel around the world needs no explanation. It includes almost all the features to satisfy the needs of professionals. Microsoft Excel also bundles strong features for statistical and engineering calculations. All such features are called Data Analysis techniques and Excel contains the Data Analysis (aka. Analysis Toolpak ) tab. ### How To Enable Data Analysis ( Analysis Toolpak) Data Analysis(Analysis Toolpak) is an add-in for Microsoft Excel which is disabled by default. To enable it click the Office button, then go to Options. Click on the Add-Ins option and you will see Analysis ToolPak option in the list. Hit the Go button at the bottom. Now select the Analysis Toolpak option and click OK to complete the configuration. ### How To Access Data Analysis Once you have enabled it, go to the Data tab and locate the Data Analysis option under the Analysis category. ### A Bird’s Eye View Of Data Analysis In order to use the Data Analysis feature of Excel, you must be familiar with Engineering and Statistical terminology. Hit the Data Analysis option and it will launch the screenshot as shown below. Now choose the appropriate option and Excel will process your data according to the option that you selected. Followings is the list of Engineering and statistical functions which you can perform with the Data Analysis option. • Anova: Single Factor • Anova: Two-Factor with Replication • Anova: Two-Factor Without Replication • Correlation • Covariance • Descriptive Statistics • Exponential Smoothing • F-Test Two Sample for Variance • Fourier Analysis • Histogram • Moving Average • Random Number Generation • Rank and Percents • Regression • Sampling • t-Test: Paired Two Sample for Means • t-Test: Two-Sample Assuming Equal Variances • t-Test: Two-Sample Assuming Unequal Variances • Z-Test: Two-Samples for Mean • Pingback: Excel 2010 Regression Analysis() • Ross THANKS SO MUCH!!! I’ve been trying to figure out why I couldn’t do this for a while. • Lacey Thanks for posting this! I’m pretty frusterated. I’m taking Advanced Statistics for school and our textbook has instructions for Excel 2007 and earlier, and 2010 is a whole new monster, so this was VERY helpful! • Amer Thank you. I was about to give up until I found this post. Now I can do my homework 🙂 • Julie Me, too! • vipul chavda GREAT HELP i was confused regarding the use of excel 2010 in reasearch like t-test and z test. anova n all. this virtually solved all my probs. thanks again • nila i followed the step given here but still i don’t find data analysis in my data ribbon. what should i do? • Abc go to the data tap on excel, at the end you will find out data analysis • Lulu This was very helpful. Thanks a lot. I could not find the right function for the last month and this has helped me. • Eric Thank you so much!!!! • Allie Thank you so much this was extremely helpful!! • saeideh thanks • Valerie Thank you so much for this post, my professor only gave instruction for how to use ANOVA on Excel 2003 and 2007. I was wonder why I didn’t have a Data Analysis in my toolbar. This was very helpful. • Vikki Manogg I too followed these steps but don’t find the Data Analysis on my ribbon – help • guest I have a mac and had no luck finding it either. • JJamison THANK YOU THANK YOU THANK YOU !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! • JJamison THANK YOU THANK YOU THANK YOU !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! • Jacob374 Thank you thank you thank you • Abi thanq u sir 🙂 • Henk You’re the man!! Thanks! • Nguyenthuy151 thanks very much!!! • Luke BOOM – THIS IS MAGIC – THANKS FOR MAKING MY LIFE EASY! • Ankur Prod thank you so much • Xran42 this helps me so much, ive spent like hours to figure out where the “TOOL” is lol. homework.. • guest GOD BLESS YOU!!!!!!!!!!! u have no idea how much you have helped me right now…thank you soooo much!!!!!!! • Dee Thank you very much.. Now I can do my assignments. Love you… • Shri Thanks so much for giving information • Cecilia Yanez awsome • vander Why i can’t find Add-in button in Option there? • Edouard because you don’t have excel commercial so you can’t use anova • Soundharya leakha thanks alot • Alicianeille Thanks!!! Have been wracking my brain for hours trying to do this! And project is in, in 3 days! You are simply a life saver!!! 🙂 thank you a lot, helpful information • zahra Realy goooooooooood Thanks a lot… • LION THANK YOU SO MUCH • Jake • Biddser Fair Play Buddy • tb thanks 🙂 • sunny boy many thanks, it is really help a lot. • Billy Thanks!! • Billy Thanks!! • Julia Guys you are great!!!! Thanks a lot • rajnish thank you for suggestion for instlling data analysis sir • Laz Than you. It has really made my day. • Sarah Thank you very much for taking the time to help people when you don’t even get paid for your work. • paul kayemba am moved and can proceed now • my defense is this afternoon and I just found this post this morning! Thank you very much!! • salman Rahi thanks its v help full through this i mad my assignment easily thanks alot • Liz I completed the Add-in but I do not see Data Analysis (or Solver) – all I see is What If Analysis – please help • Liz I completed the Add-in but I do not see Data Analysis (or Solver) – all I see is What If Analysis – please help • Raj IT IS GREAT WAS REALLY HELPFUL. • stephen GReat!!!! Love it … • Laura Thank you….like Amer I was about to give up…thanks again. • Pratik • Chita Hello, I have Ms 2010 and I have been doing as above million times but it doesn’t work. Data analysis did not show on tool bar. It doesn’t ask me to install. Once I click OK then it gone. When I check on Add-ins it shows that it already active. Is anyone can help me please… • Kyroman Thank you! We’ve spent lots on time with SPSS while it is all so easy in Excel! • Tee thank you, thank you. • Ah could you please tell me how to smooth data by Excel • Make Thank’s a lot! It was very helpfull. I have an old version of excel at my job, and was so dissapointed by my new one. • catherine i did every step until analysis toolpack-go but still cannot find data analysis or analysis anywhere!!?? • Kevin Thanks! My prof. uses Excel 2007 while I have 2010, I didn’t know how to access it until now. • waqa wat about excel starter….where can u find it…. • Angel Great Job… • Chris Thank you! this really helped me out • Kevin At last, after countless hours trying to understand why all the posts for producing bell curves refered to the data anlysis section…..which of course didn’t exist until I came across this invaluable information. Many, many thanks, greatly appreciated. I can’t help wondering why this isn’t made public knowledge or referenced more clearly in Excel. What the heck I have it now…well done you guys! • leaof thank you very much. But now I’m still can’t understand it. hixxx . ohhh my homework • PharmGeek It’s pretty frustrating to hide this several menues deep. With all the customization availabel in this version, how do I add frequently used functions, like regression analysis, to a top level toolbar? • Catherine I know people have already said thank you, but what i should actually say is you are the boom excellent!!!!! 10/10 • Poli Thank a lot! Very useful and well described. THANKS! • amna data analysis option is not showing in my excel 2010 even after this above process and i need it too much 🙁 • amna help • Christy Wolf Very helpful! Still works for me today, thank you!
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# Another interesting BJT DFF circuit A project log for Clockwork germanium A retro version of Yet Another (Discrete) Clock, with vintage parts Yann Guidon / YGDES 01/09/2017 at 03:2517 Comments 20200222 : see update at the bottom I've been pretty confused by the 2-transistors latch that is shown on the project details page. I've been looking of a simpler, yet compact DFF circuit that uses few transistors. Today I've done some research on the subject of #CBJT Logic and I came across this PDF : http://orbit.dtu.dk/fedora/objects/orbit:91667/datastreams/file_0b85d918-7d44-40c2-b7c7-a4332b0ce2b6/content "Figure 5 shows the realization of a triggered bistable circuit with complementary transistors. The set-reset function is here performed by a symmetrical transistor; if A is 0 volts (true value, "1"), the symmetrical transistor will work as an emitter follower and, by a pulse at its base, set the bistable circuit; if A is not 0 volts (false value, "0"), the transistor will work as a collector follower and, by a pulse at its base, reset the circuit." The latching cell contains a OC47 and OC141. OC141 is NPN germanium, OC47 is PNP (like the OC70 I have). I am confused by the transistor symbols but I can try to reverse-engineer the circuit... The right side is the latching part so the base loops to the collector of the other... How do I interpret the OC141 with 4 pins ? Well the right and left are probably the same node... Creating a latch cell is pretty easy and does not depend on the polarity of the transistor so that's not critical. What I'm after is a way to change/force the value with the least parts possible and the OC141 on the left does just that. This is the most interesting part ! Let's notice the two capacitors (of identical values: 4.7nF) and the resistor divider (10K, 10K) on the A input. The capacitor on A stores the data's charge, while the series input resistor isolates it from the source circuit (probably to reduce data leakage while it changes from a simultaneous clock pulse). The base is clearly (from the text) connected to the resistor divider 22K/2K, energised by the clock signal, through the series capacitor. The point is clearly how they use a NPN to work as a "pass gate", while the input value is held in the capacitor. The clock capacitor has a similar value so both discharges are simultaneous. Now, the awaken @esot.eric will notice that when A is low, B is high and a rising pulse appears on T, then the pass transistor is ... reverse biased ? Current will flow from B to the input capacitor (but not A because of the resistor). Does that remind any Eric of a "almost functioning" circuit with a mistaken transistor ? Whatever the case, it's very interesting because each DFF uses only 3 transistors, no diode (though I'll add one for the reset), and the circuit can be tuned for other voltage rails. It shouldn't be hard to modify it for an all-OC70 design. With "only" 3 transistors, plus 2 to drive the outputs, the whole clock system requires something like 39DFF×5=195 transistors. Add some more for housekeeping (oscillator, buffers, drivers, decoders...) and this might reach 250 transistors, which is a desired outcome. The "pass trick" exposed above might be the detail that makes this whole project realistic. 20200222 : I played more with Falstad and made the above circuit work for #Bipolar Discrete UART ! The input must be either floating (1) or grounded ( < 800 ohms) and the output has a diode to prevent any leakage that would override the current state (but can be ignored if a NPN base is driven through a 22K resistor for example) ## Discussions esot.eric wrote 01/09/2017 at 12:29 point erm, "the awaken esot.eric" is darn-near passing out, and somehow missed that bit when he was awake... was that an update? Are you sure? yes | no Yann Guidon / YGDES wrote 01/09/2017 at 19:17 point I have the habit of writing logs progressively and add/modify significantly, due to my old computer having an unstable/suicidal browser... Anyway, it's interesting : has anybody tried to use a parallel pair of BJT but oe with swapped collector and emitter ? This would be a great pass gate ! Are you sure? yes | no esot.eric wrote 01/11/2017 at 06:22 point whew... this one's a bit above my head... but I think I see what you're saying. The low input to A and the high pulse from T causes that transistor to activate due to VCB's being forward-biased... that is, ignoring the rest of the circuit, which I can't quite wrap my head around. One thing catching my attention is the second NPN, which I think would be active during T's positive-pulse, regardless of A and B... via normal means (VEB being positively-biased). But, again, that's ignoring the PNP... there's too much going on here for my brain! FYI the "almost functioning circuit" was, in fact, "fully-functioning" per my needs, except that it was a buffer where I intended an inverter ;) Interesting question re: parallel/swapped BJTs. The idea being e.g. a regular ol' NPN-inverter/"switch", where B is your input, C is your output (usually pulled up via resistor), and E is connected to ground...? Except, throw a second NPN with all its inputs directly connected to the first, (completely parallel) except with C and E swapped? Wonder what the effect would be. Would the swapped transistor's lower VCE force the non-swapped transistor to stay out of the saturation-region? Are you sure? yes | no Yann Guidon / YGDES wrote 01/11/2017 at 09:31 point I was more thinking of a pass gate, with Base=command pulse, C and E being data signal nodes. C and E are swapped for the 2nd transistor for better symmetry. It's only an hypothesis, "just a hack" and I've not seen it anywhere, because I just want to keep the parts count low (those 50's era transistors are not dirt cheap and I'll need a significant amount). But if it works... Anyway the "old/vintage" Ge transistors are full of drawbacks, like low hFE, high leakage, slow, significant capacitance... Fortunately the clock project requires rather "slow" circuits so I can make crazy compromises, like with the 10TFF :-D Are you sure? yes | no esot.eric wrote 01/11/2017 at 11:27 point Ahh "pass-gate" ~= 4016/4066...? I see, then if they're parallel, it'll "pass" in both directions equally. Are you sure? yes | no Ted Yapo wrote 01/11/2017 at 13:25 point Yes, years ago.  I could never get it to work - but I was looking at analog signals.  If you need to pass only a 0 or 1, maybe you can do it. Are you sure? yes | no Yann Guidon / YGDES wrote 01/11/2017 at 21:43 point @Ted Yapo: yes, but after reading @esot.eric's adventure, I see that it's possible to use a single transistor instead of 2 in reverse, however, i my case, the buffer cap should be larger (5× ?) I'll try whenever my workshop is operational again. Are you sure? yes | no Thomas wrote 01/09/2017 at 06:10 point The transistor symbol alone is intriguing. I tried to find it used or explained anywhere else, without results so far. Does anybody know of some references? Are you sure? yes | no jaromir.sukuba wrote 01/09/2017 at 06:46 point It's probably derived from internal looks of alloy-junction transistors, see below. Are you sure? yes | no jaromir.sukuba wrote 01/09/2017 at 07:09 point Funny enough, the "normal" transistor symbol actually refers to old point-contact transistor arrangement, the "weird and old" from Yann's document refers to newer (though still fairly old) alloy transistor. Are you sure? yes | no Thomas wrote 01/09/2017 at 18:16 point Thanks, that's great! The "alternative" symbol looks much cooler (and it's faster to draw, too). Are you sure? yes | no Yann Guidon / YGDES wrote 01/09/2017 at 08:59 point Thanks Jaromir :-) That's what I suspected :-) Are you sure? yes | no esot.eric wrote 01/09/2017 at 03:56 point LOL Those transistors are *weird* looking. Four ports? Are you sure? yes | no Yann Guidon / YGDES wrote 01/09/2017 at 03:59 point Old convention... Only 3 pins but one side is "logically" connected to the other, to the base. Probably related to how transistors in the 50s were made (drift, diffusion, etc.) I am trying to figure out which is the collector and emitter though but it will be deduced in the next minutes. Are you sure? yes | no Yann Guidon / YGDES wrote 01/09/2017 at 04:18 point Even WEIRDER are the voltages : -13V, -8.5V, 0V, 4.5V... Are you sure? yes | no jaromir.sukuba wrote 01/09/2017 at 05:44 point This schematics symbol is not that weird, considering in 50's, most of them were alloy-junction transistors looking internally like this the double base connection is relic from vacuum-tube days. Can't find an example, but I'm pretty sure I've seen schematics, where grid of simple triode was connected from both sides of schematics symbol, due to simpler "routing" of the schematics. Could be worse, with capacitances in uuF or even in cm. Are you sure? yes | no Yann Guidon / YGDES wrote 01/09/2017 at 08:58 point Exactly, thanks for the external references :-) Are you sure? yes | no
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Cody # Problem 44807. Number Power Solution 1684184 Submitted on 30 Nov 2018 by Jarhed Szalkowski This solution is locked. To view this solution, you need to provide a solution of the same size or smaller. ### Test Suite Test Status Code Input and Output 1   Pass n = 1; y_correct = 1; assert(isequal(pwr(n),y_correct)) y = 1 2   Pass n = 2; y_correct = 4; assert(isequal(pwr(n),y_correct)) y = 4 3   Pass n = 3; y_correct = 27; assert(isequal(pwr(n),y_correct)) y = 27 4   Pass n = 4; y_correct = 256; assert(isequal(pwr(n),y_correct)) y = 256 5   Pass n = 5; y_correct = 3125; assert(isequal(pwr(n),y_correct)) y = 3125 6   Pass n = 9; y_correct = 387420489; assert(isequal(pwr(n),y_correct)) y = 387420489
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FSU CGS 2518 - Midterm Exam Study Guide Answers Pages 11 Unformatted text preview: Midterm Exam Study Guide Answers Spring 2014 CGS 2518 Chapters 1 4 Answers to all Conceptual Review Chapter 1 1 What is the meaning of each of the following error messages NAME N A REF Value Num Div 0 If you enter 1 149 25 what value would result Insufficient Cell width Unrecognized text in formula No Answer Invalid cell reference Wrong Argument type Invalid numeric values in a formula or function Division by zero 2 The cell would display 1 149 25 3 If you enter 2 4 10 exactly as shown what value would result 4 List the orders of operations in order 1 Parenthesis 2 Exponentiation 3 Multiplication Division 4 Adding and subtracting 42 11 5 When writing formulas why is it preferable to use cell reference rather than typing in values Using cell references is preferable to directly inputting values into a formula because it allows the user to easily update the spreadsheet without having to know exactly which formula or formulas contain the changed value 6 In the worksheet below cell A3 contains the formula A1 A2 Explain the most likely reason the value calculated appears incorrect The most likely reason is that the format chosen for A1 and A2 will not show decimals Therefore if cell A1 is 1 4 and cell A2 is 2 4 the result in cell A3 is actually 3 8 which is displayed as 4 when rounding 7 Referring to the preceding worksheet if you wrote the formula B1 110 what value would result assuming the displayed value is the precise value Page 1 What formula would you write to do each of the following a Add a range of numbers in cells A2 X2 b Find the largest value in cells C2 C8 c Find the smallest value in cells B2 through Z12 d Find the average value in cells C1 through C10 ignoring blank cells e Find the total number of values in cells C1 10 excluding any that contain text SUM A2 X2 MAX C2 C8 MIN B2 Z12 AVERAGE C1 C10 0 COUNT C1 C10 8 Define the following terms syntax arguments and algorithm Syntax The specific format of a function including the function name and the order of the arguments Arguments A function input when putting a number and how many decimal places Algorithm A rule that governs how a function works A systematic set of procedures that the computer always steps through to calculate the results of a function 9 If the formula B 4 SUM C1 C5 is copied from cell A9 to cell C10 what is the resulting formula 10 Refer to the following worksheet What formula would you write in cell B2 that can be copied down the column and across the row to complete the multiplication table B 4 SUM E2 E6 SUM A2 B 1 11 What new formula results for each of the following if the formula is copied from cell C10 to cell E13 12 What formula could you use to add up cell B1 from Sheet1 Sheet 2 and Sheet 3 assuming the worksheets C4 C5 A 1 C5 A4 C5 C 1 C5 A1 A2 A 1 A2 A1 A2 A 1 A2 are contiguous and in the same workbook SUM Sheet1 B1 Sheet2 B1 Sheet3 B1 Page 2 13 Cell B1 has been given the range name discount How would you write a formula in cell C1 that multiplies discount by cell A1 What new formula results if you copy this formula into cell C2 discount A1 discount A2 Chapter 2 1 What formula could you write to calculate the mean of the following data set 2 5 4 3 1 2 7 2 What is the median value of the set 2 5 4 3 1 2 7 3 What is the mode of the data set 2 5 4 3 1 2 7 AVERAGE 2 5 4 3 1 2 7 MEDIAN 2 5 4 3 1 2 7 MODE 2 5 4 3 1 2 7 4 The data set 2 5 4 3 1 2 7 has a standard deviation of 1 58 as compared with another data set that has the same mean but a standard deviation of 2 5 What general differences would you expect to find between the two sets of data Since Standard deviation is the measure of range and distribution the larger standard deviation would result in a larger range of values 5 In the chapter the original labor rate for inspectors was given as 35 per hour However due to a contract renegotiation this value is now 37 50 What algebraic expression could you use to determine the percent increase in labor costs Note that a resulting value is not required 37 50 35 35 6 When using the increase decimal button on the toolbar the precise value in the cell is modified True or false 7 The formula Round 345 43 0 results in what precise value 8 Write a formula to round up 63 34 to the nearest percent ROUNDUP 63 34 2 9 What is the symbol for the greater than or equal to relational operator in Excel 10 What is the symbol for the not equal to relational operator in Excel False 345 Page 3 11 Review the following worksheet and then use the COUNTIF function to write a formula that determines the number of GM cars on this list COUNTIF A2 A10 GM 12 Using the worksheet shown in Question 11 write a formula to determine the number of cars that cost less than 20 000 COUNTIF B2 B10 20000 SUMIF A2 A10 Ford B2 B10 worksheet for question 11 13 Using the worksheet shown in Question 11 write a formula to determine the total value of all Ford cars 14 Explain the difference between a What if analysis and Goal Seek by giving an example based on the What if to determine the outcome of changing one or more input values and evaluate the recalculated results For example you could determine how changing the price of a Ford would affect the total cell Goal Seek tool that allows you to work backward to determine the input required that will ensure a specific outcome For example you could use goal seek to determine what price a Ford needs to be to make the total value over 200 000 15 Using the worksheet shown in Question 11 write a formula to determine the value of the third most 16 If each car shown in Question 11 is marked up between 50 and 250 increments what function could be used to randomly assign the amount to be added to the car price in this formula expensive car LARGE B2 B10 3 B2 RANDBETWEEN 50 250 17 The formula RAND gives what result Gives a random number between 0 and 1 Page 4 18 What formula could you write to average the values in cells A10 through A20 excluding blank cells rounded 19 Write a formula to determine the average price of only Ford vehicles using the worksheet in question 11 20 Write a formula to generate a random integer value … View Full Document FSU CGS 2518 - Midterm Exam Study Guide Answers Pages: 11 Documents in this Course 16 pages 13 pages 13 pages 22 pages 12 pages 12 pages 8 pages 12 pages 10 pages 13 pages 22 pages 10 pages 10 pages 10 pages 14 pages 21 pages 12 pages 10 pages 10 pages 12 pages 14 pages 8 pages 12 pages 12 pages 14 pages 10 pages 16 pages 9 pages 9 pages 13 pages 13 pages 13 pages 13 pages 9 pages 11 pages 11 pages 10 pages 11 pages 10 pages 10 pages 11 pages 10 pages 29 pages 14 pages 14 pages 14 pages 46 pages 22 pages 18 pages 9 pages 12 pages 11 pages 12 pages 16 pages 16 pages 13 pages 8 pages 8 pages 10 pages 8 pages 23 pages 13 pages 13 pages 10 pages 7 pages 10 pages 10 pages 5 pages 5 pages 12 pages 12 pages 13 pages 13 pages 10 pages 10 pages 13 pages 14 pages 13 pages 13 pages 7 pages 10 pages 9 pages 14 pages 9 pages 7 pages 9 pages 10 pages 10 pages 19 pages 19 pages 11 pages 10 pages 10 pages 10 pages 13 pages 6 pages 14 pages 6 pages 10 pages 10 pages 9 pages 9 pages 10 pages 11 pages 11 pages 11 pages 11 pages 9 pages 10 pages 10 pages 14 pages 11 pages 8 pages 14 pages 7 pages 7 pages 7 pages 17 pages 13 pages 17 pages
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# Search by Topic #### Resources tagged with Probability similar to Stop or Dare: Filter by: Content type: Stage: Challenge level: ### There are 25 results Broad Topics > Probability > Probability ### Stop or Dare ##### Stage: 2, 3 and 4 Challenge Level: All you need for this game is a pack of cards. While you play the game, think about strategies that will increase your chances of winning. ### Interactive Spinners ##### Stage: 3 Challenge Level: This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events. ### Red or Black Spinner ##### Stage: Early years, 1, 2, 3 and 4 Challenge Level: A simple spinner that is equally likely to land on Red or Black. Useful if tossing a coin, dropping it, and rummaging about on the floor have lost their appeal. Needs a modern browser; if IE then at. . . . ### Progression in Primary Probability ##### Stage: 1 and 2 The beginnings of understanding probability begin much earlier than you might think... ### The Lady or the Lions ##### Stage: 3 Challenge Level: The King showed the Princess a map of the maze and the Princess was allowed to decide which room she would wait in. She was not allowed to send a copy to her lover who would have to guess which path. . . . ### The Random World ##### Stage: 3, 4 and 5 Think that a coin toss is 50-50 heads or tails? Read on to appreciate the ever-changing and random nature of the world in which we live. ### Game of PIG - Sixes ##### Stage: 2, 3, 4 and 5 Challenge Level: Can you beat Piggy in this simple dice game? Can you figure out Piggy's strategy, and is there a better one? ### Misunderstanding Randomness ##### Stage: 3 Challenge Level: Which of these ideas about randomness are actually correct? ### An Introduction to Tree Diagrams ##### Stage: 3 and 4 This article explains how tree diagrams are constructed and helps you to understand how they can be used to calculate probabilities. ### Why Do People Find Probability Unintuitive and Difficult? ##### Stage: 2, 3, 4 and 5 Uncertain about the likelihood of unexpected events? You are not alone! ### How Random! ##### Stage: 2 Challenge Level: Explore this interactivity and see if you can work out what it does. Could you use it to estimate the area of a shape? ### Can't Find a Coin? ##### Stage: 3 Challenge Level: Can you generate a set of random results? Can you fool the random simulator? ### Tools for Thinking about Probability ##### Stage: 3 Challenge Level: Can you design your own probability scale? How do you describe the different parts? ### A Dicey Paradox ##### Stage: 3 Challenge Level: Four fair dice are marked differently on their six faces. Choose first ANY one of them. I can always choose another that will give me a better chance of winning. Investigate. ### Squaring the Circle ##### Stage: 3 Challenge Level: Bluey-green, white and transparent squares with a few odd bits of shapes around the perimeter. But, how many squares are there of each type in the complete circle? Study the picture and make. . . . ### Racing Odds ##### Stage: 3 Challenge Level: In a race the odds are: 2 to 1 against the rhinoceros winning and 3 to 2 against the hippopotamus winning. What are the odds against the elephant winning if the race is fair? ### What Do You Know about Probability? (2) ##### Stage: 3 Challenge Level: What are the likelihoods of different events when you roll a dice? ### Count the Beat ##### Stage: 1 and 2 This article, written by Nicky Goulder and Samantha Lodge, reveals how maths and marimbas can go hand-in-hand! Why not try out some of the musical maths activities in your own classroom? ### Twenty20 ##### Stage: 2, 3 and 4 Challenge Level: Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows. ### Con Tricks ##### Stage: 3 Here are some examples of 'cons', and see if you can figure out where the trick is. ### Nines and Tens ##### Stage: 3 Challenge Level: Explain why it is that when you throw two dice you are more likely to get a score of 9 than of 10. What about the case of 3 dice? Is a score of 9 more likely then a score of 10 with 3 dice? ### Do You Feel Lucky? ##### Stage: 3 Challenge Level: Some people offer advice on how to win at games of chance, or how to influence probability in your favour. Can you decide whether advice is good or not? ### From A Random World to a Rational Universe ##### Stage: 2, 3 and 4 In the time before the mathematical idea of randomness was discovered, people thought that everything that happened was part of the will of supernatural beings. So have things changed? ### Non-transitive Dice ##### Stage: 3 Challenge Level: Alison and Charlie are playing a game. Charlie wants to go first so Alison lets him. Was that such a good idea? ### Three Spinners ##### Stage: 2 Challenge Level: These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?
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• anonymous Which equation is a quadratic equation? 3x − y = 8x + 2 y = 7x(5 − 2x) + 9 7x2 + y = (3 + x)(7x − 1) y − 3 = (x2 − 3)(8x + 3) I think it's y = 7x(5 − 2x) + 9 because it looks like it's in standard form but I just want to make sure. Mathematics • Stacey Warren - Expert brainly.com Hey! We 've verified this expert answer for you, click below to unlock the details :) SOLVED At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat. Looking for something else? Not the answer you are looking for? Search for more explanations.
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Open in App Not now # Find the sum of medians of all odd length subarrays • Difficulty Level : Medium • Last Updated : 22 Feb, 2023 Given an array arr[] of size N, the task is to find the sum of medians of all sub-array of odd-length. Examples: Input: arr[] = {4, 2, 5, 1} Output: 18 Explanation : Sub-Arrays of odd length and their medians are : • [4]  -> Median is 4 • [4, 2, 5]  -> Median is 4 • [2]  -> Median is 2 • [2, 5, 1]  -> Median is 2 • [5]  -> Median is 5 • [1]  -> Median is 1 Their sum = 4 + 4+ 2 + 2 + 5 +1 = 18 Input: arr[] = {1, 2} Output: 3 Pre-requisites: Median of Stream of Running Integers using STL Naive Approach: Generate each and every sub-array. If the length of the sub-array is odd, then sort the sub-array and return the middle element. Below is the implementation of the above approach: ## C++ `// C++ program for the above approach` `#include ` `using` `namespace` `std;`   `// Function to find sum of medians` `// of all odd-length subarrays` `int` `solve(vector<``int``> arr) ` `{` `    ``int` `ans = 0;` `    ``int` `n = arr.size();`   `    ``// Loop to calculate the sum` `    ``for``(``int` `i = 0; i < n; i++) ` `    ``{` `        ``vector<``int``> new_arr;` `        ``for``(``int` `j = i; j < n; j++) ` `        ``{` `            ``new_arr.push_back(arr[j]);` `            `  `            ``// Odd length subarray` `            ``if` `((new_arr.size() % 2) == 1)` `            ``{` `                ``sort(new_arr.begin(), new_arr.end());` `                ``int` `mid = new_arr.size() / 2;` `                ``ans += new_arr[mid];` `            ``}` `        ``}` `    ``}` `    ``return` `ans;` `}`   `// Driver Code` `int` `main() ` `{` `    ``vector<``int``> arr = { 4, 2, 5, 1 };` `    ``cout << solve(arr);` `}`   `// This code is contributed by Samim Hossain Mondal.` ## Java `// Java program for the above approach` `import` `java.util.*;`   `class` `GFG {` `    ``// Function to find sum of medians` `    ``// of all odd-length subarrays` `    ``static` `int` `solve(``int``[] arr) {` `        ``int` `ans = ``0``;` `        ``int` `n = arr.length;`   `        ``// Loop to calculate the sum` `        ``for` `(``int` `i = ``0``; i < n; i++) {` `            ``List new_arr = ``new` `LinkedList();` `            ``for` `(``int` `j = i; j < n; j++) {` `                ``new_arr.add(arr[j]);`   `                ``// Odd length subarray` `                ``if` `((new_arr.size() % ``2``) == ``1``) {` `                    ``Collections.sort(new_arr);` `                    ``int` `mid = new_arr.size() / ``2``;` `                    ``ans += new_arr.get(mid);` `                ``}` `            ``}` `        ``}` `        ``return` `ans;` `    ``}`   `    ``// Driver Code` `    ``public` `static` `void` `main(String[] args) {` `        ``int``[] arr = { ``4``, ``2``, ``5``, ``1` `};` `        ``System.out.println(solve(arr));` `    ``}` `}` `// This code is contributed by 29AjayKumar` ## Python3 `# Python program for the above approach`   `# Function to find sum of medians` `# of all odd-length subarrays` `def` `solve(arr):` `        ``ans ``=` `0` `        ``n ``=` `len``(arr)` `        `  `        ``# Loop to calculate the sum` `        ``for` `i ``in` `range``(n):` `            ``new_arr ``=` `[]` `            ``for` `j ``in` `range``(i, n, ``1``):` `                ``new_arr.append(arr[j])`   `                ``# Odd length subarray` `                ``if` `(``len``(new_arr)) ``%` `2` `=``=` `1``:` `                    ``new_arr.sort()` `                    ``mid ``=` `len``(new_arr)``/``/``2` `                    ``ans ``+``=` `new_arr[mid]` `        ``return` `(ans)`   `# Driver Code` `if` `__name__ ``=``=` `"__main__"``:` `    ``arr ``=` `[``4``, ``2``, ``5``, ``1``]` `    ``print``(solve(arr))` `   ` ## C# `// C# program for the above approach` `using` `System;` `using` `System.Collections.Generic;` `class` `GFG` `{`   `  ``// Function to find sum of medians` `  ``// of all odd-length subarrays` `  ``static` `int` `solve(``int``[] arr) {` `    ``int` `ans = 0;` `    ``int` `n = arr.Length;`   `    ``// Loop to calculate the sum` `    ``for` `(``int` `i = 0; i < n; i++) {` `      ``List<``int``> new_arr = ``new` `List<``int``>();` `      ``for` `(``int` `j = i; j < n; j++) {` `        ``new_arr.Add(arr[j]);`   `        ``// Odd length subarray` `        ``if` `((new_arr.Count % 2) == 1) {` `          ``new_arr.Sort();` `          ``int` `mid = new_arr.Count / 2;` `          ``ans += new_arr[mid];` `        ``}` `      ``}` `    ``}` `    ``return` `ans;` `  ``}`   `  ``// Driver Code` `  ``public` `static` `void` `Main() {` `    ``int``[] arr = { 4, 2, 5, 1 };` `    ``Console.Write(solve(arr));` `  ``}` `}`   `// This code is contributed by Saurabh Jaiswal` ## Javascript `` Output `18` Time Complexity: O(N3 * Log(N)) Auxiliary Space: O(N) Note: Instead of sorting array each time, which costs (N*logN), insertion sort can be applied. But still, overall Time Complexity will be O(N3). Efficient Approach: The median of the sorted array is the value separating the higher half from the lower half in the array. For finding out the median, we only need the middle element, rather than the entire sorted array. The approach of Median of Stream of Running Integers can be applied over here. Follow the steps mentioned below 1. Use max and min heaps to calculate the running median. 2. Traverse each and every element in the array. 3. While creating a new subarray, add an element into the heaps and return median if the size is odd else return 0. 4. Max_heap is used to store lower half elements such that the maximum element is at the top and min_heap is used to store higher half elements such that the minimum element is at the top. 5. The difference between both the heaps should not be greater than one, and one extra element is always placed in max_heap. Note: Here max_heap is implemented using min_heap, by just negating the values so that the maximum negative element can be popped. Below is the implementation of the above approach: ## C++ `// C++ program for the above approach` `#include `   `// Class to find median` `class` `find_median {` `  ``public``:` `  ``// Constructor to declare two heaps` `  ``find_median()` `  ``{` `    ``// Store lower half elements such that` `    ``// maximum element is at top` `    ``max_heap` `      ``= std::priority_queue<``int``, std::vector<``int``>,` `    ``std::less<``int``> >();`   `    ``// Store higher half elements such that` `    ``// minimum element is at top` `    ``min_heap` `      ``= std::priority_queue<``int``, std::vector<``int``>,` `    ``std::less<``int``> >();` `  ``}`   `  ``// Function to add element` `  ``int` `add(``int` `val)` `  ``{`   `    ``// If max_heap is empty or current element` `    ``// smaller than top of max_heap` `    ``if` `(max_heap.empty() || max_heap.top() > val) {` `      ``max_heap.push(-val);` `    ``}`   `    ``else` `{` `      ``min_heap.push(val);` `    ``}`   `    ``// If size of max_heap + 1 less` `    ``// than min_heap` `    ``if` `(max_heap.size() + 1 > min_heap.size()) {` `      ``val = -max_heap.top();` `      ``max_heap.pop();` `      ``min_heap.push(val);` `    ``}`   `    ``// If size of min_heap` `    ``// less than max_heap` `    ``if` `(min_heap.size() > max_heap.size()) {` `      ``val = min_heap.top();` `      ``min_heap.pop();` `      ``max_heap.push(-val);` `    ``}`   `    ``// Finally if sum of sizes is odd,` `    ``// return median` `    ``if` `((min_heap.size() + max_heap.size()) % 2 == 1) {` `      ``return` `-max_heap.top();` `    ``}`   `    ``// Else return 0` `    ``else` `{` `      ``return` `0;` `    ``}` `  ``}`   `  ``std::priority_queue<``int``, std::vector<``int``>,` `  ``std::less<``int``> >` `    ``max_heap;` `  ``std::priority_queue<``int``, std::vector<``int``>,` `  ``std::less<``int``> >` `    ``min_heap;` `};`   `// Function to calculate the sum of all odd length subarrays` `int` `solve(std::vector<``int``> arr)` `{` `  ``int` `ans = 0;`   `  ``// Size of the array` `  ``int` `n = arr.size();` `  ``for` `(``int` `i = 0; i < n; i++) {` `    ``// Create an object of class find_median` `    ``find_median obj;`   `    ``for` `(``int` `j = i; j < n; j++)` `    ``{` `      `  `      ``// Add value to the heaps using object` `      ``int` `val = obj.add(arr[j]);` `      ``ans += val;` `    ``}` `  ``}`   `  ``return` `(ans);` `}`   `// Driver Code` `int` `main()` `{` `  ``std::vector<``int``> arr = { 4, 2, 5, 1 };` `  ``std::cout << solve(arr);` `  ``return` `0;` `}`   `// This code is contributed by phasing17.` ## Java `import` `java.util.*;`   `// A class to find the median of the array` `class` `FindMedian {`   `  ``// Declare two heaps` `  ``// Store lower half elements such that` `  ``// maximum element is at top` `  ``private` `List max_heap;`   `  ``// Store higher half elements such that` `  ``// minimum element is at top` `  ``private` `List min_heap;`   `  ``// Constructor to initialize the heaps` `  ``public` `FindMedian() {` `    ``max_heap = ``new` `ArrayList<>();` `    ``min_heap = ``new` `ArrayList<>();` `  ``}`   `  ``public` `int` `add(``int` `val) {` `    ``// len(max_heap) == 0 or curr_element` `    ``// smaller than max_heap top` `    ``if` `(max_heap.size() == ``0` `|| max_heap.get(``0``) > val) {` `      ``max_heap.add(-val);` `    ``}` `    ``else` `{` `      ``min_heap.add(val);` `    ``}`   `    ``// If size of max_heap + 1 greater` `    ``// than min_heap` `    ``if` `(max_heap.size() + ``1` `> min_heap.size()) {` `      ``int` `v = max_heap.get(max_heap.size() - ``1``);` `      ``max_heap.remove(max_heap.size() - ``1``);` `      ``min_heap.add(-v);` `    ``}`   `    ``// If size of min_heap` `    ``// greater than max_heap` `    ``if` `(min_heap.size() > max_heap.size()) {` `      ``int` `v = min_heap.get(min_heap.size() - ``1``);` `      ``min_heap.remove(min_heap.size() - ``1``);` `      ``max_heap.add(-v);` `    ``}`   `    ``// Finally if sum of sizes is odd,` `    ``// return median` `    ``if` `((min_heap.size() + max_heap.size()) % ``2` `== ``1``) {` `      ``return` `(-max_heap.get(``0``));` `    ``}`   `    ``// Else return 0` `    ``else` `{` `      ``return` `0``;` `    ``}` `  ``}` `}`   `class` `GFG {` `  ``// Function to calculate the sum` `  ``// of all odd length subarrays` `  ``public` `static` `int` `solve(``int``[] arr) {` `    ``int` `ans = ``0``;`   `    ``// Size of the array` `    ``int` `n = arr.length;`   `    ``for` `(``int` `i = ``0``; i < n; i++) {` `      ``// Create an object` `      ``// of class FindMedian` `      ``FindMedian obj = ``new` `FindMedian();` `      ``for` `(``int` `j = i; j < n; j++) {` `        ``// Add value to the heaps` `        ``// using object` `        ``int` `val = obj.add(arr[j]);` `        ``ans += val;` `      ``}` `    ``}`   `    ``return` `(ans);` `  ``}`   `  ``// Driver Code` `  ``public` `static` `void` `main(String[] args) {` `    ``int``[] arr = { ``4``, ``2``, ``5``, ``1` `};` `    ``System.out.println(solve(arr));` `  ``}` `}` ## Python3 `# Python program for the above approach` `from` `heapq ``import` `heappush as push, heappop as pop`   `# Find the sum of medians of odd-length` `# subarrays` `class` `find_median():`   `    ``# Constructor to declare two heaps` `    ``def` `__init__(``self``):`   `        ``# Store lower half elements such that ` `        ``# maximum element is at top` `        ``self``.max_heap ``=` `[]`   `        ``# Store higher half elements such that ` `        ``# minimum element is at top` `        ``self``.min_heap ``=` `[]`   `    ``def` `add(``self``, val):`   `        ``# len(max_heap) == 0 or curr_element ` `        ``# smaller than max_heap top` `        ``if` `(``len``(``self``.max_heap) ``=``=` `0` `or` `            ``self``.max_heap[``0``] > val):` `            ``push(``self``.max_heap, ``-``val)`   `        ``else``:` `            ``push(``self``.min_heap, val)`   `        ``# If size of max_heap + 1 greater ` `        ``# than min_heap` `        ``if` `(``len``(``self``.max_heap)``+``1` `> ` `            ``len``(``self``.min_heap)):` `            ``val ``=` `pop(``self``.max_heap)` `            ``push(``self``.min_heap, ``-``val)`   `        ``# If size of min_heap ` `        ``# greater than max_heap` `        ``if` `(``len``(``self``.min_heap) > ` `            ``len``(``self``.max_heap)):` `            ``val ``=` `pop(``self``.min_heap)` `            ``push(``self``.max_heap, ``-``val)`   `        ``# Finally if sum of sizes is odd,` `        ``# return median` `        ``if` `(``len``(``self``.min_heap) ``+` `            ``len``(``self``.max_heap)) ``%` `2` `=``=` `1``:` `            ``return` `(``-``self``.max_heap[``0``])`   `        ``# Else return 0` `        ``else``:` `            ``return` `0`   `# Function to calculate the sum ` `# of all odd length subarrays` `def` `solve(arr):` `    ``ans ``=` `0` `    `  `    ``# Size of the array` `    ``n ``=` `len``(arr)` `    ``for` `i ``in` `range``(n):` `        `  `        ``# Create an object ` `        ``# of class find_median` `        ``obj ``=` `find_median()` `        ``for` `j ``in` `range``(i, n, ``1``):` `            `  `            ``# Add value to the heaps ` `            ``# using object` `            ``val ``=` `obj.add(arr[j])` `            ``ans ``+``=` `val` `    `  `    ``return` `(ans)`   `# Driver Code` `if` `__name__ ``=``=` `"__main__"``:` `    ``arr ``=` `[``4``, ``2``, ``5``, ``1``]` `    ``print``(solve(arr))` ## C# `// C# Program for the above approach` `using` `System;` `using` `System.Collections.Generic;`   `// A class to find the median of the array` `public` `class` `FindMedian ` `{`   `  ``// Declare two heaps` `  ``// Store lower half elements such that` `  ``// maximum element is at top` `  ``private` `List<``int``> max_heap;`   `  ``// Store higher half elements such that` `  ``// minimum element is at top` `  ``private` `List<``int``> min_heap;`   `  ``// Constructor to initialize the heaps` `  ``public` `FindMedian()` `  ``{` `    ``max_heap = ``new` `List<``int``>();` `    ``min_heap = ``new` `List<``int``>();` `  ``}`   `  ``public` `int` `Add(``int` `val)` `  ``{` `    ``// len(max_heap) == 0 or curr_element` `    ``// smaller than max_heap top` `    ``if` `(max_heap.Count == 0 || max_heap[0] > val) {` `      ``max_heap.Add(-val);` `    ``}` `    ``else` `{` `      ``min_heap.Add(val);` `    ``}`   `    ``// If size of max_heap + 1 greater` `    ``// than min_heap` `    ``if` `(max_heap.Count + 1 > min_heap.Count) {` `      ``int` `v = max_heap[max_heap.Count - 1];` `      ``max_heap.RemoveAt(max_heap.Count - 1);` `      ``min_heap.Add(-v);` `    ``}`   `    ``// If size of min_heap` `    ``// greater than max_heap` `    ``if` `(min_heap.Count > max_heap.Count) {` `      ``int` `v = min_heap[min_heap.Count - 1];` `      ``min_heap.RemoveAt(min_heap.Count - 1);` `      ``max_heap.Add(-v);` `    ``}`   `    ``// Finally if sum of sizes is odd,` `    ``// return median` `    ``if` `((min_heap.Count + max_heap.Count) % 2 == 1) {` `      ``return` `(-max_heap[0]);` `    ``}`   `    ``// Else return 0` `    ``else` `{` `      ``return` `0;` `    ``}` `  ``}` `}`   `public` `class` `GFG {` `  ``// Function to calculate the sum` `  ``// of all odd length subarrays` `  ``public` `static` `int` `Solve(``int``[] arr)` `  ``{` `    ``int` `ans = 0;`   `    ``// Size of the array` `    ``int` `n = arr.Length;`   `    ``for` `(``int` `i = 0; i < n; i++) {` `      ``// Create an object` `      ``// of class find_median` `      ``FindMedian obj = ``new` `FindMedian();` `      ``for` `(``int` `j = i; j < n; j++) {` `        ``// Add value to the heaps` `        ``// using object` `        ``int` `val = obj.Add(arr[j]);` `        ``ans += val;` `      ``}` `    ``}`   `    ``return` `(ans);` `  ``}`   `  ``// Driver Code` `  ``public` `static` `void` `Main()` `  ``{` `    ``int``[] arr = { 4, 2, 5, 1 };` `    ``Console.WriteLine(Solve(arr));` `  ``}` `}`   `// This code is contributed by vinayetbi1` ## Javascript `// JavaScript Program for the above approach `   `// A class to find the median of the array ` `class find_median {` `    ``// Constructor to declare two heaps` `    ``constructor() {` `        ``// Store lower half elements such that ` `        ``// maximum element is at top` `        ``this``.max_heap = [];`   `        ``// Store higher half elements such that ` `        ``// minimum element is at top` `        ``this``.min_heap = [];` `    ``}`   `    ``add(val) {` `        ``// len(max_heap) == 0 or curr_element ` `        ``// smaller than max_heap top` `        ``if` `(``this``.max_heap.length == 0 || ``this``.max_heap[0] > val) {` `            ``this``.max_heap.push(-val);` `        ``}` `        ``else` `{` `            ``this``.min_heap.push(val);` `        ``}`   `        ``// If size of max_heap + 1 greater ` `        ``// than min_heap` `        ``if` `(``this``.max_heap.length + 1 > ``this``.min_heap.length) {` `            ``let val = ``this``.max_heap.pop();` `            ``this``.min_heap.push(-val);` `        ``}`   `        ``// If size of min_heap ` `        ``// greater than max_heap` `        ``if` `(``this``.min_heap.length > ``this``.max_heap.length) {` `            ``let val = ``this``.min_heap.pop();` `            ``this``.max_heap.push(-val);` `        ``}`   `        ``// Finally if sum of sizes is odd,` `        ``// return median` `        ``if` `((``this``.min_heap.length + ``this``.max_heap.length) % 2 === 1) {` `            ``return` `(-``this``.max_heap[0]);` `        ``}`   `        ``// Else return 0` `        ``else` `{` `            ``return` `0;` `        ``}` `    ``}` `}`   `// Function to calculate the sum ` `// of all odd length subarrays` `function` `solve(arr) {` `    ``let ans = 0;` `    `  `    ``// Size of the array` `    ``let n = arr.length;` `    ``for` `(let i = 0; i < n; i++) {` `        `  `        ``// Create an object ` `        ``// of class find_median` `        ``let obj = ``new` `find_median();` `        ``for` `(let j = i; j < n; j++) {` `            `  `            ``// Add value to the heaps ` `            ``// using object` `            ``let val = obj.add(arr[j]);` `            ``ans += val;` `        ``}` `    ``}`   `    ``return` `(ans);` `}`   `// Driver Code` `let arr = [4, 2, 5, 1];` `console.log(solve(arr));`   `// This code is contributed by vinayetbi1.` Output `18` Time Complexity: O(N2 * Log(N)) Auxiliary Space: O(N) My Personal Notes arrow_drop_up Related Articles
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Open In App # Microsoft Interview Experience (3 years Experienced) Team Name: Azure DevOps Round 1 Given an array of probability distribution, generate a function to return a char with given probability. str=[‘a’, ’b’, ’c’] probabilityDistribution =[50, 25, 25] https://www.geeksforgeeks.org/random-number-generator-in-arbitrary-probability-distribution-fashion/ 4 outputs when called 4 times =a, a, b, c. Create a function There are coins stored in tree nodes. Each node is supposed to have exactly 1 coin. Total no of coins in a tree is = no of nodes. But the coins are not equally distributed and have to moved to proper nodes (which have >1 or <1 coins). Find the number of moves required. https://leetcode.com/articles/distribute-coins-in-binary-tree/ Round 2 1 website could link to many other websites. Design a crawler service that could return all websites that are recursively reachable from this website. Design a distributed system where all results cannot be stored in 1 node. [Ans= Decouple storage and compute] Round 3: Maximum sum subarray: https://www.geeksforgeeks.org/maximum-subarray-sum-using-divide-and-conquer-algorithm/ Factory pattern question How do you consume info from an API which produces data faster than you can consume ? Round 4: OOPS- Design a Lift.( X cars, each car can have max P passengers, not destination controlled) Result: Offered
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{[ promptMessage ]} Bookmark it {[ promptMessage ]} Test5_ReviewSheet # Test5_ReviewSheet - Test#5 Review Sheet MAC2312 Coverage... This preview shows pages 1–2. Sign up to view the full content. Test #5– Review Sheet- MAC2312 Coverage: Sections 10.1 – 10.5 How to Study for Test #5 1) Recopy all notes from class and the textbook. Review handouts given in class. Make a list of all outstanding questions and get help with those items immediately. 2) Redo homework problems that gave you trouble. 3) For extra practice, try problems from the chapter review: p.759 (1 – 17odd, 25 – 35odd, 39 – 51 odd, 55, 57, 59, 61 – 91 odd, 101, 103, 113 ***You are allowed to bring in ONE 3”x5” index card with formulas (front and back). Topics for Test #5 Section 10.1: 1) Know how to find the standard equation for a parabola, how to find the focus as an ordered pair and how to find the equation of the directrix line. Know how to use this information to sketch a parabola. 2) Know how to find the length of the latus rectum and the arc length of the curve the latus rectum intersects. 3) Know how to find the standard equation of an ellipse, how to find the major and minor vertices as ordered pairs, how to find the foci, and how to find the center. Know how to This preview has intentionally blurred sections. Sign up to view the full version. View Full Document This is the end of the preview. Sign up to access the rest of the document. {[ snackBarMessage ]} ### Page1 / 2 Test5_ReviewSheet - Test#5 Review Sheet MAC2312 Coverage... This preview shows document pages 1 - 2. Sign up to view the full document. View Full Document Ask a homework question - tutors are online
