question stringlengths 200 50k | answer stringclasses 1
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14011 (number)
14,011 (fourteen thousand eleven) is an odd five-digits prime number following 14010 and preceding 14012. In scientific notation, it is written as 1.4011 × 104. The sum of its digits is 7. It has a total of 1 prime factor and 2 positive divisors. There are 14,010 positive integers (up to 14011) that are... | HuggingFaceTB/finemath | |
# Intuitive proofs that $\lim\limits_{n\to\infty}\left(1+\frac xn\right)^n=e^x$
At this link someone asked how to prove rigorously that $$\lim_{n\to\infty}\left(1+\frac xn\right)^n = e^x.$$
What good intuitive arguments exist for this statement?
Later edit: . . . where $e$ is defined as the base of an exponential fu... | HuggingFaceTB/finemath | |
# Root system
In mathematics, a root system is a configuration of vectors in a Euclidean space satisfying certain geometrical properties. The concept is fundamental in the theory of Lie groups and Lie algebras. Since Lie groups (and some analogues such as algebraic groups) and Lie algebras have become important in man... | open-web-math/open-web-math | |
# Find function such that $\sum y_i\le\sum x_i\Rightarrow\sum f(y_i)\le\sum f(x_i)$
What kind of a function $f$ must be to satisfy the following?
If $\sum_{i=1}^{n} y_i \leq \sum_{j=1}^{n} x_j$, where $x_j, y_i \in [0,1],\forall i,j$ then $$\sum_{i=1}^{n} f(y_i) \leq \sum_{j=1}^{n} f(x_j).$$
Any help would be apprec... | open-web-math/open-web-math | |
# How to Find Volume and Surface Area of Cubes? (+FREE Worksheet!)
Here you can learn how to find the volume and surface area of cubes using cubes volume and surface area formulas.
## Step-by-step guide to finding the Volume and Surface Area of Cubes
• A cube is a three-dimensional solid object bounded by six square... | HuggingFaceTB/finemath | |
# Find area
Find area of a rectangle with a length of 58 foot and a width of 49 foot?
A = 2842 ft2
### Step-by-step explanation: Did you find an error or inaccuracy? Feel free to write us. Thank you! #### You need to know the following knowledge to solve this word math problem:
We encourage you to watch this tutor... | HuggingFaceTB/finemath | |
# pubdoc_11_17592_1700
advertisement
```Lec(4)
College of sciences for women ((())) Dept. of computer sciences
Year 2014-2015
Computer graphic
3nd stage
18-11-2014
Introduction to computer algorithm :
Before getting started in computer graphics algorithms we need
to know what the term 'computer algorithm' means. An
al... | HuggingFaceTB/finemath | |
# ANALOGY
Let us first try to define analogy: the word ‘Analogy' means 'correspondence/ similarity’. In analogy questions, a specific relationship is given & another similar relationship has to be identified from the given options.
Types of Analogies
In reasoning, generally we come across two types of analogies: Alph... | HuggingFaceTB/finemath | |
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The October issue of the Notices of the Amer. Math. Soc. has an article about the OEIS.
Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
A208720 Number of n-bead necklaces labeled with numbers 1..7 allowing reversal, with no adjacent b... | HuggingFaceTB/finemath | |
Understand the problem
Show that among all quadrilaterals of a given perimeter the square has the largest area.
Source of the problem
Indian National Mathematical Olympiad 1986
Geometry
Easy
Suggested Book
An Excursion in Mathematics
Do you really need a hint? Try it first!
Start with a quadrilateral with sides $a,... | HuggingFaceTB/finemath | |
Excel statistical functions: LOGEST
Note
Office 365 ProPlus is being renamed to Microsoft 365 Apps for enterprise. For more information about this change, read this blog post.
Summary
This article describes the LOGEST function in Microsoft Office Excel 2003 and in later versions of Excel. It illustrates how the fun... | HuggingFaceTB/finemath | |
# Gravitational constant
The gravitational constant $~G\;$ is a fundamental physical constant, a gravitational interaction constant.
## Introduction
According to the Newton's law of universal gravitation, the force of gravitational attraction between two material points with gravitational masses m1 and m2, which are... | HuggingFaceTB/finemath | |
# Let $f:\mathbb R \to \mathbb R$ be continuous. Then which of the following statements implies that $f(0)=0$?
Let $f:\mathbb R \to \mathbb R$ be continuous. Then which of the following statements implies that $f(0)=0$?
(A)$\lim_{n \to \infty}\int_{0}^{1}f(x)^n dx=0.$
(B)$\lim_{n \to \infty}\int_{0}^{1}f(x/n) dx=0.$... | HuggingFaceTB/finemath | |
Anda di halaman 1dari 2
Miss Hopkins: Lesson Plan for the Week of October 6-10, 2014
Page 1 of 2
Monday Tuesday Wednesday Thursday Friday
Objectives SWBAT:
Divide decimals
TEKS:
6.3E Multiply an
divide positive
rational numbers
fluently
SWBAT:
Divide decimals
TEKS:
6.3E Multiply an
divide positive
rational numbers
f... | HuggingFaceTB/finemath | |
# PID math demystified, part