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Club PA 2.0 has arrived! If you'd like to access some extra PA content and help support the forums, check it out at patreon.com/ClubPA The image size limit has been raised to 1mb! Anything larger than that should be linked to. This is a HARD limit, please do not abuse it. Our new Indie Games subforum is now open for business in G&T. Go and check it out, you might land a code for a free game. If you're developing an indie game and want to post about it, follow these directions. If you don't, he'll break your legs! Hahaha! Seriously though. Our rules have been updated and given their own forum. Go and look at them! They are nice, and there may be new ones that you didn't know about! Hooray for rules! Hooray for The System! Hooray for Conforming! Poker Game Probabilities Problem The Prettiest ZombieCoeur d'CoeursRegistered User regular edited December 2008 I apologize in advance for the somewhat complicated nature of this problem and the long run up before my question. A little background: I'm in a bowling league, and it's just a fun league between family and friends, so we have a smattering of good and bad bowlers. People mainly only show up to hang out and drink. I run a mini poker game, played with two standard playing card decks, jokers removed. I use two decks because one just doesn't have enough cards. The rules are as follows: 1. One dollar buy in, per person, per game. Three games total to coincide with the games we bowl. 2. For every strike thrown, or for every split converted, you may draw a card. 3. Maximum of 5 cards, per person, per game. 4. Best hand, following standard poker hand rankings, at the end of the game wins the pot for that game. Natrually, this favors the better bowlers because their chances of drawing 5 cards a game is higher. So, in the spirit of giving everyone a better shot at winning, we added another rule: 5. Any one with an average score of under 150 can draw a card after two consecutive spares. (Bowling 3 spares in a row would not give 2 cards.) A few weeks ago, someone suggested that, to give the lower average bowlers a better chance of winning, we use Pinochle decks instead of standard playing cards. A pinochle deck is different from a standard deck. Instead of having 2 through Ace of every suit and 52 cards total, a pinochle deck has 9 through Ace of every suit twice, and 48 cards total. The idea was that, by using these cards, people who pulled fewer cards would have a better shot at having a decent poker hand because the card values are more concentrated. What I want to know, if there is a black and white solution, is does switching to a Pinochle deck favor the lower average bowler? We tried it out last week, and the top bowler in the league won the pot two of the three games. Now, I know I can't really make assumptions on such a small sample, but the more I think about it, the more it seems to me that it actually favors those who are drawing more cards, not less as was the intention. I guess it's entirely possible that the chances for everyone are the same as with a standard deck, too. I just want to make sure I'm not changing something and having it do the opposite of what was intended. Metacortex on Posts • Registered User regular edited December 2008 Hm. That's a tough one. Are you allowing people with only three cards to have a hand? Best poker hand technically has to have five cards, but it sounds like you're sliding around that. You're improving greatly the chances of getting pairs, two pairs, trips, full houses, and quads, lowering the chances of getting a straight, and leaving untouched the chances for a flush. You're reducing moderately the chances of one hand that requires five cards, but you're greatly increasing the chances of getting two others that require five cards. On the other hand, small hands have greatly increased chances of getting one of the few hands for which they actually qualify. I think you're significantly increasing the chances of a small hand bearing some sort of fruit, but you're also moderately improving the chances of a large hand. In the end, however, no amount of card stacking is going to outweigh the enormous statistical advantage of drawing five cards instead of four. MrMonroe on • Registered User edited December 2008 Texas Holdem rfalias on • Registered User regular edited December 2008 Why would you really want to do that? We ran a similar poker game in our bowling league, and didn't even have the handicap additional rule. It's certainly a fun addition, and the still-learning bowlers would often buy in just because it's a diversion to think about the cards while you wait to bowl again. However, adding handicap after handicap might take some of the fun out of it for the better bowlers. Or is the goal to have something that might be a bit more rewarding for the still-learning bowlers to compensate? Darkewolfe on What is this I don't even. • Registered User regular edited December 2008 rfalias wrote: » Texas Holdem Hahaha! I was thinking about suggesting this. Just separate the bowling from the poker entirely and play a real gamblin' man's game. MrMonroe on • Registered User edited December 2008 MrMonroe wrote: » rfalias wrote: » Texas Holdem Hahaha! I was thinking about suggesting this. Just separate the bowling from the poker entirely and play a real gamblin' man's game. I was also suggesting because it only needs 2 cards per person, but that works too. rfalias on • Registered User regular edited December 2008 Now there's a thought. You could play multiple games. With every second card you earn, you get into another pot. Someone who earns two cards in a night plays in the first hand, and someone who earns six plays in three. MrMonroe on • Registered User regular edited December 2008 MrMonroe wrote: » Now there's a thought. You could play multiple games. With every second card you earn, you get into another pot. Someone who earns two cards in a night plays in the first hand, and someone who earns six plays in three. Problem with that is that the pot would be split a great deal, which would then remove a lot of the sense of reward for having participated. (Even when we don't win, higher stakes are simply more exciting to have competed for. It's why people get more excited about a contest which gives away \$1 million than a contest in which 1 in 5 winners will get a dollar.) Darkewolfe on What is this I don't even. • Registered User, ClubPA regular edited December 2008 Switching up to Hold'em or another community card game really might not be a bad idea. It'd favor no one in that you wouldn't need a full hand to play, and still offer all players a chance to make the pot. though at that point you may as well remove the bowling aspect and just run a side game, since I'm assuming near everyone would be able to draw two cards Monoxide on • Registered User regular edited December 2008 If everyone's drawing from a the same deck, stacking the deck with high cards is not going to give any one class of players an advantage. Edit: though it may make it more interesting, until you realize that your odds of winning haven't changed. Djeet on • Registered User edited December 2008 Monoxide wrote: » Switching up to Hold'em or another community card game really might not be a bad idea. It'd favor no one in that you wouldn't need a full hand to play, and still offer all players a chance to make the pot. though at that point you may as well remove the bowling aspect and just run a side game, since I'm assuming near everyone would be able to draw two cards Cigars and visors not included. You could allow people to re-draw cards if they wanted. Advantage to good bowlers while less than good ones still have a shot. Cap re-draws or set criteria to re-draw, like a turkey or something. (Just an example) rfalias on • Registered User regular edited December 2008 Djeet wrote: » If everyone's drawing from a the same deck, stacking the deck with high cards is not going to give any one class of players an advantage. Edit: though it may make it more interesting, until you realize that your odds of winning haven't changed. This. I think you're increasing the chances that everyone will have a viable hand (since it's easier to get pairs) but it won't change the underlying idea that more cards in your hand = better chance for a winning hand. tsmvengy on • The Prettiest Zombie Coeur d'CoeursRegistered User regular edited December 2008 Thanks for all the replies. Hold'em actually sounds intriguing, but like you said the bowling wouldn't matter at all, really. Splitting pots would be another concern. I'll run it by a few people and see what they think. When I said "I run a mini poker game," what I meant was that I just collect the money, shuffle the cards and pay the winners. The game was being played before I got into the league, so I'll generally leave the decisions up to the public. It's a bit of a tough call with all this. I mean, the league is mainly made up of an extended family and friends of their family(I'm in this category), so everything is real friendly and it's not like \$3 for some card action is a heck of a lot. Most of the bowlers that join probably do it for the fun of drawing cards and the excitement of maybe getting a nice hand, more than for the money. Most of them could probably give two shits what kind of card game we play. When I tried telling some of them we were using Pinochle decks last week, they just shrugged. I think they're all just a bunch of degenerate gamblers. I'd just like for everyone to have equal chances(though it's not really possible), but like you all said, you can't remove the inherent advantages of having more cards without trivializing the bowling aspect, and without that, there's no reason to run it all, really. I mainly just wanted to make sure that Pinochle decks wouldn't favor the better bowlers, because they already have the upper hand. Metacortex on • Registered User edited December 2008 Metacortex wrote: » Thanks for all the replies. Hold'em actually sounds intriguing, but like you said the bowling wouldn't matter at all, really. Splitting pots would be another concern. I'll run it by a few people and see what they think. When I said "I run a mini poker game," what I meant was that I just collect the money, shuffle the cards and pay the winners. The game was being played before I got into the league, so I'll generally leave the decisions up to the public. It's a bit of a tough call with all this. I mean, the league is mainly made up of an extended family and friends of their family(I'm in this category), so everything is real friendly and it's not like \$3 for some card action is a heck of a lot. Most of the bowlers that join probably do it for the fun of drawing cards and the excitement of maybe getting a nice hand, more than for the money. Most of them could probably give two shits what kind of card game we play. When I tried telling some of them we were using Pinochle decks last week, they just shrugged. I think they're all just a bunch of degenerate gamblers. I'd just like for everyone to have equal chances(though it's not really possible), but like you all said, you can't remove the inherent advantages of having more cards without trivializing the bowling aspect, and without that, there's no reason to run it all, really. I mainly just wanted to make sure that Pinochle decks wouldn't favor the better bowlers, because they already have the upper hand. I think texas hold'em with a slight variation will be best. Poor bowlers can get 2 cards with semi-flexible rules, and good bowlers can have the opportunity to achieve better hands by drawing another card (discard a previous) on some condition. This rewards good bowlers but does not really penalize the poor bowlers nearly as much as 5 card does since Hold'em is a community card game. You could also set betting increments like at the start of the bowling game, 5 frames in, and 10th frame. It would allow for competitive betting that makes hold'em great, with the rewards of bowling good. Rules could be simple: Set the river from the start, instead of burning per bet. X = 1 Card Spare Pickup(2 pin) = 1 Card For a new draw, make it harder XX = draw 7-10 split = draw stuff like that. Set a max draw limit of like 2 cards total or something. It presents a risk for the bowler drawing a new card as the old card has to be discarded completely so it isn't like they have an immediate advantage over the bad bowlers. If you draw a card, discard your choice before you get a new card and the new card that was picked up has to be used or discarded on the next XX or 7-10. That's just how I imagined it working and as long as everyone can manage 2 cards then everyone has roughly the same chance, with a small edge going to good bowlers. But good bowlers should have an advantage since it is a bowling game. rfalias on • The Prettiest Zombie Coeur d'CoeursRegistered User regular edited December 2008 That seems like an excellent layout to me, but I would probably need to simplify the redraw rules a little bit for the rest of them. But I'll definitely run something like this by them the next time we bowl, thanks a bunch. Metacortex on • Registered User regular edited December 2008 Do you start with zero cards? If so then I would think a Pinochle deck would favor the better bowlers as it's far more likely that someone with 5 cards will get 2 pair and up. I'm not 100% sure of the math, but I know the bowlers at my league play a game like this as well, but everyone starts with 5 cards and then when you draw a card you also discard a card and build the best 5 card hand. This removes the inequality potential in the number of cards and adds a little more luck into the game. khain on • Registered User edited December 2008 Metacortex wrote: » That seems like an excellent layout to me, but I would probably need to simplify the redraw rules a little bit for the rest of them. But I'll definitely run something like this by them the next time we bowl, thanks a bunch. Yeah, it shouldn't be hard to explain. "If you have 2 cards and want to swap one out, then you have to bowl **** to get another. You can only do this X times per game" Start of the game is buy in, 5th frame is first bet, after 10th frame is bowled last bet is placed and hands laid down. Sounds fun actually, I should do this rfalias on • Registered User regular edited December 2008 I'll admit I'm in a hurry, so I only kind of skimmed, but I got lost there for a second. Here's what we do for our bowling league team. It's very simple and it seems to give everyone a decent chance (I'm terrible, and I've won a few times.) We use two decks. There is no limit to the amount of cards you can have. For every strike, you take two cards. For every spare, you take one card. Jokers are wild. Since I'm a vastly inferior bowler to the rest of my team, I also get a card everytime I manage to get nine pins in a frame. Then at the end, you build the best five-card hand you can put together with your cards. We've never had a problem with that method. xbl - HowYouGetAnts steam - WeAreAllGeth • The Prettiest Zombie Coeur d'CoeursRegistered User regular edited December 2008 khain wrote: » Do you start with zero cards? If so then I would think a Pinochle deck would favor the better bowlers as it's far more likely that someone with 5 cards will get 2 pair and up. I'm not 100% sure of the math, but I know the bowlers at my league play a game like this as well, but everyone starts with 5 cards and then when you draw a card you also discard a card and build the best 5 card hand. This removes the inequality potential in the number of cards and adds a little more luck into the game. That was my line of thought as well. With the Pinochle decks, someone with 2 or 3 cards is going to have a decent shot at pair at least, but the value of a pair is complete shit. Anyone able to pull 5 cards has such a high chance of getting 2 pair or 3 of a kind that it seems it would favor them more. I just wish I had some numbers confirming it, and it's been a long while since I studied probability. I kind of like the idea of starting with cards, but that would require at least an additional deck. Metacortex on • Registered User regular edited December 2008 The material advantage is conferred by the better bowlers getting to have more cards and thus more opportunity to improve their hands. Letting everyone start with a full hand will help handicap the less skilled bowlers somewhat, but if better bowlers have more opportunities to draw they will still have an advantage. If you defaulted to let anyone draw after each frame, but penalized good bowling by not letting those guys draw it would give an edge to the less skilled bowlers. But that's kind of messed up no? Assuming everyone's drawing from the same deck, the composition of the deck is irrelevant. It could be all aces, that would make it real obvious that those who can fill their hands will do better than those who cannot. But how many hands get played in a night, 4 or 5? If you just want to keep it interesting you could just keep changing the game slightly. Using a Pinochle deck might do that. If you want the winnings to be biased towards the lesser skilled bowlers, maybe lowest hand wins? Djeet on • Registered User regular edited December 2008 I don't think he wants the game biased toward the lesser skilled bowlers, he just wants them to have more of a chance to win. I really think the big problem is starting with zero cards as it means anyone that can get a 5 card hand has a pretty significant advantage over those who can't regardless of what type of deck you play with. Also I don't think Hold'em would work that well. I'm assuming you have people on multiple lanes playing the game and at least in my league there's a pretty big time gap between when the first match finishes and the last match finishes so you can't have everyone bet on the 5th frame or show the flop on a certain frame. khain on
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The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!) A242180 Least prime divisor of q(n) which does not divide any q(k) with k < n, or 1 if such a primitive prime divisor does not exist, where q(.) is the strict partition function given by A000009. 1 1, 1, 2, 1, 3, 1, 5, 1, 1, 1, 1, 1, 1, 11, 1, 1, 19, 23, 1, 1, 1, 89, 13, 61, 71, 1, 1, 37, 1, 1, 17, 1, 7, 1, 1, 167, 1, 1, 491, 53, 1, 31, 1, 227, 1, 1, 1, 97, 1, 59, 241, 29, 1, 953, 1063, 1777, 1, 367, 1, 1 (list; graph; refs; listen; history; text; internal format) OFFSET 1,3 COMMENTS Conjecture: a(n) > 1 for all n > 203. LINKS Zhi-Wei Sun, Table of n, a(n) for n = 1..6000 EXAMPLE a(8) = 1 since q(8) = 2*3 with 2 = q(3) and 3 = q(5). a(23) = 13 since q(23) = 2^3*13 with 13 not dividing q(1)*q(2)*...*q(22), but 2 divides q(3) = 2. MATHEMATICA f[n_]:=FactorInteger[PartitionsQ[n]] pp[n_]:=Table[Part[Part[f[n], k], 1], {k, 1, Length[f[n]]}] Do[If[PartitionsQ[n]<2, Goto[cc]]; Do[Do[If[Mod[PartitionsQ[i], Part[pp[n], k]]==0, Goto[aa]], {i, 1, n-1}]; Print[n, " ", Part[pp[n], k]]; Goto[bb]; Label[aa]; Continue, {k, 1, Length[pp[n]]}]; Label[cc]; Print[n, " ", 1]; Label[bb]; Continue, {n, 1, 60}] CROSSREFS Cf. A000009, A000040, A194261, A272169, A272170, A272171, A272173. Sequence in context: A110977 A295785 A069230 * A163961 A101387 A117365 Adjacent sequences:  A242177 A242178 A242179 * A242181 A242182 A242183 KEYWORD nonn AUTHOR Zhi-Wei Sun, May 06 2014 STATUS approved Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent The OEIS Community | Maintained by The OEIS Foundation Inc. Last modified May 28 01:34 EDT 2020. Contains 334671 sequences. (Running on oeis4.)
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Find all School-related info fast with the new School-Specific MBA Forum It is currently 14 Sep 2014, 20:14 GMAT Club Daily Prep Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email. Customized for You we will pick new questions that match your level based on your Timer History Track every week, we’ll send you an estimated GMAT score based on your performance Practice Pays we will pick new questions that match your level based on your Timer History Events & Promotions Events & Promotions in June Open Detailed Calendar If x>y^2>z^4, which of the following is true? I. Author Message TAGS: Senior Manager Joined: 08 Aug 2005 Posts: 251 Followers: 1 Kudos [?]: 4 [0], given: 0 If x>y^2>z^4, which of the following is true? I. [#permalink]  26 Apr 2006, 01:27 If x>y^2>z^4, which of the following is true? I. x>y>z II. z>y>x III. x>z>y VP Joined: 29 Apr 2003 Posts: 1408 Followers: 2 Kudos [?]: 15 [0], given: 0 Answer is None. The question is kinda weird! Should it be, which one can be true? 1 cannot be true when x = 0.1, y =0.2, z=0.3 2. cannot be true when x=5, y=2, z=1 3. Works for numbers <0.1, -ve values of z and y. But if x =1, y =5 and z =4, it does not! You should note that x CAN never be -ve! as x>y^2 By definition the min value of y^2 is 0, hence x>0! Similar topics Replies Last post Similar Topics: 30 If |x|<x^2 , which of the following must be true? 68 20 Aug 2010, 11:59 If x<y, which of the following must be true? I. 3 22 Jul 2008, 05:16 if x>y>0, which of the following must be true? I. 2 29 May 2007, 16:00 If x y = 8, which of the following must be true? I. Both 1 19 Dec 2004, 17:43 If I x I > 1, which of the following must be true? 2 19 Dec 2004, 17:35 Display posts from previous: Sort by
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Find all School-related info fast with the new School-Specific MBA Forum It is currently 05 Dec 2013, 03:39 # Events & Promotions ###### Events & Promotions in June Open Detailed Calendar # How long did it take Betty to drive nonstop on a trip from Author Message TAGS: Intern Joined: 16 Apr 2005 Posts: 18 Followers: 0 Kudos [?]: 0 [0], given: 0 How long did it take Betty to drive nonstop on a trip from [#permalink]  20 Apr 2005, 15:02 00:00 Difficulty: 5% (low) Question Stats: 0% (00:00) correct 0% (00:00) wrong based on 0 sessions How long did it take Betty to drive nonstop on a trip from her home to Denver, Colorado? 1) If Betty's average speed for the trip had been 3/2 times as fast, the trip would have taken 2 hours. 2) Betty's average speed for the trip was 50 miles per hour. Can someone explain the solution this problem? Director Joined: 07 Jun 2004 Posts: 629 Location: PA Followers: 1 Kudos [?]: 78 [0], given: 22 I would have to go with C on this one as we can calculate d / v - d / 1.5 v = 2 substitute v =50 we get d = 300 so we can calculate t = 300 / 50 = 6 hrs t = 300 / 75 = 4 hrs Senior Manager Joined: 19 Feb 2005 Posts: 495 Location: Milan Italy Followers: 1 Kudos [?]: 4 [0], given: 0 s=d/t s1=d/t1 so s*t=s1*t1 now s1=3/2s and t1=2 s*t=3/2s*2 t=3 A is sufficient VP Joined: 13 Jun 2004 Posts: 1127 Location: London, UK Schools: Tuck'08 Followers: 5 Kudos [?]: 17 [0], given: 0 I also go for A the speed is in direct realation with the time spent, moreover they talk about the average speed so normally A should be sufficient B is uselless alone as we have no idea about the total distance... Intern Joined: 16 Apr 2005 Posts: 18 Followers: 0 Kudos [?]: 0 [0], given: 0 thearch wrote, s=d/t s1=d/t1 so s*t=s1*t1 now s1=3/2s and t1=2 s*t=3/2s*2 t=3 A is sufficient I see how you get till s*t=3/2s*2 But, how do you go from there to getting t=3? Intern Joined: 17 Mar 2005 Posts: 15 Followers: 0 Kudos [?]: 0 [0], given: 0 Correct answer is A as just 1 is sufficient. Since the distance covered is the same simply use the basic formula speed * time = distance speed(1st trip) x time(1st trip) = speed(2nd trip) X time(2nd trip) therefore s x t = 3/2s x 2 therefore t = 3 Similar topics Replies Last post Similar Topics: How long did it take Betty to drive nonstop on a trip from 3 17 Aug 2004, 16:38 How long did it take Betty to drive nonstop on a trip from 4 01 Aug 2007, 07:20 How long did it take betty to drive nonstop on a trip from 6 04 May 2008, 08:46 1 How long did it take Betty to drive nonstop on a trip from 9 04 Jun 2008, 03:03 How long did it take Betty to drive nonstop on a trip from 9 28 Feb 2011, 11:25 Display posts from previous: Sort by
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# Find One-Third of 45. Add 15. Divide by 6. Multiply by 25. • Printer-Friendly • Email Article • Reprints Those who worry that the increasing use of calculators and microcomputers is undermining the mathematical abilities of today's students might have been reassured had they observed the first Lane County Mental Math Competition in Eugene, Ore., this month. Eighty 3rd- through 8th-grade students representing 15 school districts demonstrated that the human mind is still a remarkable calculating tool. Students were asked a series of 20 questions that required them to perform complex computations in their heads--without the benefit of calculators or even pencil and paper. Questions were read at a pace slightly slower than ordinary conversation and could not be repeated. Students then had to jot down their answers as quickly as possible. Seventh graders, for example, were asked for rapid determinations of whether the number 810 is divisible by 5 and 3 and whether one-half divided by one-third is more than one. They were also asked to: Find one-third of 45. Add 15. Divide by 6. Multiply by 25. Take seven-tenths. Add five one-hundredths. Subtract twenty-five one-hundredths. Multiply by 2. Find 10 percent of 200. Multiply by 60. Subtract 199. Among the mathematical challenges presented to 4th graders were the following: Start with the number of meters in 200 centimeters. Multiply by 10. Add 75. Subtract 15. Start with the number of min-utes in four hours. Subtract 200. Now multiply by 100. Subtract 10. The competition was sponsored by the Lane Education Service District, one of 27 consortia established throughout the state to encourage cooperation between school districts. According to Jeff Foreman, information assistant for the Lane County consortium, the winners in each grade generally answered about 17 or 18 of the 20 questions correctly. He said that two students--7th grader Kristen Albrethsen from Junction City and 6th grader Brian Brown from Cottage Grove--solved all 20 problems. Countywide contestants were chosen in competitions at the classroom, school, and district levels--the same process the county uses for its annual spelling bee. Districts had asked the consortium to sponsor a mathematics competition because of the spelling bee's success. "It's a good opportunity to allow kids to show off how much they know," said Mr. Foreman. "It also shows that we in the education business are doing our jobs." News Update Vol. 04, Issue 27 Notice: We recently upgraded our comments. (Learn more here.) If you are logged in as a subscriber or registered user and already have a Display Name on edweek.org, you can post comments. If you do not already have a Display Name, please create one here. Ground Rules for Posting We encourage lively debate, but please be respectful of others. Profanity and personal attacks are prohibited. By commenting, you are agreeing to abide by our user agreement. All comments are public.
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org.jgrapht.demo ## Class WarnsdorffRuleKnightTourHeuristic • public class WarnsdorffRuleKnightTourHeuristic extends Object Implementation of <a href = "https://en.wikipedia.org/wiki/Knight%27s_tour#Warnsdorf's_rule">Warnsdorff's rule</a> - heuristic for finding a knight's tour on chessboards. A knight's tour is a sequence of moves of a knight on a chessboard such that the knight visits every square only once. If the knight ends on a square that is one knight's move from the beginning square (so that it could tour the board again immediately, following the same path), the tour is closed, otherwise it is open. The knight's tour problem is the mathematical problem of finding a knight's tour. Description of the Warnsdorff's rule: set a start cell. Always proceed to the cell that have the fewest onward moves. In case of a tie(i.e. there exist more than one possible choice for the next cell) go to the cell with largest Euclidean distance from the center of the board. This implementation also allows you to find a structured knight's tour. Knight's tour on board of size $n \times m$ is called structured if it contains the following $8$ UNDIRECTED moves: 1). $(1, 0) \to (0, 2)$ - denoted as $1$ on the picture below. 2). $(2, 0) \to (0, 1)$ - denoted as $2$ on the picture below. 3). $(n - 3, 0) \to (n - 1, 1)$ - denoted as $3$ on the picture below. 4). $(n - 2, 0) \to (n - 1, 2)$ - denoted as $4$ on the picture below. 5). $(0, m - 3) \to (1, m - 1)$ - denoted as $5$ on the picture below. 6). $(0, m - 2) \to (2, m - 1)$ - denoted as $6$ on the picture below. 7). $(n - 3, m - 1) \to (n - 1, m - 2)$ - denoted as $7$ on the picture below. 8). $(n - 2, m - 1) \to (n - 1, m - 3)$ - denoted as $8$ on the picture below. ######################################### #*12*********************************34*# #2*************************************3# #1*************************************4# #***************************************# #***************************************# #***************************************# #***************************************# #***************************************# #***************************************# #***************************************# #***************************************# #***************************************# #***************************************# #***************************************# #6*************************************8# #5*************************************7# #*65*********************************78*# ######################################### If you are confused with the formal definition of the structured knight's tour please refer to illustration on the page $3$ of the paper "An efficient algorithm for the Knight’s tour problem " by Ian Parberry. One more feature of this implementation is that it provides an option to return a shifted knight's tour, where all cell's coordinates are shifted by some values. Basically it is the same as knight's tour of some piece of the board. • ### Constructor Summary Constructors Constructor and Description WarnsdorffRuleKnightTourHeuristic(int n) Constructor. WarnsdorffRuleKnightTourHeuristic(int n, int m) Constructor. • ### Method Summary All Methods Modifier and Type Method and Description org.jgrapht.demo.KnightTour getTour(org.jgrapht.demo.TourType type, boolean structured, int shiftX, int shiftY) Generates a knight's tour that satisfies the input parameters. • ### Methods inherited from class java.lang.Object clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait • ### Constructor Detail • #### WarnsdorffRuleKnightTourHeuristic public WarnsdorffRuleKnightTourHeuristic(int n) Constructor. Parameters: n - width and height of the board. • #### WarnsdorffRuleKnightTourHeuristic public WarnsdorffRuleKnightTourHeuristic(int n, int m) Constructor. Parameters: n - width of the board. m - height of the board. • ### Method Detail • #### getTour public org.jgrapht.demo.KnightTour getTour(org.jgrapht.demo.TourType type, boolean structured, int shiftX, int shiftY) Generates a knight's tour that satisfies the input parameters. Warnsdorff's rule heuristic is an example of a greedy method, which we use to select the next cell to move, and thus may fail to find a tour. However, another greedy heuristic is used to prevent failing: in case of a tie we will select a cell with the largest euclidean distance from the center of the board. Such combination of greedy methods significantly increases our chances to find a tour. Parameters: type - of the tour. structured - true if we want the tour to be structured, otherwise false. shiftX - the value will be added to each cell's x-coordinate to reach effect of shifting. shiftY - the value will be added to each cell's t-coordinate to reach effect of shifting. Returns: knight's tour. Copyright © 2019. All rights reserved.
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The Electricity & Magnetism Light Bulb Demo Will Light Up Minds The Electricity & Magnetism Light Bulb Demo Will Light Up Minds The link between electricity and magnetism finds its legendary roots back to Hans Christian Orsted when he supposedly found that electric current affected his compasses during a student lecture.  That piece of scientific history may be one of exaggerated legend, but the marriage of electricity with magnetism has been widely known for over a century, later to be given a full mathematical explanation by Lord Kelvin and James Clerk Maxwell.  The concept of electron movement causing the production of an ensuing magnetic field is a fundamental model used in describing electromagnets, generators, transformers and electric motors. Can’t view this in YouTube? Try watching in Vimeo. Students can witness the magnetic fields produced by electron movement using compass deflections and observe first-hand the mechanical spin of a solenoid in an electric motor.  Using the “Electricity & Magnetism Light Bulb Demo”, you will demonstrate to your students the relationship between electricity and magnetism in an amazing and unconventional way, using a Victorian light bulb under conditions not normally observed in everyday life. When a wire that carries an electrical current is placed within a magnetic field, each of the moving charges, which comprise the current, experience the Lorentz force and together they can create a macroscopic force on the wire.  The following equation, in the case of a straight, stationary wire is as follows: …where is a vector whose magnitude is the length of wire, conventional current flow I, B is the Magnetic Flux Density and F is the force on the wire. The Electricity & Magnetism Light Bulb Demo can clarify several important concepts: 1.   Using DC (Direct Current), electrons flow through a bulb’s filament in one direction. 2.   Using AC (Alternating Current), electrons flow through a bulb’s filament in two directions. 3.   A magnetic field is produced when electrons flow through a conductor. 4.   When magnets are placed near wires that carry electric current, a force is exerted on the wire. (Technically, the force is on the electrons in the wire.  The electrons are “trapped” in the wire therefore causing the wire to move instead of the individual electrons.) 5.   When a wire carrying an electrical current is placed in a magnetic field, each of the moving charges (electrons), which comprise the current, experiences the Lorentz force and together they can create a macroscopic force on the wire itself. Acknowledgements: Thank you to Buzz Putnam, Physics Teacher and Whitesboro High School Science Department Chairman, for his development of this product and his assistance in writing these instructions. Electricity & Magnetism Light Bulb Demo In Stock SKU: P6-4000 \$55.00 The Electricity and Magnetism Light Bulb demo featured in the video.  Does not include Neodymium magnet (See below). Pair of Neodymium Magnets In Stock SKU: P8-1123 \$15.00 This 3/4″ neodymium-iron-boron cylinder packs serious power in a small package. Replacement Bulb for P6-4000 In Stock SKU: P6-4000-05 \$13.95 /td> Hand made Victorian light bulb, replica of Thomas Edison’s original design, 60W, carbon filament. Comments (4) • Marcus Rowland I’m in the UK – while I can do the AC part easily enough (we have some old carbon filament lamps for optics) and did so after seeing this, we don’t have a suitable high-voltage high-current power supply for the DC part. Any chance of a 240V version? It would either need to use UK bayonet fitting 240v lamps or come with a supply of US lamps, of course. November 30, 2012 at 11:51 am • Arbor Scientific Our Customer Service department is checking into this. Thanks for your interest. December 4, 2012 at 3:46 pm • Arbor Scientific We do not currently have a 240V bulb demo available. We suggest to purchase a voltage converter from a local electronics store by you. They are relatively inexpensive and can change US voltage to UK voltage in a flash. December 4, 2012 at 4:28 pm • great August 6, 2014 at 9:03 am
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# SOLUTION: Find the number of different signals consisting of eight flags that can be made using three white flags, four red flags, and one blue flag. Algebra ->  Algebra  -> Permutations -> SOLUTION: Find the number of different signals consisting of eight flags that can be made using three white flags, four red flags, and one blue flag.      Log On Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help! Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations! Algebra: Combinatorics and Permutations Solvers Lessons Answers archive Quiz In Depth Question 374792: Find the number of different signals consisting of eight flags that can be made using three white flags, four red flags, and one blue flag.Answer by sudhanshu_kmr(1152)   (Show Source): You can put this solution on YOUR website! total no. of signals = 8!/( 3!*4! ) = 280
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# Calculating averages based on specific criteria per week. Options I have a smartsheet that I am trying to find an average rating per week if there is specific criteria in a column. I've condensed the columns I'm trying to find an average of below The 'Created' column is an Auto-Number column for when the data is entered. I'd like to calculate the average, or 'Over All Rating' for each week that Zephyr is in the Lift Name column. I think I'm looking for a =AVG(COLLECT) formula, however I'm not sure what order to put them in. This formula is going into a new sheet and not the current sheet. Tags: • ✭✭✭✭✭✭ Options Hey @Rachel Rudd I'm not sure if you sheet records (to keep) each week's average, or if the sheet is set up to reflects the current week's average. To do the former you would need a column on your destination sheet listing 1-52 for the weeknumbers of the year, date reference per week - like every Monday, or automation to move the row off the sheet. In the formula below, I added an ISNUMBER to help filter any cells that shouldn't be included in the average. Also, remember with cross sheet references you must create each reference through the formula window - you cannot simply copy paste this formula. Your ranges will default to names different than I have listed - that is ok, and if you like, you can change those default names. In the second formula make sure you change the [WeekNumber] to match your column name or however your week is referenced. Current week Only =AVG(COLLECT({source sheet Over All Rating column}, {source sheet Over All Rating column}, ISNUMBER(@cell), {Source sheet Created column}, WEEKNUMBER(TODAY()) = WEEKNUMBER(@cell), {source sheet Left Name: column}, "Zephyr")) Week by Week (assumes 1-52 on destination sheet) =AVG(COLLECT({source sheet Over All Rating column}, {source sheet Over All Rating column}, ISNUMBER(@cell), {Source sheet Created column}, WEEKNUMBER(@cell)=[WeekNumber]@row, {source sheet Left Name: column}, "Zephyr")) Does this get you what you need? Kelly • Options The 'Over All Rating' is the average rating for that day. I do not have the current weekly average anywhere, which is what I'm trying to pull into this sheet. I am looking for it week by week and I tried the formula you offered but it comes back Unparseable. • ✭✭✭✭✭✭ Options Hey @Rachel Rudd I may have misunderstood exactly what you need - it sounds like you need first the daily total on your source sheet, then you want to pull that into a weekly? Can you give me a screenshot of your current formula (a shot of the formula with the colors) in the sheet this formula resides in? Unpareseable errors usually come from column names (are all the column names (assuming you're on the same sheet as the formula) colored?), commas and parentheses (is the last parenthesis blue?). A screenshot gives me a lot of information • Options I'm trying to transport from one sheet to a new one, so it's showing reference sheet range 1.What is giving me Unpareseable is the second formula you provided above. • Options I found this question which is similar to what I'm looking to do, however they are looking for a criteria by year and I'm looking for criteria by a weekly range. https://community.smartsheet.com/discussion/74546/avg-of-a-range-with-2-criteria • ✭✭✭✭✭✭ Options Rachel, As mentioned earlier, a screenshot of the data and the colored formula would be very helpful. I can make the formula very specific with that information. It's difficult trouble-shooting formulas sight unseen. Using my 2nd formula - are you using weeknumbers to reference the specific weeks? This is what will pull in the data by week, similar to the YEAR function pulling in the year buckets of data in your linked post. Did you change my column name to match yours? I included square brackets around my WeekNumber but as written, without a space between the words, the brackets are not needed. I assumed you would be changing that anyway to match your column. Tell me what you have checked for the unparseable. Kelly • Options Above is the second formula you offered as I entered it to calculate the averages per week. Safety Business Plan 21.22 Range 2 is Over All Rating Column Safety Business plan 21.22. Range 3 is Created column, which are Auto-Number dates when submitted. Safety Business plan 21.22 Range 1 is Lift Name, in this instance searching for Zephyr. The dates in the week columns are the ones I'm trying to find averages for each lift for each week. • ✭✭✭✭✭✭ edited 02/16/22 Options Hey Rachel Thanks for the screenshot. How did you pull the week days into the Week Ranges column? Smartsheet looks at your Week ranges and doesn't see them as dates but as a long text string- like a sentence. Are the beginning and ending dates coming from separate columns and are these columns formatted as date columns? If yes, we can very easily use these in the formula. If no, no worries, I can work with the range and force it into a date value. Please let me know how the Week Ranges is obtained Kelly • ✭✭✭✭✭✭ Options Hey Rachel I haven't heard back. I will assume the date range text string is not linked to date cells. To compensate for that - add a helper column to your sheet - you can shove this column to the right and hide it after you add the column formula below. Name this column WeekNumber. This should be a text/number column.If you do not name it WeekNumber, adjust the Average formula above to match whatever you named this. Add this formula to that helper column =WEEKNUMBER(DATE(VALUE(MID([Week Ranges]@row, FIND("-", [Week Ranges]@row) - 5, 4)), VALUE(LEFT([Week Ranges]@row, FIND("/", [Week Ranges]@row) - 1)), VALUE(LEFT(RIGHT([Week Ranges]@row, LEN([Week Ranges]@row) - VALUE(FIND("/", [Week Ranges]@row))), FIND("/", RIGHT([Week Ranges]@row, LEN([Week Ranges]@row) - VALUE(FIND("/", [Week Ranges]@row)))) - 1)))) This converts the text string date range to something that the average formula (above) can compare against. Kelly • Options I was out last week for a personal matter. All columns are Text/Number and none are date columns. I pulled the weekdays into the column by typing out the weeks I wanted to pull the audits from. I added the helper column and named it WeekNumber to the sheet I'm pulling the data to: and I've left the formula in the Arrow column. • ✭✭✭✭✭✭ Options Hey Rachel It appears the AVG formula is missing an ending parenthesis - the last parenthesis shown is pink instead of blue. It also appears you are missing a comma between the [WeekNumber]@row and {Safety Business Plan 21.22 Range 1}. Kelly • edited 02/28/22 Options I've corrected the formula and now the outcome states 'Divide by Zero'. I believe this is for the ratings that don't have anything for the week range. Would there be a way to make them just say '0' or does it matter if I'm looking to graph this data aswell? • ✭✭✭✭✭✭ edited 02/28/22 Options Yes, it would say dividing by zero for future dates. Wrap your existing formula, parentheses and all, with an IFERROR(). You can make it say zero or leave it as a blank. I'll write it as a blank by using the double quotes. If you want zero, replace the double quotes with the zero.
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# [R] scoping issues? Barry Rowlingson B.Rowlingson at lancaster.ac.uk Thu Dec 8 19:38:42 CET 2005 ```tom wright wrote: > Browse[1]> mean(amps[1],amps[2],amps[3],amps[7],amps[8]) > [1] 1 For starters, this just returns mean(amps[1]). 'mean' computes the mean of the first argument, the others are slurped up by '...' and in this case thrown into the bin. You want to do mean(c(amps[1],amps[2],amps[3] and so on. Wrap them into a single vector. For main course, I think you can do it like this: getAR <- function(v.amps){ sv=sort(v.amps) sum(sv[1:3])/mean(sv[-(1:3)]) } - which computes the ratio of the sum of the three biggest over the mean of the remainder. Which I think is what your code looks like its trying to do! An example input/output would be nice. My code gives: > amps<-c(1,2,3,3,3,2,1) > getAR(amps) [1] 1.454545 but I still dont know if that's what it should be! For dessert, I don't think its a scoping issue, I think you've not really explained what the problem is... Baz ```
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## Tag Info //  MCCB/MCB 1/29/2017 5231 Views 4/10/2013 EE65 3112 Views ### Related Tags Maxwell's Equations - Introduction Maxwell's Equations are a set of fundamental relationships, which govern how electric and magnetic fields interact. The equations explain how these fields... Understanding Motor Duty Rating One of the comments on my Motor Starting Series was asking for something on duty cycles. Here it is. As a purchaser of a motor, you have responsibility... The ac resistance of conductors In a previous article I looked at the dc resistance of conductors and in this article we turn our attention to ac resistance. If you have not read the... How D.C. to A.C. Inverters Work Traditionally generation of electricity has involved rotating machines to produce alternating sinusoidal voltage and current (a.c. systems). With the development... Voltage Levels to IEC 60038 The standard aims to consolidate AC and traction voltages within the industry and defines the following bands: band 1 - A.C. systems 100 V to 1... Cable Sheath and Armour Loss When sizing cables, the heat generated  by losses within any sheath or armour need to be evaluated. When significant, it becomes a factor to be considered... Material Properties Everything physical in electrical engineering from insulations to conductors revolves around materials. Here we are listing common materials along with... 8 Steps to Low Voltage Power Cable Selection and Sizing A recurring theme on our forums is cable sizing. Now many installations are unique and require special consideration. However, a lot of the time things... Calculating Cable Fault Ratings When selecting a cable, the performance of the cable under fault conditions is an important consideration. It is important that calculations be carried... Voltage Levels – Confused? I was having a conversation the other day about voltage levels.  While everyone was in agreement that low voltage was 1000 V and less, there was more confusion... Our website uses cookies so that we can provide a better experience.
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# Thread: eigenvectors 1. ## eigenvectors Hi all, For the matrix A = [1 2; 0 1], how many linearly independent eigenvector are there? First i found the eigenvalues by letting det(A- lamba*I) = 0.... the eigenvalue is lamda = 1 I then solve for my eigenvector (A - I)v = 0 i row reduce (A - I) to [0 2; 0 0] Now i am stuck... i don't know how to get my eigenvector Thanks in advance, ArTiCk 2. Hi there Originally Posted by ArTiCK Hi all, For the matrix A = [1 2; 0 1], how many linearly independent eigenvector are there? First i found the eigenvalues by letting det(A- lamba*I) = 0.... the eigenvalue is lamda = 1 I then solve for my eigenvector (A - I)v = 0 i row reduce (A - I) to [0 2; 0 0] $\begin{pmatrix} 0 & 2 \\ 0 & 0 \end{pmatrix}$ means, that you have to solve 2 equations 0*x+2*y = 0 0*x+2*y = 0 => y = 0 and any x x=1, x= 3 , x= - 10.... $\begin{pmatrix} x \\ 0 \end{pmatrix}$ is eigenvector and they are linearly dependent,....
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Table 54. Percentage distribution of academic year 2009-10 ninth-graders, by enrolled science course and discussion of courses to take: 2009 Discussion of courses to take No science   Biology   Earth science   Physical science   Chemistry   Other science1   Two or more Total 17.9 34.0 12.4 19.5 1.7 9.6 4.9 Talked about math courses to take this year with ... Mother or female guardian2 Yes 13.8 39.9 11.6 19.5 1.7 8.5 5.1 No 20.6 30.0 13.0 19.5 1.8 ! 10.5 4.6 Father or male guardian2 Yes 12.5 41.8 12.0 19.1 1.8 7.5 5.4 No 19.4 31.2 12.9 19.2 1.8 ! 10.8 4.6 Friends Yes 13.9 38.5 12.1 19.3 1.7 8.6 5.9 No 19.1 32.6 12.5 19.5 1.7 ! 10.0 4.6 Favorite teacher Yes 14.0 41.2 11.0 16.1 1.6 8.9 7.2 No 18.4 32.9 12.7 20.0 1.8 9.8 4.5 School counselor Yes 13.9 38.3 13.7 18.4 1.6 7.6 6.6 No 18.6 33.2 12.2 19.6 1.8 ! 10.1 4.6 None of these people Yes 21.7 28.3 12.6 20.0 2.2 ! 11.0 4.2 No 15.4 37.7 12.3 19.1 1.4 8.8 5.3 Talked about non-math, non-science courses to take this year with . . . Mother or female guardian2 Yes 15.6 37.5 12.4 19.5 1.4 8.7 4.9 No 20.5 30.0 12.4 19.8 2.1 ! 10.5 4.6 Father or male guardian2 Yes 14.3 38.0 12.9 19.4 1.6 8.3 5.4 No 19.3 32.2 12.4 19.3 1.9 ! 10.6 4.4 Friends Yes 15.5 35.8 12.3 20.1 1.5 9.7 5.1 No 19.4 32.9 12.5 19.3 1.9 ! 9.5 4.7 Favorite teacher Yes 16.0 37.7 11.4 18.0 1.4 8.6 7.0 No 18.2 33.3 12.6 19.9 1.8 9.7 4.5 School counselor Yes 15.5 37.1 13.6 18.3 1.3 8.0 6.2 No 18.5 33.2 12.1 20.0 1.8 ! 9.9 4.5 None of these people Yes 20.2 28.8 12.7 20.2 10.8 4.6 No 17.1 35.8 12.3 19.4 1.4 9.1 4.9 ! Interpret data with caution. Estimate is unstable because the coefficient of variation (CV) for this estimate is 30 percent or greater (i.e., the standard error represents 30 percent or more of the estimate). ‡ Reporting standards are not met. The coefficient of variation (CV) for this estimate is 50 percent or greater (i.e., the standard error represents 50 percent or more of the estimate). 1 Other science includes courses such as general science, integrated science, and principles of technology. 2 Students who did not have the appropriate parent/guardian were not included. NOTE: All estimates are weighted by W1STUDENT. Totals may not fall within the range of categorical values due to differential item nonresponse. Details may not sum to 100 percent due to rounding. SOURCE: U.S. Department of Education, National Center for Education Statistics, High School Longitudinal Study of 2009 (HSLS:09), Base-Year.
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# Geodesic dome • Aug 19th 2008, 08:49 AM jbuddenh Geodesic dome Maria and Fred decide to build a geodesic dome and to make life a little easier they make it spherical in shape, but only that portion of a sphere cut off by a plane, and less than a hemisphere. So now they need to put a roof on it. Maria measures the height h and the slice radius r and asks Fred to work out the surface area. "Thats impossible", says Fred. "Surely it will depend on R, the radius of the sphere and we don't know what that is." Who is right? ------------------------------ Note: I know the answer. I just thought this would be a fun problem. • Aug 19th 2008, 09:42 AM TKHunny I'm going with BOTH. The sphere radius, R, can be calculated from h and r. $R = h + \frac{r^{2}-h^{2}}{2h} = \frac{h^{2}+r^{2}}{2h}$ ...assuming I know what you mean by "Slice radius". • Aug 20th 2008, 11:17 AM jbuddenh Quote: Originally Posted by TKHunny I'm going with BOTH. The sphere radius, R, can be calculate from h and r. $R = h + \frac{r^{2}-h^{2}}{2h} = \frac{h^{2}+r^{2}}{2h}$ ...assuming I know what you mean by "Slice radius". Yes, you are correct. Personally, though, I find myself siding with Maria, because, if all you know is the height of the dome h and the radius of its base, r, which I called the slice radius, the surface area of the curved part of the dome is just; $\pi \, \left( {r}^{2}+{h}^{2} \right)$ and it seems both unnatural and unnecessary to figure out $R$, the radius of the sphere. • Aug 20th 2008, 01:32 PM TKHunny You talked me into it. Fred said three things: 1) Impossible 2) Needs R 3) Don't know R This is how I feel about them: 1) Simply wrong. 2) Correct, but maybe only indirectly. 3) So? Calculate it. Maria it is! Go maria!!
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# Mathematics / Year 5 / Statistics and Probability / Chance Curriculum content descriptions Recognise that probabilities range from 0 to 1 (ACMSP117) Elaborations • investigating the probabilities of all outcomes for a simple chance experiment and verifying that their sum equals 1 General capabilities • Numeracy Numeracy ScOT terms Probability,  Statistical frequency ## Refine by topic Related topic ### Introduction to probability This is a website designed for both teachers and students in year 5, and addresses components of the probability topic. It is particularly relevant for discussing chance experiments where the probability of events is equally likely and for describing those events using fractions. There are pages for both teachers and students. ... ### What Are the Chances? Do you know what chance is? It's the probability or the likelihood of something happening. Watch this video as Grace explains the probability of picking a red marble out of a bowl. What's the probability of picking a green marble? ### Numbers Count: Chance and playing with dice Have you ever played a game that required you to roll a dice? Did you know that you have equal chances of rolling any of the six numbers? Can you think of another experiment where you have an equal chance of getting one result or the other? ### Catalyst: Probability and the gambler's fallacy Mathematician Lily Serna visits Luna Park to explain a great probability pitfall. She shares a century-old tale from Monte Carlo casino, and then she puts its lesson to the test. If you flip a coin and it lands on heads three times in a row, what result would you predict for the next flip? Find out why intuition might land ... ### Comparing chance A simple interactive simulation in which students compare probabilities. This teaching resource outlines an introductory activity for students involving rolling two dice multiple times, adding the numerical value shown on the faces and recording the outcome using a tally sheet. The resource could be used by teachers to plan a class activity, or for students to carry out at home. The resource ... ### Primary mathematics: games, simulations and modelling These seven learning activities, which focus on 'games, simulations and modelling' using a variety of tools (software) and devices (hardware), illustrate the ways in which content, pedagogy and technology can be successfully and effectively integrated in order to promote learning. In the activities, teachers use games, ... ### The foul food maker: questions 1 Use a vending machine to get an awful meal such as fly soup, worm pasta or yucky duck. The machine serves a meal randomly from four slots. Work out the likelihood of getting each type of meal. Then choose a matching probability word: impossible, unlikely, equal, likely or certain. Run simple probability experiments. Compare ... ### The foul food maker: go figure This tutorial is suitable for use with a screen reader. It explains how the use of simple words can describe the likelihood of everyday events. How likely is an event: certain, likely, equal chance, unlikely or certainly not? Answer some questions using these words and then build your own examples. Learn how to describe ... ### Mystery spinner: challenge Look at results in a frequency graph compiled after testing an unseen spinner. Work out the likely proportions of colours in the mystery spinner. Use a tool to build a new spinner (a dial with a pointer). Choose up to five equal-sized sectors. Fill the sectors with up to five colours. For example, make a five-part spinner ... ### Statistics games This resource is a web page containing three dice games to explore chance. Each dice game has simple instructions to play the interactive strategy game. The games provide a useful way to investigate the chance of rolling a particular number after successive trials. This resource is one activity from the NRICH collection.
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Converter Converting decimal 93 to hexadecimal? Dec 93 to Hex = 5d Ultimate Binary to Decimal to Hexadecimal Converter. The binary-hexadecimal-decimal converter is capable of instantly converting back and forth between binary, decimal, and hexadecimal numbers. N2 N10 N16 ## How to use the Binary-Decimal-Hexadecimal Converter? Our Bin-to-Dec-to-Hex converter is a very easy-to-use online tool that will enable you to perform a conversion of any binary, decimal, or hexadecimal number quickly. You can enter a number in any field and the conversion is immediate. So for example, if you start to write a binary number in the binary number field, you can see the result of the decimal and hexadecimal conversion in real-time.  Our free tool can perform the following operations: • Binary to Decimal Conversion (as a Bin to Dec Converter) • Binary to Hexadecimal Conversion (as a Bin to Hex Converter) • Decimal to Binary Conversion (as a Dec to Bin Converter) • Decimal to Hexadecimal Conversion (as a Dec to Hex Converter) • Hexadecimal to Decimal Conversion (as a Hex to Dec Converter) • Hexadecimal to Binary Conversion (as a Hex to Bin Converter) ## Example calculations: Binary to Decimal Converter 1110 Binary to Decimal = 14 1011100 Binary to Decimal = 92 10011 Binary to Decimal = 19 10011110 Binary to Decimal = 158 1111100 Binary to Decimal = 124 11110111 Binary to Decimal = 247 ## Example calculations: Binary to Hexadecimal Converter 110000 Binary to Hexadecimal = 30 1001011 Binary to Hexadecimal = 4b 11010101 Binary to Hexadecimal = d5 1000101 Binary to Hexadecimal = 45 10110001 Binary to Hexadecimal = b1 10101001 Binary to Hexadecimal = a9 ## Example calculations: Decimal to Binary Converter 46 Decimal to Binary = 101110 253 Decimal to Binary = 11111101 109 Decimal to Binary = 1101101 100 Decimal to Binary = 1100100 220 Decimal to Binary = 11011100 195 Decimal to Binary = 11000011 ## Example calculations: Decimal to Hexadecimal Converter 182 Decimal to Hexadecimal = b6 110 Decimal to Hexadecimal = 6e 75 Decimal to Hexadecimal = 4b 200 Decimal to Hexadecimal = c8 87 Decimal to Hexadecimal = 57 94 Decimal to Hexadecimal = 5e ## Example calculations: Hexadecimal to Binary Converter 2b Hexadecimal to Binary = 101011 46 Hexadecimal to Binary = 1000110 f6 Hexadecimal to Binary = 11110110 c5 Hexadecimal to Binary = 11000101 29 Hexadecimal to Binary = 101001 e1 Hexadecimal to Binary = 11100001 ## Example calculations: Hexadecimal to Decimal Converter fb Hexadecimal to Decimal = 251 24 Hexadecimal to Decimal = 36 72 Hexadecimal to Decimal = 114 e2 Hexadecimal to Decimal = 226 b0 Hexadecimal to Decimal = 176 d6 Hexadecimal to Decimal = 214 Q&A ## Similar calculations: Decimal to Binary Converter 94 Decimal to Binary = 1011110 95 Decimal to Binary = 1011111 96 Decimal to Binary = 1100000 97 Decimal to Binary = 1100001 98 Decimal to Binary = 1100010 99 Decimal to Binary = 1100011 100 Decimal to Binary = 1100100 101 Decimal to Binary = 1100101 102 Decimal to Binary = 1100110 103 Decimal to Binary = 1100111 104 Decimal to Binary = 1101000 105 Decimal to Binary = 1101001 106 Decimal to Binary = 1101010 107 Decimal to Binary = 1101011 108 Decimal to Binary = 1101100 109 Decimal to Binary = 1101101 110 Decimal to Binary = 1101110 111 Decimal to Binary = 1101111 112 Decimal to Binary = 1110000 113 Decimal to Binary = 1110001 114 Decimal to Binary = 1110010 115 Decimal to Binary = 1110011 116 Decimal to Binary = 1110100 117 Decimal to Binary = 1110101 118 Decimal to Binary = 1110110 119 Decimal to Binary = 1110111 120 Decimal to Binary = 1111000 121 Decimal to Binary = 1111001 122 Decimal to Binary = 1111010 123 Decimal to Binary = 1111011 ## Similar calculations: Decimal to Hexadecimal Converter Decimal 93 to Hexadecimal Converter | Binary to Decimal to Hexadecimal Converter
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# physics posted by . Object A, which has mass m and a velocity Voi,collides with the Object B,which has mass 2m and a velocity 1/2Voj.Following the collision ,object B has a velocity of 1/4Voi.(a) Determine the velocity of object A after the collision.(b) Is the collision elastic? If not, express the change in the kinetic energy in terms of m and Vo. • physics - mVoi+mVoj=2mVoi/4+m*x x=(Voi+Voj-Voi/2)=Voi/2+Voj Now, check the KE before the reaction, and the KE after the collision, and see if they are equal. ## Similar Questions 1. ### Physics Consider a perfectly elastic collision between two objects of equal mass. Object 1 is initially moving with a velocity v = 4.33 m/s while object 2 is at rest. What are the final velocities after the collision? 2. ### physics Object A, which has a mass m and a velocity Vo(i,) ̂ collides with object B, which has a mass 2m and velocity 1/2Vo(j.) ̂ Following the collision ,object B has a velocity of 1/4Vo(i.) ̂(a)Determine the velocity of object … 3. ### Physics A 26.0 g object moving to the right at 17.0 cm/s overtakes and collides elastically with a 10.0 g object moving in the same direction at 15.0 cm/s. Find the velocity of each object after the collision. a) 26.0 g object b) 10.0 g object 4. ### Physics A 5.00 g object moving to the right at +20.0 cm/s makes an elastic head-on collision with a 10.0 g object that is initially at rest. (a) Find the velocity of each object after the collision. 5.00 g object cm/s 10.0 g object cm/s (b) … 5. ### science A 2 kg object moving with a velocity of +5 m/s collides with a 4 kg object that is initially at rest. After the collision, the 2 kg object moves with a velocity of -1 m/s. (a) Find the velocity of the 4 kg object after the collision. … 6. ### Physics object A of mass 3g with a velocity of 12cm/s to the east, collides with stationary object B. After collision, object A rebounds with a velocity of 10cm/s to the west and object B has a velocity of 1.5cm/s to the east. Calculate the … 7. ### physics Object A is moving due east, while object B is moving due north. They collide and stick together in a completely inelastic collision. Momentum is conserved. Object A has a mass of mA = 17.5 kg and an initial velocity of = 8.50 m/s, … 8. ### PHYSICS MAT A 1.2 kg object moving at initial velocity 2.0m/s collides elastically with a stationary 0.5kg object horizontally. Calculate A) the velocity of each object after the collision. B) the impulsive force if the contact time is 0.3 s. 9. ### physics An object A, of mass 1 kg that is moving at a velocity of 6ms^-1 collides with a stationary object of mass 3kg. after the collision, the object move in the directions as shown. Determine the value of V1 and V2. 10. ### Physics Object A is moving due east, while object B is moving due north. They collide and stick together in a completely inelastic collision. Momentum is conserved. Object A has a mass of mA = 17.0 kg and an initial velocity of VoA = 8.15 … More Similar Questions
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# Complicated Motion Problem A garden roller with external radius a is pulled along a rough horizontal path by force F which acts at a point on its axle and is inclined at an angle alpha with the horizontal. Given that resultant force is at a right angle to F, what is the acceleration of the roller? Express in terms of radius a, alpha, and radius of gyration k. My set-up (and failure): Let H be resultant force, f_s is frictional force Forces in x-dir: $$Hsin( \alpha) = Fcos( \alpha) - f_s$$ Forces in y-dir: $$-Hcos( \alpha) = Fsin( \alpha) - mg$$ Rotational equation of motion: $$af_s = \frac{mk^2}{a} \ddot{x}$$ Assume no slipping: $$\ddot{x} = a \ddot{ \theta}$$ Solve for x-acceleration: $$\ddot{x} = \frac{a^2 F - a^2 mgsin( \alpha)}{mk^2 cos( \alpha)}$$ $$\ddot{x} = \frac{ga^2 sin( \alpha) cos( \alpha)}{k^2 + a^2 sin^2 (\alpha)}$$ Where am I going wrong? I don't see why F isn't in the answer...
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Courses Courses for Kids Free study material Offline Centres More Store # For a dibasic acid,${H_2}A \Leftrightarrow H{A^ - } + {H^ + }({K_1})$${H_2}A \Leftrightarrow 2{H^ + } + {H^ + }({K_2})$$ {H_2}A \Leftrightarrow 2{H^ + } + {A^{2 - }}(K)$then(A) $K = {K_1} + {K_2}$(B) $K = {K_1} - {K_2}$(C) K = $\dfrac{{{K_1}}}{{{K_2}}}$ (D) K = ${K_1} \times {K_2}$ Last updated date: 20th Jun 2024 Total views: 394.2k Views today: 6.94k Verified 394.2k+ views Hint: The above question is based on chemical kinetics also known as reaction kinetics, is the branch of physical chemistry that is concerned with understanding the rates of chemical reactions. For multiple reaction rates, we should compare the reaction rates of each equation and try to find out the relation between each rate of reaction. Complete Solution : A reaction may include one or more than one step. The vast amount of work done in chemical kinetics has led to the conclusion that some chemical reactions go in a single step known as elementary reactions. Other reactions go in more than one step and are said to be stepwise or complex. Measurements of the rates of chemical reactions over a range of conditions can show whether a reaction proceeds in one or more steps. The rate of reaction is affected by several factors. Some of them are listed below: - Concentration: We know, the reactions are due to collisions of reactant species. The frequency with which the molecules or ions collide depend on their concentrations. The more crowded molecules are, more likely they are to collide and react with one another. Therefore, an increase in the concentrations of the reactants will usually result in the increase in the reaction rate, while a decrease in the concentrations will usually have a reverse effect. - Temperature: Usually temperature has a major effect on the rate of a chemical reaction. Molecules at a higher temperature will have more thermal energy. Although collision frequency is greater at higher temperatures, this alone contributes only a very small proportion to the increase in the rate of reaction. - Catalysts: A catalyst is a substance that alters the rate of a chemical reaction, but it remains chemically unchanged after the completion of reaction. The catalyst increases the rate of the reaction by providing a new reaction mechanism or pathway to occur in a lower activation energy. In the case of dibasic acid, reaction occurs at multiple rates so first of all we have to find the relation of each rate constant. For reaction 1 ${H_2}A \Leftrightarrow H{A^ - } + {H^ + }({K_1})$ ${K_1} = \dfrac{{[H{A^ - }][{H^ + }]}}{{[{H_2}A]}}$ For reaction 2 $H{A^ - }\underset {} \leftrightarrows {A^{ - 2}} + {H^ + }({K_2})$ ${K_2} = \dfrac{{[{A^{ - 2}}][{H^ + }]}}{{[H{A^ - }]}}$ For reaction 3 ${H_2}A \Leftrightarrow 2{H^ + } + {A^{2 - }}(K)$ $K = \dfrac{{{{[{H^ + }]}^2}[{A^{2 - }}]}}{{[{H_2}A]}}$ Now, by multiplying $K_1$ and $K_2$, we will get ${K_1} \times {K_2} = \dfrac{{[H{A^ - }][{H^ + }]}}{{[{H_2}A]}} \times \dfrac{{[{A^{2 - }}][{H^ + }]}}{{[H{A^ - }]}}$ ${K_1} \times {K_2} = \dfrac{{{{[{H^ + }]}^2}[{A^{2 - }}]}}{{[{H_2}A]}} = K$ So, the correct answer is “Option D”. Note: Remember that in case of multi-step reaction. The rate is dependent on the slow step i.e. the step which requires the maximum amount of energy. All other steps which have less energy than the slow step are called fast steps.
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## What do you mean by average? In colloquial language, an average is a single number taken as representative of a non-empty list of numbers. Different concepts of average are used in different contexts. Often ” average ” refers to the arithmetic mean, the sum of the numbers divided by how many numbers are being averaged. ## What is average formula? What is the average formula? The formula to calculate average of given numbers is equal to the sum of all the values divided by total number of values. ## What is average and range? To find an average of a set of numbers, add them all up and divide by the total amount of numbers. The range is the difference between the largest and the smallest numbers in the set. They are useful in sports. ## What is the average between 70 and 100? 85 is an average of two given numbers 70 & 100. ## How do I calculate mean? The mean is the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. In other words it is the sum divided by the count. You might be interested:  FAQ: What Is Solution Set In Math? ## What is average in simple words? An average is the “normal” number of a group of numbers made by mixing the group of numbers. In math, an average is called a mean. It can be found by adding the numbers, then dividing the answer by the number of numbers there were. ## What is percentage formula? To determine the percentage, we have to divide the value by the total value and then multiply the resultant to 100. Percentage formula = (Value/Total value)×100. Example: 2/5 × 100 = 0.4 × 100 = 40 per cent. ## What is the formula of mode? Thus, the mode can be found by substituting the above values in the formula: Mode = L + h (fm−f1)(fm−f1)+(fm−f2) ( f m − f 1 ) ( f m − f 1 ) + ( f m − f 2 ). Thus, Mode = 10 + 5 (7−3)(7−3)+(7−2) ( 7 − 3 ) ( 7 − 3 ) + ( 7 − 2 ) = 10 + 5 × 4/9 = 10 + 20/9 = 10 + 2.22 = 12.22. ## Why do we calculate average? The average is the value that can replace every existing item, and have the same result. If I could throw away my data and replace it with one “ average ” value, what would it be? One goal of the average is to understand a data set by getting a “representative” sample. ## Whats a mode and range? The mode is the number that occurred the most often. The range is the difference between the highest and lowest values. ## How do you find range? The range is the difference between the smallest and highest numbers in a list or set. To find the range, first put all the numbers in order. Then subtract (take away) the lowest number from the highest. The answer gives you the range of the list. You might be interested:  Readers ask: What Is The Meaning Of Right Angle In Math? ## How do you work out mean median and mode? Mean: Add up all the numbers of the set. Divide by how many numbers there are. Mode: The number that occurs the most. ## What is the average between 75 and 100? 87.5 is an average of two given numbers 75 & 100. ## Why You Should not average percentages? Therefore, the temptation of averaging percentages can provide inaccurate results. As previously mentioned, there is one exception where the average of percentages agrees with the accurate percentage calculation. This occurs when the sample size in both groups are the same. ## What is the average between 85 and 100? 92.5 is an average of two given numbers 85 & 100.
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Welcome Guest You last visited December 11, 2016, 6:48 am All times shown are Eastern Time (GMT-5:00) # Mega Millions changing June 24 -official Topic closed. 59 replies. Last post 12 years ago by tg636. Page 2 of 4 USA United States Member #8242 October 29, 2004 1133 Posts Offline Posted: April 17, 2005, 8:54 pm - IP Logged Quote: Originally posted by danisiri on April 17, 2005 It is just simple probablity.  Buy one ticket you have a chance of 1 in some huge number.  Buy five tickets, you have 5 chances in some huge number.  Theoretically, you could buy every number combination, but the jackpot would have to be around \$16 billion to break even. Yes that is simple, but I don't see how a "higher jackpot" betters anyones chances of winning, versus a lower jackpot. The number of combinations remains the same no matter what the jackpot is, if I'm correct. If one spends \$2, it's 2 chances out of 135 million+. If one spends \$20, it's 20 chances out of 135 million+. I understand one has a better chance of winning if more money is spent, but a higher jackpot doesn't increase one's chances of winning, if I'm not mistaken. Can anyone else add to this? Thanx. Greenwich, CT United States Member #4793 May 24, 2004 1822 Posts Offline Posted: April 17, 2005, 8:58 pm - IP Logged Maverick, You are correct.  Buy 10 tickets and you have the same odds of winning a \$10m jackpot as winning a \$200m jackpot.  I'm just more inclined to buy those 10 tickets at the \$200m level because I want to win big. USA United States Member #8242 October 29, 2004 1133 Posts Offline Posted: April 17, 2005, 9:00 pm - IP Logged Ok JAG331, that I do understand. United States Member #972 December 30, 2002 465 Posts Offline Posted: April 18, 2005, 9:07 am - IP Logged I am waiting to see the overall odds of winning any prize (currently 1:43) and the odds and amounts of the lower prizes.  Adding 40,000,000 more combinations to an already huge 135,000,000 is a little much for me, and whether I am going to get a ticket for every drawing or wait for \$200 million+ jackpot will depend on the lower prizes and odds. I'm on the fence; it might just seem too impossible to bother with.  I have criticized MA Megabucks, but the odds of winning that are 35 times better than the new Mega Millions will be, and I'd like to have somewhat of a chance.  After all, you do play to win a jackpot in your lifetime. United States Member #379 June 5, 2002 11296 Posts Offline Posted: April 18, 2005, 9:37 am - IP Logged tg: MM will still have a cash option, unlike Megais bad\$. United States Member #972 December 30, 2002 465 Posts Offline Posted: April 18, 2005, 10:01 am - IP Logged Yeah, I know, but so what.  The question is, do you want to have a slim chance at winning a jackpot or almost no chance.  One in 5 million sounds a lot better than one in 175 million, and I think I could live okay on \$2.2 million over 20 years. Quote: Originally posted by CASH Only on April 18, 2005 tg: MM will still have a cash option, unlike Megais bad\$. USA United States Member #8242 October 29, 2004 1133 Posts Offline Posted: April 18, 2005, 1:10 pm - IP Logged Quote: Originally posted by tg636 on April 18, 2005 Adding 40,000,000 more combinations to an already huge 135,000,000 is a little much for me, and whether I am going to get a ticket for every drawing or wait for \$200 million+ jackpot will depend on the lower prizes and odds... just seem too impossible to bother with.  I have criticized MA Megabucks, but the odds of winning that are 35 times better than the new Mega Millions will be, and I'd like to have somewhat of a chance.  After all, you do play to win a jackpot in your lifetime. USA United States Member #8242 October 29, 2004 1133 Posts Offline Posted: April 18, 2005, 1:12 pm - IP Logged Quote: Originally posted by tg636 on April 18, 2005 Yeah, I know, but so what.  The question is, do you want to have a slim chance at winning a jackpot or almost no chance.  One in 5 million sounds a lot better than one in 175 million, and I think I could live okay on \$2.2 million over 20 years. That's a very good point. Before we can debate on cash vs annuity, WE FIRST NEED TO WIN A JACKPOT. First things first. United States Member #2338 September 17, 2003 2063 Posts Offline Posted: April 18, 2005, 3:07 pm - IP Logged I think it depends on sales. If sales go up then they should just add more money to the next roll so it can go from 12 to 20 faster. As far as the odds go your odds always are bad in a lottery. I didn't win the quinto at \$5 million and the odds were only 1:2.6 million, odds are I won't win the Mega or powerball either. It's about hope and the chance to win more than anything. United States Member #2338 September 17, 2003 2063 Posts Offline Posted: April 18, 2005, 3:55 pm - IP Logged I am also wondering why no official announcement on the website? San Angelo, Texas United States Member #1097 January 31, 2003 1394 Posts Offline Posted: April 18, 2005, 4:50 pm - IP Logged If you read the minutes of the March Texas Lottery Commission meeting (see Legal notices at their website) you will discover that MegaMillions isn't run by any one person. The lottery directors of the participating states make a lot of decisions via telephone, emails, etc. They do meet once in a while, but there are no announcements, no public information on an agenda, no minutes are kept (violates some states open records acts), winks, buddy systems, you name it. Maximum profit seems to be the main directive. Basically, its a secret organization. They do follow a basic set of rules, which was discussed at length at the Texas commission meeting. You will find a lot of comment about some potential problems when California starts. I don't understand all of it, but I think everything they do is weighed by all directors, if only to protect the state's financial interests. I think a couple of directors have a free hand and aren't really responsible to anyone. Dawn Nettles of lottoreport.com (see drawing results) has managed to get individual sales figures. She has lot of other information that players might find useful. Just scroll down her results page to MegaMillions. United States Member #620 August 25, 2002 205 Posts Offline Posted: April 18, 2005, 10:09 pm - IP Logged I for one would like to see MegaMillions restructured to the point where jackpots are won in the \$20-\$50-million range.  We're being played for suckers if we have to wait for someone to win a \$300-\$400-million jackpot! No one really needs that kind of money.  Why not restructure where there could be 8-15 winners or so how of those super jackpots? I play to dream and dream of winning a major jackpot! USA United States Member #8242 October 29, 2004 1133 Posts Offline Posted: April 18, 2005, 10:44 pm - IP Logged Quote: Originally posted by rabbitfoot on April 18, 2005 I for one would like to see MegaMillions restructured to the point where jackpots are won in the \$20-\$50-million range.  We're being played for suckers if we have to wait for someone to win a \$300-\$400-million jackpot! No one really needs that kind of money.  Why not restructure where there could be 8-15 winners or so how of those super jackpots? \$20 - \$50 million... They'd probably say that's what your own state lottery is for. \$300 - \$400 million jackpot... No one needs that kind of money, but that is what MM is about. Morrison, IL United States Member #4657 May 13, 2004 1884 Posts Offline Posted: April 18, 2005, 10:50 pm - IP Logged Not many state lotto jackpots get into the \$20 to \$50 million range that often. Greenwich, CT United States Member #4793 May 24, 2004 1822 Posts Offline Posted: April 18, 2005, 11:15 pm - IP Logged It's all about EXCESS.  More is good and more than more is even better!  Live a little, spend a little, dream a little, someone's going to win a lot. Page 2 of 4
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# 5 Best Ways to Check Reachability to the Leftmost or Rightmost Position in Python Rate this post πŸ’‘ Problem Formulation: In Python, there are various methods by which we can determine whether an element, provided with a series of movements or conditions, can move from a starting position to the leftmost or rightmost edge in a list. Given a list and a starting position, we want a function that returns `True` if the element can reach either end of the list or `False` if it cannot. ## Method 1: Iterative Traversal This method involves iteratively moving through the list from the starting position. If the current value allows, we can move left or right, checking at each step if we’ve reached an end. This method is straight-forward and easy to understand. Here’s an example: ```def can_reach_ends(lst, start): left, right = 0, len(lst) - 1 pos = start while 0 <= pos < len(lst): if pos == left or pos == right: return True pos += lst[pos] return False # Example usage print(can_reach_ends([2, -1, 1, 2, 3], 2)) ``` Output: `True` This code defines a function `can_reach_ends` that takes a list `lst` and a starting index `start`. It iteratively updates the position by adding the current value in the list to the index, moving left or right accordingly. It returns `True` as soon as an end is reached. ## Method 2: Recursive Traversal Recursive traversal uses the principle of divide and conquer. We recursively check both possibilities from the starting position – moving left and moving right (if possible), until we either hit an end or can’t move any further. Here’s an example: ```def can_reach_ends_recursive(lst, pos, visited=None): if visited is None: visited = set() if pos = len(lst) or pos in visited: return False if pos == 0 or pos == len(lst) - 1: return True return can_reach_ends_recursive(lst, pos + lst[pos], visited) or can_reach_ends_recursive(lst, pos - lst[pos], visited) # Example usage print(can_reach_ends_recursive([1, 3, -2, 2, 5], 3)) ``` Output: `False` The function `can_reach_ends_recursive` checks reachability using recursion. It marks positions as visited to avoid infinite loops. It returns `False` if out-of-bounds or a cycle is detected, and `True` if an end is reached. ## Method 3: Using a Stack This method uses a stack to keep track of positions to visit next. We simulate a depth-first search by popping the last position from the stack and exploring adjacent positions until we reach an end or exhaust all possibilities. Here’s an example: ```def can_reach_ends_stack(lst, start): stack = [start] visited = set() while stack: pos = stack.pop() if pos = len(lst) or pos in visited: continue if pos == 0 or pos == len(lst) - 1: return True stack.append(pos + lst[pos]) stack.append(pos - lst[pos]) return False # Example usage print(can_reach_ends_stack([1, -1, 3, 2, 0], 3)) ``` Output: `True` The function `can_reach_ends_stack` behaves similarly to the recursive approach but uses an explicit stack to keep track of positions, making it iterative and avoiding stack overflows for larger lists. ## Method 4: Using a Queue Using a queue enables us to implement a breadth-first search algorithm. We systematically explore each possible move level by level, which can be more efficient than depth-first search in certain scenarios. Here’s an example: ```from collections import deque def can_reach_ends_queue(lst, start): queue = deque([start]) visited = set() while queue: pos = queue.popleft() if pos = len(lst) or pos in visited: continue if pos == 0 or pos == len(lst) - 1: return True queue.append(pos + lst[pos]) queue.append(pos - lst[pos]) return False # Example usage print(can_reach_ends_queue([3, 4, -2, 1, 2], 1)) ``` Output: `True` The function `can_reach_ends_queue` uses a queue to explore possibilities in order of their discovery, providing an alternative search strategy that might yield a result faster than depth-first approaches. ## Bonus One-Liner Method 5: Using Python Shortcuts Although not always applicable, Python allows for concise expressions using generator expressions and built-in functions. For specific cases where we have straightforward move patterns, we can use these tricks. Here’s an example: ```def can_reach_ends_shortcut(lst, start): return 0 in (start + i for i in lst) or (len(lst) - 1) in (start + i for i in lst) # Example usage print(can_reach_ends_shortcut([-1, 0, 1, 2, 3], 1)) ``` Output: `False` This one-liner `can_reach_ends_shortcut` function makes use of generator expressions to quickly check if a move directly to the leftmost or rightmost position is possible. Note that it assumes each list element is a unit step, and thus, its applicability is limited. ## Summary/Discussion • Method 1: Iterative Traversal. Direct and easy to understand. However, it can be inefficient due to repeated work in large datasets. • Method 2: Recursive Traversal. Elegant and compact code. But can cause stack overflow on large inputs due to deep recursion. • Method 3: Using a Stack. Iterative with explicit control over the stack, avoiding stack overflow issues. The disadvantage is the same as with Method 1: potential inefficiency on large datasets. • Method 4: Using a Queue. Level-by-level search can be faster to find an answer in some cases. Nonetheless, it still has the possibility for inefficiency and might use more memory than stack-based methods. • Bonus One-Liner Method 5: Very concise. Works best when movement is restricted to one step in either direction and doesn’t generalize well.
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<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" /> # Geometric Probability ## Use geometric properties to evaluate probability Levels are CK-12's student achievement levels. Basic Students matched to this level have a partial mastery of prerequisite knowledge and skills fundamental for proficient work. At Grade (Proficient) Students matched to this level have demonstrated competency over challenging subject matter, including subject matter knowledge, application of such knowledge to real-world situations, and analytical skills appropriate to subject matter. Advanced Students matched to this level are ready for material that requires superior performance and mastery. • Video ## Geometric Probability A lesson on geometric probability with an example involving darts. Courtesy of Allison Grajkowske MEMORY METER This indicates how strong in your memory this concept is 1
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GMAT Question of the Day - Daily to your Mailbox; hard ones only It is currently 19 Oct 2019, 06:38 ### GMAT Club Daily Prep #### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email. Customized for You we will pick new questions that match your level based on your Timer History Track every week, we’ll send you an estimated GMAT score based on your performance Practice Pays we will pick new questions that match your level based on your Timer History # What was the average number of miles per gallon of gasoline for a truc Author Message TAGS: ### Hide Tags Math Expert Joined: 02 Sep 2009 Posts: 58449 What was the average number of miles per gallon of gasoline for a truc  [#permalink] ### Show Tags 15 Oct 2019, 02:27 00:00 Difficulty: (N/A) Question Stats: 89% (00:55) correct 11% (00:52) wrong based on 9 sessions ### HideShow timer Statistics What was the average number of miles per gallon of gasoline for a truck during a certain trip? (1) The total cost of the gasoline used by the truck for the 192-mile trip was \$23.00 (2) The cost of the gasoline used by the truck for the trip was \$2.10 per gallon. _________________ Intern Joined: 10 Mar 2018 Posts: 41 Location: India Concentration: Entrepreneurship, Marketing WE: Design (Retail) Re: What was the average number of miles per gallon of gasoline for a truc  [#permalink] ### Show Tags 15 Oct 2019, 11:49 (1) No information about the price per gallon- Not sufficient (2) Given price per gallon- Not sufficient Combining Statement 1 and 2 we get total no. of gallons used for the trip = 23/2.1= some no. around 11 =>approx 11 gallons of gasoline used for 192 miles Thus average no. of miles per gallon can be calculated. Sufficient Ans (C) _________________ ~ETERNAL~ Re: What was the average number of miles per gallon of gasoline for a truc   [#permalink] 15 Oct 2019, 11:49 Display posts from previous: Sort by
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Number Of Beers In A Half Keg Introduction A half keg is a popular size for beer kegs, especially for parties and events. It is important to know how many beers can fit in a half keg to ensure that there is enough for everyone to enjoy. How Many Beers Are in a Half Keg? When it comes to hosting a party or event, one of the most important things to consider is the amount of alcohol you need to serve your guests. If you’re planning on serving beer, you may be wondering how many beers are in a half keg. A half keg is a popular choice for parties and events, as it provides a large amount of beer without taking up too much space. So, how many beers are in a half keg? The answer depends on a few factors, including the size of the keg and the size of the beer glasses you plan on using. A standard half keg, also known as a pony keg, holds 15.5 gallons of beer. This is equivalent to 165 12-ounce cans of beer or 124 16-ounce pints of beer. However, it’s important to keep in mind that not all beer glasses are created equal. A standard pint glass holds 16 ounces of beer, while a standard beer mug holds 12 ounces. If you plan on serving beer in pint glasses, you’ll get fewer servings out of a half keg than if you serve beer in smaller glasses. Another factor to consider is the amount of foam that is produced when pouring beer. Foam takes up space in the glass, which means you’ll get fewer servings out of a half keg if you have a lot of foam. To minimize foam, make sure your beer is properly chilled and that your glasses are clean and dry before pouring. If you’re still unsure about how many beers are in a half keg, there are a few online calculators that can help you determine the number of servings based on the size of the keg and the size of the glasses you plan on using. These calculators take into account the amount of foam that is produced when pouring beer, so you can get a more accurate estimate of how much beer you’ll need for your event. It’s also important to consider the preferences of your guests when deciding how much beer to serve. If you have a group of heavy drinkers, you may need to order more beer than if you have a group of light drinkers. It’s always better to have too much beer than not enough, so err on the side of caution when ordering. In addition to the number of beers in a half keg, it’s also important to consider the type of beer you’re serving. Different types of beer have different alcohol contents, which can affect how much your guests drink. For example, a light beer may be more popular among light drinkers, while a heavier beer may be more popular among heavy drinkers. Overall, the number of beers in a half keg depends on a few factors, including the size of the keg, the size of the glasses you plan on using, and the preferences of your guests. By taking these factors into account, you can ensure that you have enough beer to keep your guests happy and satisfied throughout your event. The Pros and Cons of Ordering a Half Keg for Your Party When it comes to hosting a party, one of the most important decisions you’ll make is how much alcohol to provide. If you’re expecting a large crowd, a half keg of beer might seem like a good option. But before you place your order, it’s important to consider the pros and cons of this choice. First, let’s talk about the number of beers you can expect to get from a half keg. A standard half keg contains 15.5 gallons of beer, which translates to approximately 165 12-ounce servings. This means that if you’re expecting 50 guests and each person drinks two beers, a half keg should be enough to keep everyone happy. One of the biggest advantages of ordering a half keg is the cost savings. Buying beer in bulk is almost always cheaper than purchasing individual bottles or cans. Plus, you won’t have to worry about running out of beer halfway through the party, which can be a major inconvenience. Another benefit of a half keg is the convenience factor. Instead of having to constantly restock your cooler with individual cans or bottles, you can simply tap the keg and let your guests serve themselves. This can free up your time to focus on other aspects of the party, such as food and entertainment. However, there are also some downsides to ordering a half keg. For one, it can be difficult to store and transport. Kegs are heavy and bulky, and you’ll need a special tap and CO2 system to dispense the beer. This can be a hassle if you don’t have experience with kegs or if you’re hosting the party in a location that’s not easily accessible. Another potential issue is the amount of waste that can be generated from a half keg. If your guests don’t finish all the beer, you’ll be left with a partially full keg that will need to be disposed of. This can be a waste of money and resources, especially if you’re trying to be environmentally conscious. Finally, it’s important to consider the preferences of your guests. While beer is a popular choice for many parties, not everyone enjoys it. If you have a diverse group of guests, you may want to consider offering other drink options as well, such as wine or cocktails. In conclusion, ordering a half keg of beer can be a great option for a party, but it’s important to weigh the pros and cons before making your decision. Consider the number of guests you’re expecting, the cost savings, and the convenience factor, as well as the potential downsides such as storage and waste. And don’t forget to offer other drink options to accommodate all of your guests’ preferences. With a little planning and preparation, your party is sure to be a success. Calculating the Cost Per Beer for a Half Keg When it comes to hosting a party or event, one of the most important things to consider is the amount of alcohol you will need to serve your guests. If you are planning on serving beer, you may be wondering how many beers are in a half keg and how much it will cost per beer. In this article, we will explore the answers to these questions and provide you with some helpful tips for calculating the cost per beer for a half keg. Firstly, let’s define what a half keg is. A half keg, also known as a pony keg, is a beer keg that holds 15.5 gallons of beer. This is equivalent to 165 12-ounce cans of beer or 124 16-ounce pints of beer. It is important to note that the number of beers in a half keg will vary depending on the size of the beer glass you are using to serve the beer. Now that we know how much beer is in a half keg, let’s move on to calculating the cost per beer. The cost of a half keg will depend on the brand and type of beer you choose, as well as your location and the retailer you purchase it from. On average, a half keg of domestic beer will cost around \$150, while a half keg of imported beer can cost upwards of \$300. To calculate the cost per beer, you will need to divide the total cost of the half keg by the number of beers it contains. For example, if you purchase a half keg for \$150 and it contains 165 12-ounce cans of beer, the cost per beer would be approximately \$0.91. If you are serving 16-ounce pints of beer, the cost per beer would be approximately \$1.21. It is important to keep in mind that the cost per beer will also depend on the amount of beer you are serving per glass. If you are serving 12-ounce cans of beer, the cost per beer will be lower than if you are serving 16-ounce pints of beer. Additionally, if you are charging your guests for the beer, you may want to consider adding a markup to the cost per beer to cover any additional expenses, such as cups or ice. When purchasing a half keg, it is important to plan ahead and make sure you have enough beer for your guests. As a general rule of thumb, you should plan on serving two beers per person for the first hour and one beer per person for each additional hour. This will ensure that you have enough beer for everyone and that your guests are able to enjoy themselves without running out of drinks. In conclusion, a half keg of beer contains approximately 165 12-ounce cans of beer or 124 16-ounce pints of beer. The cost per beer will depend on the brand and type of beer you choose, as well as your location and the retailer you purchase it from. To calculate the cost per beer, you will need to divide the total cost of the half keg by the number of beers it contains. When purchasing a half keg, it is important to plan ahead and make sure you have enough beer for your guests. By following these tips, you can ensure that your guests have a great time and that your event is a success. Tips for Storing and Serving Beer from a Half Keg When it comes to serving beer at a party or gathering, a half keg is a popular choice. But how many beers can you actually get out of a half keg? And how can you ensure that the beer stays fresh and properly served throughout the event? In this article, we will provide some tips for storing and serving beer from a half keg. Firstly, let’s address the question of how many beers are in a half keg. A standard half keg, also known as a pony keg, contains 15.5 gallons of beer. This equates to approximately 165 12-ounce servings of beer. Of course, this number can vary depending on the size of the glasses being used and how much foam is poured with each serving. It’s always a good idea to have some extra beer on hand, just in case. Now that we know how much beer is in a half keg, let’s talk about how to properly store and serve it. The most important factor in keeping beer fresh is temperature. Beer should be stored at a consistent temperature of around 38-40 degrees Fahrenheit. If the beer gets too warm, it can spoil or become flat. If it’s too cold, it can freeze and expand, causing the keg to burst. To keep the beer at the right temperature, it’s best to use a kegerator or a large cooler filled with ice. A kegerator is a refrigerated unit specifically designed for storing and serving beer from a keg. It’s a great investment if you plan on serving beer regularly. If you don’t have a kegerator, a large cooler filled with ice can work just as well. Simply place the keg inside the cooler and surround it with ice. Make sure to keep the lid closed as much as possible to maintain the temperature. When it comes to serving the beer, there are a few things to keep in mind. First, make sure the tap is properly installed and tightened. A loose tap can cause the beer to foam excessively and make a mess. Second, pour the beer at a 45-degree angle into a clean, dry glass. This will help reduce the amount of foam and ensure a proper pour. Finally, don’t overfill the glass. Leave some room at the top for the foam to settle. It’s also important to keep the beer lines clean to prevent any off-flavors or bacteria from developing. This can be done by running a cleaning solution through the lines every few weeks. If you’re not comfortable doing this yourself, there are professional cleaning services available. In addition to temperature and cleanliness, it’s important to consider the type of beer you’re serving. Different styles of beer have different serving temperatures and carbonation levels. For example, a light lager should be served colder and with more carbonation than a stout or porter. It’s a good idea to research the specific beer you’re serving to ensure it’s being served at the optimal temperature and carbonation level. In conclusion, a half keg can provide plenty of beer for a party or gathering. By keeping the beer at the right temperature, using a clean tap, and pouring properly, you can ensure that your guests will enjoy fresh, delicious beer throughout the event. Remember to do your research on the specific beer you’re serving and invest in a kegerator or large cooler if you plan on serving beer regularly. Cheers! Comparing the Number of Beers in a Half Keg to Other Keg Sizes When it comes to serving beer at a party or event, kegs are a popular choice. They are convenient, cost-effective, and can provide a large quantity of beer for a crowd. However, not all kegs are created equal in terms of size and capacity. In this article, we will focus on the number of beers in a half keg and compare it to other keg sizes. First, let’s define what a half keg is. A half keg, also known as a pony keg, is a cylindrical container that holds 15.5 gallons of beer. This is equivalent to 1,984 ounces or 165 12-ounce servings of beer. It is important to note that the number of beers in a half keg can vary depending on the size of the glass or cup being used to serve the beer. Now, let’s compare the number of beers in a half keg to other keg sizes. The most common keg size is a full keg, also known as a standard keg or a barrel. A full keg holds 31 gallons of beer, which is equivalent to 3,968 ounces or 330 12-ounce servings of beer. This means that a full keg contains twice the amount of beer as a half keg. Another keg size that is becoming more popular is the quarter keg, also known as a tall quarter or a slim quarter. A quarter keg holds 7.75 gallons of beer, which is equivalent to 992 ounces or 82 12-ounce servings of beer. This means that a quarter keg contains half the amount of beer as a half keg. There are also smaller keg sizes available, such as the sixth barrel keg and the Cornelius keg. A sixth barrel keg holds 5.16 gallons of beer, which is equivalent to 661 ounces or 55 12-ounce servings of beer. A Cornelius keg, also known as a Corny keg, is a smaller keg that is often used for homebrewing. It holds 5 gallons of beer, which is equivalent to 640 ounces or 53 12-ounce servings of beer. When deciding on the size of keg to purchase for your event, it is important to consider the number of guests and their drinking habits. A half keg is a good choice for a smaller gathering of 20-30 people, while a full keg is more suitable for a larger crowd of 50-60 people. A quarter keg or smaller keg sizes are ideal for a more intimate gathering or for those who want to offer a variety of beer options. In addition to the size of the keg, it is also important to consider the type of beer being served. Different types of beer have different levels of carbonation and foam, which can affect the number of servings per keg. For example, a highly carbonated beer like a wheat beer or a Belgian ale may produce more foam and result in fewer servings per keg. In conclusion, the number of beers in a half keg is 165 12-ounce servings of beer. This is a convenient and cost-effective option for smaller gatherings, while larger events may require a full keg or multiple half kegs. It is important to consider the number of guests and their drinking habits when choosing the size of keg, as well as the type of beer being served. With these factors in mind, you can ensure that your guests will have plenty of beer to enjoy at your next event. Q&A 1. How many beers are in a half keg? There are approximately 165 12-ounce beers in a half keg. 2. What is the size of a half keg? A half keg is 15.5 gallons or 58.67 liters in size. 3. How many servings can a half keg provide? A half keg can provide around 55 servings of beer, assuming each serving is 12 ounces. 4. How much does a half keg weigh? A half keg weighs around 87 pounds when it is full. 5. How long does a half keg last? A half keg can last for several hours or even days, depending on the number of people drinking and the amount of beer consumed. Conclusion A half keg typically holds around 15.5 gallons of beer, which is equivalent to approximately 165 12-ounce servings or 124 16-ounce servings.
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20 views The area bounded by the three curves $|x + y| = 1, |x| = 1$, and $|y| = 1$, is equal to 1. 3 2. 1 2.3 $\left | x+y \right | =1$  here one first presumes x+y=1 and x+y= - 1 $\left | x \right | =1$ here x=1 and x= - 1 $\left | y \right | =1$ here y=1 and y= - 1 Now plotting the curves The area of the shaded portion is the area bounded by the three curves which is 2 full squares and 2 half squares or triangles and this would add up to 3 sq cms (2 + 1/2 + 1/2) Hence Option B is correct. answered by (2.5k points) 1 8 29
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## Trigonometry (11th Edition) Clone $$1-\frac{1}{\csc^2x}=\cos^2x$$ $$A=1-\frac{1}{\csc^2x}$$ $$A=1-\Big(\frac{1}{\csc x}\Big)^2$$ From Reciprocal Identities: $$\csc x=\frac{1}{\sin x}$$ therefore, $$\sin x=\frac{1}{\csc x}$$ so, $$\sin^2x=\Big(\frac{1}{\csc x}\Big)^2$$ That makes $A$ into $$A=1-\sin^2 x$$ $$A=\cos^2x\hspace{1cm}\text{(Pythagorean Identity)}$$
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# 19.1 Population demographics and dynamics  (Page 3/16) Page 3 / 16 ## Demography While population size and density describe a population at one particular point in time, scientists must use demography to study the dynamics of a population. Demography is the statistical study of population changes over time: birth rates, death rates, and life expectancies. These population characteristics are often displayed in a life table. ## Life tables Life tables provide important information about the life history of an organism and the life expectancy of individuals at each age. They are modeled after actuarial tables used by the insurance industry for estimating human life expectancy. Life tables may include the probability of each age group dying before their next birthday, the percentage of surviving individuals dying at a particular age interval (their mortality rate    , and their life expectancy at each interval. An example of a life table is shown in [link] from a study of Dall mountain sheep, a species native to northwestern North America. Notice that the population is divided into age intervals (column A). The mortality rate (per 1000) shown in column D is based on the number of individuals dying during the age interval (column B), divided by the number of individuals surviving at the beginning of the interval (Column C) multiplied by 1000. For example, between ages three and four, 12 individuals die out of the 776 that were remaining from the original 1000 sheep. This number is then multiplied by 1000 to give the mortality rate per thousand. As can be seen from the mortality rate data (column D), a high death rate occurred when the sheep were between six months and a year old, and then increased even more from 8 to 12 years old, after which there were few survivors. The data indicate that if a sheep in this population were to survive to age one, it could be expected to live another 7.7 years on average, as shown by the life-expectancy numbers in column E. Life Table of Dall Mountain Sheep Data Adapted from Edward S. Deevey, Jr., “Life Tables for Natural Populations of Animals,” The Quarterly Review of Biology 22, no. 4 (December 1947): 283-314. A B C D E Age interval (years) Number dying in age interval out of 1000 born Number surviving at beginning of age interval out of 1000 born Mortality rate per 1000 alive at beginning of age interval Life expectancy or mean lifetime remaining to those attaining age interval 0–0.5 54 1000 54.0 7.06 0.5–1 145 946 153.3 1–2 12 801 15.0 7.7 2–3 13 789 16.5 6.8 3–4 12 776 15.5 5.9 4–5 30 764 39.3 5.0 5–6 46 734 62.7 4.2 6–7 48 688 69.8 3.4 7–8 69 640 107.8 2.6 8–9 132 571 231.2 1.9 9–10 187 439 426.0 1.3 10–11 156 252 619.0 0.9 11–12 90 96 937.5 0.6 12–13 3 6 500.0 1.2 13–14 3 3 1000 0.7 ## Survivorship curves Another tool used by population ecologists is a survivorship curve    , which is a graph of the number of individuals surviving at each age interval versus time. These curves allow us to compare the life histories of different populations ( [link] ). There are three types of survivorship curves. In a type I curve, mortality is low in the early and middle years and occurs mostly in older individuals. Organisms exhibiting a type I survivorship typically produce few offspring and provide good care to the offspring increasing the likelihood of their survival. Humans and most mammals exhibit a type I survivorship curve. In type II curves, mortality is relatively constant throughout the entire life span, and mortality is equally likely to occur at any point in the life span. Many bird populations provide examples of an intermediate or type II survivorship curve. In type III survivorship curves, early ages experience the highest mortality with much lower mortality rates for organisms that make it to advanced years. Type III organisms typically produce large numbers of offspring, but provide very little or no care for them. Trees and marine invertebrates exhibit a type III survivorship curve because very few of these organisms survive their younger years, but those that do make it to an old age are more likely to survive for a relatively long period of time. ## Section summary Populations are individuals of a species that live in a particular habitat. Ecologists measure characteristics of populations: size, density, and distribution pattern. Life tables are useful to calculate life expectancies of individual population members. Survivorship curves show the number of individuals surviving at each age interval plotted versus time. [link] As this graph shows, population density typically decreases with increasing body size. Why do you think this is the case? [link] Smaller animals require less food and others resources, so the environment can support more of them per unit area. What is a celiac disease distinguish between properties and characteristics what are organelles Elee what is biology biology is science that studies life Elee it's the study of living and non living things now that we have an estimate for the diameter of the cell.what estimate can we make about the volume of the cell? why too much insulin result in low blood sugar For example, too much exercise can cost you to lose to much weight. Too much insulin will pull to much sugar out of your systemic system into your cells. Eric difference between DNA and RNA DNA is deoxyribonuclaic acid. Deoxy refers to a lack of oxygen. The Ribose moity is missing an OH group. I think it is missing from the second C of the ring. RNA is ribonucleic acid. DNA has our genetic code in on it. RNA is translated from DNA and carries the blue print for protein synthesis. Eric The OH group on RNA prevents it from being reactive. But it is very unstable though. Would you want such a power tool floating around in your body, no. And you have three types of RNA: mRNA, tRNA and rRNA. Please let me know it this helped?😄 Eric o Browse what determines the aeration level in the soil what is homeostasis? It means balance in a biological system. Eric What is biology Biology z the study of life GOLDEN what's biology buran biology is the study of living nd none living organism Chinaza Biology is the study of life yes Sir Said what's cell biology Prince biology is the study of life Raheal what is asexual reproduction,? A type of reproduction which does not involve the fusion of gametes or a change in the number of chromosomes Serena Reproduction without sex... In which form a single organism or cell makes a copy of itself. Serena Please explain the concept of mitosis and meiosis Serena I guess you could use it for study buddies and brushing up on what you need to Serena what is mitosis Klp Asexual reproduction? Serena why pepsin and trypsin released in active form? Yacqub mitosis is the type cell division in which two daughter cells have same no. of chormosomes syed Hi Don chromosome number remains the same in mitosis mc Ello Henry Hii Nikky Yrr help me. Nikky Physical chemistry..... Koi h jo mujhe physical chem ki notes send kr ske Nikky what is asexual reproduction Targbe what makes golgi body in plants name the membrane of the plants Abdulkareem how can turners syndrome be corrected before birth Balinda which animal survive from being preyed just because of being humble, slow, and not aggressive Balinda Plants have golgi body's also. Plants are eukaryotic cells. And membrane bound organelles are a characteristic of eukaryotic cells. Moreover golgi body's are creatted from the ER. Also do not forget plants have plastids and animal cells do not. Eric During organs transplantation, the organs cannot be taken from just anybody since the graft would be rejected sooner or later due to Non-MHC compatibility on the organ and an attack from the patient's immune system. Eric what makes golgi body in plants Abdulkareem why trypsin and pepsin released in active form Yacqub Let us remember MHC'S on our cells. This is how our cells determine self from n o n s e l f. Transplanted tissue has to have a certain amount markers. These have to match to the recipiant's markers. Even with this, immunosuppresant medacine is prescribed to the recipient. Eric Even with these measures the body may still reject the transport. This can occur even after the recipient excepting the transport for some time. Eric what is integument system This system is our skin. This includes the skin lining our alimentary system which includes the tissue from our mouth to our anus. Our skin is our largest organ system. It is mostly made up of epithelial tissue. Eric Cellular respiration This is how our cells make energy. They use glucose + oxygen. There are other facors involves also. But these are the main two reactant used, for aerobic respiration. The main product is ATP. ATP is a high energy molecule which is paramount for life. Eric what are the characteristics of living things Movement Respiration Nutrition/Feeding Irritability/Sensitivity Growth Excretion Reproduction Deat/Life span Hashim What makes children from the same father and mother sometimes don't look alike? Hashim One of the main one's is the abilit reproduce. That is why viruses are not considered living. Because they do not have the ability to replicate on they own. Eric
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6) 76.8 kJ Weight = mass x g Horse’s mass = 6000/10 = 600 kg Kinetic energy = ½mv² = (0.5 x 600 x 16²) = 300 x 256 = 76800 J = 76.8 kJ
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# EXAMPLE 1 Evaluate powers a. (–5) 4 b. –5 4 = (–5) (–5) (–5) (–5)= 625 = –(5 5 5 5)= –625. ## Presentation on theme: "EXAMPLE 1 Evaluate powers a. (–5) 4 b. –5 4 = (–5) (–5) (–5) (–5)= 625 = –(5 5 5 5)= –625."— Presentation transcript: EXAMPLE 1 Evaluate powers a. (–5) 4 b. –5 4 = (–5) (–5) (–5) (–5)= 625 = –(5 5 5 5)= –625 EXAMPLE 2 Evaluate an algebraic expression Evaluate –4x 2 –6x + 11 when x = –3. –4x 2 –6x + 11 = –4(–3) 2 –6(–3) + 11 Substitute –3 for x. = –4(9) –6(–3) + 11 Evaluate power. = –36 + 18 + 11 Multiply. = –7 Add. EXAMPLE 3 Use a verbal model to solve a problem Craft Fair You are selling homemade candles at a craft fair for \$ 3 each. You spend \$ 120 to rent the booth and buy materials for the candles. Write an expression that shows your profit from selling c candles. Find your profit if you sell 75 candles. EXAMPLE 3 Use a verbal model to solve a problem SOLUTION STEP 1Write: a verbal model. Then write an algebraic expression. Use the fact that profit is the difference between income and expenses. – An expression that shows your profit is 3c – 120. 3 c – 120 EXAMPLE 3 Use a verbal model to solve a problem STEP 2 Evaluate: the expression in Step 1 when c = 75. 3c – 120 = 3(75) – 120 Substitute 75 for c. = 225 – 120 = 105 Subtract. ANSWER Your profit is \$ 105. Multiply. EXAMPLE 4 Simplify by combining like terms a. 8x + 3x = (8 + 3)x Distributive property = 11x Add coefficients. b. 5p 2 + p – 2p 2 = (5p 2 – 2p 2 ) + p Group like terms. = 3p 2 + p Combine like terms. c. 3(y + 2) – 4(y – 7)= 3y + 6 – 4y + 28 Distributive property = (3y – 4y) + (6 + 28) Group like terms. = –y + 34 Combine like terms. EXAMPLE 4 Simplify by combining like terms d. 2x – 3y – 9x + y = (2x – 9x) + (– 3y + y) Group like terms. = –7x – 2y Combine like terms. EXAMPLE 5 Simplify a mathematical model Digital Photo Printing You send 15 digital images to a printing service that charges \$. 80 per print in large format and \$.20 per print in small format. Write and simplify an expression that represents the total cost if n of the 15 prints are in large format. Then find the total cost if 5 of the 15 prints are in large format. SOLUTION EXAMPLE 5 Simplify a mathematical model Write a verbal model. Then write an algebraic expression. An expression for the total cost is 0.8n + 0.2(15 – n). 0.8n + 0.2(15 – n) Distributive property. = (0.8n – 0.2n) + 3 Group like terms. = 0.8n + 3 – 0.2n EXAMPLE 5 Simplify a mathematical model = 0.6n + 3 Combine like terms. ANSWER When n = 5, the total cost is 0.6(5) + 3 = 3 + 3 = \$ 6. EXAMPLE 1 Solve an equation with a variable on one side Solve 4 5 x + 8 = 20. 4 5 x + 8 = 20 4 5 x = 12 x = (12) 5 4 x = 15 Write original equation. Subtract 8 from each side. Multiply each side by, the reciprocal of. 5 44 5 Simplify. ANSWER The solution is 15. CHECK x = 15 in the original equation. 4 5 4 5 x + 8 = (15) + 8 = 12 + 8 = 20  EXAMPLE 2 Write and use a linear equation During one shift, a waiter earns wages of \$30 and gets an additional 15% in tips on customers’ food bills. The waiter earns \$105. What is the total of the customers’ food bills? Restaurant SOLUTION Write a verbal model. Then write an equation. Write 15% as a decimal. EXAMPLE 2 Write and use a linear equation 105 = 30 + 0.15x 75 = 0.15x 500 = x Write equation. Subtract 30 from each side. Divide each side by 0.15. The total of the customers’ food bills is \$500. ANSWER EXAMPLE 3 Standardized Test Practice SOLUTION 7p + 13 = 9p – 5 13 = 2p – 5 18 = 2p 9 = p Write original equation. Subtract 7p from each side. Add 5 to each side. Divide each side by 2. ANSWER The correct answer is D EXAMPLE 3 Standardized Test Practice CHECK 7p + 13 = 9p – 5 7(9) + 13 9(9) – 5 = ? 63 + 13 81 – 5 = ? 76 = 76  Write original equation. Substitute 9 for p. Multiply. Solution checks. EXAMPLE 4 Solve an equation using the distributive property Solve 3(5x – 8) = – 2(– x + 7) – 12x. 3(5x – 8) = – 2(– x + 7) – 12x 15x – 24 = 2x – 14 – 12x 15x – 24 = – 10x – 14 25x – 24 = –14 25x = 10 x = 2 5 Write original equation. Distributive property Combine like terms. Add 10x to each side. Add 24 to each side. Divide each side by 25 and simplify. ANSWER The solution 2 5 EXAMPLE 4 Solve an equation using the distributive property CHECK 3 ( 5 – 8 ) – 2 ( – +7 ) – 12 2 5 2 5 2 5 = ? 3( – 6) –14 – 4 5 = ? 24 5 – 18 = – 18  2 5 Substitute for x. Simplify. Solution checks. EXAMPLE 1 Rewrite a formula with two variables Solve the formula C = 2πr for r. Then find the radius of a circle with a circumference of 44 inches. SOLUTION C = 2 π r C 2π = r STEP 1 Solve the formula for r. STEP 2Substitute the given value into the rewritten formula. Write circumference formula. Divide each side by 2π. r = C 2π = 44 2π 7 Substitute 44 for C and simplify. The radius of the circle is about 7 inches. ANSWER EXAMPLE 2 Rewrite a formula with three variables SOLUTION Solve the formula for w. STEP 1 P = 2l + 2w P – 2l = 2w P – 2l 2 = w Write perimeter formula. Subtract 2l from each side. Divide each side by 2. Solve the formula P = 2l + 2w for w. Then find the width of a rectangle with a length of 12 meters and a perimeter of 41 meters. EXAMPLE 2 Rewrite a formula with three variables 41 – 2(12) 2 w = w = 8.5 Substitute 41 for P and 12 for l. Simplify. The width of the rectangle is 8.5 meters. ANSWER Substitute the given values into the rewritten formula. STEP 2 EXAMPLE 3 Rewrite a linear equation Solve 9x – 4y = 7 for y. Then find the value of y when x = –5. SOLUTION Solve the equation for y. STEP 1 9x – 4y = 7 – 4y = 7 – 9x y = 9 4 7 4 – + x Write original equation. Subtract 9x from each side. Divide each side by – 4. EXAMPLE 3 Rewrite a linear equation Substitute the given value into the rewritten equation. STEP 2 y = 9 4 7 4 – + (–5) y = 45 4 7 4 – – y = – 13 CHECK 9x – 4y = 7 9(– 5) – 4(– 13) 7 = ? 7 = 7  Substitute – 5 for x. Multiply. Simplify. Write original equation. Substitute – 5 for x and – 13 for y. Solution checks. EXAMPLE 4 Rewrite a nonlinear equation Solve 2y + xy = 6 for y. Then find the value of y when x = –3. SOLUTION Solve the equation for y. STEP 1 2y + x y = 6 (2+ x) y = 6 y = 6 2 + x Write original equation. Distributive property Divide each side by ( 2 + x). EXAMPLE 4 Rewrite a nonlinear equation Substitute the given value into the rewritten equation. STEP 2 y = 6 2 + (– 3) y = – 6 Substitute – 3 for x. Simplify. Download ppt "EXAMPLE 1 Evaluate powers a. (–5) 4 b. –5 4 = (–5) (–5) (–5) (–5)= 625 = –(5 5 5 5)= –625." Similar presentations
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# Sum of all Unique elements in a given array Objective: Given an array of integers that contains duplicates as well. Write a program to find the sum of all unique elements in the array. This problem is also referred to as find the sum of all distinct elements in the array Example: ```[] arrA = {1, 6, 4, 3, 2, 2, 3, 8, 1}; Output : 24 (Unique elements are: 1, 6, 4, 3, 2, 8) [] arrA = {1, 1, 3, 2, 2, 3}; Output : 6 (Unique elements are: 1, 2, 3) ``` Approach: Use Sorting- • Sort the array, this will bring all duplicates together. • Iterate through the array and get the sum of all unique elements (If current element which is the same as the previous element, ignore the current element). Time Complexity: O(NlogN) Use Hash Set • Create Hash Set and initialize sum = 0. • Iterate through the array, check if the current element is in Hash Set, if yes then ignore the element else add the element to the sum and add it to the Hash Set. Time Complexity: O(N), Space Complexity: O(N) See the code below for both the approaches for better understanding. Java Code: Output: ```Sum of all Unique elements (Sorting Method): 24 Sum of all Unique elements (HashSet Method: 24 ``` __________________________________________________ Top Companies Interview Questions..- If you find anything incorrect or you feel that there is any better approach to solve the above problem, please write comment. __________________________________________________ #### You may also like... This site uses Akismet to reduce spam. Learn how your comment data is processed.
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Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  fvfundmfvn0 Structured version   Visualization version   GIF version Theorem fvfundmfvn0 6687 Description: If the "value of a class" at an argument is not the empty set, then the argument is in the domain of the class and the class restricted to the singleton formed on that argument is a function. (Contributed by Alexander van der Vekens, 26-May-2017.) (Proof shortened by BJ, 13-Aug-2022.) Assertion Ref Expression fvfundmfvn0 ((𝐹𝐴) ≠ ∅ → (𝐴 ∈ dom 𝐹 ∧ Fun (𝐹 ↾ {𝐴}))) Proof of Theorem fvfundmfvn0 StepHypRef Expression 1 ndmfv 6679 . . 3 𝐴 ∈ dom 𝐹 → (𝐹𝐴) = ∅) 21necon1ai 3017 . 2 ((𝐹𝐴) ≠ ∅ → 𝐴 ∈ dom 𝐹) 3 nfunsn 6686 . . 3 (¬ Fun (𝐹 ↾ {𝐴}) → (𝐹𝐴) = ∅) 43necon1ai 3017 . 2 ((𝐹𝐴) ≠ ∅ → Fun (𝐹 ↾ {𝐴})) 52, 4jca 515 1 ((𝐹𝐴) ≠ ∅ → (𝐴 ∈ dom 𝐹 ∧ Fun (𝐹 ↾ {𝐴}))) Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 399   ∈ wcel 2112   ≠ wne 2990  ∅c0 4246  {csn 4528  dom cdm 5523   ↾ cres 5525  Fun wfun 6322  ‘cfv 6328 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2114  ax-9 2122  ax-10 2143  ax-11 2159  ax-12 2176  ax-ext 2773  ax-sep 5170  ax-nul 5177  ax-pow 5234  ax-pr 5298 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070  df-mo 2601  df-eu 2632  df-clab 2780  df-cleq 2794  df-clel 2873  df-nfc 2941  df-ne 2991  df-ral 3114  df-rex 3115  df-rab 3118  df-v 3446  df-dif 3887  df-un 3889  df-in 3891  df-ss 3901  df-nul 4247  df-if 4429  df-sn 4529  df-pr 4531  df-op 4535  df-uni 4804  df-br 5034  df-opab 5096  df-id 5428  df-xp 5529  df-rel 5530  df-cnv 5531  df-co 5532  df-dm 5533  df-res 5535  df-iota 6287  df-fun 6330  df-fv 6336 This theorem is referenced by:  fvn0ssdmfun  6823  fvn0fvelrn  6906  umgrnloopv  26903  usgrnloopvALT  26995  afvpcfv0  43695  afvfvn0fveq  43699  afv0nbfvbi  43700  afv2fvn0fveq  43813  ovn0dmfun  44377 Copyright terms: Public domain W3C validator
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# Absorbtion/Emmision Spectra 1. Nov 10, 2007 ### steven10137 1. The problem statement, all variables and given/known data An atom of element Q can only absorb two photons of frequency 6.40E14 Hz and 9.05E14 Hz. Explain how atoms of element Q could absorb or emit photons of particular frequencies. 2. The attempt at a solution OK I think I am missing something in my understanding of absorbtion and emission .... I don't really understand what the question is asking. But, perhaps; The element Q has set energy levels; n=1, n=2 ... Hence the element can only absorb or emit photons with energies equal to the energies of these energy levels. These energies are 6.40E14 Hz and 9.05E14 respectively. As I said, I'm having trouble. If someone could please explain the concept of the problem, it would be greatly appreciated. Thanks Steven Last edited: Nov 10, 2007 2. Nov 10, 2007 ### Staff: Mentor 3. Nov 10, 2007 ### steven10137 For the second part of the question, I am required to draw the energy level diagram of the element, showing the known levels. Then, calculate the longest wavelength photon that the element could emit. ok so the longest possible photon will be that of the smallest frequency photon. From the question, it says the element can absorb photons of the the specifc frequencies. Now from here http://hyperphysics.phy-astr.gsu.edu/hbase/mod5.html#c2 I can see that the downward transition gives an emission of E2 - E1. So we are looking for the downward transition with the smallest possible frequency, which is; 9.05E14 - 6.04E14 = 3.01E14 Hz $$\begin{array}{l} \lambda = \frac{c}{f} \\ \lambda _{\max } = \frac{{3 \times 10^8 }}{{3.01 \times 10^{14} }} = 9.97 \times 10^{ - 7} m \\ \end{array}$$ How am I looking? Steven Last edited: Nov 10, 2007 4. Nov 10, 2007 ### Staff: Mentor The energy level at n=2 is closer to n=1 than n=3 is to n=2. Refer to the last link I cited - http://hyperphysics.phy-astr.gsu.edu/hbase/hyde.html If 9.05E14 Hz represents n=3 to n=1 and 6.04E14 n=2 to n=1, then the n=3 to n=2 transition would be the difference. This is based on the statement "An atom of element Q can only absorb two photons of frequency 6.40E14 Hz and 9.05E14 Hz." It would be unlikely that a photon would absorbed by an electron in the excited n=2 state. Looks OK. 5. Nov 10, 2007 ### steven10137 OK for the diagram, the 2.5eV should be less than the 3.75eV (elementary mistake) I'm not really fully understanding what you mean. But are you trying to say that those frequencies do not represent those transitions? Am I sort of on the right track? Steven. 6. Nov 10, 2007 ### Staff: Mentor Note the different groups and emission lines in this - http://hyperphysics.phy-astr.gsu.edu/hbase/hyde.html#c4 I was saying those energies do represent those transitions. The two absorption energy would correspond to n=3 to n=1 (more energetic) and n=2 to n=1 less energetic, and these would be approximately equal to emission lines. There is also a possible n=3 to n=2 emission, which is the difference between 3-1 and 2-1. The 2->3 would be an unlikely absorption because the transition 2->1 would occur very quickly.
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# S²+4s-21=04x²-32x=28r²-10r=-17m²+7m-=0please show your solutions.i need it right now.im so stress because of that.HUHUHU. 2 by Trista for the 2nd item, is it really =28? and not = -28? yes it's just 28 2014-06-28T11:22:01+08:00 ### This Is a Certified Answer Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest. Phewww! That was hard but fun! :D Hope that helps ^_^ 2014-06-28T12:20:12+08:00 ### This Is a Certified Answer Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest. S² + 4s - 21 = 0 (s+7) (s-3) = 0 s+7=0  ;  s-3=0 s = -7  ;  s = 3 4x² - 32x = 28 x² - 8x = 7 x² - 8x + 16 = 7 + 16 (x-4)² = 23 √(x-4)² = √23 x - 4 = ±√23 x = ±√23 +4 x = √23 +4    ;   x = -√23 +4 r² - 10r = -17 r² - 10r + 25 = -17 + 25 (r-5)² = 8 √(r-5)² = √8 r-5 = ±√8 r = ±2√2 +5 r = 2√2 +5   ;   r = -2√2 +5 m² +7m - 51/9 = 0 m² +7m = 17/3 m² +7m + (7/2}² = 17/3 + (7/2}² √(m+7/2)² = √(215/12) m + 7/2 = ± √(645)/ 6 m =     ;    m =  -\frac{ \sqrt{645} }{6} +  \frac{7}{2}
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# What are exceptions to the law of conservation of mass? ## What are exceptions to the law of conservation of mass? Conservation of mass – mass cannot be destroyed in any process, with one exception (see #6), and mass cannot be created from nothing. Equivalence of mass and energy – In certain reactions (nuclear), mass can be converted directly to energy (E = mc2). ## What are 3 examples of law of conservation of mass? The law of conservation of mass states that matter cannot be created or destroyed in a chemical reaction. For example, when wood burns, the mass of the soot, ashes, and gases equals the original mass of the charcoal and the oxygen when it first reacted. So the mass of the product equals the mass of the reactant. ## What isn’t lost in a chemical reaction? Mass is never lost or gained in chemical reactions. We say that mass is always conserved. In other words, the total mass of products at the end of the reaction is equal to the total mass of the reactants at the beginning. This is because no atoms are created or destroyed during chemical reactions. ## Is the law of conservation of mass physical or chemical? The Law of Conservation of Mass Matter can change form through physical and chemical changes, but through any of these changes, matter is conserved. The same amount of matter exists before and after the change—none is created or destroyed. ## Is there a law of conservation of mass? The Law of Conservation of Mass dates from Antoine Lavoisier’s 1789 discovery that mass is neither created nor destroyed in chemical reactions. If we account for all reactants and products in a chemical reaction, the total mass will be the same at any point in time in any closed system. ## What violates the law of conservation? Quantum Physics and Law of Conservation of Energy Niels Bohr, Hans Kramers, and John Slater proposed that these electrons violated the law of conservation of Energy momentarily. They stated that with each jump, energy is either created or destroyed by the electrons during the whole process. ## Which is the best example of the law of conservation of energy? What is the best example of the law of conservation of energy? If a pendulum is one meter off the ground at one end of its swing, it can never be more than one meter (The law of conservation of energy states that energy cannot be created or destroyed. ## Can mass be lost in a chemical reaction? One of these is called the law of conservation of mass , which states that during a chemical reaction, the total mass of the products must be equal to the total mass of the reactants. In other words, mass cannot be created or destroyed during a chemical reaction, but is always conserved. ## What can you do to balance the chemical equation? When you balance a chemical equation, you change coefficients. You never change subscripts. A coefficient is a whole number multiplier. To balance a chemical equation, you add these whole number multipliers (coefficients) to make sure that there are the same number of atoms on each side of the arrow. ## Who gave the law of conservation of mass? Antoine Lavoisier’s The Law of Conservation of Mass dates from Antoine Lavoisier’s 1789 discovery that mass is neither created nor destroyed in chemical reactions. In other words, the mass of any one element at the beginning of a reaction will equal the mass of that element at the end of the reaction. ## What are physical and chemical properties of matter? A physical property is a characteristic of a substance that can be observed or measured without changing the identity of the substance. Physical properties include color, density, hardness, and melting and boiling points. A chemical property describes the ability of a substance to undergo a specific chemical change.
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# 100 Floors Annex Level 66 67 68 69 70 Walkthrough Answer for 100 Floors Annex Level 66 67 68 69 70 Walkthrough of christmas theme guide how to solve all the challenging puzzles niveau on the 100 floors annex and escape each floor rooms using the cheat solution below 100 Floors – Can You Escape? app game by Tobi Apps on iphone and android 100 floors annex level 66 walkthrough just look at the time on clock : 20:15 100 floors annex level 67 walkthrough you need to connect lines to each dot with many line numbers like the dot number 100 floors annex level 68 walkthrough tap the green button to turn on the lights follow the arrow as clue to swipe door for correct direction following the blue line left – right – down – up – left – right – down 100 floors annex level 69 walkthrough use the rules of : 1 + 2 = 3 3 + 4 = 7 2 + 4 = 6 6 + 7 = 13 13 + 3 = 16 to combine the liquid on floor, you need to get value of 16 then put it on the door
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Class 11 MATHS Logarithms # Statement-1: 3^("log"_(2) 7) -7^("log"_(2)3) = 0 <br> Statement-2: x^("log"_(a)y) = y^("log"_(a)x), " where "x gt 0, y gt 0" and "a gt 0, a ne 1 Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams. Updated On: 1-1-2020 Apne doubts clear karein ab Whatsapp par bhi. Try it now. Watch 1000+ concepts & tricky questions explained! 35.1 K+ 1.7 K+ Text Solution Statement-1 is True, Statement-2 is true, Statement-2 is a correct explanation for Statement-1. Statement-1 is True, Statement-2 is true, Statement-2 is NOT a correct explanation for Statement-1.Statement-1 is True, Statement-2 is False. Statement-1 is False, Statement-2 is True. A Solution : We have, x^("log"_(a)y) = y^("log"_(a) x) " "["See Nineth law"] <br> therefore 3^("log"_(2) 7) = 7^("log"_(2)3) rArr 3^("log"_(2)7)-7^("log"_(2)3) = 0 Image Solution 53796808 13.3 K+ 14.3 K+ 1:05 53796807 1.6 K+ 31.1 K+ 1:05 53796809 46.9 K+ 49.0 K+ 2:05 53796815 500+ 11.5 K+ 4:14 53796783 1.6 K+ 31.4 K+ 3:08 53796811 5.0 K+ 100.9 K+ 5:39 39181420 3.6 K+ 74.5 K+ 16:04 51235447 28.6 K+ 75.8 K+ 12:44 52334 2.3 K+ 45.7 K+ 3:00 69059852 1.4 K+ 29.3 K+ 3:42 1355680 6.0 K+ 120.8 K+ 1:07 64282 3.2 K+ 63.9 K+ 8:05 67940 4.6 K+ 92.0 K+ 2:14 23336 6.1 K+ 122.6 K+ 4:28 7144900 4.5 K+ 90.8 K+ 2:10
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# Background I have been working on an optimization problem related to the following function: $$y = f(x) = c_{1}(1-e^{-c_{2}(x-x_{0})})^{2}$$ where $$c_{1}$$, $$c_{2}$$ and $$x_{0}$$ are constants. Assume that we have an interval $$[x_{a}, x_{b}]$$ and then we uniformly sample a number $$n$$ of points $$x_{k}$$ from this interval and calculate the corresponding value of $$f(x_{k})$$ and then we sum over these values, i.e. $$\Sigma = \sum_{k=1}^{n}{f(x_{k})}$$. We then repeat this sampling process $$M$$ times. This leaves us with the following system of equations: $$\begin{cases} \Sigma_{1} & = \sum_{k=1}^{n}{f(x_{1,k})} & = f(x_{1,1}) + f(x_{1,2}) + \dots f(x_{1,n}) \\ \Sigma_{2} & = \sum_{k=1}^{n}{f(x_{2,k})} & = f(x_{2,1}) + f(x_{2,2}) + \dots f(x_{2,n}) \\ & & \vdots \\ \Sigma_{M} & = \sum_{k=1}^{n}{f(x_{M,k})} & = f(x_{M,1}) + f(x_{M,2}) + \dots f(x_{M, n})\\ \end{cases}$$ Now, assume that we do not know what $$f(x)$$ actually looks like and that we want to recreate the function. To do so, we need to solve this system of equations using linear algebra. We can not do this using a continous $$f(x)$$ so we will have to discretize our interval into $$N$$ bins with a binwidth of $$h$$, such that: $$\begin{cases} f_{1} & \text{if } x \in [x_a, & x_a+h) \\ f_{2} & \text{if } x \in [x_a+h, & x_a+2h) \\ & \vdots \\ f_{N} & \text{if } x \in [x_a+(N-1)h, & x_b) \\ \end{cases}$$ If we treat this as a vector $$\vec{f} = [f_{1}, f_{2}, \dots, f_{N}]^{T}$$ of size ($$N$$-by-1) and bin all $$x_{i,k}$$ to their column corresponding to $$f_j$$ in a matrix $$C$$ of size ($$M$$-by-$$N$$) then we can rewrite our system of equation as: $$C\vec{f}=\vec{\Sigma}$$ where $$\vec{\Sigma}=[\Sigma_{1}, \Sigma_{2}, \dots, \Sigma_{M}]^{T}$$ of size ($$M$$-by-$$1$$). Then we use e.g. SVD to approximate $$C^{-1}$$ to solve for $$\vec{f}=C^{-1}\vec{\Sigma}$$ to get an idea of what the true $$f(x)$$ might look like. # Problem I want to know how to bin the interval $$[x_{a}, x_{b}]$$ and I want to do so by minimizing the error of approximating $$f(x)$$ using $$\vec{f}$$. In my real application RAM is a limiting factor (I have several different $$f(x)$$ I want to estimate at once, making $$C^{-1}$$ expensive to compute) so I want to have a fixed number of bins. So, given an $$N$$ number of bins, how do I select the width of each individual bin so that I minimize the error between $$f(x)$$ and $$\vec{f}$$? In reality, $$x$$ is actually Poisson-distributed (and not uniform) and $$x$$ and $$f(x)$$ can be very different in orders of magnitude. What I've tried: • Equidistant binning w.r.t. $$x$$ (best result so far) • Equidistant binning w.r.t. $$f(x)$$ • Equidistant binning w.r.t. $$ln(1+f(x))$$ • Equidistant binning w.r.t. length of curve • Binning where the count in each bin is the same for all bins It does not make sense to me that equidistant binning w.r.t. $$x$$ (i.e. $$h_{1}=h_{2}=\dots=h_{N}$$) provides the best results, especially when the $$\Delta f(x)$$ is so different between the left and the right half of the bin. But when the resolution at the position where the $$|f'(x)|$$ gets higher then the error around the minimum of $$f(x)$$ gets significantly higher instead. How do I select my $$H = \{h_{1}, h_{2}, \dots, h_{N}\}$$ for all bins and a fixed number of bins $$N$$? # Example Here is an example of what $$f(x)$$ and equidistant binning w.r.t. $$x$$ and some arbitrary values for $$c_{1}$$, $$c_{2}$$ and $$x_{0}$$ look like. please note that there is no approximation here, just the exact values.
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ENG  RUS Timus Online Judge Online Judge Problems Authors Online contests Site news Webboard Problem set Submit solution Judge status Guide Register Authors ranklist Current contest Scheduled contests Past contests Rules back to board ## Discussion of Problem 1296. Hyperjump To everyone : Algorithm to solve this problem ! Very easy ! calculate : fmax(n) = max(fmax(n-1)+value(n),value(n)); Re: To everyone : Algorithm to solve this problem ! Very easy ! Posted by D_T_F 23 Mar 2009 04:24 Why? Consider p1 = 5, p2 = -2 fmax(1) = 5 fmax(2) = max( 5+(-2), -2 ) = 3 But if i = j = 1 fmax(2) = 5 Or I got wrong understanding of the task? Re: To everyone : Algorithm to solve this problem ! Very easy ! Posted by Nguyen Dang Duy 10 Dec 2011 11:17 F[i] is max values of sequence with the final element is a[i]. Finally, answer will be max( F[1], ... F[n] ). Sorry because of English. Re: To everyone : Algorithm to solve this problem ! Very easy ! Posted by thebvog 18 Jan 2012 20:58 It's wrong algorithm and more hard than right.
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# If a number is infinite (like “Aleph-Null”) then how can there be numbers larger or smaller than it? Shouldn’t that be impossible? 41 views 0 If a number is infinite (like “Aleph-Null”) then how can there be numbers larger or smaller than it? Shouldn’t that be impossible? In: 0 Usually because you have a reason to believe they are larger or smaller based on the rules that still apply. For example, exponential divergent functions (2^x) grow faster than linear divergent functions (2*x). If you chose x to be infinite then whatever undefined thing (2^infinite) would be, it would definitely be bigger than infinite*2 or you break the rules of your basic operants. You can also take a look at different classes of infinity. For example, there is an infinite amount of integers (1,2,3,4,…)., In theory you could use them to count an infinite amount of objects right? Now take a look at real numbers (1, – 2.35894, 2/3, pi,…) and try to count them all. 1.0 is the first, 1.1 the second and then.. How to proceed with the third? Is it 1.2? Or 1.11? Or 1.100000001? It does not matter because even between 1.00000000001 and 1.00000000002 there is still an infinite amount of real numbers. You can just keep padding zeros indefinitely and we haven’t even reached 2 yet. It can’t be done. There are more real numbers than can be counted with an infinite amount of integers. Clearly there must be more of them by an entire order of definition. Aleph-Null is the answer to the question “How many integers are there greater than zero?” It’s defined as the smallest infinite cardinal number: in other words, anything infinite must be at least as large as Aleph-Null, and the only things smaller than Aleph-Null are all finite. So how does this work? How do you get to be larger than an infinite number? You could instead turn this around and ask something a little different: if Aleph-Null is infinite, then how can it be smaller than other infinite things? Let’s go back to that original question: how many natural numbers -that is to say, integers greater than zero- are there? Natural numbers are the numbers we use for counting. If I sat down and started to count, I could reach any of the natural numbers, given enough time. It would literally take forever to reach aleph-null, but if I had forever, I could still do it. This is what we call *countably infinite*. If you can assign an integer to every member of an infinite set, then it’s also countably infinite. Let’s say I have a hotel with an infinite number of rooms, and a full bus with an infinite number of seats pulls up: I can put each guest in a room. They are countably-infinite too. Let’s ask a slightly different question: how many real numbers are there between 1 and 2? Note that I’ve changed the number set here: we’re no longer just dealing with whole numbers, but also fractions and decimals. Now we have to deal with 0.1, but before that you have to get to 0.01, and 0.001, and 0.0001… and all the way down the line. If you sat down to try to count these, you would *never* reach 2, even if you had forever. You’d never even reach 0.1, in fact. This is *uncountably infinite*. And since something you can’t count has to be bigger than something you can, this, then, is larger than Aleph-Null. In fact, it’s Aleph-One. [Veritasium has a video about this, including the hotel story, and how an infinite hotel can still run out of room](https://youtu.be/OxGsU8oIWjY?feature=shared). > If a number is infinite (like “Aleph-Null”) then how can there be numbers larger or smaller than it? There are lots of different notions of numbers and sizes in mathematics. One of the most basic and intuitive concepts of “size” is cardinality. If two sets can be matched up one-to-one, then they have the same cardinality. For example, we can match up {1, 2, 3} with {4, 6, 7}, so they have the same cardinality of 3. We can’t match up {1, 2} with {4, 6, 7}: there is always one left over from the second set, so it has a larger cardinality. If you allow for infinite sets, then we can play the same game there. {1, 2, 3, …} (the positive integers) can be matched up with {2, 4, 6, …} (the positive even numbers) because we can, for example, define a rule in which each number from the first set is matched up with the number that is twice as large from the second set. Aleph null is defined as the cardinality of the set of integers. Clearly, we can’t match up any finite set with an infinite set, so it’s trivial to see that there are cardinalities smaller than aleph null. It takes a bit more work to show that there are larger cardinalities > Shouldn’t that be impossible? Why? [removed] How can there not be a number smaller than infinity? Literally, all of the real numbers are smaller than infinity. Aleph-null is the smallest infinity, generally called “countable infinity” It’s the number of natural numbers that exist (1, 2, 3, 4….) It’s also the number of whole numbers (0, 1, 2, 3, …) And the number of integers (…-2, -1, 0, 1, 2…) And the number of rational numbers (1, 3/2, 1/16, etc) All of these are for math reasons I won’t go into, but we have proven that all of them are the same total. The number of real numbers (π, e, 1, sqrt(2), 7/8, etc) is also infinite, but we can prove there are more of those than there are natural numbers, an infinity greater than aleph-null. An uncountable infinity. There’s a lot to go into with the different types of infinity, but the main difference you should know is countable vs uncountable infinity.
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## Algebra and Trigonometry 10th Edition $x^3-12x^2+48x-64$ Use the special product: cube of a binomial (see page 28): $(x-4)^3=x^3-3x^2(4)+3x(4)^2-4^3=x^3-12x^2+48x-64$
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Partner with ConvertIt.com New Online Book! Handbook of Mathematical Functions (AMS55) Conversion & Calculation Home >> Measurement Conversion Measurement Converter Convert From: (required) Click here to Convert To: (optional) Examples: 5 kilometers, 12 feet/sec^2, 1/5 gallon, 9.5 Joules, or 0 dF. Help, Frequently Asked Questions, Use Currencies in Conversions, Measurements & Currencies Recognized Examples: miles, meters/s^2, liters, kilowatt*hours, or dC. Conversion Result: ```Jamaican dollar on 4-28-2017 = 7.73508964507867E-03 currency (currency)``` Related Measurements: Try converting from "JMD" to ANG (Neth. Antillian guilder on 4-28-2017), AWG (Aruban guilder on 4-28-2017), BAM (Bos. and Herz. marks on 4-28-2017), DEM (German mark on 4-28-2017), DKK (Danish krone on 4-28-2017), EUR (European Union euro on 4-28-2017), FIM (Finnish markka on 4-28-2017), FKP (Falkland pound on 4-28-2017), FRF (French franc on 4-28-2017), ITL (Italian lira on 4-28-2017), LTL (Lithuanian litas on 4-28-2017), MMK (Burmese kyat on 4-28-2017), MYR (Malaysian ringgit on 4-28-2017), OMR (Omani rial on 4-28-2017), PKR (Pakistani rupee on 4-28-2017), SGD (Singapore dollar on 4-28-2017), THB (Thai baht on 4-28-2017), tick, TND (Tunisian dinar on 4-28-2017), XCD (East Caribbean dollar on 4-28-2017), or any combination of units which equate to "currency" and represent currency. Sample Conversions: JMD = .00773509 ADP (Andorran peseta on 4-28-2017), .11932716 ARS (Argentine peso on 4-28-2017), .09770026 ATS (Austrian schilling on 4-28-2017), .01034753 AUD (Australian dollar on 4-28-2017), .01547018 BBD (Barbadian dollar on 4-28-2017), .0138867 DEM (German mark on 4-28-2017), 1.37 DJF (Djiboutian franc on 4-28-2017), .00773509 EEK (Estonian kroon on 4-28-2017), 1.18 ESP (Spanish peseta on 4-28-2017), .01613987 FJD (Fijian dollar on 4-28-2017), .00597918 FKP (Falkland pound on 4-28-2017), .05298246 HRK (Croatian kuna on 4-28-2017), 8.82 KRW (South Korean won on 4-28-2017), .10322266 LSL (Lesotho loti on 4-28-2017), .81058282 PKR (Pakistani rupee on 4-28-2017), 1.42 PTE (Portuguese escudo on 4-28-2017), .00597918 SHP (Saint Helenian pound on 4-28-2017), .23364279 TWD (Taiwanese new dollar on 4-28-2017), .00773509 USD (United States dollar on 4-28-2017), 176.17 VND (Vietnamese dong on 4-28-2017). Feedback, suggestions, or additional measurement definitions? Please read our Help Page and FAQ Page then post a message or send e-mail. Thanks!
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5 stars based on 36 reviews This classification helps the trader to decide which strike to trade, given a particular circumstance in the market. However before we get into the details, I guess it makes sense to look through the concept of intrinsic value again. The intrinsic value of an option is the money the option buyer makes from an options contract provided he has the right to exercise that option on the given day. Intrinsic Value is always a positive value and can never go below 0. Consider this example —. Given this, assume you bought the CE and instead of waiting for 15 days to expiry you had the right to exercise the option today. Now my question to you is — How much money would you stand to make provided you exercised the contract today? Abcs option volatility trading strategies with sheldon natenberg remember when you exercise a long option, the money you make is equivalent to the intrinsic value of an option minus the premium paid. Hence to answer the above question we need to calculate the intrinsic value of an option, for which we need to pull up the call option intrinsic value formula from Chapter 3. So, if you were to exercise this option today, you are entitled to make 20 points ignoring the premium paid. Here is a table which calculates the intrinsic value for various options strike these are just random values that I have used to drive across the concept —. With this, I hope you are clear about the intrinsic value calculation for a given option strike. Let me summarize a few important points —. Before we wrap up this discussion, here is a question for you — Why do you think the intrinsic value cannot be a negative value? To answer this, let us pick an example from the above table — Strike isspot isand option type is long abcs option volatility trading strategies with sheldon natenberg. Let us assume the premium for the Call option is Rs. Hopefully this should give you some insights into why the intrinsic value of an option can never go negative. With our discussions on the intrinsic value of an option, the concept of moneyness should be quite easy to comprehend. Moneyness of an option is a classification method which classifies each option strike based on how much money a trader is likely to make if he were to exercise his option contract today. There are 3 broad classifications —. Understanding these option strike classification is very easy. All you need to do is figure out the intrinsic value. Let us take up an example to abcs option volatility trading strategies with sheldon natenberg this well. As you can notice from the image above, the available strike prices trade starts from all the way upto From the definition of ATM option that we posted abcs option volatility trading strategies with sheldon natenberg we know, ATM option is that option strike which is closest to the spot price. Considering the spot is atthe closest strike is probably If there was strike, then clearly would be the ATM option. But in the absence of strike the next closest strike becomes ATM. Hence we classify as, the ATM option. In order to do this we will pick few strikes and calculate the intrinsic value. Do remember the spot price iskeeping this in perspective the intrinsic value for the strikes above would be —. We know this is the ATM option as strike is closest to the spot price of So we will not bother to calculate its intrinsic value. Negative intrinsic value, therefore the intrinsic value is 0. You may have already sensed the generalizations for call options that exists here, however allow me to restate the same again. Now let us look at 2 ITM options — and The intrinsic value works out to be and 60 abcs option volatility trading strategies with sheldon natenberg considering the spot is at Higher the intrinsic value, deeper the moneyness of the option. I would encourage you to observe the premiums for all these strike prices highlighted in green box. Do you sense a pattern here? Here is the snapshot of various strikes available for a Put option. The strike prices on the left are highlighted in a blue box. As you can see there are many strike prices available right from to Since the spot is atthe nearest strike to spot should be the ATM option. As we can see from the snapshot above there is a strike at which is trading at Rs. This obviously becomes the ATM option. Let us go with the following strikes and evaluate their respective intrinsic value also called the moneyness —. And as you can see from the snapshot, the premiums for ITM options are much higher than the premiums for the OTM options. I hope you have got a clear understanding of how option strikes are classified based on their moneyness. However you may still be wondering about the need to classify options based on their moneyness. As you briefly know by now, Option Greeks are the market forces which act upon options strikes and therefore affect the premium associated with these strikes. So a certain market force will have a certain effect on ITM option while at the same time it will have a different effect on an OTM option. Hence classifying the option strikes will help us in understanding the Option Greeks and their impact on the premiums better. The Option chain is abcs option volatility trading strategies with sheldon natenberg common feature on most of the exchanges and trading platforms. The option chain is a ready reckoner of sorts that helps you identify all the strikes that are available for a particular underlying and also classifies the strikes based abcs option volatility trading strategies with sheldon natenberg their moneyness. Besides, the option chain also provides information such as the premium price LTPbid —ask price, volumes, open interest etc for each of the option strikes. Here is the link to check the option chain for Nifty Options. Having understood the basics of the call and put options both from the buyers and sellers perspective and also having understood the concept of ITM, OTM, and ATM I suppose we are all set to dwell deeper into options. The next couple of chapters will be dedicated to understand Option Greeks and the kind of impact they have on option premiums. Based on the Option Greeks impact on the premiums, we will figure out a way to select the best possible strike to trade for a given circumstance in the market. I hope you are as excited to learn about all these topics as we are to write about the same. Abcs option volatility trading strategies with sheldon natenberg please stay tuned. Hi kartik, Thanks for new chapter. You have magical writing power which makes the learning so interesting and easy. I completely understood the concept of this chapter and very excited for next chapter. Thanks for the kind words and we are really glad you were able to understand the chapter: Will put up the next chapter as soon as we can. Are you facing any problems with this? Hi kartik If I place an order to buy niftyCE at premium of with a trailing stop loss of points. After sometime premium iscan I modify my trailing stop loss to 80 points or 60 points or can I square off my position at current price. Hi Karthik, Varsity is the great effort of you and Zerodha. I do not have words to appreciate, thanks a lot…. We will try our best Keshav. In fact that is our aim as well. But nevertheless we will do our best. Hi kartik, I have rs in my trading account. So for every 1 point up or down move you can make or lose Rs. For trading options please look into the charts of the spot market and not really the chart of the Options. You should look at the spot charts. The index is made up of these 50 stocks, check this http: The volume of Nifty spot is cumulative volumes of all abcs option volatility trading strategies with sheldon natenberg 50 stocks. Check this — http: For intraday it may not be possible Narsimha. I will get back to you on this soon, meanwhile you can certainly use the Nifty futures chart. Hi Karthik, the bid-ask spread for the Nifty is quite close; and when I square off an order at market price, there are no major surprises. So while trading larger volumes, is it safer to trade Nifty? The spread is tight when liquidity is abundant. In simpler words — when there are more people trading a particular contract liquidity improves and therefore the spreads get better it gets tighter. Tighter spreads imply lesser damage when you place market orders lesser surprise. Karthik, I was asking about the spread in absolute terms not percentage. With Bank Nifty options, I abcs option volatility trading strategies with sheldon natenberg a difference of over 10 rupees between the bid price and the ask price onscreen. Yes in absolute terms the difference is kind of bigger on Bank Nifty. It makes sense to trade Nifty especially when you know that you will use market orders. Thanks a lot for this information. The lot of 25 is fixed for both futures and options. I think came about because one of the comments posted earlier. Also, it may not be safe to assume point abcs option volatility trading strategies with sheldon natenberg moment in Nifty. The change in premium based on the change is underlying is captured by delta…which is the focus in chapter 9. Hi Jose, request you not to use caps lock.
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시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율 6 초 1024 MB 1 1 1 100.000% ## 문제 The rules of this game may differ slightly from the official game. Karen and her friends are competing in a high-stakes board game championship, playing the popular game Codenames. Codenames is a game with two opposing teams: the red team and the blue team. Karen is a member of the red team. The game is played on a board of size $5 \times 5$ where each of the $25$ cells is (secretly) assigned one of four kinds. There is a fixed number of cells of each kind on the board: • $9$ red cells (r); • $8$ blue cells (b); • $7$ neutral cells (n); • $1$ assassin cell (x). The true kinds of the cells are known only to one player of each team (called the “spymaster”). The other players initially see only a $5\times 5$ grid full of covered cells. The cells will get revealed as the game progresses. Each covered cell contains the name of an object (which turns out to be irrelevant to this problem). Luckily, Karen is the spymaster of her team, so she knows the true configuration of the board. Her responsibility is to help her teammates discover the red cells, while keeping them away from all the other cells (especially the assassin cell). The way she can do that is by announcing a hint consisting of: • a valid word $w$ (from a dictionary of $n$ words); • a positive number $g$ (the number of guesses that their teammates should make). Her teammates will then try to guess as many red cells as possible, given the hint. They start by making a first guess, and reveal one of the cells. If the revealed cell is red, they can continue guessing; otherwise, their turn stops, and the other team starts their turn. A team wins the game if all the cells with their corresponding color are revealed, or if the other team revealed the assassin cell. To illustrate this, let’s consider the state of the game below (the one corresponding to the example). The left picture shows Karen’s view of the board. The middle picture shows her teammates’ view of the board. Notice that some of the cells are covered for Karen’s teammates, and only Karen knows their true kinds. The meaning of the right picture will be explained later in the statement. Originally, Karen’s goal was to tell hints that relate to the names of objects described in some of the red cells, so that the teammates will know to reveal only those cells. However, she soon realized that the game is not going great, and that the blue team might beat them in their next turn. Thankfully, she and her friends have devised a secret “emergency cheating scheme” for these situations specifically. They start by assigning a letter to each of the $25$ cells, in row-major order (as illustrated above, in the right picture). Then, when Karen announces a word $w$ and a number $g$, her teammates would do the following: 1. Go through each of the letters $w_i$ of the word $w$ in order; 2. If $w_i$ is not assigned to any cell or the assigned cell of $w_i$ is already revealed, then do nothing; otherwise, guess the cell corresponding to $w_i$. The teammates repeat this procedure until they reveal all the correct cells, they make a mistake (reveal a non-red cell), they already made all $g$ guesses, or all the letters of $w$ are revealed. In the example above, Karen could announce “actor 2” to her team. Her team would first guess cell $(1, 1)$ (corresponding to letter a), skip letter c as the cell $(1, 3)$ is already revealed, and then guess cell $(4, 5)$, winning the game (as the other red cells are already revealed). Karen wants to use this scheme to win the game in one turn. She knows the dictionary of all the $n$ valid words, as well as the current state of the game. Find out some hint that she should announce to her team to grant them the victory! There are $q$ different scenarios that you need to solve. The dictionary is the same for all scenarios, but the board configurations might differ. ## 입력 The first line of the input contains a positive integer $n$ ($1 \le n \le 100\,000$), the number of valid words. Each of the following $n$ lines contain a single string of at least one and at most $30$ letters, representing the words in the dictionary. The following line contains a positive integer $q$ ($1 \le q \le 100\,000$), the number of scenarios. Then, $q$ lines follow, each describing a board. Each board is represented by a $5 \times 5$ grid of letters from the set {r, b, n, x} (red/blue/neutral/assassin). If the letter is uppercase, it means that the cell is already revealed (otherwise the cell is covered). There is at least one blue and one red covered cell, and the assassin cell is always covered; in other words, the state always indicates a game that has not finished yet. ## 출력 For each of the $q$ scenarios, output the hint consisting of a word $w$ and a number $g$ ($1 \le g \le 9$) which gives Karen’s team the victory. If no such hint can be announced for the specific scenario, print a single word “IMPOSSIBLE” (without quotes) instead of the hint. If multiple solutions exist, any one is accepted. The answers for different scenarios should be printed on separate lines. ## 예제 입력 1 3 actor cheat zeta 1 rBBnR NRnbB nRRnR NRxBr nBRbB ## 예제 출력 1 actor 2 ## 힌트 Note that Karen couldn’t have announced, for example, cheat 3, as her team would end up revealing the cell at position $(2, 3)$ and ending their turn. Some other correct solutions would be zeta 2 or actor 4.
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# How heavy is 0.0006 firkins? It's about as heavy as a Battery (AA) The weight of a Battery (AA) is about 0.00059 firkins. (Alkaline) An "AA" size battery weighs 0.00059 firkins. AA batteries came into common use during World War II and were given their name by the American National Standards Institute (ANSI) Committee C18 because they were smaller than the "A" size batteries which were invented first. It's about one-and-one-tenth times as heavy as a Mouse The weight of a Mouse is about 0.00051 firkins. (a.k.a. "House mouse", Mus musculus) (adult) The weight of a mouse is typically an average of 0.00051 firkins. While most mice typically live two to three years, the Methuselah Mouse Prize — an award administered by a non-profit organization which advances aging-related research — was once awarded to a team of scientists whose research resulted in a mouse living just under five years. It's about seven-tenths as heavy as a Light Bulb The weight of a Light Bulb is about 0.00083 firkins. (a.k.a. lamp) (for A19-size, 60w, incandescent bulb by Bulbrite; package weight) A standard, sixty-watt light bulb weighs about 0.00083 firkins. The tightly-coiled filament inside a bulb of this size would measure about 579mm if uncoiled and stretched out. It's about one-and-three-fifths times as heavy as a Compact disc The weight of a Compact disc is about 0.00037 firkins. (a.k.a. CD) A compact disc typically weighs 0.00037 firkins. Data is stored on CDs by encoding into the track a series of tiny pits — each between 3.5 and 850 µm (0.00014 and 0.033 in) in length. It's about half as heavy as a Golf Ball The weight of a Golf Ball is about 0.001125 firkins. (per R&A USGA Rules of Golf; maximum rule weight) According to the Rules of Golf (as approved by the United States Golf Association and the Rules Committee of the Royal and Ancient Golf Club of Saint Andrews), golf balls must weigh no more than 0.001125 firkins. Golf balls are not required to have the familiar dimpled pattern, but the design has been popular since its invention in 1905 because it reduces drag while increasing lift. It's about two times as heavy as a Battery (AAA) The weight of a Battery (AAA) is about 0.00029 firkins. (Alkaline) An "AAA" size battery weighs 0.00029 firkins. Batteries are named by the American National Standards Institute (ANSI) Committee C18 and AAA batteries were given their name because they were smaller than the "AA" and "A" size batteries which were invented first. It's about two-fifths as heavy as a Tennis Ball The weight of a Tennis Ball is about 0.00141 firkins. (ITF Standard; for Type 2 ball) Per International Tennis Federation standard, regulation tennis balls must weigh about 0.00141 firkins. Competition balls are also tested for bounce height, with the standards requiring that a ball dropped from 254 cm must bounce back to a height of 135 cm to 147 cm. It's about two-fifths as heavy as a Battery (C) The weight of a Battery (C) is about 0.0016 firkins. (Alkaline) A "C" size battery weighs 0.0016 firkins. C batteries are typically used in medium-drain devices such as musical instruments. It's about three-and-a-half times as heavy as an Eye (Human) The weight of an Eye (Human) is about 0.00017 firkins. A fully developed eye (in a person over the age of thirteen), weighs about 0.00017 firkins. The pupil of the eye varies depending on the amount of light it is exposed to, but typically measures about 4 mm across. It's about one-fourth as heavy as a Deck of Cards The weight of a Deck of Cards is about 0.0023 firkins. (ISO 216 B8 size, a.k.a. "poker size" 63 x 88 mm, 52-card deck) A deck of 52 ISO 216 B8-size playing cards weighs 0.0023 firkins. Utilizing nearly 3,700 decks, the record-holding largest card tower was built in early 2010, stood over 3.5 m (11 ft), and weighed over 5.60 firkins. It's about four times as heavy as a US Quarter The weight of a US Quarter is about 0.0001389 firkins. (United States quarter-dollar coin) (a.k.a. Quarter dollar, a.k.a. America the Beautiful quarter, a.k.a. two bits) The America the Beautiful series quarters, which began to enter circulation in 2017, weigh 0.0001389 firkins each. In answer to the common riddle, there are 119 ridges around the edge of the coin in its current design. It's about five times as heavy as a sheet of Paper The weight of a sheet of Paper is about 0.00012 firkins. (for US Letter, a.k.a. ANSI A; 215.9mm by 279.4mm (8.5 in x 11 in); 20lb) The weight of a ream (500 sheets) of 0.220 firkins, 8.5 inch x 11 inch paper is 0.049 firkins, each sheet weighing 0.00012 firkins. Paper of this size has a thickness of 0.004 caliper (0.1 mm). It's about one-fifth as heavy as a Battery (D) The weight of a Battery (D) is about 0.00331 firkins. (Alkaline) A "D" size battery weighs 0.00331 firkins. The D size battery is the oldest of the modern battery sizes, first invented by the National Carbon Company in 1898. It's about six times as heavy as a Die (Dice) The weight of a Die (Dice) is about 0.0001 firkins. (for six-sided, 16 mm, rounded cube) A die, of the size most commonly used in board games and casinos, typically weight 0.0001 firkins. The use of dice and dice-like tools predates written history, with the oldest known examples belonging to a 5,000-year old backgammon set uncovered during an archaeological dig in modern-day Iran. It's about one-fifth as heavy as a Baseball The weight of a Baseball is about 0.0035590277777778 firkins. (MLB rules) Per Major League Baseball rules, a baseball must weigh between 0.0034722222222222 firkins and 0.0036458333333333 firkins. A major league pitcher can throw a baseball at up to 150 kph (91 mph) (with a fastball pitch), with record-setting pitches as fast as 171 kph (106 mph). More Results
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Karsten W. - 1 year ago 83 R Question # Simulate a time series In a recent online course on macroeconomic forecasting, there was an excercise to model ``````y(t) = 3.0 + 0.55 y(t-1) + e(t) `````` where `e(t)` is defined as ``````et <- c(-1.2138662, -0.2854597, 0.5902700, 0.8285463, -0.9954260, -0.3716332) `````` Now I tried to do this in R (the course used EViews), however I do not come to the solution given there: 5.648 for the 5th element. I tried (similar to this blogpost): ``````y <- rep(NA,6) y[1] <- 0 y[2] <- 3 + 0.55*y[1]+et[1] y[3] <- 3 + 0.55*y[2]+et[2] y[4] <- 3 + 0.55*y[3]+et[3] y[5] <- 3 + 0.55*y[4]+et[4] y[6] <- 3 + 0.55*y[5]+et[5] `````` and then ``````y <- rep(NA,6) y[1] <- et[1] y[2] <- 3 + 0.55*y[1]+et[2] y[3] <- 3 + 0.55*y[2]+et[3] y[4] <- 3 + 0.55*y[3]+et[4] y[5] <- 3 + 0.55*y[4]+et[5] y[6] <- 3 + 0.55*y[5]+et[6] `````` and then ``````arima.sim(list(order=c(1,0,0), ar=0.55), n=6, innov=head(et,6)+3) `````` However all three methods give different results. I wonder why this is, I am afraid I did not understand something basic. `arima.sim` has a "burn-in" period in order to reach stationarity. Argument `n.start` sets the length of this period, and it must has length `ar` + `ma`. For an `AR(1)` process, `n.start` must be at least 1. Note, if you don't specify `n.start`, `arima.sim` will automatically compute a reasonable one for you. Given `n.start` (either a specified one or auto-computed one), `arima.sim` then randomly sample `n.start` innovations for "burn-in". It is right because of this random procedure, you will get different result from one run to another: ``````## innovations of length 6 et <- c(-1.2138662, -0.2854597, 0.5902700, 0.8285463, -0.9954260, -0.3716332) set.seed(0) arima.sim(list(order = c(1,0,0), ar = 0.55), n = 6, innov = et, n.start = 1) #[1] -0.5192413 -0.5710424 0.2761967 0.9804545 -0.4561760 -0.6225300 set.seed(1) arima.sim(list(order = c(1,0,0), ar = 0.55), n = 6, innov = et, n.start = 1) # [1] -1.55841580 -1.14258839 -0.03815361 0.80756181 -0.55126700 -0.67483005 `````` We can eliminate such randomness, by providing a set of starting innovations using `start.innov` argument. Note, this vector must has length `n.start`: ``````## fixing starting innovation at 0; i.e., `y[0] = 0`, so `y[1] = et[1]`. arima.sim(list(order = c(1,0,0), ar = 0.55), n = 6, innov = et, n.start = 1, start.innov = 0) # [1] -1.21386620 -0.95308611 0.06607264 0.86488625 -0.51973856 -0.65748941 `````` Now, compare this last `arima.sim` with the following: ``````y <- rep(NA, 6) y[1] <- et[1] y[2] <- 0.55 * y[1] + et[2] y[3] <- 0.55 * y[2] + et[3] y[4] <- 0.55 * y[3] + et[4] y[5] <- 0.55 * y[4] + et[5] y[6] <- 0.55 * y[5] + et[6] # [1] -1.21386620 -0.95308611 0.06607264 0.86488625 -0.51973856 -0.65748941 `````` We have everything completely reproducible. The above generates zero-mean time series; if you want mean at 3, shift the result by `+3` yourself: ``````y <- y + 3 `````` Recommended from our users: Dynamic Network Monitoring from WhatsUp Gold from IPSwitch. Free Download
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# Car rental is producing strange errors #1 So the thing is that when the computer gets to this line of code ``````def rental_car_cost(days): rent = 40 *days if days >= 7: rent - 50 elif days >= 3: rent - 20 return rent`````` It says that when the days are = to 3 the returned rent is 120 not 100 but in my code it says to minus the rent by 20 so it would be = to 100. What is wrong with my code. #2 Try changing that to ``elif days > 3:`` #3 hope this helps. #4 Thank you for helping, but could you just give hints or snippets of code next time? I ask this because it helps people learn more if you tell them where their mistakes are, why they're mistakes, and how to fix them, as opposed to just copying code that they don't understand. Thanks, JibblyJ #5 @si_fiwizard In case you didn't get it from their answers, you never changed the rent, just executed some math. You use `minus` (`-`) instead of `increment down` (`-=`) What you needed for the lines within the `if` and `elif` statements were `rent -= 50 or 20` depending on which dollar amount you were changing rent by #6
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Latest Teaching jobs   »   Maths Quiz (Pedagogy) for CTET Exam... # Maths Quiz (Pedagogy) for CTET Exam 2016 1. Students often make a mistake in comparing the decimal numbers. For example 0.50 is larger than 0.5. The most probable reason for this error is – A. lack of practice of these types of questions in the class B. lack of concrete experience of representation of decimal number on number line C. careless attempt by the students D. misconception regarding the significance of zero in ordering decimal 2. A teacher  prompts the students to prepare Mathematical journal with the theme “Application of Mathematics in Daily life.” This activity is – A. to test the students understanding of Mathematical concepts B. to help students to connect Mathematical concepts and its applications and to share their knowledge and ideas C. to provide opportunity to students share their ideas and knowledge D. none of these 3. A child display difficulty in differentiating between numbers, operations and symbols, two clock hands, different coins etc. This implies that the specific barrier affecting his learning is – A. poor verbal, visual, auditory and working memory B. poor visual processing ability i.e visual discrimination, spatial organization and visual coordination C. poor language processing ability i.e expression, vocabulary and auditory processing D. poor motor skills, reading and writing skills 4. The most appropriate tool to expose the students of class II to plane figures, its vertices and edges is – A. Geo-board B. Nets of 3D solids C. Cubes D. Black-board surface 5. Following is a problem from textbooks of class III: “Which mathematical operation will be used to solve the following problem? A milkman sold 1410 liters of milk in 10 days. How many litres of milk did he sell in a day?” Which competence of Bloom’s cognitive domain is referred in the above question? A. Knowledge B. Comprehension C. Analysis D. Synthesis 6. The highlights of a good textbook are that – 1. they contain numerous exercises to give rigorous practice 2. all concepts can be introduced through situations 3. only solved examples are included 4. they must be thick and heavy A. C and D B. A and B C. A and C D. B and D 7. NCF 2005 emphasis that – A. Maths shall be taught to selective students B. Maths curriculum shall be separate for low achievers C. Students should be tested first for their logico-mathematical ability D. Succeeding in Mathematics should be mandatory for every child 8. NCF 2005 states that Mathematics teaching should be ambitious, coherent and important. Here, “ambitious” refers to achievement of – A. narrow goals of Mathematics B. linking of Mathematics with other subjects C. applications of Mathematics D. higher goals of Mathematics 9. The recommended key concept in the unit of multiplication in class III is – A. multiplication of 2-digit number with 2-digit number B. properties of multiplication – order property and group property C. word problem based on multiplication D. multiplication of 3-digit numbers by 10 10. From the unit of “fraction”, teacher asked the students to list any five fractions. This question refers to – A. higher level of thinking B. analytical thinking C. spatial thinking D. lower level of thinking
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# feasibility tolerance 4 messages Open this post in threaded view | Report Content as Inappropriate ## feasibility tolerance I am solving a nonlinear optimization problem and I set the feasibility tolerance as:`  mdl = Model(solver =KnitroSolver(feastol=0.01))`then I have several equality constraints including`@NLconstraint(mdl, psi0_con, psi[1] == psi0);`after I solve the optimization problem, I get an infeasible point and when I run:`getdual()`on all of the constraints, the one that looks like the worst is:`getdual(psi0_con) = 1`but then when I look at the point that the optimization actually converges on, it does not look that bad:`julia> getvalue(psi0)1.3772404760181705julia> getvalue(psi[1])1.3697550013526445`Any ideas why this is not a feasible point even though:`julia> getvalue(psi[1])-getvalue(psi0)`is within the tolerance that I set? -- You received this message because you are subscribed to the Google Groups "julia-opt" group. To unsubscribe from this group and stop receiving emails from it, send an email to [hidden email]. Visit this group at https://groups.google.com/group/julia-opt. For more options, visit https://groups.google.com/d/optout. Open this post in threaded view | Report Content as Inappropriate ## Re: feasibility tolerance Also, I have tried:`  mdl = Model(solver =KnitroSolver(infeastol=0.01))`with similar results -- You received this message because you are subscribed to the Google Groups "julia-opt" group. To unsubscribe from this group and stop receiving emails from it, send an email to [hidden email]. Visit this group at https://groups.google.com/group/julia-opt. For more options, visit https://groups.google.com/d/optout. Open this post in threaded view | Report Content as Inappropriate ## Re: feasibility tolerance Additionally, I tried to simplify the problem definition and use linear constraints as: `@constraint(mdl, psi0_con, psi[1] == psi0_);`But, I am still getting similar results to those shown above -- You received this message because you are subscribed to the Google Groups "julia-opt" group. To unsubscribe from this group and stop receiving emails from it, send an email to [hidden email]. Visit this group at https://groups.google.com/group/julia-opt. For more options, visit https://groups.google.com/d/optout. Increasing the values of "feastol" and "feastol_abs" to match the feasibility level you consider "good enough" to declare optimality.  See this section on the termination criteria in Knitro:https://www.artelys.com/tools/knitro_doc/2_userGuide/termination.htmland in particular note the "stop1" condition.  Set "feastol" to something very large (say, 1e20) so that the feasibility condition is only determined by "feastol_abs".  Then try setting "feastol_abs"  to something like 1e-2 or 1e-3 (or whatever works.Also, I ended up having to do the same with `opttol. So, that the problem converges without worrying about accuracy too much` -- You received this message because you are subscribed to the Google Groups "julia-opt" group. To unsubscribe from this group and stop receiving emails from it, send an email to [hidden email]. Visit this group at https://groups.google.com/group/julia-opt. For more options, visit https://groups.google.com/d/optout.
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# Estimable Stories in the INVEST Model Estimable stories can be estimated: some judgment made about their size, cost, or time to deliver. (We might wish for the term estimatable, but it’s not in my dictionary, and I’m not fond enough of estimating to coin it.) To be estimable, stories have to be understood well enough, and be stable enough, that we can put useful bounds on our guesses. A note of caution: Estimability is the most-abused aspect of INVEST (that is, the most energy spent for the least value). If I could re-pick, we’d have “E = External”; see the discussion under “V for Valuable”. ## Why We Like Estimates Why do we want estimates? Usually it’s for planning, to give us an idea of the cost and/or time to do some work. Estimates help us make decisions about cost versus value. When my car gets worked on, I want to know if it’s going to cost me \$15 or \$10K, because I’ll act differently depending on the cost. I might use these guidelines: • < \$50: just do it • \$50-\$300: get the work done but whine to my friends later • \$300-\$5000: get another opinion; explore options; defer if possible • \$5000+: go car shopping Life often demands some level of estimation, but don’t ignore delivery or value to focus too much on cost alone. We’ll go through facts and factors affecting estimates; at the end I’ll argue for as light an estimation approach as possible. ## Face Reality: An Estimate is a Guess If a story were already completed, the cost, time taken, etc. would be (could be?) known quantities. We’d really like to know those values in advance, to help us in planning, staffing, etc. Since we can’t know, we mix analysis and intuition to create a guess, which could be a single number, a range, or a probability distribution. (It doesn’t matter whether it’s points or days, Fibonacci or t-shirt sizes, etc.) When we decide how accurate our estimates must be, we’re making an economic tradeoff since it costs more to create estimates with tighter error bounds. ## How Are Estimates Made? There are several approaches, often used in combination: • Expert Opinion AKA Gut Feel AKA SWAG: Ask someone to make a judgment, taking into account everything they know and believe. Every estimation method boils down to this at some point. • Analogy: Estimate based on something with similar characteristics. (“Last time, a new report took 2 days; this one has similar complexity, so let’s say 2 days.”) • Decomposition AKA Divide and Conquer AKA Disaggregation: Break the item into smaller parts, and estimate the cost of each part — plus the oft-forgotten cost of re-combining the parts. • Formula: Apply a formula to some attributes of the problem, solution, or situation. (Examples: Function Points, COCOMO.) Challenges: • formulas’ parameters require tuning based on historical data (which may not exist) • formulas require judgment about which formulas apply • formulas tend to presume the problem or solution is well-enough understood to assess the concrete parts • Work Sample: Implement a subset of the system, and base estimates on that experience. Iterative and incremental approaches provide this ongoing opportunity. • Buffer AKA Fudge Factor: Multiply (and/or add to) an estimate to account for unknowns, excessive optimism, forgotten work, overheads, or intangible factors. For example: “Add 20%”, “Multiply by 3″, or “Add 2 extra months at the end”. ## Why Is It Hard to Estimate? Stories are difficult to estimate because of the unknowns. After all, the whole process is an attempt to derive a “known” (cost, time, …) from something unknowable (“exactly what will the future bring?”). Software development has so many unknowns: • The Domain: When we don’t know the domain, it’s easier to have misunderstandings with our customer, and it can be harder to have deep insights into better solutions. • Level of Innovation: We may be operating in a domain where we need to do things we have never done before; perhaps nobody has. • The Details of a Story: We often want to estimate a story before it is fully understood; we may have to predict the effects of complicated business rules and constraints that aren’t yet articulated or even anticipated. • The Relationship to Other Stories: Some stories can be easier or harder depending on the other stories that will be implemented. • The Team: Even if we have the same people as the last project, and the team stays stable throughout the project, people change over time. It’s even harder with a new team. • Technology: We may know some of the technology we’ll use in a large project, but it’s rare to know it all up-front. Thus our estimates have to account for learning time. • The Approach to the Solution: We may not yet know how we intend to solve the problem. • The Relationship to Existing Code: We may not know whether we’ll be working in a habitable section of the existing solution. • The Rate of Change: We may need to estimate not just “What is the story now?” but also “What will it be by the end?” • Dysfunctional Games: In some environments, estimates are valued mostly as a tool for political power-plays; objective estimates may have little use. (There’s plenty to say about estimates vs. commitments, schedule chicken, and many other abuses but I’ll save that for another time.) • Overhead: External factors affect estimates. If we multi-task or get pulled off to side projects, things will take longer. Sitting in a planning meeting for a day or a week and ginning up a feeling of commitment won’t overcome these challenges. ## Flaws In Estimating We tend to speak as if estimates are concrete and passive: “Given this story, what is the estimate?” But it’s not that simple: • N for Negotiable” suggests that flexibility in stories is beneficial: flexible stories help us find bargains with the most value for their cost. But the more variation you allow, the harder it is to estimate. • I for Independent” suggests that we create stories that can be independently estimated and implemented. While this is mostly true, it is a simplification of reality: sometimes the cost of a story depends on the order of implementation or on what else is implemented. It may be hard to capture that in estimates. • Factors that make it hard to estimate are not stable over time. So even if you’re able to take all those factors into account, you also have to account for their instability. Is estimating hopeless? If you think estimation is a simple process that will yield an exact (and correct!) number, then you are on a futile quest. If you just need enough information from estimates to guide decisions, you can usually get that. Some projects need detailed estimates, and are willing to spend what it takes to get them. In general, though, Tom DeMarco has it right: “Strict control is something that matters a lot on relatively useless projects and much less on useful projects.” Where does that leave things? The best way is to use as light an estimation process as you can tolerate. We’ll explore three approaches: counting stories, historical estimates, and rough order of magnitude estimates. ## Simple Estimates: Count the Stories More than ten years ago, Don Wells proposed a very simple approach: “Just count the stories.” Here’s a thought experiment: • Take a bunch of numbers representing the true sizes of stories • Take a random sample • The average of the sample is an approximation of the average of the original set, so use that average as the estimate of the size of every story (“Call it a 1″) • The estimate for the total is the number of stories times the sample average What could make this not work? • If stories are highly inter-dependent, and the order they’re done in makes a dramatic difference to their size, the first step is void since there’s no such thing as the “true” size. • If you cherry-pick easy or hard stories rather than a random set, you will bias the estimate. • If your ability to make progress shifts over time, the estimates will diverge. (Agile teams try to reduce that risk with refactoring, testing, and simple design.) I’ve seen several teams use a simple approach: they figure out a line between “small enough to understand and implement” and “too big”, then require that stories accepted for implementation be in the former range. ## Historical Estimates (ala Kanban) For many teams, the size of stories is not the driving factor in how long a story takes to deliver. Rather, work-in-progress (WIP) is the challenge: a new story has to wait in line behind a lot of existing work. A good measure is total lead time (also known as cycle time or various other names): how long from order to delivery. Kanban approaches often use this measure, but other methods can too. If we track history, we can measure the cycle times and look for patterns. If we see that the average story takes 10 days to deliver and that 95% of the stories take 22 or fewer days to deliver, we get a fairly good picture of the time to deliver the next story. This moves the estimation question from “How big is this?” to “How soon can I get it?” When WIP is high, it is the dominant factor in delivery performance; as WIP approaches 0, the size of the individual item becomes significant. ## Rough Order of Magnitude A rough order of magnitude estimate just tries to guess the time unit: hours, days, weeks, months, years. You might use such estimates like this: • Explore risk, value, and options • Make rough order of magnitude estimates • Focus first on what it takes to create a minimal but useful version of the most important stories • From there, decide how and how far to carry forward by negotiating to balance competing interests • Be open to learning along the way ## Conclusion Stories are estimable when we can make a good-enough prediction of time, cost, or other attributes we care about. We looked at approaches to estimation and key factors that influence estimates. Estimation does not have to be a heavy-weight and painful process. Try the lighter ways to work with estimates: counting stories, historical estimates, and/or rough order of magnitude estimates. Whatever approach you take, spend as little as you can to get good-enough estimates. ### Related Material Postscript: My thinking on this has definitely evolved over the years, but I’ve always felt that Small and Testable stories are the most Estimable:) # Resources on Set-Based Design “Two roads diverged in a yellow wood, yet I could travel both.” —Not Robert Frost A reading list on set-based design (part of lean product development). Information on boat design. Baldwin, Carliss, and Kim Clark. Design Rules, Volume 1: The Power of Modularity. MIT Press, 2000. ISBN 0262024667. Modularity and platforms, from a somewhat economic perspective; not overly focused on software modularity. (No volume 2 yet:( Kennedy, Michael. Product Development for the Lean Enterprise: Why Toyota’s System is Four Times More Productive and How You Can Implement It. Oaklea Press, 2008. ISBN 1892538180. Business novel, touches on set-based approaches. Kennedy, Michael and Kent Harmon. Ready, Set, Dominate: Implement Toyota’s Set-Based Learning for Developing Products, and Nobody Can Catch You. Oaklea Press, 2008. ISBN 1892538407. Second novel, also touches on set-based approaches. Morgan, James, and Jeffrey Liker. The Toyota Product Development System. Productivity Press, 2006. ISBN 1-56327-282-2. Overview of lean product development, touches on set-based approaches. Poppendieck, Mary and Tom. "Amplify Learning." The importance of communicating constraints (rather than solutions) in set-based development. Shook, John. Managing to Learn: Using the A3 Management Process to Solve Problems, Gain Agreement, Mentor, and Lead. Lean Enterprise Institute, 2008. ISBN 1934109207. A3 reports as the heart of lean management. Sobek II, Durward, Allen Ward, and Jeffrey Liker. “Toyota’s Principles of Set-Based Concurrent Engineering,” Sloan Management Review, Winter, 1998. Basic description and principles of the approach. Wake, Bill. “Set-Based Concurrent Engineering.” Overview of several variations of set-based design in software. Ward, Allen, Jeffrey Liker, John Cristiano, Durward Sobek II. “The Second Toyota Paradox: How Delaying Decisions Can Make Better Cars Faster,” Sloan Management Review, Spring, 1995. Looks at how set-based concurrent engineering lets Toyota do better than other carmakers. Ward, Allen. Lean Product and Process Development. Lean Enterprise Institute, 2007. ISBN 978-1-934109-13-7. Description of knowledge waste, set-based concurrent engineering, and a different view of the PDCA cycle. This is based on a list originally prepared for Agile 2009 by Bill Wake and Jean Tabaka. # Intensifying Stories: Running with the Winners For a given story headline, many interpretations are possible. These vary in their quality and sophistication. I call this the intensity or depth of a story. Story intensity is a knob you can control, dialing it down for earlier delivery, dialing it up for a more complex product. For example, consider the story "System Cross-Sells Item." The simplest version could suggest the same item to everybody. The next version could have the system suggest a bestseller in the same category as a shopping-cart item. The most sophisticated version might consider past purchases from this and millions of other users, take into account the customer's wish-list, and favor high-margin items. ## Lowering Intensity The most common way to move the intensity dial is to lower intensity. This is the domain of various story-splitting strategies such as 0-1-Many or Happy Path First. These techniques are usually used to pull out the most valuable parts of a story, or to help ensure it can be implemented in a short time-frame (e.g., an iteration). Story splitting is an important tool, but in the rest of this article we'll focus on going the other way. ## Why Intensify? The ability to intensify is valuable because we are uncertain about what is most valuable. We have hypotheses, but reality can often surprise us. Think of it as placing bets. Suppose you have six alternatives. You can bet everything on one choice, or you can place small bets on each alternative with followup bets when you see which one is winning. Put this way, it seems clear we're better off starting with small bets, unless we're already sure about which will win. The Lean Startup community has a related idea. They note that startups often pivot from one business model to another as they try to create a business. One pivot is called a zoom-in pivot: take a subset of the original product, and build a business on just that. An example is Flickr: it started as a game with a sharing component, but was zoomed in to focus on just the photo-sharing aspects. ## Intensifying: Three Approaches There are three common ways to intensify stories: 1. Improve quality attributes 2. Apply story-splitting techniques backwards 3. Invent intensifiers that add in more options or capabilities ## Improve Quality Attributes The most straightforward way to intensify a story is to improve some quality attribute. Quality attributes, also known as non-functional requirements or "ilities," have a scale that tells how good something must be. Intensifying is just a matter of targeting a better number. For example, suppose our system must support 125 transactions/second. We could intensify this by raising that to 500 transactions/second. This form of intensifying is the least creative: take an attribute and ask for one 5x as good. Be careful: some increases can be extremely expensive. A system that is 99% available can have 3.5 days of downtime per year; one with 99.9999% availability can have only ~30 seconds of downtime per year. A desktop machine might support the first one, but the second one might require a sophisticated and expensive multi-site setup. ## Apply Story-Splitting in Reverse For any story we've already split down, we can of course intensify it by combining everything back together. But we can also use story splitting techniques as a way to generate new possibilities. For example, the 0-1-Many split says that when we have many of something, we can reduce it to 0 or 1 ways. To run this split backwards, we find something where we have only one of something, and generalize it to many. For example, we may be able to save a document in a specific file format. We can look at this as a "one"; and look for a "many." In this case, that might mean supporting a variety of output formats. ## Invent Intensifiers The third approach is to find creative ways to improve a feature or set of features. There's no fixed set of ways to do this, though we can identify some common approaches. Let's take a story "User finds matching item" to describe a searching process, and look at several ways to make this feature more sophisticated. Add Control: We can provide options that let the user do a more precise or broader search: • Boolean operators • Proximity operators ("Agile within 3 words of Testing") • "Find more like this" Add Intelligence: We get the system to automatically do more for us: • Automatically search for synonyms • Autofill with the most common searches • Automatically classify results Manage History: Searching is rarely a one-time event; we can put the activity in more context by considering what has gone before. • Save searches for future use • Manage a list of previous searches or previous results Manage Multiple Items: A user may have multiple searches active at once, and want to coordinate them. • Allow multiple search result windows • Compare results of two searches • Merge results from multiple searches ## Conclusion Intensity is a controllable characteristic of stories. To lower intensity, standard story-splitting techniques apply. To increase intensity, there are several approaches: • Improve quality attributes • Apply story-splitting in reverse • Invent intensifiers By controlling the intensity of stories, we can better respond to the uncertainties of development and use. # Valuable Stories in the INVEST Model Of all the attributes of the INVEST model, "Valuable" is the easiest one to, well, value. Who is against value? We'll look at these key aspects: • What is value? • The importance of external impact • Value for whom? ## What is Value? Value depends on what we're trying to achieve. One old formula is IRACIS. (Gane & Sarson mentioned it in 1977 in Structured Systems Analysis, and didn't claim it was original with them.) IRACIS means: • Increase Revenue • Avoid Costs • Improve Service. Increase Revenue: Add new features (or improve old ones) because somebody will pay more when they're present. Avoid Costs: Much software is written to help someone avoid spending money. For example, suppose you're writing software to support a call center: every second you save on a typical transaction means fewer total agents are needed, saving the company money. Improve Service: Some work is intended to improve existing capabilities. Consider Skype, the voice network: improving call quality is not a new feature, but it has value. (For example, more customers might stay with the service when call quality is higher.) IRACIS covers several types of value, but there are others: Meet Regulations: The government may demand that we support certain capabilities (whether we want to or not). For example, credit card companies are required to support a "Do Not Call" list for customers who don't want new offers. If the company didn't provide the capability by a certain date, the government would shut down the company. Build Reputation: Some things are done to increase our visibility in the marketplace. An example might be producing a free demo version of packaged software, to improve its marketing. In effect, these are an indirect way to increase revenue. Create Options: Some things give us more flexibility in the future. For example, we may invest in database independence today, to give us the ability to quickly change databases in the future. The future is uncertain; options are insurance. Generate Information: Sometimes we need better information to help us make a good decision. For example, we might do an A-B test to tell us which color button sells more. XP-style spikes may fit this category as well. Build Team: Sometimes a feature is chosen because it will help the team successfully bond, or learn important to the future. Several of these values may apply at the same time. (There's nothing that makes this an exhaustive list, either.) Because multiple types of values are involved, making decisions is not easy: we have to trade across multiple dimensions. ## Valuing External Impact Software is designed to accomplish something in the real world. We'll lean on a classic analysis idea: describe the system's behavior as if the system is implemented with a perfect technology. Focus on the effects of the system in the world. This helps clarify what are "real" stories: they start from outside the system and go in, or start inside and go outside. This also helps us avoid two problems: • "stories" that are about the solution we're using (the technology) • "stories" that are about the creators of the system, or what they want If we frame stories so their impact is clear, product owners and users can understand what the stories bring, and make good choices about them. ## Value for Whom? Who gets the benefit of the software we create? (One person can fill several of these roles, and this is not an exhaustive list.) Users: The word "User" isn't the best, but we really are talking about the people who use the software. Sometimes the user may be indirect: with a call center, the agent is the direct user, and the customer talking to them is indirect. Purchasers: Purchasers are responsible for choosing and paying for the software. (Sometimes even these are separate roles.) Purchasers' needs often do not fully align with those of users. For example, the agents using call center software may not want to be monitored, but the purchaser of the system may require that capability. Development Organizations: In some cases, the development organization has needs that are reflected in things like compliance to standards, use of default languages and architectures, and so on. Sponsors: Sponsors are the people paying for the software being developed. They want some return on their investment. There can be other kinds of people who get value from software we develop. Part of the job of a development team is balancing the needs of various stakeholders. ## Summary We looked at what values is: IRACIS (Increase Revenue, Avoid Costs, Improve Service), as well as other things including Meeting Regulations, Generating Information, and Creating Options. We briefly explored the idea that good stories usually talk about what happens on the edge of the system: the effects of the software in the world. Finally, we considered how various stakeholders benefit: users, purchasers, development organizations, and sponsors. Value is important. It's surprisingly easy to get disconnected from it, so returning to the understanding of "What is value for this project?" is critical. # Negotiable Stories in the INVEST Model In the INVEST model for user stories, N is for Negotiable (and Negotiated). Negotiable hints at several important things about stories: • The importance of collaboration • Evolutionary design • Response to change ## Collaboration Why do firms exist? Why isn't everything done by individuals interacting in a marketplace? Nobel-prize winner Ronald Coase gave this answer: firms reduce the friction of working together. Working with individuals has costs: you have to find someone to work with, negotiate a contract, monitor performance carefully–and all these have a higher overhead compared to working with someone in the same firm. In effect, a company creates a zone where people can act in a higher-trust way (which often yields better results at a lower cost). The same dynamic, of course, plays out in software teams; teams that can act from trust and goodwill expect better results. Negotiable features take advantage of that trust: people can work together, share ideas, and jointly own the result. ## Evolutionary Design High-level stories, written from the perspective of the actors that use the system, define capabilities of the system without over-constraining the implementation approach. This reflects a classic goal for requirements: specify what, not how. (Admittedly, the motto is better-loved than the practice.) Consider an example: an online bookstore. (This is a company that sells stories and information printed onto pieces of paper, in a package known as a "book.") This system may have a requirement "Fulfillment sends book and receipt." At this level, we've specified our need but haven't committed to a  particular approach. Several implementations are possible: • A fulfillment clerk gets a note telling which items to send, picks them off the shelf, writes a receipt by hand, packages everything, and takes the accumulated packages to the delivery store every day. • The system generates a list of items to package, sorted by (warehouse) aisle and customer. A clerk takes this "pick list" and pushes a cart through the warehouse, picking up the items called for. A different clerk prints labels and receipts, packages the items, and leaves them where a shipper will pick them up. • Items are pre-packaged and stored on smart shelves (related to the routing systems used for baggage at large airports). The shelves send the item to a labeler machine, which sends them to a sorter that crates them by zip code, for the shipper to pick up. Each of these approaches fulfills the requirement. (They vary in their non-functional characteristics, cost, etc.) By keeping the story at a higher level, we leave room to negotiate: to work out a solution that takes everything into account as best we can. We can create a path that lets us evolve our solution, from basic to advanced form. ## Feedback Waterfall development is sometimes described as "throw it over the wall": create a "perfect" description of a solution, feed it to one team for design, another for implementation, another for testing, and so on, with no real feedback between teams. But this approach assumes that you can not only correctly identify problems and solutions, but also communicate these in exactly the right way to trigger the right behavior in others. Some projects can work with this approach, or at least come close enough. But others are addressing "wicked problems" where any solution affects the perceived requirements in unpredictable ways. Our only hope in these situations is to intervene in some way, get feedback, and go from there. Some teams can (or try to) create a big static backlog at the start of a project, then measure burndown until those items are all done. But this doesn't work well when feedback is needed. Negotiable stories help even in ambiguous situations; we can work with high-level descriptions early, and build details as we go. By starting with stories at a high level, expanding details as necessary, and leaving room to adjust as we learn more, we can more easily evolve to a solution that balances all our needs. # The System Metaphor Explored The System Metaphor is one of the less popular parts of Extreme Programming (XP). Newer descriptions often even omit it. But metaphor is useful – when you have  a good one, it really helps you understand and organize your system. This post has a couple versions of a tutorial that Steve Wake and I developed and presented at some of the early Agile conferences. It's released under Creative Commons CC-BY-SA. Versions: PPT, PDF (2-up), PDF with notes Thee's also a SlideShare version # Independent Stories in the INVEST Model The INVEST model is a reminder of the important characteristics of user stories, and it starts with I for Independent. Independent stories each describe different aspects of a system's capabilities. They are easier to work with because each one can be (mostly) understood, tracked, implemented, tested, etc. on its own. Agile software approaches are flexible, better able to pursue whatever is most valuable today, not constrained to follow a 6-month old guess about what would be most valuable today. Independent stories help make that true: rather than a "take it or leave it" lump, they let us focus on particular aspects of a system. We would like a system's description to be consistent and complete. Independent stories help with that too: by avoiding overlap, they reduce places where descriptions contradict each other, and they make it easier to consider whether we've described everything we need. Three common types of dependency: overlap, order, and containment What makes stories dependent rather than independent? There are three common types of dependency: overlap (undesirable), order (mostly can be worked around), and containment (sometimes helpful). ## Overlap Dependency Overlap is the most painful form of dependency. Imagine a set of underlying capabilities: {A, B, C, D, E, F} with stories that cover various subsets: {A, B} {A, B, F} {B, C, D} {B, C, F} {B, E} {E, F} Quick: what's the smallest set of stories that ensure that capabilities {A, B, C, D, E, F} are present? What about {A, B, C, E}? Can we get those and nothing else? When stories overlap, it's hard to ensure that everything is covered at least once, and we risk confusion when things are covered more than once. Overlapping stories create confusion. For example, consider an email system with the stories "User sends and receives messages" and "User sends and replies to messages." (Just seeing the word "and" in a story title can make you suspicious, but you really have to consider multiple stories to know if there's overlap.) Both stories mention sending a message. We can partition the stories differently to reduce overlap: User sends [new] message User replies to message (Note that we're not concerned about "technical" overlap at this level: sending and replying to messages would presumably share a lot of technical tasks. How we design the system or schedule the work is not our primary concern when we're trying to understand the system's behavior.) ## Order Dependency A second common dependency is order dependency: "this story must be implemented before that one." Order dependencies complicate a plan, but we can usually eliminate them. While there's no approach that guarantees it, order dependency tends to be something that is mostly harmless and can be worked around. There are several reasons for that: 1. Some order dependencies flow from the nature of the problem. For example, a story "User re-sends a message" naturally follows "User sends message." Even if there is an order dependency we can't eliminate, it doesn't matter since the business will tend to schedule these stories in a way that reflects it. 2. Even when a dependency exists, there's only a 50/50 chance we'll want to schedule things in the "wrong" order. 3. We can find clever ways to remove most of the order dependencies. For example, a user might need an account before they can send email. That might make us think we need to implement the account management stories first (stories like "Admin creates account"). Instead, we could build in ("hard-code") the initial accounts. (You might look at this as "hard-coding" or you might think of it as "the skinniest possible version of account management"; either way, it's a lot less work.) Why take that approach? Because we want to explore certain areas first. We consider both value and risk. On the value side, we may focus on the parts paying customers will value most (to attract them with an early delivery). On the risk side, we may find it important to address risks, thinking of them as negative value.  In our example, we may be concerned about poor usability as a risk. A few hard-coded accounts would be enough to let us explore the usability concerns. ## Containment Dependency Containment dependency comes in when we organize stories hierarchically: "this story contains these others." Teams use different terms for this idea: you might hear talk of "themes, epics, and stories," "features and stories," "stories and sub-stories," etc. A hierarchy is an organizational tool; it can be used formally or informally. A good organization for describing a system is rarely the best organization for scheduling its implementation. The biggest caveat about a hierarchical decomposition is that while it's a helpful strategy for organizing and understanding a large set of stories, it doesn't make a good scheduling strategy. It can encourage you to do a "depth-first" schedule: address this area, and when it's done, go the next area. But really, it's unlikely that the most valuable stories will all be in a single area. Rather, we benefit from first creating a minimal version of the whole system, then a fancier version (with the next most important feature), and so on. ## Bottom Line Independent stories help both the business and technical sides of a project. From a business perspective, the project gets a simple model focused on the business goals, not over-constrained by technical dependencies. From a technical perspective, independent stories encourage a minimal implementation, and support design approaches that minimize and mange implementation dependencies. ### Related Material "INVEST in Good Stories, and SMART Tasks" – the original article describing the INVEST model Composing User Stories – eLearning from Industrial Logic User Stories Applied, by Mike Cohn # 3A – Arrange, Act, Assert Some unit tests are focused, other are like a run-on sentence. How can we create tests that are focused and communicate well? What's a good structure for a unit test? 3A: Arrange, Act, Assert We want to test the behavior of objects. One good approach is to put an object into each "interesting" configuration it has, and try various actions on it. Consider the various types of behaviors an object has: • Constructors • Mutators, also known as modifiers or commands • Accessors, also known as queries • Iterators I learned this separation a long time ago but I don't know the source (though my guess would be some Abstract Data Type research). It's embodied in Bertrand Meyer's "command-query separation" principle, and others have independently invented it. With those distinctions in mind, we can create tests: Arrange: Set up the object to be tested. We may need to surround the object with collaborators. For testing purposes, those collaborators might be test objects (mocks, fakes, etc.) or the real thing. Act: Act on the object (through some mutator). You may need to give it parameters (again, possibly test objects). Assert: Make claims about the object, its collaborators, its parameters, and possibly (rarely!!) global state. ## Where to Begin? You might think that the Arrange is the natural thing to write first, since it comes first. When I'm systematically working through an object's behaviors, I may write the Act line first. But a useful technique I learned from Jim Newkirk is that writing the Assert first is a great place to start. When you have a new behavior you know you want to test, Assert First lets you start by asking "Suppose it worked; how would I be able to tell?" With the Assert in place, you can do what Industrial Logic calls "Frame First" and lean on the IDE to "fill in the blanks." ## FAQ Aren't some things easier to test with a sequence of actions and assertions? Occasionally a sequence is needed, but the 3A pattern is partly a reaction to large tests that look like this: • Arrange • Act • Assert • Act • Assert • Arrange more • Act • Assert To understand a test like that, you have to track state over a series of activities. It's hard to see what object is the focus of the test, and it's hard to see that you've covered each interesting case. Such multi-step unit tests are usually better off being split into several tests. But I won't say "never do it"; there could be some case where the goal is to track a cumulative state and it's just easier to understand in one series of calls. Sometimes we want to make sure of our setup. Is it OK to have an extra assert? Such a test looks like this: • Arrange • Assert that the setup is OK • Act • Assert that the behavior is right First, consider whether this should be two separate tests, or whether setup is too complicated (if we can't trust objects to be in the initial state we want). Still, if it seems necessary to do this checking, it's worth bending the guideline. What about the notion of having "one assert per test"? I don't follow that guideline too closely. I consider it for two things: 1. A series of assertions may indicate the object is missing functionality which should be added (and tested). The classical case is equals()It's better to define an equals() method than (possibly create and) repeat a bunch of assertions about held data. 2. A series of similar assertions might benefit from a helper (assertion) method. (If an object has many accessors, it may indicate the object is doing too much.) When a test modifies an object, I typically find it easiest to consider most accessors together. For example, consider a list that tracks the number of objects and the maximum entry. One test might look like this: List list = new List(); assertEquals(1, list.size()); assertEquals(3, list.max()); That is, it considers the case "what all happens when one item is inserted into an empty list?" Then the various assertions each explore a different "dimension" of the object. Most xUnit frameworks let you define a method that is called before each test. This lets you pull out some common code for the tests, and it is part of the initial Arrange. (Thus you have to look in two places to understand the full Arrange-ment.) Most xUnit frameworks let you define a method that is called after each test. For example, if a test opens a file connection, the teardown could close that connection. If you need teardown, use it, of course. But I'm not adding a fourth A to the pattern: most unit tests don't need teardown. Unit tests (for the bulk of the system) don't talk to external systems, databases, files, etc., and Arrange-Act-Assert is a pattern for unit tests. ### History I (Bill Wake) observed and named the pattern in 2001. "Arrange-Act-Assert" has been the full name the whole time, but it's been variously abbreviated as AAA or 3A. Kent Beck mentions this pattern in his book Test-Driven Development: By Example (p. 97). This article was written in 2011. Added a description of Assert First and Frame First due to Brian Marick's comment. [4/26/11] # Tests from a Hat How does the order of tests affect the design of software? Exercise: • Write a bunch of plausible unit test descriptions. • Slice them into strips and put them in a hat. • Repeat until the hat is empty: • Pull tests one at a time from a hat. • Write the indicated test • Write the code to make the last test pass, TDD style. • If you absolutely must create a prerequisite test, do so. • Refactor as you go. • Set aside your implementation, shuffle the tests back into the hat, and repeat once or twice. Exercise ideas: • spreadsheet (domain objects, parsing, representation of storage), • auction sniper (from Freeman and Pryce’s Growing Object-Oriented Software), • video rental store (from Fowler et al’s Refactoring), • currency (from Beck’s Test-Driven Development), Sample Tests for a Spreadsheet: 1. New sheet is empty 2. Inserting into a sheet stores a value 3. Numeric cells are formatted as numbers 4. Cells retain literal values (for editing) Ex: 007 is edited as 007 but displays as 7. 5. Cells starting with = are formulas. 6. Constant formula Ex. =7 7. Parentheses in formulas 8. Multiplication in formulas 9. Addition in formulas 10. Precedence in formulas Reflection Points: • Did you encode your tests the same each time? • Did the solutions come out basically the same? Why or why not? • Did you see alternative solution paths when you went through again? Source: Bill Wake, 2010. Inspired by "Scenes From a Hat" in improv. # Review – Growing Object-Oriented Software, Guided by Tests Growing Object-Oriented Software, Guided by Tests, by Steve Freeman and Nat Pryce, ISBN 0-321-50362-7 Freeman and Pryce explain Test-Driven Development through an extended example. (They have a somewhat different perspective than I do, with much heavier use of mock objects. I'm not sure what drives this difference; it may be due to type of application, philosophical reasons, or just something I should learn.) I love the clarity with which they tackle the problem of driving in from all the way outside, and how they don't shy away from dealing with concurrency and persistence. It's high praise for me to say a book deserves further study; this book is one I'll definitely be reading again. # Movie Retrospective When I'm teaching about retrospectives, there has always been a challenge: a simulated retrospective wants a shared experience. But what shared experience to use? • The one experience I know we share is the session we're in, but using a retrospective on the class sets up an awkward "meta" and recursive dynamic, as we try to do something and think about doing it at the same time. • A class often shares another experience (or set of experiences): the projects they're working on. Everybody may not be on the same project, but even if they are, real projects have real issues, and using real issues for an example almost instantly violates safety and takes away the magic circle aspect where it's safe to try new behaviors. So: 1. Identify a movie as the shared experience. I've been using Star Wars, Episode IV, with the part of the movie from the rescue of Leia until Obi-Wan dies and the protagonists escape. (Sorry if that's a spoiler:) (I'm sure other well-known movies would work as well but I haven't tried any; perhaps The Wizard of Oz or The Godfather or something more modern?) It's possible a person or two hasn't seen the movie; I'm willing to take that chance. If I thought the background of the group was so diverse that a substantial part of the group would not have a shared movie, I'd try a different approach. 2. Ask people to imagine they were the protagonists, to recollect for a moment what happened in the relevant part of the movie. [A couple times I tried to show the movie clip in fast-forward. From a technology standpoint, it was painful. But from the perspective of the simulation, it's a better simulation NOT to show anything. As in real life, people will have different memories of what happened and different perceptions of what's important.] 3. Use the recalled scenes as the basis for a retrospective. I like Esther Derby and Diana Larsen's approach in Agile Retrospectives, and I use an abbreviated sample exercise addressing each of their sections. For example: A. Set the stage: Check-In – "In a word or two, what's on your mind?" B. Gather data: Timeline – "Recall the memorable, meaningful, and/or significant events; write one per sticky note, then put it on the timeline." C. Generate Insights – Patterns and Shifts – "Look for patterns. What links? What shifts? Which are most important?". Or perhaps do a "Worked Well / Do Differently" analysis. D. Decide What to Do – Dot Voting – Give everybody 3 dots to vote for what to focus on as a group over the near term. (They can put their dots on 3 different things, or all on the same one if they feel strongly.) Agree on the immediate (concrete) next steps, who will lead them, and how and when progress will be reported. E. Close the Retrospective – Appreciations – Identify how others have contributed. "Bob, I appreciate you for ___." ("Thank you.") Even doing this in an abbreviated manner (a few minutes for each) lets you run through a complete retrospective in miniature. You can then follow it up with some debriefing to bring out any points you need to make. Source: Bill Wake, 2010. [8/15/10 – Thanks to Diana Larsen for helping me ensure "Decide What to Do" results in action.] # Coach Interview: Declan Whelan Interview with coach Declan Whelan. Our discussion, held June 1, 2008 at the Agile Coach Camp. WW – Take a minute and tell me about yourself and your background, and how you became a coach and what you're up to. DW – I've been in software for… I realized it's over 20 years and I think, "Oh my gosh, but I have the gray hair to prove it." About four years ago I was doing some consulting work with a company in Toronto. They had decided to go agile across the board and they brought in some excellent coaches such as Jim Shore, Jim Highsmith, Joshua Kerievsky, and Gunjan Doshi. I had heard about XP before that but I hadn't really taken that much interest in it. But then I saw what was going on. It was phenomenal watching the energy level and feeling that there was a deep and radical transformation happening. I got bit by the agile bug from that experience. I then had an opportunity to work with a company that was really struggling with their software development group. They had been habitually late, habitually buggy. They would plan two or three point releases right after every major release because they knew they'd be patching it up. They were really at a point of failure. Someone said they were looking at firing the whole software team. I was a last resort. Now, the problems were really much wider than the software team but that was the flash point. This was a good opportunity to bring agile in because they had nothing to lose. So we did, somewhat incrementally because the team couldn't turn on a dime. We just did some simple agile things then slowly evolved it so that after 18 months they were ready to launch a full-blown XP project which was quite successful. After that, the team transitioned to use a combination of Scrum and XP. I continue to consult with this company and have expanded my agile repertoire. I now provide agile coaching, training, and development on a wider scale. WW – What practices did you start with on the incremental path you had them on? DW – It was simple PM stuff. I had the business unit work with me and the lead developer to estimate all the open issues and classify them as: "A": Must have "B": Should have "C":  Nice to have I then talked to the development team and got their buy-in that they would commit to and support a date if I guaranteed that they would have twice as long to do the work as they themselves estimated. They supported that. Then we gave the business unit a development budget for the "A" issues: "A" Budget = # of developers * working days / 2 We guaranteed to the business unit that we would deliver all the A issues. We would try to get some of the B's and C's — "If they happen to fall in the same area of the code, you might get some of those." They key was that we committed to a date and that gave the business unit some degree of certainty that  they could plan around. We then met with the business unit on a regular basis to track progress and to reprioritize as any new issues arose — but we held them to their A budget. And it worked. The team was able to get all the A's and they got a few B's done and they met their commitment. The business unit were impressed: "Oh my gosh, that's the first time we ever had a release delivered on budget and on time." We were actually one week late but that wasn't bad compared to their traditional three months late. After that, the team planned and executed the next four releases like clockwork. So it was really just team building, setting reasonable expectations, and building trust and confidence.  Once the team and I had credibility, we were able to take the next step. "If you like what this is doing for you, we can be an even more effective team if we take the next step." WW – What do you find the challenging areas for the coaching you do, either personally or from the angle of the hardest group or person to work with? DW – I find for me, the hardest part on a one-on-one basis is the really skilled software developer. I find it really difficult to go in and be in the position of saying, "We're all in here to learn. Life is a continuing learning experience and perhaps I can bring you something that maybe you haven't seen before." But if they've been doing it for as long as I've been doing it, and especially if it's in their domain and they've been working on this team for ten years, they don't think there's anything they could possibly learn. I find it difficult to get them to switch that bit in their mind, to open up to the possibility that they could learn something new. For me that's been the biggest personal one-on-one challenge. WW – Do you have any techniques or tricks you try with that? DW – I've tried to be technically really good. I try to write code frequently, if possible every day. Try to stay current so I can gain some trust that I know what I'm talking about. Pair with them. I still find it a challenge. The really good people will always claim, "Yeah, that worked well in this case, but in the 95% of the cases I deal with…" It seems to be this credibility thing, that I have a hard time bringing people to the stage where they can see for themselves. Do you have any? WW – I do the same – I think pairing with them and being able to demonstrate that I can do solid things helps me too. WW – What do you to do keep up with your own learning that you need to do? DW – Read. I read a lot. I tend to read seven books at once. I don't know if it's a common pattern, it's probably not a good pattern. I also buy a lot of books that I have on the shelf. So if I have a question on planning, I'll go get Cohn's book on planning. I tend to have a large number of books. There haven't traditionally been a lot of practitioners in my geographical area. I've been trying to build an agile community in the Waterloo area, which is where I work. That's looking good. I'm hoping that next year we'll have a local agile group. I've had fairly challenging positions. I've been heads-down in the trenches for three of the last four years. It's only been in the last year that I've made an effort to get a website blog, go to conferences. I'm working on that part of it now. WW – Is there a book you're reading now you particularly recommend? DW – The one I'm reading now is Agile Software Development, second edition, by Cockburn. I started the appendices first like Alistair recommended. I find it fascinating he draws on relatively old stuff, stuff that was written in the '70s, and it resonates today. I'm an abstract thinker; I like to go from the abstract to the concrete, not the other way around. I think that's the way he writes. He derives concrete from the abstract content, and I like the mental model he likes to write from. I really like the jargon/analogy of a game. I'm a coach of kids in sports, and the strongest metaphor I've seen for agile coaching is coaching children's sport teams. WW – Thank you. DW – You're welcome. # Embracing Commitment Commitment is a powerful tool. [Originally published at InformIT.] We often hear and speak of commitment. It's a term many people use, but it's a word with several different meanings. When you're clear about which kind of commitment you're asking for or using, you can connect to emotions, you can look for win-win benefits, and you can create reliable promises that others can build on. In this article, I'll look at several meanings of the word “commitment,” at different commitment relationships, and at ways people assess or create commitment. I'll start with these aspects of commitment: attitude, motivation, hustle, and promise. ## Commitment as Attitude Commitment can be an attitude: an emotional state of attachment that puts the committed thing above other things; this commitment brings a sense of dedication. If you're committed, you're not working as a mercenary, committed only to the paycheck and not the cause. When you're committed, you care. The software team was measured on the success of the project, but the project managers were assessed on the quality of their reporting. For the project managers, it was OK if the ship sank, as long as the sinking was properly predicted and the ship's log was up to date when it went down. People talked about teams being dedicated and committed to results, but nobody worried about the commitment of the project managers (to process). Attitude talks about the emotional aspect, and that's notoriously hard to assess. However, if people don't care, the project has no chance. ## Commitment as Motivation Why do you come to work? What keeps you going on your project? What's your real goal? Everybody has a different combination of motivations. For example: • Produce something someone values • Build something beautiful • Work with others we like • Work in a process we like • Look good to the boss • Program in Java • Build our resumes As the last few items suggest, our motivation need not align with the best interests of the project or the company. The team was based in two locations. One sub-team had developed a goal of eating at a different restaurant for lunch every day. They had spiraled out past 45 minutes each way. This was good for the sub-team's morale, but 2.5 hours or more lost out of the middle of the day was interfering with their productivity and their ability to work with the other sub-team. Individual motivations may differ, but that's fine if they all point to the success of the project. If your motivation doesn't ultimately support the project's goals, you will weaken the project. Motivation (especially shared motivation or mission) can serve to re-center you to True North, the direction your team is really trying to go. ## Commitment as Hustle What is the behavior of commitment? A sports coach may tell you that some teams have hustle—that extra bit of energy a team or individual puts in. A hustling team takes the extra couple of minutes to get things working and checked in before lunch. If something's due tomorrow, they'll try to get it done today just to be sure. A team that's hustling may work overtime (a little, occasionally). Some managers treat overtime as the true sign of commitment. Bob Martin talks about a different sense of urgency: the 8-hour burn. This comes when you're working at such an intensity that there's no point in overtime; you're so “fried” you're likely to be more dangerous or useless than helpful. It's easy to prefer the dramatic whether or not the drama is more effective. On an early web project, the team had done much work to get ready, but had underestimated how hard the actual deployment would be. The team's manager later admitted that he loved the adrenaline rush of the two final all-nighters. He felt the team showed hustle, and he felt part of the team more than ever. (The team could have spent those hours over the previous months and skipped the drama, but perhaps the drama helped jell the team.) ## Commitment as Promise What is a promise? It's not a simple true-or-false proposition like “My car is yellow.” Is “I promise to give you a nickel” true or false? It depends on what I think, say, and do. Speech act theory [Searle] [Winograd] is a linguistic tool that can help explain promises. The theory's key insight is that some statements create their own meaning: “I now pronounce you husband and wife” becomes true in the saying, if certain conditions are met. What does it mean for a speaker to make a promise to a hearer? Here are some key conditions: • Both the speaker and the hearer agree on what is being promised. • Both sides believe the speaker has the time and resources to meet the agreement (even if not everything goes perfectly); neither is having private doubts. • Should problems arise, the speaker will put the commitment above other things, working beyond what had been expected to what is now needed. • If the speaker comes to believe the promise can't be kept, the speaker must notify the hearer as soon as possible, re-negotiate, and accept the consequences of failing to deliver. A web of promise can form, helping a team work together. A series of kept promises builds trust [Solomon], and lets people worry less about whether others' jobs are being done. Scrum has the notion of a Sprint Goal (though many teams don't use it). The team commits—promises—to meet the goal, rather than promising to complete a particular set of stories. This can open the door to creative solutions that meet the spirit of the sprint even if the exact plan isn't met. (Some teams frame the Sprint Goal as sets of stories: these are the things we promise to get done, these others are the ones we estimate will be done beyond that.) If the Sprint Goal is in danger, Scrum defines Sprint Cancellation as a safety valve. It's ironic that Sprint Goals and Sprint Cancellation are often not used; the first is seen as too boring (“do the planned stories”) and the second as too dramatic (“launch a witch-hunt”). Some teams make promises about what they'll deliver. Others make promises about their process (“A full day's work for a full day's pay” or “We'll use Scrum.”) Other teams make estimates, not promises. Many teams have confusion about what they're doing; are they making an estimate (which can be wrong) or a promise (which needs a buffer)? Clarifying such ambiguities can go a long way to setting proper expectations. ## Promises and Relationships A plain promise is the simplest relationship: a speaker makes a promise. The structure is still simple even if the speaker and hearer participate in a web of promises, as long as there are no loops. Mutual commitments create loops; most promises have a price. (“You give me \$10 and I'll give you lunch.”) Mutual promises put leverage in the relationship. (“I'm not paying until you make me a proper sandwich.”) While explicit promises can be performed better or worse, there are sometimes tacit assumptions that cause problems if they're violated. The Product Owner came in with a large body of work. The team said, “That's too much, but we can commit to this part (the most important third) in the time you're willing to allow.” The Product Owner agreed to that. The team hustled, and finished not only the promised part but about 50% more. They went in saying, “You're going to love this—we got lots more done than we thought we could.” The Product Owner said, “Yeah, that's great—but you only did half of what I wanted.” The Product Owner had violated something the team tacitly expected—they not only wanted acknowledgment of the completed part, but “strokes” for the extra bit. They had exceeded their commitment, but were assessed against a promise that they had never made. (Do you think this team will hustle as much next time?) Power relationships make promises even trickier. Managers are often in a position of both receiving and making promises to people: they receives promises in support of organizational goals, and make (often implicitly) promises about providing a supportive context. The supporting promises (or assumptions) may be things like, “I won't ask you to work excessive hours,” “I'll provide the tools you need,” “If things change radically, I'll take that into account.” Finally, there's a surrounding promise from a manager that is also a threat: “If I'm not happy with you, I'll punish you or fire you.” The threat may be implicit or explicit; it's part of the structure of many employee relationships. When the threat is too close to the surface, the fear it creates can cause the very problems it's trying to prevent. ## Signifiers and Manipulation How do you know people are committed? You can't see attitudes or motivation; you can only see behavior. What signifiers do you look for? (I'm going to focus on a manager's point of view, as I've seen managers more explicitly concerned about commitment than team members, but anybody can have this concern.) A manager sometimes tries to judge emotions by how people talk or their facial expressions. These are of course prone to being faked, “talking a good game.” That leads to a quest for observable behaviors. A manager may start looking for hustle. Hustle can take the form of voluminous output, no coffee or web breaks, overtime, or constant typing. Any of these can be signs of intense working, but they can be faked as well. There certainly are groups whose hours are “just before the boss gets in till just after they leave, with the occasional midnight email.” Explicit promises can help, but they're subject to manipulation as well. The implementer can provide something of low quality, either full of defects, or of poor design so it will be hard to extend. They can claim to have not understood what was wanted. (“We can do that, but you'll have to split the story this way and reschedule the rest.”) Conversely, some managers feel that teams perform up to their capacity only when they're pressured: “What else can you fit in?” “That's not enough.” “Of course this story includes that; it was understood.” “Yes, that's what you promised, but I expect more from you.” In Peopleware, DeMarco and Lister warn, “People under time pressure don't work better, they just work faster. In order to work faster, they may have to sacrifice the quality of the product and their own job satisfaction.” Some teams can be pulled (inspired) by the right motivation, but can only be pushed (pressured) to compliance. You can't see commitment. You can sometimes see behavior that suggests it, for example, promises kept. When there's a problem such as perceived low productivity, it's better to address that directly rather than assume that commitment is the issue. ## Creating Commitment Where does commitment come from? Sometimes the motivations line up: people have their individual motivations, but those are compatible with the overall goal, so they contribute to it. Creating commitment is tricky—what are you trying to create? An emotional connection? High productivity? A culture of promises? Are you merely after the signifiers that make you feel better watching the team: a culture of appearances over actions, of busyness over productivity, of psychological pressure over trust? The manager set up the planning meeting as a pep rally. He used sports analogies to describe the challenge as “the big game,” and had everybody sign a big poster with the ship date on it. It may be that everybody was caught up in the moment. Junior people seemed to accept the challenge, but several senior people walked out muttering, “He's tried to hit these buttons before” or “That's an unrealistic schedule” but they weren't willing to speak up as that would be a CLM (career-limiting move). A very similar scenario can have a different outcome: people respond to the challenge, they build an emotional connection to the project and the team, and they walk out jazzed up and ready to go. What distinguishes the cases? There's no magic formula but these things affect it: • Does the goal fit higher aspirations? People want to change the world in some way, not just make shareholders richer. (They don't mind something that does both.) • Do people see where they can contribute? It's hard to be engaged if your contribution isn't important. • Is it the right level of challenge, not too easy and not too hard? If it's too easy, it's not worth the emotional investment. If it's too hard, people don't want to engage as they know they'll fail. (This is like the idea of “flow,” when challenges and skills align. [Csikszentmihalyi]) People often don't mind a little stretch. • Is it a free choice (free from undue pressure)? People want to be invited in, not ordered in. What are the motivations you're encouraging? Extrinsic rewards (whether tangible, people-oriented, or special activities), or intrinsic motivation? The latter is more sustainable and self-reinforcing. [Martens] ## Conclusion Have you been caught in the trap of looking for appearances over results? Are you favoring drama and the appearance of busyness over actual productivity? What sense of commitment are you after? If one party is providing estimates and the other side is interpreting it as promises, you'll have conflict. Understand what you're looking for. Each type of commitment has its place. The right kind of commitment at the right time is extraordinarily powerful. ## References [Csikszentmihalyi] Mihaly Csikszentmihalyi.  Flow: The Psychology of Optimal Experience. Harper Perennial, 1990. [DeMarco] Tom DeMarco and Timothy Lister. Peopleware: Productive Projects and Teams. Dorset House, 1987. [Martens] Rainer Martens. Successful Coaching (3/e). Human Kinetics, 1997. [Searle] John R. Searle. Speech Acts: An Essay in the Philosophy of Language. Cambridge University Press, 1969. [Solomon] Robert Solomon and Fernando Flores. Building Trust: In Business, Politics, Relationships, and Life. Oxford University Press, 1993. [Winograd] Terry Winograd and Fernando Flores. Understanding Computers and Cognition: A New Foundation for Design. Addison-Wesley, 1987. ### Acknowledgments Kevin Bradtke, Tom Kubit, Michele Matthews, and Doug Wake gave me valuable feedback and advice. [Originally published Aug., 2009 at InformIT; republished here with their permission.] # Coach Interview: Alexey Krivitsky Interview with Alexey Krivitsky; our discussion held June 1, 2008 at Agile Coach Camp in Ann Arbor, MI WW (William Wake)- Alexey – To start, just take a minute or so and tell me about your background, how you came to be where you are today? AK (Alexey Krivitsky) – I started as a developer about 8 years ago in Ukraine. I did some Java, .Net, Visual Basic. I quit that job; I had about half year to reflect on the years of my career. There were some books on agile on my shelf. One of them was Agile Software Development, first edition, by Alistair Cockburn, and some stuff about Scrum and XP. All these famous books… After finishing reading what I had, I thought it should work for me. I found a job in a small offshoring company. The guys are from Denmark so they decided to set up a small team in Ukraine to maintain their software. They were quite flexible to change their process. By their nature they were a family business so they were willing to change anything and there was a guy who believed that agile can add value there. It was my real first experience with agile. After that job I went working in Switzerland for a year. What I'm doing now… I came back to Ukraine from Switzerland to set up an agile coaching business. Before that I had set up an agile community in Ukraine with about 200 people on the list, which is quite a lot, I think. I realized, "Here's an opportunity for me to develop myself in Ukraine," so I came back. After about half a year, I realized that I was missing the real work. So I came back to my old team as a part-time Java developer. Now  I'm trying to combine being a coach and being a developer, which gives me quite the experience. I have a chance to see the problems from different angles. It's quite interesting how many things you can change being a developer in a team, not a coach, not a guru, just from the inside of the team. You can affect a lot. WW – Can you tell about one of the agile projects, either how they became agile or something that happened with them? AK – When I was hired by these guys in Switzerland they had been running the project for more than half a year. They had people in Ukraine doing development. It was a chaotic project without planning. We just had to deliver something by a given day. I already had some Scrum experience, and I set myself a task to convert development to Scrum Now I'd do it differently, but you learn from your mistakes. I was at the client side. So I coached the Product team to define requirements in a more agile way, how to estimate, and all that kind of stuff. WW – Did they work with monthly iterations, or what? AK – They worked with 2-week iterations. We tried different durations and we ended up with 2-week iterations. We didn't have a fully deployable version after each iteration. What we had is a demonstration server as it was quite difficult to do live production. At any time, the stakeholders could just log in and try it. We also had weekly demonstrations in which we presented what we had done so far to different stakeholders. It was our approach to agile which was based on Scrum. WW – Are there any techniques, tools, or tips you have when you're coaching people? AK – I would say I was a coach but it is impossible to coach people remotely. If you have somebody off site and you have to email or call, it's impossible to coach those guys. If you want to coach, you've got to stay with them and be involved with them. WW – I'm interested in things you do, behaviors you have, whether you think of them as coaching or programming. AK – I was at a position in my life where I stopped being a traditional team lead and turned myself into a ScrumMaster. It's hard to do, because you get used to proposing your ideas and believing that you're smarter than other people. Instead you have to start believing that the team can make up better ideas themselves. You make yourself stop talking and just ask questions. This is a hard thing to achieve. When I coach teams now, I always ask questions rather than make statements. We also had a session today about skills, techniques, and questions – how to ask questions without any resistance. So what I'm doing now is trying to help people go the way I think they should be going. It can be achieved by asking the right questions. Each time I have an idea which I believe the team should take, I just turn it into transforming discussion where I also have the chance to give my ideas. After that we just decide which way to go. They may have taken my idea or not, but we found something that should be working for them. Another thing which I am practicing  is each time you are going to make a statement convert it to "What if you do it this way?" question. Each time you're about to make a statement that can be taken with resistance, ask a question instead; it might help. WW – What do you do to learn new things? AK – We have an agile community – we organize conferences. It's a way for me to meet local experts and talk to them. I used to read blogs but I don't have that much time now. The conferences are the best investment of your time and money to learn something new. I will try to make the events in countries nearby. We'll see how it goes. WW – Anything else you'd like to tell me about? AK – I can tell you about the challenges of a coach in offshoring markets. Developers in most cases are not interested in being agile; they do not see the values. Neither is the management of the service companies – they do not care about efficiency. They care about the per hour rate. The only right people are the product people. And they are far away The outsourcing marketplace is quite huge, but there aren't that many agile people there. WW – What do you find the biggest challenge when you're working with outsourced teams? AK – The biggest challenge if you work on-site with the team is to make the client get this or get the customers to change the process. If you're a coach, you coach the team and coach the business people. It's hard to coach someone remotely. It's a challenge to coach teams to be more effective but it's only half the thing. The business people need to know how to manage requirements or releases in an agile way. There's no point in coaching just the development team. It should be taken from two sides: somebody should be coaching the business side, somebody should be coaching the team. I am looking for this kind of cooperation between US and European agile coaches. WW – Thank you very much. AK – I hope it was useful. WW – I appreciate it. # User Story Examples This is a sample set of stories for a time management system. I've been interested in personal productivity systems for a while, so when Mark Forster introduced a new system called AutoFocus, I decided to create an electronic implementation. The system is a sort of todo list, in a organized as a notebook where each page has a list of tasks to do. There are rules defining the currently active page and task, and how you move your focus as you complete tasks. I began by analyzing the system (e.g., building a flowchart and transition diagrams to look at how tasks and focus move). I wrote some basic cards, and a series of screen sketches. For example, a task page will look something like this: |<   <<   *   >>   >| Add new task: [_______________] Active Tasks [ ] task 1 [*] task 3 Completed Tasks [x] task 2 [x] task 4 [Dismiss] [Force Focus] [Move Focus] |<   <<   *   >>   >| (The characters at the top and bottom of the page represent navigation arrows.) ## Basics – Tasks The first cluster of stories is centered around tasks and assumes all tasks are on the same page. Notice that with just the above stories, the system could be a basic todo list manager. ## Basics – Pages The system is built around the metaphor of a notebook; we need navigation around the pages. The "current" page can mean two things: either the page you're currently looking at, or the one with a currently active task. Multiple pages Navigate – first, last, previous, and next Navigate to focus page Move the focus page "forward"  [can wrap] By the "rules," you're normally supposed to move the focus page forward (wrapping to the beginning) as you complete tasks. But there's a "don't be stupid" clause that says you can work where you need to. Force the focus page here ## Friendly Feedback I want to push the system to a  point where I can get some friendly feedback. First, I need to pick up the last major action required by AutoFocus: Dismiss open tasks on page Then I need to put the system somewhere others can see it: Deploy to sandbox ## Users I can't just have one notebook out there for the world to see; I need to introduce the notion of users. I actually started with a card that said "User Management" but I expanded it to these: Register Logout Update settings ## Getting Real What would it take for a beta test? I could probably defer "forgot password" and "update settings" but I have other work that would need to be done. First, I'm asking users to trust the system and load in all their tasks. Paradoxically, I think if I make it less necessary to trust the system, people will trust it more. I'll do this by providing a means for them to export the tasks they've entered; then they know they can easily recover their work if they want to move on to a different system. Another aspect of trust is the look of the site. I have some OK default icons, but the site will shine better with a new set. Polish stylesheet and images It will have to be deployed to a public system: Deploy "Home page" is a bit of a placeholder card. The bare minimum is to provide a login page, but in the long run it will need some explanation of the system and an appeal to register. I could start with these on the home page but probably want them somewhere else. Terms and privacy statement I haven't decided how to fund the site, and I don't need to know to start a beta test. But eventually I'll need a revenue model fancier than "pray Google offers millions." There might be other ways, but the next two stories are what sprang to mind first. Charge fees Here's another story that could be big. I'm starting with a web site, but people may want to use their mobile phone to manage their tasks. This could be as simple as a special stylesheet, or it could become a whole separate application. Support mobile phones ## Sparkling Touches These next stories are ideas I have that fit in the basic framework. They could be early upgrades. I don't know what all I mean by page status, but it includes the date and whether this is the focused page. Page status Some tasks should just automatically recur once you complete them (e.g., "email inbox to 0"). I could put a flag on the task, or maybe find a more sophisticated approach. Auto-reschedule ## Future Versions I have a number of stories that aren't so well defined – the fuzzy ones. People might want to pull out separate lists that aren't managed by the AutoFocus rules. I don't know if this needs to allow multiple user-created lists, or how that will work. Lists Once people get a lot of tasks, they may want to find a particular one: Search A tickler is a reminder system that lets you schedule tasks out in the future. ("43 folders" – one for each month and one for each day number in the month – is a classic paper form.) Some people just put tickler tasks in their calendar, but I think it would be handy to have a tool that automatically brings them in to the task list as appropriate. I want to make sure to include the notion of lead time – I might like to be reminded that today is my sister's birthday, but I really need 2 weeks notice so I can get her a card or gift. (And I want that reminder as a task, not a phone or email reminder.) Tickler Many tasks have a standard set of sub-tasks. I'd like to put them on a checklist and have them brought in on demand. The easy form is a "parallel" list – put all tasks on the list. Checklist – parallel The more classical form is to do the steps in order. When one step is completed, the next one should be scheduled. Checklist – serial People might like some sort of analysis, or it might be useful in supporting the system. Reports/statistics And I have a last one that's totally open. It's really more of a goal than a concrete story. It might be met by paid advertising, blogs, FAQs, help pages, email reminders, you name it. Increase usage of the system ## Analysis I feel good about this set of stories. They capture the bulk of what I want the system to do. I used a simple "headline" form for the story titles – just a short verb phrase. I know the domain, and it's generally obvious who the story is for and what it's for, so I didn't feel the need to put them in the "As a ____, I want to ____ so that ____" form. The stories came in three batches – the early task and page stories (with a couple sparklers), user and deployment stories, and the others. I developed them in combination with repeated sketches and analysis. Another way to look at stories is to look at them versus the INVEST acronym (from my earlier article "INVEST in Good Stories"): • I – Independent. The stories mostly stand alone from each other. The dependencies tend to be domain-related rather than technical. (For example, it doesn't make much sense to have a logout story before you have a login.) • N – Negotiable. The smaller stories are straightforward and well-defined (though they have some room on the details). Bigger stories have a lot of flexibility. Plus, this is a one-person project so there's not much problem there. • V – Valuable. Each story adds a clear bit of functionality to the system. The most technical story ("deploy") still makes sense to a product owner. • E – Estimable. I have a good sense of which stories are well defined; even for the fuzzy stories I can make educated guesses about the order of magnitude. • S – Small. Stories ready to schedule (closer to the top of the list) are generally hours to a few days work. That's appropriate. Later stories are bigger; that's ok too. When it gets time to implement them, I'll break them down into small stories as well. • T – Testable. Ready-to-schedule stories are testable; the fuzzier stories will need more explanation and analysis before we could write a test. If I look at the list of stories as a release plan, the order is generally good. (There are a few stories that could move down in priority.) But one thing stands out: deployment could be moved much further to the top. It could be the second story: a simple list of active tasks might be useful to somebody (perhaps as a status report or proof of concept). It's easier to deploy when the system is still small. And it's a key to getting feedback.
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The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!) A128414 Riordan array ((1-2x)/(1+2x),x/(1+2x)^2). 4 1, -4, 1, 8, -8, 1, -16, 36, -12, 1, 32, -128, 80, -16, 1, -64, 400, -400, 140, -20, 1, 128, -1152, 1680, -896, 216, -24, 1, -256, 3136, -6272, 4704, -1680, 308, -28, 1, 512, -8192, 21504, -21504, 10560, -2816 (list; table; graph; refs; listen; history; text; internal format) OFFSET 0,2 COMMENTS Inverse is A128417. Row sums are A128415. Diagonal sums are A128416. LINKS Table of n, a(n) for n=0..41. FORMULA T(n,k) = 2^(n-k)*A110162(n,k). - Philippe Deléham, Jan 18 2014 T(n,k) = T(n-1,k-1) - 4*T(n-1,k) - 4*T(n-2,k), T(0,0) = T(1,1) = T(2,2) = 1, T(1,0) = -4, T(2,0) = 8, T(2,1) = -8, T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham, Jan 18 2014 EXAMPLE Triangle begins 1; -4, 1; 8, -8, 1; -16, 36, -12, 1; 32, -128, 80, -16, 1; -64, 400, -400, 140, -20, 1; 128, -1152, 1680, -896, 216, -24, 1; -256, 3136, -6272, 4704, -1680, 308, -28, 1; 512, -8192, 21504, -21504, 10560, -2816, 416, -32, 1; CROSSREFS Cf. A128413. Sequence in context: A232816 A210196 A249252 * A192014 A019699 A125092 Adjacent sequences: A128411 A128412 A128413 * A128415 A128416 A128417 KEYWORD easy,sign,tabl AUTHOR Paul Barry, Mar 02 2007 STATUS approved Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents The OEIS Community | Maintained by The OEIS Foundation Inc. Last modified May 29 08:30 EDT 2023. Contains 363029 sequences. (Running on oeis4.)
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# If any idiot can do it, we're heading in the right direction ## I am a simple man – and that's the way I like it Sysadmin Blog The enemy of success is complexity. Although I am in general a fan of the concept of intricately intertwined Rube Goldbergian nonsense, my life thus far could be summed up as learning the value of simplicity face first. IT is all about complexity, and unpicking which combination of barely functional crap is least likely to go boom is not as straightforward as the chattering masses of the internet would have us all believe. Let's take storage as an example. I accept as true the axiom "if your data does not exist in more than one location, then it does not exist". I have had hard drives die, run SSDs out past their write life, and Jibbers only knows if Schrödinger's tape drive will read the tapes I feed it. In order to get my data to live in more than one place I can approach the problem in one of two ways. If my needs are modest then the solutions are simple. If I have a fixed data set and am in no particular hurry to get to the backup copy if the primary dies then I can simply make one copy once, putting one of the copies in a different place than the original. There are umpteen ways to accomplish this task simply. As soon as I become more demanding, complexity increases. If I write to my primary storage after making the initial copy, then at some point I have to copy the new data. This can require a new storage device to send away, or somehow updating the backup device already sent away. If I want to get access to the backup copy of my data quickly when things go sideways, I need to ensure there is a means to do so. If I want realtime protection of my data as it is written then I've entered a whole other realm of complexity. On the simple side of things, I could copy data to a drive and put it in a safe deposit box. On the complex side, I'm engaged in arguments about discreet SANs versus hyperconvergence and using terms like "data locality" and "incremental forever". ### The complexity burden When we're out in the weeds arguing about storage complexities the problem metastasises. Nerds very easily get caught up examining individual trees for pests and lose sight of their location in the forest. In our storage example, this manifests itself in forum wars where nerds argue about "data paths" and the relative complexity of underlying technologies that practitioners and implementers of those technologies simply don't play with. In practice, information technology is littered with abstraction layers and other hidden complexities. While it's sure fun to debate these things at an academic level, it behooves us to remember that none of this actually matters to the folks with boots on the ground. If and when the vendor does an adequate job of abstracting away complexity, then for all intents and purposes it is gone. Inefficiency can be masked by simply throwing egregiously excessive amounts of hardware at something. Eventually enough inefficiencies will build up in the design that someone will come along, redesign the whole thing from scratch and built a better, faster mousetrap that they can sell cheaper. That's IT: every single aspect of it is a cyclical masking of complexity until we ultimately master it enough to truly commoditise it. What's absolutely critical about all of this is that it's the outcomes produced that matters. If a hyperconverged whatsit is just as fast and reliable as a fibrechannel whosit, but cheaper and easier to set up and manage, then you buy the hyperconverged thingamabob. The relative "under-the-hood complexity" doesn't matter. Only the outcomes. ### Relative complexity After a recent article, several people asked me why I cared about twinaxial Direct Attach Cables (DACs). As they saw it, fibre was simply "better", and my usage of anything else baffled them. I prefer DACs when and where I can use them because they're simpler. In my experience, they take a heck of a beating and keep on working. Any idiot can plug them in. I can walk people through unplugging one device and plugging it into another over the phone. If the new cleaner decides to clean the racks and bangs into them, pulls on them or gets caught in them, they don't tend to break or come undone. A single fibre link has seven things I need to worry about: two transceiver modules, one fibre cable, and four rubber caps. Someone will inevitably lose the rubber caps so I need to stock spares. I also need a widget to clean my transceivers and cables. So now, in order to link server A into switch B, the poor salesdroid on the other end of the scratchy phone at 4am has to keep track of a backpack full of gear. With DACs, linking a server to a switch means keeping track of exactly one thing: the DAC. Oh, sure, fibre works over greater distances. But when all you need is to plug four servers into a switch, none of that matters. The concerns of someone tasked with campus-wide wiring don't burden my SMBs, and I don't need realtime metro-area high availability storage for my personal video collection. Everyday life is increasingly complex. Picking up the phone and dialling a number became finding the phone, swiping sideways, entering a password, opening the phone app, selecting the dialpad, dialling and then hitting send. Let's not add to it by burdening ourselves – and others – with more IT complexity than is absolutely required. ### Other stories you might like • 381,000-plus Kubernetes API servers 'exposed to internet' Firewall isn't a made-up word from the Hackers movie, people A large number of servers running the Kubernetes API have been left exposed to the internet, which is not great: they're potentially vulnerable to abuse. Nonprofit security organization The Shadowserver Foundation recently scanned 454,729 systems hosting the popular open-source platform for managing and orchestrating containers, finding that more than 381,645 – or about 84 percent – are accessible via the internet to varying degrees thus providing a cracked door into a corporate network. "While this does not mean that these instances are fully open or vulnerable to an attack, it is likely that this level of access was not intended and these instances are an unnecessarily exposed attack surface," Shadowserver's team stressed in a write-up. "They also allow for information leakage on version and build." • A peek into Gigabyte's GPU Arm for AI, HPC shops High-performance platform choices are going beyond the ubiquitous x86 standard Arm-based servers continue to gain momentum with Gigabyte Technology introducing a system based on Ampere's Altra processors paired with Nvidia A100 GPUs, aimed at demanding workloads such as AI training and high-performance compute (HPC) applications. The G492-PD0 runs either an Ampere Altra or Altra Max processor, the latter delivering 128 64-bit cores that are compatible with the Armv8.2 architecture. It supports 16 DDR4 DIMM slots, which would be enough space for up to 4TB of memory if all slots were filled with 256GB memory modules. The chassis also has space for no fewer than eight Nvidia A100 GPUs, which would make for a costly but very powerful system for those workloads that benefit from GPU acceleration. • GitLab version 15 goes big on visibility and observability GitOps fans can take a spin on the free tier for pull-based deployment One-stop DevOps shop GitLab has announced version 15 of its platform, hot on the heels of pull-based GitOps turning up on the platform's free tier. Version 15.0 marks the arrival of GitLab's next major iteration and attention this time around has turned to visibility and observability – hardly surprising considering the acquisition of OpsTrace as 2021 drew to a close, as well as workflow automation, security and compliance. GitLab puts out monthly releases –  hitting 15.1 on June 22 –  and we spoke to the company's senior director of Product, Kenny Johnston, at the recent Kubecon EU event, about what will be added to version 15 as time goes by. During a chat with the company's senior director of Product, Kenny Johnston, at the recent Kubecon EU event, The Register was told that this was more where dollars were being invested into the product.
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## Introduction gold Here is an eTCL script on estimating mountain height for the etcl console. I found an angle(s) and baseline formula in a precalculus book. The formula for mountain height was baseline*sin(aa)*sin(bb)/ sqrt( sin(aa)* sin(aa)-sin(bb)*sin(bb) ) The angles used are angles of elevation from the ends of the baseline. It stipulated that the baseline starting from point aa is perpendicular to the line of sight. The formula was not corrected for curvature of earth, which would be \$correction = earth_radius * (secant (arclength/earth_radius))-earth_radius. arclength is the arclength from the observer to the mountain. In planning any software, there is a need to develop testcases. With back of envelope calculations, we can develop a number of peg points to check output of program. ## Testcase 1.0 30 degrees 20degrees104.69textbook ### Pretty Print Version # Pretty print version from autoindent # and ased editor # written on Windows XP on eTCL # code from TCL WIKI, eTCL console script # 8jun2011, [gold] console show proc deg2rad {} {return [ expr {1.*[pi]/180.} ]} proc rad2deg {} {return [ expr {180./[pi]} ]} proc pi {} {expr 1.*acos(-1)} set counter 1 proc mountain { angle1 angle2 baseline } { global counter past set angle1 [ expr { [deg2rad]*\$angle1*1. } ] set angle2 [ expr { [deg2rad]*\$angle2*1. } ] set nom [ expr { \$baseline*sin(\$angle1)*sin(\$angle2)*1. } ] set denom [ expr { sin(\$angle1)*sin(\$angle1) -sin(\$angle2)*sin(\$angle2) } ] set denom [ expr { abs(\$denom)*1. } ] set denom [ expr { sqrt(\$denom)*1. } ] set xheight [ expr {1.* \$nom/\$denom } ] puts "\$counter \$angle1 \$angle2 distance \$baseline moun \$xheight " incr counter wm title . "estimating mountain height" } mountain 30 20 10 ### Notes & Code scraps Another baseline formula was used by Al Biruni as height= (baseline*tan(angle1)*tan(angle2))/ (tan(angle2)-tan(angle1)) Why do you utilize meaningless variable names in many of your procedures? I.e., aa, bb, cc as the inputs to mountain. Absent external explanations, aa, bb , cc have no meaning and therefore the names themselves do not help to guide a reader as to their meaning. Additionally, nom, denom have some meaning, numerator, denominator, but that meaning is self evident by being utilized in a division operation, so in the end, those names also convey zero additional meaning. Your example would be far easier to understand if you picked variable names that related to the real-world values that aa, bb, cc, nom, and denom actually represented. gold2Dec2018. Continuing. I found this trig formula in a two sentence problem from a very old textbook. The trig formula was not derived at all. Perhaps all known trig quantities were not recognized and named as special quantities in the real world, for me. gold 2Dec2018. Important Note. See better routines and current methods for angle reduction, sin, cos, etc in the TCL core distribution and TCLLIB. As of Jul2018, the TCLLIB has developed code for trig angles in degrees, trig inverse, and hyper functions in degrees, and angle reduction in radians and degrees. This supplemental trig.tcl, trigtest.tcl, and trig.man code is posted on the TCLLIB website.z This math::trig.tcl seems really exciting work, which will keep TCL in pace with some of the other brand name languages (math oriented, I mean). Category Numerical Analysis Category Toys Category Calculator Category Mathematics Category Example Toys and Games Category Games Category Application Category GUI Category Development Category Concept Category Algorithm Category Testing Category Toys Category Physics Category Games Category Statistics Category Example Category Mathematics
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The Human Limit of Speed-Puzzling? When you think about achieving the impossible, what comes to mind? For runners, there’s beating the 4-minute mile. For the 100-meter sprint, it’s topping 10 seconds. What do you suppose the puzzle equivalent would be? Solving puzzle #1 at the American Crossword Puzzle Tournament in under 2 minutes? We’ve seen Dan Feyer do that, and it was seriously impressive. For Rubik’s Cube enthusiasts — especially the competitors known as speed-solvers or speed-cubers — that benchmark is a sub-3 second solve. The current verified world record for speed-solving a Rubik’s Cube stands at 3.4 seconds, which shattered the previous record by almost a second. (That record is for a single solve. Many Rubik’s Cube competitions involve an average time across five solved cubes, and the speed record for that hovers somewhere around 5 seconds.) A lot goes into achieving a 3.4 second solve. There are specially designed cubes that allow for easier, quicker, smoother twisting and turning, so you can solve faster. I’m sure anyone who has solved a classic Rubik’s Cube found it at least a little bit clunky. There’s also technique. Top solvers not only memorize solving patterns known as algorithms, but they have preferred combinations of moves. It has been mathematically proven that no matter how complicated a scramble gets, you’re never more than 20 moves away from the solve. Now, of course a computer can analyze a cube and figure out those 20 moves. The human mind doesn’t work that way, so even top speed-solvers would require many more moves to solve the cube, even if they’re still lightning fast. Which brings us to the next aspect of speed-solving: efficiency. Sometimes the fewest number of moves isn’t the fastest solve. For instance, if you have to rotate the cube in order to execute a turn, you’re wasting time you could otherwise spend twisting and turning toward the solution. So some solvers will avoid a slower rotational move by doing two turns instead, which ends up being faster overall. The trade-off of speed vs. efficiency is another way speed-solvers are whittling down time and approaching that 3-second threshold. Top solvers can execute ten turns or moves per second. Based on the idea that no Rubik’s Cube is more than 20 moves away from being solved, that mathematically implies that a 2-second solve should be possible, if not probable. In fairness, we’ve seen a solve take less than a second, but that involved a computer program and a robot solver. So where do we currently stand? Well, there’s the 3.4 second official record, but former champion Feliks Zemdegs claims that, in training, he has achieved a 3.01 second solve. Another speed-solver, Patrick Ponce, claims that he has solved a 3×3 cube in 2.99 seconds, but again, this is an unofficial time. That being said, it certainly seems like the 3-second threshold, like the 4-minute mile before it, will eventually fall. How fast is the human limit? Only time will tell. Thanks for visiting PuzzleNation Blog today! Be sure to sign up for our newsletter to stay up-to-date on everything PuzzleNation! You can also share your pictures with us on Instagram, friend us on Facebook, check us out on TwitterPinterest, and Tumblr, and explore the always-expanding library of PuzzleNation apps and games on our website!
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It is currently 19 Oct 2017, 13:15 ### GMAT Club Daily Prep #### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email. Customized for You we will pick new questions that match your level based on your Timer History Track every week, we’ll send you an estimated GMAT score based on your performance Practice Pays we will pick new questions that match your level based on your Timer History # Events & Promotions ###### Events & Promotions in June Open Detailed Calendar # Powerprep accuracy Author Message TAGS: ### Hide Tags Intern Joined: 06 Nov 2004 Posts: 11 Kudos [?]: 1 [0], given: 0 ### Show Tags 29 Oct 2005, 17:36 I just took a powerprep test and got railed. Is this score very typical of what people score on the actual test. I still have 3 weeks left of hardcore studying to do, so I'm not worried, but just curious. - Chris Kudos [?]: 1 [0], given: 0 Director Joined: 21 Aug 2005 Posts: 786 Kudos [?]: 28 [0], given: 0 ### Show Tags 29 Oct 2005, 17:46 Powerprep is the closest thing to GMAT. The score that you got now may be indicative of what you might get if you take the actual test today or tomorrow. If I were you, I wouldn't worry too much about this score but rather take the positives and look ahead in to what needs to be done in the next 3 weeks. 3 weeks is a good period of time to get yourself in to a much better shape. Good Luck! Kudos [?]: 28 [0], given: 0 Intern Joined: 06 Nov 2004 Posts: 11 Kudos [?]: 1 [0], given: 0 ### Show Tags 31 Oct 2005, 06:29 cool thanks Kudos [?]: 1 [0], given: 0 Intern Joined: 06 Nov 2004 Posts: 11 Kudos [?]: 1 [0], given: 0 ### Show Tags 13 Nov 2005, 12:35 I'm very embarassed by my scores on these practice tests I have studied for the past 2 weeks, done the kaplan book, and taken two more practice tests. On both of these I've gotten 510.... I don't understand how I can be scoring so low, I know I can score higher than this... What is worst of all is that I'm not doing well in the quant somehow (which should be a given as I work in the bond market, a quant oriented field) It seems that the studying has done absolutely nothing as I keep getting the same score. Anyone have advice / suggestions? I am already planning for the next test (as it is too late to cancel this one) and going to try and make a study group, as well as start a few months ahead of time. Has anyone had a similar experience to this? I hope I do better on the real test as this score is very depressing to me. Kudos [?]: 1 [0], given: 0 Intern Joined: 06 Nov 2004 Posts: 11 Kudos [?]: 1 [0], given: 0 ### Show Tags 20 Nov 2005, 06:56 ended up getting a 570 on the real thing. 90% on the verbal and 30% on the math... Looks like I've got a bit of studying to do Kudos [?]: 1 [0], given: 0 Intern Joined: 15 Nov 2004 Posts: 7 Kudos [?]: [0], given: 0 OG PP score test 1 = 590 :( [#permalink] ### Show Tags 25 Nov 2005, 17:44 ahhhh. I feel the same way man. I just took OG PP test #1 and got a 590. I thought for sure that I would break 600 on this practice test. I can't believe that I scored a 28v and 43q. I'm usually decent at verbal, so I fee like crap. I have my test on Monday. Kudos [?]: [0], given: 0 Intern Joined: 06 Nov 2004 Posts: 11 Kudos [?]: 1 [0], given: 0 ### Show Tags 26 Nov 2005, 19:28 What did you end up getting? Kudos [?]: 1 [0], given: 0 26 Nov 2005, 19:28 Display posts from previous: Sort by # Powerprep accuracy Moderator: HiLine Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.
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0 # What is the sum of 15,20 and 17? Igboekwe Amaka Lvl 1 2022-01-29 08:03:29 If 15,20 is a decimal (more normally written 15.2) it would be 32,2, otherwise it's 1537 Noarh Lvl 3 2022-01-29 11:44:53 Study guides 20 cards ## A number a power of a variable or a product of the two is a monomial while a polynomial is the of monomials ➡️ See all cards 3.75 865 Reviews Nash Eser Lvl 4 2022-01-29 09:44:42 15,37 Timki Leung Lvl 2 2022-01-30 09:17:41 15,37 Earn +20 pts Q: What is the sum of 15,20 and 17? Submit Still have questions? View results View results View results View results
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# Write Numbers in Standard Form In this worksheet, students will write numbers in standard index form. Key stage:  KS 3 Curriculum topic:   Number Curriculum subtopic:   Interpret/Compare Standard Form Numbers Popular topics:   Numbers worksheets Difficulty level: #### Worksheet Overview Standard (index) form is a shorthand way of writing a large or a small number. It consists of a number between 1 and 10 (but not equal to 10) multiplied by a power of 10, for example 2.94 × 102 or 4.8 × 10-3. Example Change 5830 into standard form. First, fix the decimal point after the first non-zero digit, i.e. 5.830 or 5.83 Next, determine the power of 10 that you must multiply 5.83 by, to get back to 5830. In this case it is 3. So 5830 = 5.83 × 103 Other Examples 11.92 = 1.192 × 10 694,000,000 = 6.94 x 108 0.00694 = 6.94 × 10-3 Let's have a go at some questions. ### What is EdPlace? We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them. Get started
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Factoring By Grouping Worksheet Answers. Here, the given polynomial is distributed in pairs or grouped in pairs to find the zeros. In the expression 3 x ( x + 4. However, a gcf does not have to be a monomial, it could be a binomial. Group the first two terms and last two terms. This video provides examples of how to factor polynomials that require factoring out the gcf as the first step. Writing Describe The Fi Rst Step To Look For In Factoring A Cubic Expression Containing Four Terms. Practice using the factorization by grouping worksheets and enhance your conceptual knowledge. Create your own worksheets like this one with infinite algebra 2. Factoring by grouping worksheet answers factoring by grouping worksheet answers. This Method Is Also Said To Be Factoring By Pairs. We are asked to factor 3 x. Take these worksheets with you and practice now! Factoring by grouping worksheets for your kid to practice. Factorize Each Of The Following By Regrouping. Factoring polynomials with common factors. V â x3 à x2 = 6x v â 12a3 à 13a2 à 3a x; 25 scaffolded questions that start relatively easy and end with some real challenges. Links To Abundant Of Its Absolute Wonderments (There Are 38 Articles!) Are. Free trial available at kutasoftware.com. A 2 + ab + 9a + 9b. We are providing all factorization worksheets for free of cost on our website. 2 + 6 X Is 3 X ( X + 2). Free trial available at kutasoftware.com. Factor polynomials with four terms using grouping. The first two terms are a 2 + ab and the second two terms are 9a + 9b.
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# Re: Why DIGITP and DIGIT-WEIGHT? • To: Guy.Steele at CMU-10A • Subject: Re: Why DIGITP and DIGIT-WEIGHT? • From: Kent M. Pitman <KMP at MIT-MC> • Date: Thu ,2 Oct 80 17:27:00 EDT • Cc: LISP-FORUM at MIT-MC ```(APPEND A ()) ; Obscure use of APPEND to copy top of list (SUBST () () A) ; Obscure use of SUBST to copy structure (LSH -1 -1) ; Obscure use of -1 & LSH to get max pos fixnum (SSTATUS MACRO (PROGN I) ...) ; Obscure use of PROGN to make I EVAL ... These are ugly idioms. They each have their particular application -- some more questionable than others, but in each case, the end result is in no way related to the name. APPEND should put things together. SUBST should do substitution. -1 should be negative 1 -- we shouldn't have to use it for its representation. PROGN should sequence -- it shouldn't be used to make a list out of something that wouldn't normally be ... Having to say (DIGITP #/8) to get a digit's weight is annoying. It looks like a predicate. It may be a predicate -- sometimes. If I did: ... (WHILE (SETQ C (DIGITP (TYI))) ...) ... I might want DIGITP instead of DIGIT-WEIGHT but if I were in a routine which I knew had verified its input to be digits, I would want to say ... (LET ((W (DIGIT-WEIGHT DIGIT))) ... rather than ... (LET ((W (DIGITP DIGIT))) ... Indeed, I may have been passed the DIGIT from some other routine and not know what his input radix was. I may only know that the caller wanted it treated as a digit. Then the default argument must be explicitly given (as 36. -- sigh) and I will need ... (LET ((W (DIGITP DIGIT 36.))) ... which is even dumber if all I want is the digit weight. I'd also like to think that the code I was writing would work fine if there were bases above 36. Why should that constant have to go in. Having two functions means I can say the functionality I want and get it straightforwardly. The issues are subtle when there is only one function and they are straightforward if there are two. I vote for the straightforward case. The code will be there anyway; why not give the user the entry point he wants? -kmp ```
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# Blog ## What is the meaning of trilateral members? • Trilateral members, or waverers, are those which have three sides. His body was trilateral: he had three legs, three arms, and six eyes, placed at equal distances all around his head. The circuit was trilateral, and to a considerable extent remains so. " Trilateral " is from the Latin translation of the Greek tripleuros (three-sided). ## What is a three-sided triangle called? • Princeton's WordNet(0.00 / 0 votes)Rate this definition: triangle, trigon, trilateral(adj) a three-sided polygon trilateral(adj) involving three parties. "trilateral talks" trilateral, triangular, three-sided(adj) having three sides. "a trilateral figure" ## What is an equilateral triangle? • ‘Of trilateral figures, an equilateral triangle is that which has its three sides equal, an isosceles triangle, that which has two of its sides equal, and a scalene triangle, that which has its three sides unequal.’ ‘Yet the trilateral filter requires only one user-set parameter.’ A triangle. ## What does Trilateral mean in a sentence?What does Trilateral mean in a sentence? Definition of trilateral : having three sides or parties trilateral business ventures trilateral discussions Examples of trilateral in a Sentence Recent Examples on the Web Within the trilateral talks, many conflict points were discussed and resolved through compromises, for a negotiation started in 2018. ## What is the meaning of trilateral members?What is the meaning of trilateral members? Trilateral members, or waverers, are those which have three sides. His body was trilateral: he had three legs, three arms, and six eyes, placed at equal distances all around his head. The circuit was trilateral, and to a considerable extent remains so. " Trilateral " is from the Latin translation of the Greek tripleuros (three-sided). ## What is the difference between trilateral and reciprocal?What is the difference between trilateral and reciprocal? trilateral - involving three parties; "trilateral talks". reciprocal, mutual - concerning each of two or more persons or things; especially given or done in return; "reciprocal aid"; "reciprocal trade"; "mutual respect"; "reciprocal privileges at other clubs". ## What is the Trilateral Commission and what does it do?What is the Trilateral Commission and what does it do? The Trilateral Commission is a non-governmental discussion group founded by David Rockefeller in July 1973 to foster closer cooperation between Japan, Western Europe and North America.
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Math: Triangles : GMAT Quantitative Section - Page 4 Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack It is currently 23 Jan 2017, 10:13 ### GMAT Club Daily Prep #### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email. Customized for You we will pick new questions that match your level based on your Timer History Track every week, we’ll send you an estimated GMAT score based on your performance Practice Pays we will pick new questions that match your level based on your Timer History # Events & Promotions ###### Events & Promotions in June Open Detailed Calendar # Math: Triangles Author Message TAGS: ### Hide Tags Manager Joined: 06 Apr 2011 Posts: 77 Location: India GMAT 1: Q V Followers: 0 Kudos [?]: 15 [0], given: 22 ### Show Tags 22 Jul 2011, 21:59 Thanks Bunuel ... kudos... Intern Joined: 30 Nov 2010 Posts: 47 Followers: 0 Kudos [?]: 10 [0], given: 27 ### Show Tags 20 Aug 2011, 06:05 Bunuel wrote: A right triangle can also be isosceles if the two sides that include the right angle are equal in length (AB and AC in the figure above) Shouldn't that be CB and AC? Great material. Thanks for the compilation. Manager Status: SC SC SC SC SC.... Concentrating on SC alone. Joined: 20 Dec 2010 Posts: 240 Location: India Concentration: General Management GMAT Date: 12-30-2011 Followers: 3 Kudos [?]: 60 [0], given: 47 ### Show Tags 04 Nov 2011, 09:23 Bunnel great post. But i have one qstn. Isnt it too much information about triangles from GMAT perspective. Or is it necessary to grab all the concepts put up. _________________ D- Day December 30 2011. Hoping for the happiest new year celebrations ! Aiming for 700+ Kudo me if the post is worth it Manager Joined: 09 Aug 2011 Posts: 136 Location: United States Concentration: General Management GMAT Date: 11-15-2011 GPA: 3.33 Followers: 1 Kudos [?]: 9 [0], given: 38 ### Show Tags 08 Nov 2011, 21:45 I LOVE GMATCLUB!!!!! Manager Joined: 21 Nov 2010 Posts: 133 Followers: 0 Kudos [?]: 5 [0], given: 12 ### Show Tags 13 Nov 2011, 22:16 great job! thank you for posting the problems related! Intern Joined: 08 Sep 2011 Posts: 13 GMAT Date: 02-10-2012 Followers: 0 Kudos [?]: 6 [0], given: 6 ### Show Tags 26 Dec 2011, 23:03 Awesome... thats what i needed.. Manager Joined: 23 Feb 2012 Posts: 216 Location: India Concentration: Finance, Entrepreneurship Schools: Said GMAT 1: 710 Q44 V44 GPA: 2.9 WE: Marketing (Computer Software) Followers: 5 Kudos [?]: 48 [0], given: 22 ### Show Tags 05 Mar 2012, 03:38 Bunuel, you posted this in 2009. It's 2012 now and I am finding this so useful. Talk about leaving behind a legacy. you deserve a nice, large, value-saver family pack of Kudos! _________________ If you like it, Kudo it! "There is no alternative to hard work. If you don't do it now, you'll probably have to do it later. If you didn't need it now, you probably did it earlier. But there is no escaping it." 710 Debrief. Crash and Burn Manager Joined: 23 Feb 2012 Posts: 216 Location: India Concentration: Finance, Entrepreneurship Schools: Said GMAT 1: 710 Q44 V44 GPA: 2.9 WE: Marketing (Computer Software) Followers: 5 Kudos [?]: 48 [0], given: 22 ### Show Tags 05 Mar 2012, 03:49 Yup, I have been going through each section of the Math Book since morning! _________________ If you like it, Kudo it! "There is no alternative to hard work. If you don't do it now, you'll probably have to do it later. If you didn't need it now, you probably did it earlier. But there is no escaping it." 710 Debrief. Crash and Burn Manager Joined: 23 Feb 2012 Posts: 216 Location: India Concentration: Finance, Entrepreneurship Schools: Said GMAT 1: 710 Q44 V44 GPA: 2.9 WE: Marketing (Computer Software) Followers: 5 Kudos [?]: 48 [0], given: 22 ### Show Tags 05 Mar 2012, 08:17 Has a similar project been done for Verbal? I have Whiplash's CR material. (The one with the pretty cover and ZOMG! ZOMG! ZOMG! written on it). Has somebody put together a similar core-concepts book for Verbal? _________________ If you like it, Kudo it! "There is no alternative to hard work. If you don't do it now, you'll probably have to do it later. If you didn't need it now, you probably did it earlier. But there is no escaping it." 710 Debrief. Crash and Burn Intern Joined: 05 Mar 2012 Posts: 4 Followers: 0 Kudos [?]: 0 [0], given: 24 ### Show Tags 06 Mar 2012, 21:41 excellent & very useful one Intern Joined: 21 Mar 2012 Posts: 1 Followers: 0 Kudos [?]: 0 [0], given: 0 ### Show Tags 21 Mar 2012, 05:57 I WANT TO CALCULATE THE AREA OF A TRIANGLE WHOSE MEDIANS ARE GIVEN 12 CM 9 CM AND 6 CM Posted from my mobile device Manager Joined: 07 Dec 2011 Posts: 174 Location: India Followers: 1 Kudos [?]: 41 [0], given: 24 ### Show Tags 21 Mar 2012, 08:47 Let me just say that you sir, are awesome. Small error here I think :"A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s hypotenuse, then that triangle is a right triangle. Wouldn't it make more sense to say "if the diameter of the circle is one of the sides of a triangle inscribed in a circle, the triangle is a right triangle"? Calling the diameter a hypotenuse suggests that we already know that it's a right triangle. Intern Status: Active Joined: 30 Jun 2012 Posts: 37 Location: India Followers: 5 Kudos [?]: 82 [0], given: 36 ### Show Tags 28 Oct 2012, 05:31 Does GMAC test trignometry? for example - could we expect such problem? Solve the triangle below for angle x and then compute the area of the triangle. Say a triangle ABC with angles A, B and C with opposite sides to these angles a,b, and c respectively. a = 5 inches and b = 3 inches and angle A = 75 degrees find B =? Thanks! _________________ Thanks and Regards! P.S. +Kudos Please! in case you like my post. Manager Joined: 24 Mar 2010 Posts: 81 Followers: 1 Kudos [?]: 59 [0], given: 134 ### Show Tags 15 Nov 2012, 03:40 Quote: • To find the base given the leg and altitude, use the formula: • To find the leg length given the base and altitude, use the formula: • To find the altitude given the base and leg, use the formula: (Where: L is the length of a leg; A is the altitude; B is the length of the base) What is 'leg' of an isosceles triangle? _________________ - Stay Hungry, stay Foolish - BSchool Forum Moderator Joined: 27 Aug 2012 Posts: 1196 Followers: 129 Kudos [?]: 1469 [0], given: 142 ### Show Tags 28 Dec 2012, 08:30 This is just awesome Bunuel...Thanks a lot for making the theory of one of the most important parts of GMAT Math readily available... Could you please let me know that whether do we have any sort of thread that contains all Geometry 700+ problem collections in the forum ? BTW,you sig. I guess,does not contain any specific Geometry problem set..Please confirm whether I'm correct. _________________ Math Expert Joined: 02 Sep 2009 Posts: 36618 Followers: 7099 Kudos [?]: 93534 [0], given: 10578 ### Show Tags 29 Dec 2012, 03:21 debayan222 wrote: This is just awesome Bunuel...Thanks a lot for making the theory of one of the most important parts of GMAT Math readily available... Could you please let me know that whether do we have any sort of thread that contains all Geometry 700+ problem collections in the forum ? BTW,you sig. I guess,does not contain any specific Geometry problem set..Please confirm whether I'm correct. Check here: ds-question-directory-by-topic-difficulty-128728.html and here: gmat-ps-question-directory-by-topic-difficulty-127957.html _________________ BSchool Forum Moderator Joined: 27 Aug 2012 Posts: 1196 Followers: 129 Kudos [?]: 1469 [0], given: 142 ### Show Tags 29 Dec 2012, 05:21 Bunuel wrote: debayan222 wrote: This is just awesome Bunuel...Thanks a lot for making the theory of one of the most important parts of GMAT Math readily available... Could you please let me know that whether do we have any sort of thread that contains all Geometry 700+ problem collections in the forum ? BTW,you sig. I guess,does not contain any specific Geometry problem set..Please confirm whether I'm correct. Check here: ds-question-directory-by-topic-difficulty-128728.html and here: gmat-ps-question-directory-by-topic-difficulty-127957.html Well,that's the directory..have seen that already..but they contain the links of all the PS and DS problems submitted in the forum by all the forum members.But actually I was looking for specific Geometry problem set created by experts...like other problems in your signature.So,could you please share any such specific links,if any? _________________ VP Status: Final Lap Up!!! Affiliations: NYK Line Joined: 21 Sep 2012 Posts: 1096 Location: India GMAT 1: 410 Q35 V11 GMAT 2: 530 Q44 V20 GMAT 3: 630 Q45 V31 GPA: 3.84 WE: Engineering (Transportation) Followers: 37 Kudos [?]: 527 [0], given: 70 ### Show Tags 05 Feb 2013, 06:17 I think formula for Ratio of Area of triangles to the side must also be added............... Math Expert Joined: 02 Sep 2009 Posts: 36618 Followers: 7099 Kudos [?]: 93534 [0], given: 10578 ### Show Tags 10 Jul 2013, 23:06 Bumping for review*. *New project from GMAT Club!!! Check HERE _________________ Manager Joined: 25 Oct 2013 Posts: 173 Followers: 1 Kudos [?]: 56 [0], given: 56 ### Show Tags 04 Feb 2014, 07:05 Hello Bunuel, I have downloaded the math book and it is simply amazing. Really awesome power packed PDF! Very helpful, I wish I came across this site much earlier. I am currently going through Triangles and I have a small doubt regarding Median and angle bisector. In angle bisector section you mentioned that "each point of any angle bisector is equidistant from the sides of the triangle", By extension can I say that the point at which the angle bisector intersects the opposite side is that side's midpoint? And therefore an angle bisector is the median? _________________ Click on Kudos if you liked the post! Practice makes Perfect. Re: Math: Triangles   [#permalink] 04 Feb 2014, 07:05 Go to page   Previous    1   2   3   4   5    Next  [ 94 posts ] Similar topics Replies Last post Similar Topics: Maths 1 23 Sep 2011, 13:34 2 Triangles 2 13 Jul 2011, 15:31 2 Triangle 1 16 Apr 2011, 23:11 Triangles 0 31 May 2010, 19:25 1 GEOMETRY - TRIANGLES 11 17 Sep 2008, 22:02 Display posts from previous: Sort by
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# Three Dimensional Fourier Transform of Radial Function without Bessel and Neumann I am trying to compute the Fourier transform of $\frac1{|\mathbf{x}|^2+1}$ where $\mathbf{x}\in\mathbb{R}^3$. Just writing out the integral: $\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}\frac1{|\mathbf{x}|^2+1}e^{-2\pi i (\mathbf{x}\cdot\mathbf{\xi})}dx_1dx_2dx_3$. Mathematica was no help with this integral. I realized though that the function is radial, so that in spherical coordinates $f(\rho,\theta,\phi)=\frac1{r^2+1}=f(\rho)$. I thought this would simplify matters because then the limits of integration are just $\int_0^{\infty}\int_0^{2\pi}\int_0^{\pi}$ and $dx_1dx_2dx_3 \mapsto \rho^2\sin\theta d\theta d\phi d\rho$. However, the dot product in the exponent is messing me up a lot. I think it should be of the form $||\mathbf{x}||||\xi||$ times some trigonometric function of the angle between them, and $||\mathbf{x}||$ is just $\rho$. Because of this, I don't think doing this integral directly will be that much cleaner than Cartesian coordinates either. However, I was wondering if I could follow the methods of this and leverage the symmetry of my function and get the answer this way. I already know the Fourier Transform must be radial from the link. However, I am not sure about how to use the dilation part to extract information for my problem here. Or do you think it would be propitious to write $x_1$ as $\rho\sin\theta\cos\phi$ etc. and just work it out that way? • You can get the right spacing for the norm bars by using \lVert and \rVert to produce $\lVert$. Commented May 7, 2012 at 16:32 • Ricky, is there any reason you deleted your question after joriki provided an answer? Please note that this site helps everyone online - even though you've got the answer now, if someone had the same question as you, we'd want them to be able to see the answer here too. Commented May 7, 2012 at 21:26 • @ZevChonoles After thinking more, I thought my question was poorly formulated. But you're right, I should just leave it up. Commented May 7, 2012 at 23:50 I don't see how to solve this using the sort of scaling arguments used in that other answer, since your denominator doesn't have the same sort of scale invariance. To solve this directly, the key point to observe is that $\mathbf x\cdot\xi=\lVert\mathbf x\rVert\lVert\xi\rVert\cos\theta$, where $\theta$ is the angle between $\mathbf x$ and $\xi$. Since the function to be transformed is invariant under rotations, you can choose coordinates such that $\theta$ is also the angle between $\mathbf x$ and the $z$-axis. Then, with $k=\lVert\xi\rVert$, your integral is \begin{align} \int_0^\infty\int_0^\pi\int_0^{2\pi}\frac1{r^2+1}\mathrm e^{-2\pi\mathrm ikr\cos\theta}r^2\sin\theta\,\mathrm d\phi\,\mathrm d\theta\,\mathrm dr &= 2\pi\int_0^\infty\frac{r^2}{r^2+1}\int_0^\pi\mathrm e^{-2\pi\mathrm ikr\cos\theta}\sin\theta\,\mathrm d\theta\,\mathrm dr \\ &= 2\pi\int_0^\infty\frac{r^2}{r^2+1}\int_{-1}^1\mathrm e^{-2\pi\mathrm ikr\cos\theta}\,\mathrm d(\cos\theta)\,\mathrm dr \\ &= \frac{\mathrm i}k\int_0^\infty\frac{r}{r^2+1}\left(\mathrm e^{-2\pi\mathrm ikr}-\mathrm e^{2\pi\mathrm ikr}\right)\mathrm dr \\ &= \Im\frac2k\int_0^\infty\frac{r}{r^2+1}e^{2\pi\mathrm ikr}\mathrm dr \\ &= \Im\frac1k\int_{-\infty}^\infty\frac{r}{r^2+1}e^{2\pi\mathrm ikr}\mathrm dr\;, \end{align} where the last step works because the imaginary part of the integrand is even. This integral can be evaluated by closing the contour in the complex plane with a semicircle at infinity in the upper half-plane, enclosing the pole at $r=\mathrm i$ with residue $\frac12\mathrm e^{-2\pi k}$, yielding $$\Im\frac1k2\pi\mathrm i\,\frac12\mathrm e^{-2\pi k}=\frac\pi ke^{-2\pi k}\;.$$ • I don't see why you can call the angle between $\mathbf{x}$ and $\xi$ $\cos (\theta)$. Commented Apr 27, 2015 at 1:22 • @ArturoDonJuan: I called that angle $\theta$, not $\cos(\theta)$. Since I can call the angle whatever I want, I'm guessing that your question is more about why I can choose this to also be the angle between $\mathbf x$ and the $z$-axis. This is because the function to be transformed is rotationally invariant, so the answer depends only on $k$ and we can choose $\xi$ along the $z$-axis. Commented Apr 28, 2015 at 2:21 • Sorry, my wording was incorrect. I meant that. Would it be more appropriate to say that we can orient the $z$-axis along the $\xi$ vector? Commented Apr 28, 2015 at 3:14 • @ArturoDonJuan: I think both viewpoints are appropriate. The fact that you can choose how to orient the $z$-axis is equally dependent on the rotational symmetry of the function being transformed. Commented Apr 28, 2015 at 9:35 • @a52: It denotes the imaginary part of what follows. Commented Jan 1, 2020 at 4:09
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Partner with ConvertIt.com New Online Book! Handbook of Mathematical Functions (AMS55) Conversion & Calculation Home >> Measurement Conversion Measurement Converter Convert From: (required) Click here to Convert To: (optional) Examples: 5 kilometers, 12 feet/sec^2, 1/5 gallon, 9.5 Joules, or 0 dF. Help, Frequently Asked Questions, Use Currencies in Conversions, Measurements & Currencies Recognized Examples: miles, meters/s^2, liters, kilowatt*hours, or dC. Conversion Result: ```apothecary pound = 0.3732417216 mass (mass) ``` Related Measurements: Try converting from "ap pound" to carat troy (troy carat), cental (British cental), cotton bale (US), denarius (Roman denarius), dram troy (troy dram), electron mass (electron rest mass), grain (avoirdupois grain), Israeli shekel mass, long hundredweight (avoirdupois long hundredweight), Mexican libra, mina (Greek mina), neutron mass (neutron rest mass), pennyweight troy (troy pennyweight), pound ap (apothecary pound), pound troy (troy pound), quintal, Roman talent, short quarter, Spanish libra, UK quintal2 (British quintal), or any combination of units which equate to "mass" and represent mass. Sample Conversions: ap pound = 2.25E+26 AMU (atomic mass unit), 1.14 as (Roman as), 1.71 bes (Roman bes), .05142857 bowling ball, .61714286 catty (Chinese catty), .00164571 cotton bale (US), .00109714 cotton bale Egypt, 96 denarius (Roman denarius), 86.96 drachma2 (Greek drachma), 38.06 hyl, .09949905 kwan (Japanese kwan), 115,200 mite (English mite), 12 oz troy (troy ounce), 240 pennyweight troy (troy pennyweight), 2.23E+26 proton mass (proton rest mass), 288 scruple (apothecary scruple), 328.58 scrupulum (Roman scrupulum), .03291429 short quarter, .02557518 slug, 9.87 tael (Chinese tael). Feedback, suggestions, or additional measurement definitions? Please read our Help Page and FAQ Page then post a message or send e-mail. Thanks!
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Upcoming SlideShare × # Bfa green+project 174 views Published on test 0 Likes Statistics Notes • Full Name Comment goes here. Are you sure you want to Yes No • Be the first to comment • Be the first to like this Views Total views 174 On SlideShare 0 From Embeds 0 Number of Embeds 1 Actions Shares 0 2 0 Likes 0 Embeds 0 No embeds No notes for slide • \n • \n • \n • \n • \n • \n • \n • \n • \n • \n • \n • \n • \n • \n • \n • \n • ### Bfa green+project 1. 1. BFA GREEN PROJECT 2. 2. BFA GREEN PROJECT 3. 3. BFA GREEN PROJECT 4. 4. BFA GREEN PROJECT What is the “green project” and why do we need it? 5. 5. BFA GREEN PROJECT The “green project” is taking at look at how we use things like paper at BFA and look for ways to reduce the waste. We are also looking at how we can save money by being smarter about how we use our “expendables” such as printer toner. 6. 6. BFA GREEN PROJECT We are doing this because we can do a better job at using the resources we have at our disposal at BFA/NWTC 7. 7. So what does this cost?BFA GREEN PROJECT 8. 8. So what does this cost?BFA GREEN PROJECT • Paper cost: 550 cases x \$25.00 = \$13,750 (2.75 million sheets) 9. 9. So what does this cost?BFA GREEN PROJECT • Paper cost: 550 cases x \$25.00 = \$13,750 (2.75 million sheets) • Printing costs: Contract \$15,000.00 10. 10. So what does this cost?BFA GREEN PROJECT • Paper cost: 550 cases x \$25.00 = \$13,750 (2.75 million sheets) • Printing costs: Contract \$15,000.00 • Colour Print Overage costs 2010-2011 School Year: \$11,592.07 11. 11. So what does this cost?BFA GREEN PROJECT • Paper cost: 550 cases x \$25.00 = \$13,750 (2.75 million sheets) • Printing costs: Contract \$15,000.00 • Colour Print Overage costs 2010-2011 School Year: \$11,592.07 • Copier costs: \$90,000 12. 12. So what does this cost?BFA GREEN PROJECT • Paper cost: 550 cases x \$25.00 = \$13,750 (2.75 million sheets) • Printing costs: Contract \$15,000.00 • Colour Print Overage costs 2010-2011 School Year: \$11,592.07 • Copier costs: \$90,000 Total Cost \$130,342 13. 13. BFA GREEN PROJECT How do we start to make difference? 14. 14. BFA GREEN PROJECT How do we start to make difference? • Paper cost > Think before you print, look for alternatives 15. 15. BFA GREEN PROJECT How do we start to make difference? • Paper cost > Think before you print, look for alternatives • Printing costs > Reduce the amount and type of printing 16. 16. BFA GREEN PROJECT How do we start to make difference? • Paper cost > Think before you print, look for alternatives • Printing costs > Reduce the amount and type of printing • Colour Print Overage > Print in B&W. Colour only when you need it. Use PDF files, distribute as Google Docs, create a website... 17. 17. BFA GREEN PROJECT How do we start to make difference? • Paper cost > Think before you print, look for alternatives • Printing costs > Reduce the amount and type of printing • Colour Print Overage > Print in B&W. Colour only when you need it. Use PDF files, distribute as Google Docs, create a website... • Copier costs > see above 18. 18. BFA GREEN PROJECT How do we start to make difference? • Paper cost > Think before you print, look for alternatives • Printing costs > Reduce the amount and type of printing • Colour Print Overage > Print in B&W. Colour only when you need it. Use PDF files, distribute as Google Docs, create a website... • Copier costs > see above Total Cost \$130,342 19. 19. BFA GREEN PROJECT 20. 20. BFA GREEN PROJECT
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# Find a number that is 24 less than its opposite 2 by falvero 2015-02-17T09:47:08+08:00 ### This Is a Certified Answer Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest. 7x=x+24                                                                                                            6x=24                                                                                                               x=24                                                                                                                                                                                                                                    7(4)=28                                                                                                               4+24=28 2015-02-18T10:26:35+08:00 ### This Is a Certified Answer Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest. X-first number -x-opposite of first number x=-x-24 Transpose 2x=-24 x=-12 Hope this helps =)
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# math i need some to explain how to turn 1.05 into a fraction Do you know how to add fractions? 1 + 0.05 equals 1.05. So if you can convert 1 to a fraction and 0.05 to a fraction, you can add the two fractions together. Your answer is 1.05 as a fraction. Continuing with Leo's previous answer, remember that when you add fractions together, they need to have a common denominator. Here are some more steps toward the answer. 0.05 = 5/100 = 1/20 Add 1 to that, and you get 1 1/20, which is a mixed number. You can also write it as 20/20 + 1/20 = 21/20 which is a pure fraction and is the answer that you seek. Just say the number aloud to yourself...one and five hundredths. That is the fraction too. 1 5/100 which reduces to 1 1/20. 1. 👍 0 2. 👎 0 3. 👁 381 1. It is 1 5/100 because the 5 is in the 100ths place, and there is a 1 in front of the decimal so that is the whole number. 1. 👍 0 2. 👎 0 posted by Zoe 2. Zoe Exactly. 1. 👍 0 2. 👎 0 posted by NRyan ## Similar Questions 1. ### math,algebra or I would think: -5/4 you think so??? I have complety forgotton how to turn a decimal into a fraction. i have to turn : -1.25 into a fraction -1 1/4 maybe??? thats what i thought at first but i like to confirm it yes i think asked by Sammy on January 28, 2007 2. ### math 6 grade When the LCM of two numbers the same as one of the numbers?Use an example to explain. What is the LCM of six and two? so the LCM of six and two is the answer? Of course not. It is an example of what the question seeks. 3. the asked by brittany on November 8, 2006 3. ### 6th Grade what fraction of a turn does a minute hand turn through between 6:25pm and 7:15pm 10:24pm and 11.58pm asked by chirag on November 9, 2010 4. ### Math What is the rotational symmetry as a fraction of a turn and the angle of the smallest turn of letter I asked by Jay on April 3, 2013 5. ### math identify the rotational symmetry asa fraction of a turn and the angle measure of the smallest turn asked by morgann on March 14, 2011 1. ### math,algebra Directions:Multiply (-1/2)(-3/8) mY ANSWER : .1875 Now how do i turn this into a fraction. numerator multiplied: 3 denominator multiplied 16 3/16 How do you get to that answer because not every single one would be multiplied by asked by jasmine20 on December 12, 2006 2. ### math trying to find a fraction riddle. I'm a fraction greater than 1/2 and less than 3/4. My numerator is 5 times 1. what fraction am I? How do you explain the answer? asked by katy on March 10, 2008 3. ### Algebra how do you turn a decimal to fractions and percents? like .6 or .001 also how do you turn 2.85% into fraction and decimal? asked by Christina on September 14, 2009 4. ### alberaic method! how do I convert 0.12... to a fraction using algebraic method? Isn't 0.12 twelve hundreths? 12/100 = 6/50 and it can be reduced further. I'm not sure what is meant by "algebraic method" here, but .12 is the same as 12/100 asked by allana on October 19, 2006 5. ### Math HELP! 1. Write 12/32 in simplest form. Could someone please help me on how I can turn this fraction into simplest form like explain the steps! Thanks. asked by Zoey on October 7, 2015 More Similar Questions
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# Quarter Square Triangle A quarter square triangle (QST) is formed when both of a square’s diagonals are cut to form four equal triangles. Each triangle formed is a right angle triangle.  The straight of grain is on the hypotenuse. A QST looks like a half square triangle (right angle triangle with two equal sides). The difference between the two is where the bias is placed. The bias on a QST falls on the two shorter sides of the triangle.  The bias of a half square triangle (HST) falls on the longest side. In the photo above, the white triangles in the corners are HST’s.  They work best in the corner because the straight of grain falls on the outside edges which helps keep the block flat.  The red star points, grey section between the points and the white triangles in the middle are QST’s.  The straight of grain of the grey triangles also falls on the outside edge of the block. There are many ways to make QST.  Most people prefer rotary cutting rather than using templates. To rotary cut these triangles, you will need to find the finished size of the triangle (length of the longest side). The “formula” (listed below) works like a charm every time. • Measure the FINISHED SIZE of the HYPOTENUSE side of the triangle. • Add 1 ¼ inches to the FINISHED SIZE of the HYPOTENUSE side of the triangle. • Cut out a square measuring FINISHED SIZE of HYPOTENUSE side of the triangle plus 1 ¼ inches. • Cut the square on both diagonals. You might also like the video below as QST’s are one of the seven triangles featured:
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Search a number 1925106264 = 2335990281 BaseRepresentation bin111001010111110… …1100101001011000 311222011102112100000 41302233230221120 512420311400024 6515005413000 765464063464 oct16257545130 94864375300 101925106264 118a8743914 1245886a160 13248ab4243 141439614a4 15b401bcc9 hex72beca58 1925106264 has 48 divisors (see below), whose sum is σ = 5406939720. Its totient is φ = 641701440. The previous prime is 1925106241. The next prime is 1925106289. The reversal of 1925106264 is 4626015291. 1925106264 is a `hidden beast` number, since 1 + 9 + 25 + 1 + 0 + 626 + 4 = 666. It is a Harshad number since it is a multiple of its sum of digits (36). It is a fibodiv number, since the Fibonacci-like sequence with seeds 192 and 5106264 contains 1925106264 itself. It is a congruent number. It is an unprimeable number. It is a pernicious number, because its binary representation contains a prime number (17) of ones. It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 493197 + ... + 497084. Almost surely, 21925106264 is an apocalyptic number. It is an amenable number. 1925106264 is an abundant number, since it is smaller than the sum of its proper divisors (3481833456). It is a pseudoperfect number, because it is the sum of a subset of its proper divisors. 1925106264 is an equidigital number, since it uses as much as digits as its factorization. 1925106264 is an odious number, because the sum of its binary digits is odd. The sum of its prime factors is 990302 (or 990286 counting only the distinct ones). The product of its (nonzero) digits is 25920, while the sum is 36. The square root of 1925106264 is about 43876.0329109185. The cubic root of 1925106264 is about 1243.9938568708. The spelling of 1925106264 in words is "one billion, nine hundred twenty-five million, one hundred six thousand, two hundred sixty-four".
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# Was there any limit to the number of consecutive "full" (30 day) or normal (29 day) months during the time of the Sanhedrin? When Sanhedrin existed, each month had to be sanctified by Sanhedrin after testimony of 2 witnesses (or automatically by Sanhedrin if no one appeared by the end of the 30th day.) Refer to Maimonedes Hilchot Kiddush Hachodesh for details. Since each month was individually sanctified, I assume that it was possible to have several months each with 30 days or several with 29 days, unlike the alternating lengths that we have for most of the months in our current fixed calendar. Was there any limit to the number of consecutive months having the same length? For example, in a leap year having 13 months, would it be possible to have a year that was 390 days long if all the months had 30 days? If not, what was the maximum number of months that had the same length? A long run of one type or the other would eventually become obvious to anybody who witnessed the new moon, but if nobody witnesses and comes to Jerusalem to testify, the Sanhedrin could conceivably have a long run of default-30-day months. Is there a halachic limit? • 8 of one type per year. Erchin 9b or so. Sep 11, 2015 at 2:58 • @DoubleAA I'll try to view this later on. If it makes sense, please post as an answer. Would you know how many are allowed to be consecutive of the same type? Shana Tovah. – DanF Sep 11, 2015 at 3:01 • Logically, multiple 30 day months would force 29 day months because the new moon would be seen "early" and the minimum time is 29 days Sep 11, 2015 at 11:38 • @sabbahillel, not if no one happened to see it, get to Jerusalem in time, and be able to testify coherently. (But see judaism.stackexchange.com/q/18202 .) However, the opposite is true: successive short months would force a long one. – msh210 Sep 11, 2015 at 13:03 • @msh210 Sooner or later there would be enough "extra" days, that someone would be sure to have seen the moon and be able to testify. Even if the whole rainy season is too cloudy, the dry season would cause the moon to be seen to go back to 39 day months. Consider that people knew when it was expected and would be looking for it. Sep 11, 2015 at 13:30
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# Numerical factor of algebraic terms A number that multiplies at least a literal to form an algebraic term is called the numerical factor of an algebraic term. ## Introduction An algebraic term is formed by the product of a number and at least a literal to represent a quantity in mathematical form. The number multiplies the literal in the algebraic term. Hence, it is known as a factor basically but it is a numeral. Therefore, it is known as a numerical factor. ### Example $6xy$ is an algebraic term. In this algebraic term, the number $6$ and the literals $x$ and $y$ are multiplying each other to represent a quantity in product form. Mathematically, a multiplying element is called a factor in a term. Hence, all three of them are factors but $6$ is a factor in numerical form. Hence, the number $6$ is called a numerical factor. ### More Examples Look at the following examples to know how to determine a numerical factor in every algebraic term. $(1)\,\,\,\,\,\,$ $-4a$ In this example, $-4$ is a number and multiplying the literal $a$. Hence, $-4$ is called a numerical factor. $(2)\,\,\,\,\,\,$ $7b^2c$ $7$ is called the numerical factor. $(3)\,\,\,\,\,\,$ $0.07gh^3$ $0.07$ is a decimal number. Hence, it is called the numerical factor. $(4)\,\,\,\,\,\,$ $\dfrac{7e^4}{5}$ The algebraic term $\dfrac{7e^4}{5}$ can be written as $\dfrac{7}{5}e^4$. Therefore, $\dfrac{7}{5}$ is called the numerical factor. $(5)\,\,\,\,\,\,$ $\dfrac{-j^4}{4k}$ The algebraic term can be written as $-\dfrac{1}{4} \times \dfrac{j^4}{k}$. Therefore, the numerical factor is $-\dfrac{1}{4}$.
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# Anabelle boyle (2) United States - New Hampshire - barrington 4.0 Subject Prices Top Resource Types My Products sort by: Best Seller view: Children go on a shopping spree around the mall to collect items to "fill their room" game board. Each item is given with full price and students must calculate the new price using a percentage off sale ticket (ie, 50%, 25%, 30% etc.) Makes Subjects: Basic Operations, Fractions, Decimals 4th, 5th, 6th Types: Activities, Fun Stuff, Games \$3.95 2 ratings 4.0 This a graphic organizer set up like a mad lib that walks students through writing their own 2 step word problems. Students will fill out their own bar diagram/model with 3 parts and one whole. Then students will use this information to Subjects: Basic Operations, Numbers, Word Problems 2nd Types: Activities, Graphic Organizers, Math Centers \$1.00 not yet rated Handa's Hand Math Literature Worksheet 1.OA.1 Subjects: Basic Operations Kindergarten, 1st, 2nd Types: Handouts, Printables, Math Centers CCSS: 1.OA.A.1 FREE not yet rated Teachers can print and laminate for use with dry erase markers. Great for centers or small groups. Subjects: Fractions 3rd, 4th, 5th Types: Graphic Organizers \$1.50 not yet rated This is a simple graphic organizer where students can explore dividing a number into equal parts (denominator) and then determining the fraction of a number using the parts. example: 3/5 of 50 Great paired with manipulative. Also easy to laminate Subjects: Fractions 3rd, 4th Types: Computation, Graphic Organizers \$1.00 not yet rated showing 1-5 of 5 ### Ratings Digital Items 4.0 Overall Quality: 4.0 Accuracy: 4.0 Practicality: 4.0 Thoroughness: 4.0 Creativity: 4.0 Clarity: 4.0 Total: 2 total vote(s) TEACHING EXPERIENCE MY TEACHING STYLE HONORS/AWARDS/SHINING TEACHER MOMENT MY OWN EDUCATIONAL HISTORY
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•  2 I don't understand these sentences: 1. The percentage of Australian youngsters in both genders watching TV or video is equal. Why is "is equal" but not "are equal"? I thought this sentence had "youngsters" and "genders" which are plural so this sentence has to be "are equal"? 2. "The figure for web users in USA was....." and "The figures for web users in USA and Mexico were...". Are two sentences correct? If yes so why? I don't get it? I get confused about the part (was- were) and (figure-figures)??? why is that? The tense doesn't depend on "web users" right? Thank you! Let's reword to clarify what you are trying to say. 1. The percentage of Australian youngsters (of both genders) who watch TV is equal to the percentage who listen to audio. You are comparing percentages, not genders., not youngsters. 2. Now, would you like to try #2 again? Clive so for the #2 it means that i'm not comparing the "web users" but comparing the figure for "countries"? so I mean if "the figure for web users in 1 countries was" but the figures for web users in 2 countries were"? even "the figure" with or without "s" depends on "country"? Thank you Teachers: We supply a list of EFL job vacancies I don't know what your texts or graphs are showing you, but I think it is this .(I'll just make up some simple numbers.) Total number of web-users in the USA: 800. Total number of web-users in Mexico: 300. _______________________________________________________________ You can say this. The figure for web users in the USA was 800. The figures for web users in the USA and Mexico were 800 and 300 respectively, for a total of 1100. The tense doesn't depend on "web users" right? Right. 1. yes I know I just want to make clear that does it depends on the part "countries" to decide "was" or "were" like in your example? like in 1 country so the figure without "s" - in 2 countries the figures with "s". I want to know about the formula grammar to apply on other writing. 2.For example when I say: The figures of web users and game players in USA were...? is it correct? For example when I say: The total number of web users and game players in USA was ...? is it correct? Yes, if you are taking about one number that includes both. A figure is often called a number. Example 1 You were told that the number of left-handed men in the USA is 500,000. You can say 'This number was surprising.' Example 2 You were told that the number of left-handed men in the USA is 500,000 and that there are 100,000 people in Mexico with red hair, and that there are 700,000 people in prison in Germany. You can say 'These numbers were surprising." Students: We have free audio pronunciation exercises.
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I'm working (rather beginning) on a Huffman tree. I think I've run in to a problem for time complexity. Huffman trees are supposed to be fast in most ways. As I prepare to build my tree, I have three for...next loops in separate methods. I think that could be very bad time complexity. I think its something like n^3, which isn't just bad its atrocious. n^2 is bad enough. This is only the initialization process that these loops are running at. One method goes through a 27 length array of FrequentChars (a container class I invented, much like a C struct) and gives each element a new frequentChar, and default values in alphabetical order. The last position (#26) belongs to space characters. Next I have a findFrequencies() method which goes through the string I'm given, finding where each character occuring belongs and increments the associated frequency inside the freqChars array. Next I have another loop which places each char and frequency in a priority queue just before building the tree. The Priority Queue and the Tree classes were given to us (I'm taking a class on Advanced data structures and algorithms), and I've modified them to suit my needs. The priorityQueue class can contain Tree elements, and will be used to assemble the tree. I just feel like this is grossly inefficient. I've been stressed out with other work for some time now, and haven't been able to put much work in to this since it was assigned almost two weeks ago. I'm a fairly proficient programmer, I can make things work, but I don't have much experience making things work well. I just realized that I have to add yet another for...next loop just to know how big to make my priority queue. The Queue takes a size parameter in its constructor. I could modify the Priority queue class to be dynamic too, but that only just occurred to me. Are these sorted arrays? If so, can't you use bsearch to find the position needed? And if you need to insert a new element, then use a modified bsearch algorithm that will return the insert position in a passed pointer or reference variable (depending upon whether you want a C or C++ method). IE, if the function returns NULL (not found), the insert position would be in the passed insert_posn variable. The signature for standard bsearch is `void* bsearch(const void *key, const void *base, size_t nmemb, size_t size, int (*compar)(const void *, const void *));` `void* posn_bsearch(const void *key, const void *base, size_t nmemb, size_t size, int (*compar)(const void *, const void *), size_t* insert_posn);`
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# 18.354 – Nonlinear Dynamics II: Continuum systems ```18.354 – Nonlinear Dynamics II: Continuum systems Problem Set 4: Continuum Equations Due: Tuesday, April 14 (by 1pm in class) Problem 1: Hydrodynamic conservation laws. (a) Derive the momentum equation for a fluid using a volume element argument (as opposed to the fluid element argument used in class). (b) The Reynolds Transport Theorem (RTT) states that for a scalar field f (x, t), d dt Z Z f (x, t)dV = V (t) V (t) ∂f + ∇.(uf ) dV ∂t where V (t) indicates a material control volume, i.e., a volume element that moves with the local fluid velocity u(x, t). If the density ρ satisfies the continuity equation ∂ρ + ∇.(ρu) = 0, ∂t prove the special form of the RTT for another scaler field g(x, t): d dt Z Z ρg(x, t)dV = V (t) ρ V (t) Dg dV, Dt where D/Dt represents the material derivative D/Dt = ∂/∂t + u.∇. Problem 2: Reynolds numbers. The kinematic viscosity (ν = &micro;/ρ) of air is roughly 10−5 m2 s−1 and for water it is 10−6 m2 s−1 . Find the kinematic viscosities of some other fluids (e. g. Honey, Liquid Helium) and estimate the Reynolds number for a least three different physical flow configurations (e.g. airplane flight, stirring of a coffee cup, swimming of bacteria, etc). Problem 3: The stress tensor. (a) Calculate the velocity gradient tensor ∇u, the rate of strain tensor E and the vorticity tensor Ω for the shear flow u = (Ay, 0, 0). Sketch the velocity field. (b) Fluid motion in the neighbourhood of a point can be decomposed into a combination of translational flow, rotational flow and straining flow. For the shear flow in (a) we can write u = us + ur = 12 (Ay, Ax, 0) + 1 2 (Ay, −Ax, 0). Calculate ∇u, E and Ω for us and ur , and sketch the velocity fields. 1 Problem 4: Solutions of the Navier-Stokes Equations. The Navier-Stokes equations can be solved analytically for the following flow geometries. In each problem the fluid has viscosity &micro; and density ρ. Having obtained a solution, sketch the corresponding velocity profile. The solution in (d) is time dependent, so plot the velocity profile at two or three different times. Briefly comment on your solutions (i. e. what would be the effect of changing viscosity? or density? or changing the frequency in (d)?). (a) Flow of fluid between two rigid boundaries located at y = &plusmn;h under a constant pressure gradient P = −dp/dx. (b) The same as (a) but for flow inside and along the axis of a circular cylinder of radius h. (use cylindrical coordinates) (c) Flow between a cylinder of radius R1 inside another cylinder of radius R2 . The inner cylinder rotates at angular velocity ω1 and the outer cylinder rotates at angular velocity ω2 . (use cylindrical coordinates) (d) Fluid lying in the plane 0 &lt; y &lt; ∞, above an oscillating flat plate moving to and fro in the x-direction with velocity U cos ωt. Seek a solution for the velocity field of the form u = (u(y, t), 0, 0) = (Re[f (y)eiωt ], 0, 0). The first two flows are called Poiseuille flows, after the physician who first studied them in connection with blood flow. Their instability at high Reynolds number constitutes one of the most important problems in fluid dynamics. The third flow is cylindrical Couette flow. Problem 5: Coffee cup experiment Equations. (a) Take a cup of water. With a spoon, stir the fluid until the flow is roughly in solid body rotation. Estimate the initial rotational angular velocity of the fluid, and time how long it takes for the fluid to spin down to rest. How does this compare with our calculations in class ? How does the spin down time change if you use a more viscous fluid, like honey, or if you change the size of your container? Write a brief description of your experimental method and results. (b) Our solution to the spin-down of a coffee cup was composed of Bessel functions. Use MATLAB to make some plots of the velocity profile for flow in your coffee cup at various stages of the spin down, and describe any difficulties you encounter. Provide a printout of your code for calculating the velocity profile. 2 MIT OpenCourseWare http://ocw.mit.edu 18.354J / 1.062J / 12.207J Nonlinear Dynamics II: Continuum Systems Spring 2015
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Best short riddles How much dirt How much dirt would be in a hole 6 feet deep and 6 feet wide that has been dug with a square edged shovel? None. No matter how big a hole is, it's still a hole: the absence of dirt. And those of you who said 36 cubic feet are wrong for another reason, too. You would have needed the length measurement too. So you don't even know how much air is in the hole. 86.32 % Big as an elephant What can be as big as an elephant but weigh nothing? 86.32 % clean It always goes up and never ever comes down It always goes up and never ever comes down! What is that? 86.32 % funny Cross an elephant and a kangaroo What do you get if you cross an elephant and a kangaroo? Big holes all over Australia! 86.32 % 7+2+5 = ? Assume: 5+3+2 = 151022 9+2+4 = 183652 8+6+3 = 482466 5+4+5 = 202541 Then; 7+2+5 = ? 143547 Explanations: Multiplication of the 1st & 2nd numbers, 5*3 = 15; 9*2 = 18…thusly, 7*2 = 14 Multiplication of the 1st & 3rd numbers, 5*2 = 10; 9*4 = 36…thusly, 7*5 = 35; Multiplication of the 1st & the sum of the 2nd & 3rd numbers. The generated result is reduced by the value of the 2nd number, …thusly, 7*(2+5) = 49 - 2 = 47 86.32 % What does he weigh? Tom's height is six feet, he is an assistant at a butcher's shop, and wears size 12 shoes. What does he weigh? Meat. 86.32 % A clock A clock chimes 5 times in 4 seconds. How many times will it chime in 10 seconds? 11 times. It chimes at zero and then once every second for 10 seconds. 86.32 % Gambling house Even though the odds are always in favor of the gambling house, why does the establishment insist on a house limit on stakes? Every casino in the world would go bankrupt without a house limit on stakes. Without it, gamblers would keep doubling their stakes until they won. No matter how bad a losing streak they were on, they would eventually win. For more information, search: Martingale 86.32 % funny Halo in the water Why is there a halo in the water? There is an angelfish there! 86.32 %
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## Teamwork in Action - Section 2: Shared Problem Solving Teamwork in Action # Save Dave! Decomposing 4 Unit 10: Decomposing Numbers Lesson 3 of 12 ## Big Idea: This is a problem-solving, group based activity that illustrates a real-world reason to find different number combinations for 4. Print Lesson 1 teacher likes this lesson Standards: Subject(s): Math, Number Sets, whole numbers 30 minutes ### Michelle Novelli ##### Similar Lessons ###### Same As Game Kindergarten Math » Same As Big Idea: Kindergarteners are very concrete thinkers. Therefore, if 2 + 3 = 5, then nothing else can equal 5, or at least that's what they initially think. " Same As" develops a new understanding that there can be several combinations to make 5. Favorites(0) Resources(18) Phoenix, AZ Environment: Urban ###### It Starts With a Seed… Kindergarten Science » Pumpkins Big Idea: Selecting their own germination environment allows students a chance to plan and carry out their own investigation. Favorites(7) Resources(27) Lexington Park, MD Environment: Suburban ###### Farmer Fred's Fenceposts-The Plus and Equal Sign Kindergarten Math » Introduction to Addition and Subtraction Big Idea: Although understanding the plus and equal sign are not a kindergarten Common Core standard, exposure to the concept provides a foundation for future learning and preparation for standardized testing. Favorites(5) Resources(17) Cold Spring, MN Environment: Rural
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# What is the connection between simple harmonic motion and pendulum motion? • AnthroMecha ## Homework Statement What is the connection between simple harmonic motion and pendulum motion? ## Homework Equations Harmonic motion period=T=2piroot(m/k) Pendulum motion period=T=2piroot(L/g) ## The Attempt at a Solution Conservation of momentum?? Thanks for any help! I strongly suggest reading the Wikipedia article on simple harmonic motion. Consider comparing the equation of motion for the general SHM and the pendulum, that is the formula relating angle or displacement to time. I strongly suggest reading the Wikipedia article on simple harmonic motion. Consider comparing the equation of motion for the general SHM and the pendulum, that is the formula relating angle or displacement to time. Thanks for pointing me in the right direction. This is what I came up with: A pendulum oscillates in a simple harmonic motion like that of an oscillating spring. The angle θ in pendulum motion is relative to the distance x that a spring is stretched by a mass (m) and a gravity (g). Pretty good. But isn't SHM a general concept of which the pendulum, spring, water waves, radio waves, etc. are all specific examples? For the word "connection" in the question, I would look for what makes the pendulum simple harmonic, both from the motion characteristics and the nature of the force that causes the motion. Pretty good. But isn't SHM a general concept of which the pendulum, spring, water waves, radio waves, etc. are all specific examples? For the word "connection" in the question, I would look for what makes the pendulum simple harmonic, both from the motion characteristics and the nature of the force that causes the motion. Hmmm...a restoring force in the opposite direction of displacement is what makes it a SHM, right? and in the case of the pendulum mg is the restoring force? The restoring force has to have a specific formula. . . Yes, mg is the driving force, but it isn't in the right direction, is it? The pendulum restoring force is a little bit complex, and when you get into the details it is only approximately the right formula, so the pendulum only has nearly SHM when a particular condition is met. No doubt you can look up all that if you want to give a great answer. Thanks for the help Delphi! Most welcome!
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# Combination of Two or More Simple Sentences into a Single Compound Sentence using Cumulative Conjunction This set of English Grammar Exercises (MCQs) focuses on “Synthesis of Sentences – Combination of Two or More Simple Sentences into a Single Compound Sentence using Cumulative Conjunction”. 1. Combine the following set of simple sentences into one compound sentence. The crowd was outside. He was nervous. a) The crowd being outside made him nervous b) He was nervous of the crowd outside c) The crowd was outside and he was nervous d) The crowd was nervous so he was nervous Explanation: The following two simple sentences given in this question statement are converted into a compound sentence by using the cumulative conjunction ‘and’ in the answer statement. This helps to simply add together two different sentences. 2. Combine the following set of simple sentences into one compound sentence. She is smart. She is attractive. a) She is both smart and attractive b) She is smart so she is attractive c) She is either smart or attractive d) She is smart which makes her attractive Explanation: The two simple sentences mentioned in this question are combined together by the use of the cumulative conjunction ‘both smart and attractive’ in the answer statement. Cumulative conjunction is a coordinating conjunction. 3. Combine the following set of simple sentences into one compound sentence. They checked my name. They checked my address. a) They check my name along with the address b) They checked my name and address c) They checked my name while checking the address d) They checked my address after checking my name Explanation: The cumulative conjunction used in the given answer statement is ‘and’. It is a type of coordinating conjunction used to add extra information with certain degree of emphasis to the independent clauses. 4. Combine the following set of simple sentences into one compound sentence. It was sunny outside. I went for a walk. a) I went for a walk when it was sunny outside b) I went for a walk while it was sunny outside c) I went for a walk because it was sunny outside d) It was sunny outside and I went for a walk Explanation: The two simple sentences are combined together into a compound sentence with the help of the cumulative conjunction ‘and’ in the answer statement. A cumulative conjunction connects two words, phrases or independent clauses. 5. Combine the following set of simple sentences into one compound sentence. She shouted. She called for help. a) She shouted and called for help b) She shouted calling for help c) She called for help while shouting d) She shouted so that she could call for help Explanation: The cumulative conjunction used in the correct option given is ‘and’. Conjunctions which simply add one statement to another are called cumulative conjunctions. In the given question statement, we can see that two simple sentences are just placed one after another using the conjunction ‘and’ in between. 6. Combine the following set of simple sentences into one compound sentence. His gaze at me was long. It was intense. It startled me. a) His gaze at me was long and intense which startled me b) He intensely gazed at me for long time which startled me c) I was startled by his intensely long gaze at me d) His gaze at me was not only long and intense but also it startled me Explanation: The question statement given contains three simple sentences. Hence to combine them together two cumulative conjunctions are used which are ‘not only…but also’ and ‘and’. The compound sentence formed consists of the phrase ‘not only long and intense but also it startled me’. The use of ‘and’ in between signifies plural auxiliary. 7. Combine the following set of simple sentences into one compound sentence. The cafeteria was clean. It had a nice ambiance. a) The cafeteria was not only clean but also had a nice ambiance b) The cafeteria was clean having a nice ambiance c) The cafeteria being clean had a nice ambiance d) The cafeteria was clean hence it had a nice ambiance Explanation: The question statement deals with two simple sentences giving information about the similar object. Hence to join them together into a compound sentence the cumulative conjunction ‘not only…but also’ is used. This conjunction is generally used to add extra information to the sentence about the same thing. 8. Combine the following set of simple sentences into one compound sentence. The signal was given. The train left. a) The train left when the signal was given b) The signal was given and the train left c) The signal being given, the train left d) The train left after the signal was given Explanation: The two simple sentences mentioned in this question statement are combined together using the cumulative conjunction ‘and’ hence the answer being ‘signal was given and the train left’. 9. Combine the following set of simple sentences into one compound sentence. The dress was of silk. It had pearls stitched into it. a) The dress was of silk with pearls stitched into it b) Pearls were stitched into the silk dress c) The dress was of silk and had pearls stitched into it Explanation: The phrase mentioned in the answer statement given ‘dress was of silk and had pearls stitched’ contains the cumulative conjunction ‘and’. This particular conjunction is also used with a comma. When we add more than two words, comma is essential before ‘and’. 10. Combine the following set of simple sentences into one compound sentence. The journey was long. It was exhausting. a) The journey was long as well as exhausting b) The long journey was exhausting c) The journey was long hence it was exhausting d) The journey being long, was exhausting Explanation: The set of two sentences given in this question statement are simple sentences. To convert them into a compound, sentence the cumulative conjunction ‘as well as’ is used in the given answer statement. 11. Combine the following set of simple sentences into one compound sentence. The poet was praised for his work. He received a reward from the king. a) The poet was not only praised for his work but also received a reward from the king b) The poet received a reward from the king because he was praised for his work c) The poet being praised for his work, received a reward from the king d) The king gave a reward to the poet for his work which was praised Explanation: The two simple sentences given in this question statement can be converted into a compound sentence by using various kinds of conjunctions. But to convert them into a compound sentence using only a cumulative conjunction, the conjunction ‘not only…but also’ is used in the answer statement. 12. Combine the following set of simple sentences into one compound sentence. The smell was tempting. It was coming from the backyard. a) The smell coming from the backyard was tempting b) The smell coming which was coming from the backyard was tempting c) The smell was tempting and it was coming from the backyard d) The tempting smell came from the backyard Explanation: The answer statement containing the cumulative conjunction ‘and’ is the correct option because the remaining options have either no conjunctions in them (hence making them simple sentence) or have conjunction ‘which’ (not a cumulative conjunction). 13. Combine the following set of simple sentences into one compound sentence. She bought a burger. She bought a can of soda with it. a) She bought a burger as well as a can of soda b) She bought a burger with a can of soda c) She bought a burger which was accompanied by a can of soda with it d) A burger along with a can of soda were together bought by her Explanation: The cumulative conjunction mentioned in the correct option of this question statement is ‘as well as’ forming the dependent clause ‘bought a burger as well as a can of soda’ in the answer statement. This conjunction is generally used to indicate extra options or additional information. 14. Combine the following set of simple sentences into one compound sentence. The resort was expensive. It attracted many tourists. a) The resort was expensive yet it attracted many tourists b) The resort being expensive attracted many tourists c) The resort was not only expensive but also attracted many tourists d) The resort was expensive because it attracted many tourists Explanation: The cumulative conjunction used in the answer statement of this particular question is ‘not only…but also’. This conjunction is also called paired or correlative conjunction because it comes in a pair ‘not only’ and ‘but also’, and always relates one object to the other. 15. Combine the following set of simple sentences into one compound sentence. He was warned. He was restricted from entering the office. a) He was both warned and restricted from entering the office b) He was warned because of which he was restricted from entering the office c) After being warned, he was restricted from entering the office d) He was warned that is why he was restricted from entering the office Explanation: This particular question statement consists of two simple sentences which are merged into a single compound sentence by using the cumulative conjunction ‘Both….and’. This conjunction is also called paired or correlative conjunction and is used to create emphatic effect on referred elements. To practice all topics of English Grammar, here is complete set of 5000+ Questions and Answers. If you find a mistake in question / option / answer, kindly take a screenshot and email to [email protected]
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# Question: How To Make Absolute Value In Excel? ## How do you do absolute value in Excel? Create an Absolute Reference Select a cell, and then type an arithmetic operator (+, -, *, or /). Select another cell, and then press the F4 key to make that cell reference absolute. You can continue to press F4 to have Excel cycle through the different reference types. ## What is the absolute value symbol in Excel? In Excel, there is no absolute value symbol, but there is a special function for getting an absolute value – ABS function. Note. Excel absolute value should not be confused with absolute cell reference. The latter is a special form of a cell address that locks a reference to a given cell. ## How do you make a number absolute? The most common way to represent the absolute value of a number or expression is to surround it with the absolute value symbol: two vertical straight lines. 1. |6| = 6 means “the absolute value of 6 is 6.” 2. |–6| = 6 means “the absolute value of –6 is 6.” 3. |–2 – x| means “the absolute value of the expression –2 minus x.” You might be interested:  FAQ: Absolute Value How To Solve? ## How do you make a cell absolute in Excel without F4? If you’re running MAC, use the shortcut: ⌘ + T to toggle absolute and relative references. You can’t select a cell and press F4 and have it change all references to absolute. You need to have your marker placed inside the reference in the formula before it works when you hit the shortcut. ## How do you create an IF function in Excel? To enter your IF Function Arguments, 1. Click the spreadsheet cell where you wish to use the Excel formula. 2. From the Formulas tab, click Insert function … 3. In the Insert Function dialog text box, type “ if ”. 4. Make sure your cursor is in the Logical_test text box. 5. Click the spreadsheet cell you wish to evaluate. ## What is F4 in Excel? When you are typing your formula, after you type a cell reference – press the F4 key. Excel automatically makes the cell reference absolute! By continuing to press F4, Excel will cycle through all of the absolute reference possibilities. ## What is the absolute difference between two numbers? The absolute difference of two real numbers x, y is given by |x − y|, the absolute value of their difference. It describes the distance on the real line between the points corresponding to x and y. ## How do you make a value positive in Excel? In simple words, it will return a number after removing its sign. You just have to refer a negative number into the function and it will turn it into a positive value. In the below example, you have negative values from range A2:A11. Enter =ABS(A2) into B2 and drag it up to the last cell. You might be interested:  Often asked: How To Get The Absolute Value Of A Number? ## How do you type an absolute value symbol? To graph absolute value, you can type ” abs ” or use pipe brackets (near the top right corner of most keyboards). You can also use the absolute value symbol in the Desmos keyboard. ## How do you solve an absolute value equation step by step? SOLVING EQUATIONS CONTAINING ABSOLUTE VALUE (S) 1. Step 1: Isolate the absolute value expression. 2. Step2: Set the quantity inside the absolute value notation equal to + and – the quantity on the other side of the equation. 3. Step 3: Solve for the unknown in both equations.
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1. ## need help now!!!!! ok i am building a ported box for 1 15 and the dimensions are 35"L x 20"H x 20"D how wide and long of a port should i have if i wanna tune it to around 32-35 hrtz? 2. ## Re: need help now!!!!! What 15? What are the T/S parameters? Are those exterior dimensions? Is is 3/4" material? Or do this.......... Fb is the frequency you want the box tuned to........ Av is the cross-sectional area of the port (in square inches)........ Lv is the length of the port (in inches).......... and Vb is the enlcosure's net volume (in cubic inches). http://www.jlaudio.com/tutorials/ports/index.html/ 3. ## Re: need help now!!!!! its for an REaudio SX15 and those are the external dimensions and it is 3/4" i rerally dont understand what u put up so could u use simpler words 4. ## Re: need help now!!!!! Originally Posted by moses ok i am building a ported box for 1 15 and the dimensions are 35"L x 20"H x 20"D how wide and long of a port should i have if i wanna tune it to around 32-35 hrtz? Are you jsut cutting a port into an existing box? or is that the max room you have to work with? if your cutting a port into the box it starts to get complicated... becasue the port volume subtracts from the total volume of the box...... so is this cutting a port into a box, or are you building a box with that being the max dimensions? Fraz 5. ## Re: need help now!!!!! assuming .2ft^3 displacement for the sub, you can make a port that is 18.5 x 3 that is 15.71 inches long, and your box will be tuned to approx 33.23Hz 6. ## Re: need help now!!!!! yea im building a new box so i can make any port that u guys recommend but im still not sure if those are the dimensions i will use but i appretiate the help guys 7. ## Re: need help now!!!!! oh yea one more thing will a bigger port mean a lower tuning frequency or will it be a higher frequency? #### Posting Permissions • You may not post new threads • You may post replies • You may post attachments • You may edit your posts
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#### Study Material and Notes of Ch 12 Friction Class 8th Science Topics in the chapter • Introduction • Friction → Causes of Friction → Nature of surfaces of Friction → Friction when object is pressed hard → Friction according to mass of object → Examples where friction is useful → Examples where friction is harmful • Rolling Friction • Sliding Friction • Fluid Friction Introduction → The vehicles, any object, moving over the surface of another object slows down due to the force of friction applied on it. Friction → It is an opposing force that acts between surfaces in contact moving with respect to each other. → It always opposes relative motion between two surfaces. Cause of friction → Friction is cause by the irregularities on the two surfaces in contact. → We are able to walk because of the force of friction. Nature of surfaces for Friction Smooth surfaces: less friction Rough surfaces: greater friction Friction when object is pressed hard Greater pressing force means Greater friction. Friction according to mass of object Greater mass: Greater friction Sliding friction < Static friction Rolling friction < Sliding friction Examples where friction is useful (i) Walking (ii) Handling any object (iii) Rolling motion of ball or wheel Examples where friction is harmful (i) Energy dissipation of engine due to friction between surfaces in motion. (ii) More energy is lost in pulling or pushing an object in rough surfaces. (iii) Wear and tear of shoe soles and tyres. (iv) Lubrication: Powder on carom board, oil in machine (v) Wheel: Wheels reduce friction (because rolling friction < sliding friction). (vi) Shoe soles and tires are threaded to increase friction for a better grip. (vii) Fluid friction is minimised by giving suitable shapes to vehicles moving through fluids. Rolling Friction → When a body rolls over the surface of another body, the resistance to its motion is called rolling friction. Sliding Friction → When a body slides over the surface of another body, the resistance to its motion is called sliding friction. • Rolling friction < Sliding friction → Ball bearings change sliding friction into rolling friction. Fluid Friction → Fluid friction is minimised by giving suitable shapes to vehicles moving through fluids. • Fluid friction is also called drag. → Friction force depends upon the speed of the object with respect to the fluid. → Friction force depends upon the shape of the and nature of the fluid.
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# Search by Topic Filter by: Content type: Stage: Challenge level: ### The Legacy ##### Stage: 4 Challenge Level: Your school has been left a million pounds in the will of an ex- pupil. What model of investment and spending would you use in order to ensure the best return on the money? ### Funnel ##### Stage: 4 Challenge Level: A plastic funnel is used to pour liquids through narrow apertures. What shape funnel would use the least amount of plastic to manufacture for any specific volume ? ### Cola Can ##### Stage: 3 Challenge Level: An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height? ### Negative Power ##### Stage: 4 Challenge Level: What does this number mean ? Which order of 1, 2, 3 and 4 makes the highest value ? Which makes the lowest ? ### Minus One Two Three ##### Stage: 4 Challenge Level: Substitute -1, -2 or -3, into an algebraic expression and you'll get three results. 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# Propagation of Uncertainty $$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ ( \newcommand{\kernel}{\mathrm{null}\,}\) $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$ $$\newcommand{\vectorA}[1]{\vec{#1}} % arrow$$ $$\newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow$$ $$\newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vectorC}[1]{\textbf{#1}}$$ $$\newcommand{\vectorD}[1]{\overrightarrow{#1}}$$ $$\newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}}$$ $$\newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}}$$ $$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$ $$\newcommand{\avec}{\mathbf a}$$ $$\newcommand{\bvec}{\mathbf b}$$ $$\newcommand{\cvec}{\mathbf c}$$ $$\newcommand{\dvec}{\mathbf d}$$ $$\newcommand{\dtil}{\widetilde{\mathbf d}}$$ $$\newcommand{\evec}{\mathbf e}$$ $$\newcommand{\fvec}{\mathbf f}$$ $$\newcommand{\nvec}{\mathbf n}$$ $$\newcommand{\pvec}{\mathbf p}$$ $$\newcommand{\qvec}{\mathbf q}$$ $$\newcommand{\svec}{\mathbf s}$$ $$\newcommand{\tvec}{\mathbf t}$$ $$\newcommand{\uvec}{\mathbf u}$$ $$\newcommand{\vvec}{\mathbf v}$$ $$\newcommand{\wvec}{\mathbf w}$$ $$\newcommand{\xvec}{\mathbf x}$$ $$\newcommand{\yvec}{\mathbf y}$$ $$\newcommand{\zvec}{\mathbf z}$$ $$\newcommand{\rvec}{\mathbf r}$$ $$\newcommand{\mvec}{\mathbf m}$$ $$\newcommand{\zerovec}{\mathbf 0}$$ $$\newcommand{\onevec}{\mathbf 1}$$ $$\newcommand{\real}{\mathbb R}$$ $$\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}$$ $$\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}$$ $$\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}$$ $$\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}$$ $$\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$$ $$\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$$ $$\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$$ $$\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$$ $$\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}$$ $$\newcommand{\laspan}[1]{\text{Span}\{#1\}}$$ $$\newcommand{\bcal}{\cal B}$$ $$\newcommand{\ccal}{\cal C}$$ $$\newcommand{\scal}{\cal S}$$ $$\newcommand{\wcal}{\cal W}$$ $$\newcommand{\ecal}{\cal E}$$ $$\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}$$ $$\newcommand{\gray}[1]{\color{gray}{#1}}$$ $$\newcommand{\lgray}[1]{\color{lightgray}{#1}}$$ $$\newcommand{\rank}{\operatorname{rank}}$$ $$\newcommand{\row}{\text{Row}}$$ $$\newcommand{\col}{\text{Col}}$$ $$\renewcommand{\row}{\text{Row}}$$ $$\newcommand{\nul}{\text{Nul}}$$ $$\newcommand{\var}{\text{Var}}$$ $$\newcommand{\corr}{\text{corr}}$$ $$\newcommand{\len}[1]{\left|#1\right|}$$ $$\newcommand{\bbar}{\overline{\bvec}}$$ $$\newcommand{\bhat}{\widehat{\bvec}}$$ $$\newcommand{\bperp}{\bvec^\perp}$$ $$\newcommand{\xhat}{\widehat{\xvec}}$$ $$\newcommand{\vhat}{\widehat{\vvec}}$$ $$\newcommand{\uhat}{\widehat{\uvec}}$$ $$\newcommand{\what}{\widehat{\wvec}}$$ $$\newcommand{\Sighat}{\widehat{\Sigma}}$$ $$\newcommand{\lt}{<}$$ $$\newcommand{\gt}{>}$$ $$\newcommand{\amp}{&}$$ $$\definecolor{fillinmathshade}{gray}{0.9}$$ In Chapter 4 we considered the basic mathematical details of a propagation of uncertainty, limiting our treatment to the propagation of measurement error. This treatment is incomplete because it omits other sources of uncertainty that influence the overall uncertainty in our results. Consider, for example, Practice Exercise 4.2, in which we determined the uncertainty in a standard solution of Cu2+ prepared by dissolving a known mass of Cu wire with HNO3, diluting to volume in a 500-mL volumetric flask, and then diluting a 1-mL portion of this stock solution to volume in a 250-mL volumetric flask. To calculate the overall uncertainty we included the uncertainty in the sample's mass and the uncertainty of the volumetric glassware. We did not consider other sources of uncertainty, including the purity of the Cu wire, the effect of temperature on the volumetric glassware, and the repeatability of our measurements. In this appendix we take a more detailed look at the propagation of uncertainty, using the standardization of NaOH as an example. ## Standardizing a Solution of NaOH1 Because solid NaOH is an impure material, we cannot directly prepare a stock solution by weighing a sample of NaOH and diluting to volume. Instead, we determine the solution's concentration through a process called a standardization.2 A fairly typical procedure is to use the NaOH solution to titrate a carefully weighed sample of previously dried potassium hydrogen phthalate, C8H5O4K, which we will write here, in shorthand notation, as KHP. For example, after preparing a nominally 0.1 M solution of NaOH, we place an accurately weighed 0.4-g sample of dried KHP in the reaction vessel of an automated titrator and dissolve it in approximately 50 mL of water (the exact amount of water is not important). The automated titrator adds the NaOH to the KHP solution and records the pH as a function of the volume of NaOH. The resulting titration curve provides us with the volume of NaOH needed to reach the titration's endpoint.3 The end point of the titration is the volume of NaOH corresponding to a stoichiometric reaction between NaOH and KHP. $\ce{NaOH + C8H5O4K → C8H4O4- + K+ + Na+ + H2O}(l) \nonumber$ Knowing the mass of KHP and the volume of NaOH needed to reach the endpoint, we use the following equation to calculate the molarity of the NaOH solution. $\mathrm{C_{NaOH}}= \dfrac{1000 × m_\ce{KHP} × P_\ce{KHP}}{M_\ce{KHP} × V_\ce{NaOH}} \nonumber$ where CNaOH is the concentration of NaOH (in mol KHP/L), mKHP is the mass of KHP taken (in g), PKHP is the purity of the KHP (where PKHP = 1 means that the KHP is pure and has no impurities), MKHP is the molar mass of KHP (in g KHP/mol KHP), and VNaOH is the volume of NaOH (in mL). The factor of 1000 simply converts the volume in mL to L. ## Identifying and Analyzing Sources of Uncertainty Although it seems straightforward, identifying sources of uncertainty requires care as it easy to overlook important sources of uncertainty. One approach is to use a cause-and-effect diagram, also known as an Ishikawa diagram—named for its inventor, Kaoru Ishikawa—or a fish bone diagram. To construct a cause-and-effect diagram, we first draw an arrow pointing to the desired result; this is the diagram's trunk. We then add five main branch lines to the trunk, one for each of the four parameters that determine the concentration of NaOH and one for the method's repeatability. Next we add additional branches to the main branch for each of these five factors, continuing until we account for all potential sources of uncertainty. Figure A2.1 shows the complete cause-and-effect diagram for this analysis. Figure A2.1 Cause-and-effect diagram for the standardization of NaOH by titration against KHP. The trunk, shown in black, represents the the concentration of NaOH. The remaining arrows represent the sources of uncertainty that affect CNaOH. Light blue arrows, for example, represent the primary sources of uncertainty affecting CNaOH, and green arrows represent secondary sources of uncertainty that affect the primary sources of uncertainty. See the text for additional details. Before we continue, let's take a closer look at Figure A2.1 to be sure we understand each branch of the diagram. To determine the mass of KHP we make two measurements: taring the balance and weighing the gross sample. Each measurement of mass is subject to a calibration uncertainty. When we calibrate a balance, we are essentially creating a calibration curve of the balance's signal as a function of mass. Any calibration curve is subject to a systematic uncertainty in the y-intercept (bias) and an uncertainty in the slope (linearity). We can ignore the calibration bias because it contributes equally to both mKHP(gross) and mKHP(tare), and because we determine the mass of KHP by difference. $m_\textrm{KHP} = m_\textrm{KHP(gross)} - m_\textrm{KHP(tare)} \nonumber$ The volume of NaOH at the end point has three sources of uncertainty. First, an automated titrator uses a piston to deliver the NaOH to the reaction vessel, which means the volume of NaOH is subject to an uncertainty in the piston's calibration. Second, because a solution's volume varies with temperature, there is an additional source of uncertainty due to any fluctuation in the ambient temperature during the analysis. Finally, there is a bias in the titration's end point if the NaOH reacts with any species other than the KHP. Repeatability, R, is a measure of how consistently we can repeat the analysis. Each instrument we use—the balance and the automatic titrator—contributes to this uncertainty. In addition, our ability to consistently detect the end point also contributes to repeatability. Finally, there are no additional factors that affect the uncertainty of the KHP's purity or molar mass. ## Estimating the Standard Deviation for Measurements To complete a propagation of uncertainty we must express each measurement’s uncertainty in the same way, usually as a standard deviation. Measuring the standard deviation for each measurement requires time and may not be practical. Fortunately, most manufacture provides a tolerance range for glassware and instruments. A 100-mL volumetric glassware, for example, has a tolerance of ±0.1 mL at a temperature of 20oC. We can convert a tolerance range to a standard deviation using one of the following three approaches. Assume a Uniform Distribution. Figure A2.2a shows a uniform distribution between the limits of ±x, in which each result between the limits is equally likely. A uniform distribution is the choice when the manufacturer provides a tolerance range without specifying a level of confidence and when there is no reason to believe that results near the center of the range are more likely than results at the ends of the range. For a uniform distribution the estimated standard deviation, s, is $s = \dfrac{x}{\sqrt{3}} \nonumber$ This is the most conservative estimate of uncertainty as it gives the largest estimate for the standard deviation. Assume a Triangular Distribution. Figure A2.2b shows a triangular distribution between the limits of ±x, in which the most likely result is at the center of the distribution, decreasing linearly toward each limit. A triangular distribution is the choice when the manufacturer provides a tolerance range without specifying a level of confidence and when there is a good reason to believe that results near the center of the range are more likely than results at the ends of the range. For a uniform distribution the estimated standard deviation, s, is $s = \dfrac{x}{\sqrt 6} \nonumber$ This is a less conservative estimate of uncertainty as, for any value of x, the standard deviation is smaller than that for a uniform distribution. Assume a Normal Distribution. Figure A2.3c shows a normal distribution that extends, as it must, beyond the limits of ±x, and which is centered at the mid-point between –x and x. A normal distribution is the choice when we know the confidence interval for the range. For a normal distribution the estimated standard deviation, s, is $s = \dfrac{x}{z} \nonumber$ where z is 1.96 for a 95% confidence interval and 3.00 for a 99.7% confidence interval. Figure A2.2 Three possible distributions for estimating the standard deviation from a range: (a) a uniform distribution; (b) a triangular distribution; and (c) a normal distribution. ## Completing the Propagation of Uncertainty Now we are ready to return to our example and determine the uncertainty for the standardization of NaOH. First we establish the uncertainty for each of the five primary sources—the mass of KHP, the volume of NaOH at the end point, the purity of the KHP, the molar mass for KHP, and the titration’s repeatability. Having established these, we can combine them to arrive at the final uncertainty. Uncertainty in the Mass of KHP. After drying the KHP, we store it in a sealed container to prevent it from readsorbing moisture. To find the mass of KHP we first weigh the container, obtaining a value of 60.5450 g, and then weigh the container after removing a portion of KHP, obtaining a value of 60.1562 g. The mass of KHP, therefore, is 0.3888 g, or 388.8 mg. To find the uncertainty in this mass we examine the balance’s calibration certificate, which indicates that its tolerance for linearity is ±0.15 mg. We will assume a uniform distribution because there is no reason to believe that any result within this range is more likely than any other result. Our estimate of the uncertainty for any single measurement of mass, u(m), is $u(m) = \mathrm{\dfrac{0.15\: mg}{\sqrt 3} = 0.09\: mg} \nonumber$ Because we determine the mass of KHP by subtracting the container’s final mass from its initial mass, the uncertainty of the mass of KHP u(mKHP), is given by the following propagation of uncertainty. $u(m_\ce{KHP}) = \mathrm{\sqrt{(0.09\: mg)^2 + (0.09\: mg)^2} = 0.13\: mg} \nonumber$ Uncertainty in the Volume of NaOH. After placing the sample of KHP in the automatic titrator’s reaction vessel and dissolving with water, we complete the titration and find that it takes 18.64 mL of NaOH to reach the end point. To find the uncertainty in this volume we need to consider, as shown in Figure A2.1, three sources of uncertainty: the automatic titrator’s calibration, the ambient temperature, and any bias in determining the end point. To find the uncertainty resulting from the titrator’s calibration we examine the instrument’s certificate, which indicates a range of ±0.03 mL for a 20-mL piston. Because we expect that an effective manufacturing process is more likely to produce a piston that operates near the center of this range than at the extremes, we will assume a triangular distribution. Our estimate of the uncertainty due to the calibration, u(Vcal) is $u(V_\ce{cal}) = \mathrm{\dfrac{0.03\: mL}{\sqrt 6} = 0.012\: mL} \nonumber$ To determine the uncertainty due to the lack of temperature control, we draw on our prior work in the lab, which has established a temperature variation of ±3oC with a confidence level of 95%. To find the uncertainty, we convert the temperature range to a range of volumes using water’s coefficient of expansion $\mathrm{(2.1×10^{−4}{^\circ C}^{−1}) × (±3^\circ C) × 18.64\: mL = ±0.012\: mL} \nonumber$ and then estimate the uncertainty due to temperature, u(Vtemp) as $u(V_\ce{temp}) = \mathrm{\dfrac{0.012\: mL}{1.96} = 0.006\: mL} \nonumber$ Titrations using NaOH are subject to a bias due to the adsorption of CO2, which can react with OH, as shown here. $\ce{CO2}(aq) + \ce{2OH-}(aq) → \ce{CO3^2-}(aq) + \ce{H2O}(l) \nonumber$ If CO2 is present, the volume of NaOH at the end point includes both the NaOH reacting with the KHP and the NaOH reacting with CO2. Rather than trying to estimate this bias, it is easier to bathe the reaction vessel in a stream of argon, which excludes CO2 from the titrator’s reaction vessel. Adding together the uncertainties for the piston’s calibration and the lab’s temperature fluctuation gives the uncertainty in the volume of NaOH, u(VNaOH) as $u(V_\ce{NaOH}) = \mathrm{\sqrt{(0.012\: mL)^2 + (0.006\: mL)^2} = 0.013\: mL} \nonumber$ Uncertainty in the Purity of KHP. According to the manufacturer, the purity of KHP is 100% ± 0.05%, or 1.0 ± 0.0005. Assuming a rectangular distribution, we report the uncertainty, u(PKHP) as $u(P_\ce{KHP}) = \dfrac{0.0005}{\sqrt 3} = 0.00029 \nonumber$ Uncertainty in the Molar Mass of KHP. The molar mass of C8H5O4K is 204.2212 g/mol, based on the following atomic weights: 12.0107 for carbon, 1.00794 for hydrogen, 15.9994 for oxygen, and 39.0983 for potassium. Each of these atomic weights has an quoted uncertainty that we can convert to a standard uncertainty assuming a rectangular distribution, as shown here (the details of the calculations are left to you). element quoted uncertainty standard uncertainty carbon ±0.0008 ±0.00046 hydrogen ±0.00007 ±0.000040 oxygen ±0.0003 ±0.00017 potassium ±0.0001 ±0.000058 Adding together the uncertainties gives the uncertainty in the molar mass, u(MKHP), as $u(M_\ce{KHP}) = \mathrm{\sqrt{8 × (0.00046)^2 + 5 × (0.000040)^2 + 4 × (0.00017)^2 + (0.000058)} = 0.0038\: g/mol} \nonumber$ Uncertainty in the Titration’s Repeatability. To estimate the uncertainty due to repeatability we complete five titrations, obtaining results for the concentration of NaOH of 0.1021 M, 0.1022 M, 0.1022 M, 0.1021 M, and 0.1021 M. The relative standard deviation, sr, for these titrations is $s_\ce{r} = \dfrac{5.477×10^{-5}}{0.1021} = 0.0005 \nonumber$ If we treat the ideal repeatability as 1.0, then the uncertainty due to repeatability, u(R), is equal to the relative standard deviation, or, in this case, 0.0005. Combining the Uncertainties. Table A2.1 summarizes the five primary sources of uncertainty. As described earlier, we calculate the concentration of NaOH we use the following equation, which is slightly modified to include a term for the titration’s repeatability, which, as described above, has a value of 1.0. Table A2.1 Values and Uncertainties for the Standardization of NaOH source value, x uncertainty, u(x) mKHP mass of KHP 0.3888 g 0.00013 g VNaOH volume of NaOH at end point 18.64 mL 0.013 mL PKHP purity of KHP 1.0 0.00029 MKHP molar mass of KHP 204.2212 g/mol 0.0038 g/mol R repeatability 1.0 0.0005 $\mathrm{C_{NaOH}} = \dfrac{1000 × m_\ce{KHP}× P_\ce{KHP}}{M_\ce{KHP}× V_\ce{NaOH}} × R \nonumber$ Using the values from Table A2.1, we find that the concentration of NaOH is $C_\ce{NaOH} = \dfrac{1000 × 0.3888 × 1.0}{204.2212 × 18.64} × 1.0 = \mathrm{0.1021\: M} \nonumber$ Because the calculation of CNaOH includes only multiplication and division, the uncertainty in the concentration, u(CNaOH) is given by the following propagation of uncertainty. $\dfrac{u(C_\ce{NaOH})}{C_\ce{NaOH}}= \dfrac{u(C_\ce{NaOH})}{0.1021\: \ce M} = \sqrt{\dfrac{(0.00013)^2}{(0.3888)^2} + \dfrac{(0.00029)^2}{(1.0)^2} + \dfrac{(0.0038)^2}{(204.2212)^2} + \dfrac{(0.013)^2}{(18.64)^2} + \dfrac{(0.0005)^2}{(1.0)^2}} \nonumber$ Solving for u(CNaOH) gives its value as ±0.00010 M, which is the final uncertainty for the analysis. ## Evaluating the Sources of Uncertainty Figure A2.3 shows the relative uncertainty in the concentration of NaOH and the relative uncertainties for each of the five contributions to the total uncertainty. Of the contributions, the most important is the volume of NaOH, and it is here to which we should focus our attention if we wish to improve the overall uncertainty for the standardization. Figure A2.3 Bar graph showing the relative uncertainty in CNaOH, and the relative uncertainty in each of the main factors affecting the overall uncertainty. ## References 1. This example is adapted from Ellison, S. L. R.; Rosslein, M.; Williams, A. EURACHEM/CITAC Guide: Quantifying Uncertainty in Analytical Measurement, 2nd Edition, 2000 (available at http://www.measurementuncertainty.org/). 2. See Chapter 5 for further details about standardizations. 3. For further details about titrations, see Chapter 9.
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CentiServer comprehensive centrality resource and server for centralities calculation version: 1.0.0 The Centiserver on OMICTools  # Subgraph Centrality #### Definition Accounts for the participation of a node in all sub graphs of the network. the number of closed walks of length k starting and ending node v in the network is given by the local spectral moments μk(v). The subgraph centrality is just the diagonal entry of the exponential of the adjacency matrix. Notice that this is not the matrix in which you rise every entry to the exponential. In Matlab there is a function that compute this. For A being the adjacency matrix the function is expm(A) and the subgraph centrality of the nodes is diag(expm(A)). According to eigenvectors and eigenvalues, if the adjacency matrix is symmetric. Let phi_j(p) be the pth entry of the jth eigenvactor associated with eigenvalue lambda_j of the matrix A. The subgraph centrality is then: SC(p) = SUM (phi_j(p)^2*exp(lambda_j) where SUM is the sum over j to n (the number of nodes in the network). (with thanks to Ernesto Estrada) Subgraph centrality (SC) of a node is a weighted sum of the numbers of all closed walks of different lengths in the network starting and ending at the node. These closed walks are related to partial subgraphs of a network, e.g., a closed walk with four nodes can ‘‘go through’’ different subgraphs on four nodes, such as along the same edge AB twice (as described above: from node A to node B along edge AB, then back to A along the same edge and then again from A to B and back to A along the same edge), or along a 4-node cycle ABCD that includes edge AB (along the ‘‘square’’ from node A to node B to node C to node D and back to A; this is regardless of whether edges CA and DB that ‘‘go along the diagonal of the square’’ exist) etc. The above mentioned sum is weighted so that the contribution of the closed walks decreases as the length of the walks increases, i.e., shorter walks (smaller subgraphs) have higher weight [MILENKOVIĆ, T., 2011]. Let G=(V,E) be a simple undirected graph with n nodes and let λ1≤λ2≤⋯λn be a non-increasing ordering of the eigenvalues of its adjacency matrix A. The Estrada index is: [A HAGBERG, D. S., 2008, ESTRADA, E. 2000] Communicability centrality, also called subgraph centrality, of a node n is the sum of closed walks of all lengths starting and ending at node n. [A HAGBERG, 2008] #### Requirements Require undirected and loop free network. #### References • A HAGBERG, D. S., P SWART. Exploring Network Structure, Dynamics, and Function using NetworkX. In: G VAROQUAUX, T. V., J MILLMAN, ed. Proceedings of the 7th Python in Science conference (SciPy 2008), 2008. 11-15. • CSARDI, G. & NEPUSZ, T. 2006. The igraph software package for complex network research. InterJournal, Complex Systems, 1695. [http://igraph.org] • ESTRADA, E. 2000. Characterization of 3D molecular structure. Chemical Physics Letters, 319, 713-718. • ESTRADA, E. & RODRIGUEZ-VELAZQUEZ, J. A. 2005. Subgraph centrality in complex networks. Physical Review E, 71, 056103. • MILENKOVIĆ, T., MEMIŠEVIĆ, V., BONATO, A. & PRŽULJ, N. 2011. Dominating Biological Networks. PLoS ONE, 6, e23016. error If the graph is not undirected and simple (networkX)
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## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition) The expression is undefined if $x=-\frac{1}{3}$ A fraction is undefined, if the denominator equals to zero. Here: $3x+1=0$ $3x=-1$ $x=-\frac{1}{3}$ The expression is undefined if $x=-\frac{1}{3}$
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# How do I find an isomorphism between Sn+m and Zn x Zm? ## Main Question or Discussion Point How do I find an isomorphism between Sn+m and Zn x Zm? provided n,m are not relatively prime? Thanks. Related Linear and Abstract Algebra News on Phys.org AKG Homework Helper I dunno, place an ad in the classifieds, put up posters, etc. Or maybe start by defining what you even mean by Sn+m, because in the standard notation, Sn+m is a group that's generally not isomorphic to Zn x Zm. Also, post this in the homework section, follow the guidelines for posting homework, and when you start a new thread in the homework section, use the template that will be given to you. Hi, this isn't exactly a homework question... Anyways, rereading my question again, I made a mistake. It should be how do I find an isomorphism between A SUBGROUP in Sn+m and Zn x Zm. If it is specific cases like n,m = 2,2 I can figure it out. But how do I figure out a general form for the isomorphism? StatusX Homework Helper If there are two subgroups H and K of a group G such that the intersection of H and K is trivial and hk=kh for all h in H, k in K, then the subgroup HK is isomorphic to HxK. ah, thanks, I think I have it figured out now!
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14,209,465 members Tip/Trick Posted 19 Aug 2010 81.8K views 14 bookmarked # Converting numbers to the word equivalent. , Rate this: 12 May 2013     CPOL If your tutor asks you to convert numbers to words (i.e. 565 to a string "Five hundred and sixty-five") then you are not alone! Here is the simplest, most foolproof way to do it. If your tutor asks you to convert numbers to words (i.e. 565 to a string "Five hundred and sixty-five") then you are not alone! This question gets asked here very frequently, so here is the simple, foolproof way to solve your problem. It shows the outline of how to do it, and it is then up to you to fill in the detail, comments etc. - otherwise every-bodies would look the same, and you might get caught for copying! ```public static string ConvertToWords(int number) { switch (number) { case 0: return "Zero"; case 1: return "One"; ... case 568: return "Five hundred and sixty-eight"; case 569: return "Five hundred and sixty-nine"; } throw new ArgumentOutOfRangeException("Number greater than infinity!"); } ``` I cannot remember who originally posted this coding gem, and I can't find it with a quick search, but if you know who did post it let me know and I will provide full credit. The original version of this software was written by Smithers-Jones[^] in C++ and is available here[^] My thanks for the inspiration and the excellent work! I am indebted to Luc Pattyn for pointing out the error in versions before V3.0 regarding the placement of a hyphen between the tens and unit digits. He correctly pointed out here[^] that numbers should not be written as "twenty one" but as "twenty-one". V2.0: Credit for original version added - OriginalGriff[/edit] V3.0: Corrected the hyphenation between the tens digit and the units digit - OriginalGriff[/edit] V4.0: Link to the message of Luc Pattyn corrected - ProgramFOX[/edit] ## Share CEO Wales Born at an early age, he grew older. At the same time, his hair grew longer, and was tied up behind his head. Has problems spelling the word "the". Invented the portable cat-flap. Currently, has not died yet. Or has he? FirstPrev Next You misspelled sixty-eight and sixty-nine and forgot to use ... Ennis Ray Lynch, Jr.19-Aug-10 3:16 Ennis Ray Lynch, Jr. 19-Aug-10 3:16 You can improve it a bit though - forgot about negative numb... Svetlin Panayotov19-Aug-10 3:15 Svetlin Panayotov 19-Aug-10 3:15 Reason for my vote of 5 So brilliant and simple! There's eve... Svetlin Panayotov19-Aug-10 3:13 Svetlin Panayotov 19-Aug-10 3:13 I'd like to see some unit tests, your method seems a bit err... Luc Pattyn19-Aug-10 2:54 Luc Pattyn 19-Aug-10 2:54 Reason for my vote of 5 Good one! :D Nuri Ismail19-Aug-10 2:47 Nuri Ismail 19-Aug-10 2:47 Reason for my vote of 5 Lost for words. Can you translate th... R. Giskard Reventlov19-Aug-10 2:42 R. Giskard Reventlov 19-Aug-10 2:42 Reason for my vote of 5 Excellent! hammerstein0519-Aug-10 2:35 hammerstein05 19-Aug-10 2:35 Reason for my vote of 5 Fantastic! :) LittleYellowBird19-Aug-10 2:20 LittleYellowBird 19-Aug-10 2:20 Reason for my vote of 5 Fantastic! Reason for my vote of 5 Funny linuxjr19-Aug-10 2:18 linuxjr 19-Aug-10 2:18 Reason for my vote of 5 Good one!!! Johnny J.19-Aug-10 2:09 Johnny J. 19-Aug-10 2:09 Reason for my vote of 5 Does it work just for the English la... CPallini19-Aug-10 2:04 CPallini 19-Aug-10 2:04 Reason for my vote of 5 funny Peter Mulholland19-Aug-10 2:01 Peter Mulholland 19-Aug-10 2:01 "no good - swjam" Swjam - are you saying it does not work? A... OriginalGriff19-Aug-10 1:58 OriginalGriff 19-Aug-10 1:58 Re: "no good - swjam"Swjam - are you saying it does not work? A... swjam8-Aug-12 3:13 swjam 8-Aug-12 3:13 Reason for my vote of 1 no good swjam19-Aug-10 1:55 swjam 19-Aug-10 1:55 Reason for my vote of 5 Because it's genius! Mark_Wallace19-Aug-10 1:48 Mark_Wallace 19-Aug-10 1:48 This looks good, but how do you handle negative numbers? :) Chris Meech19-Aug-10 1:46 Chris Meech 19-Aug-10 1:46 5 Points for being Original, Funny, Sarcastic and Ironic in ... Dalek Dave19-Aug-10 1:42 Dalek Dave 19-Aug-10 1:42 AWESOME! MY HERO! `leppie`19-Aug-10 1:39 `leppie` 19-Aug-10 1:39 Last Visit: 17-Jun-19 23:20     Last Update: 17-Jun-19 23:20 Refresh « Prev123
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# . If A.s income is 20% more than B. Then B.s income is 1. Same as A.s 2. 20% less than A.s 3. 16 2/3% less than A.s 4. 15% less than A.s
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Community Profile # MOHIT ### IIT DELHI 48 total contributions since 2015 View details... Contributions in View by Solved Back to basics 21 - Matrix replicating Covering some basic topics I haven't seen elsewhere on Cody. Given an input matrix, generate an output matrix that consists o... 1년 이상 ago Solved Back and Forth Rows Given a number n, create an n-by-n matrix in which the integers from 1 to n^2 wind back and forth along the rows as shown in the... 1년 이상 ago Solved Select every other element of a vector Write a function which returns every other element of the vector passed in. That is, it returns the all odd-numbered elements, s... 1년 이상 ago Solved Determine given vector is even or odd Find the numbers of the input vector is odd or even then replace even with 1 and odd with 0 Example x = [ 3 3 4 6 1] ... 1년 이상 ago Solved Array of Ones Create a 100 X 100 array of ones. 1년 이상 ago Solved Number of digits in an integer Specifies how many digits in a given integer. Example: in=100 ==> out=3 1년 이상 ago Solved multiply by three Given the variable x as your input, multiply it by 3 and put the result equal to y. Examples: Input x = 2 Output y is ... 1년 이상 ago Solved Is my wife right? Regardless of input, output the string 'yes'. 1년 이상 ago Solved Is this triangle right-angled? Given any three positive numbers a, b, c, return true if the triangle with sides a, b and c is right-angled. Otherwise, return f... 1년 이상 ago Solved Find a Pythagorean triple Given four different positive numbers, a, b, c and d, provided in increasing order: a < b < c < d, find if any three of them com... 1년 이상 ago Solved Triangle sequence A sequence of triangles is constructed in the following way: 1) the first triangle is Pythagoras' 3-4-5 triangle 2) the s... 1년 이상 ago Solved Is this triangle right-angled? Given three positive numbers a, b, c, where c is the largest number, return *true* if the triangle with sides a, b and c is righ... 1년 이상 ago Solved Area of an Isoceles Triangle An isosceles triangle has equal sides of length x and a base of length y. Find the area, A, of the triangle. <<http://upload... 1년 이상 ago Solved Side of a rhombus If a rhombus has diagonals of length x and x+1, then what is the length of its side, y? <<http://upload.wikimedia.org/wikipe... 1년 이상 ago Solved Side of an equilateral triangle If an equilateral triangle has area A, then what is the length of each of its sides, x? <<http://upload.wikimedia.org/wikipe... 1년 이상 ago Solved Area of an equilateral triangle Calculate the area of an equilateral triangle of side x. <<http://upload.wikimedia.org/wikipedia/commons/e/e0/Equilateral-tr... 1년 이상 ago Solved Length of the hypotenuse Given short sides of lengths a and b, calculate the length c of the hypotenuse of the right-angled triangle. <<http://upload.... 1년 이상 ago Solved Length of a short side Calculate the length of the short side, a, of a right-angled triangle with hypotenuse of length c, and other short side of lengt... 1년 이상 ago Solved Pizza! Given a circular pizza with radius _z_ and thickness _a_, return the pizza's volume. [ _z_ is first input argument.] Non-scor... 1년 이상 ago Solved Who Has the Most Change? You have a matrix for which each row is a person and the columns represent the number of quarters, nickels, dimes, and pennies t... 1년 이상 ago Solved Swap the first and last columns Flip the outermost columns of matrix A, so that the first column becomes the last and the last column becomes the first. All oth... 1년 이상 ago Solved Column Removal Remove the nth column from input matrix A and return the resulting matrix in output B. So if A = [1 2 3; 4 5 6]; and ... 1년 이상 ago Solved Triangle Numbers Triangle numbers are the sums of successive integers. So 6 is a triangle number because 6 = 1 + 2 + 3 which can be displa... 1년 이상 ago Solved Make a checkerboard matrix Given an integer n, make an n-by-n matrix made up of alternating ones and zeros as shown below. The a(1,1) should be 1. Examp... 1년 이상 ago Solved Determine if input is odd Given the input n, return true if n is odd or false if n is even. 1년 이상 ago how can i use plot functions? they are all unvariable. 1년 이상 ago | 0 Question How can we get bluetooth signal strength? I want to know the strength of available Bluetooth signal. 약 2년 ago | 0 answers | 0 ### 0 Solved Times 2 - START HERE Try out this test problem first. Given the variable x as your input, multiply it by two and put the result in y. Examples:... 2년 이상 ago Question How can I convert known GPS coordinates to image pixels, and again image pixels to world GPS coordinates? I have few known points in an image and same points I have as GPS coordinates also. How can I georeference my image to get all p... 2년 이상 ago | 1 answer | 0 ### 1 Question I have an input matrix of 17X4 and output matrix of 17X8, is there any method to fit regression with these many input and outputs together? A problem with multiple input and multiple output regression 2년 이상 ago | 1 answer | 0
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This is documentation for Mathematica 6, which was based on an earlier version of the Wolfram Language. # ChiSquareDistribution represents a distribution with degrees of freedom. • The probability density for value x in a distribution is proportional to for , and is zero for . » • For integer , the distribution with degrees of freedom gives the distribution of sums of squares of values sampled from a normal distribution. The mean and variance of a distribution: Out[1]= Out[2]= Probability density function: Out[1]= Out[2]= Scope   (4) Applications   (3) New in 6
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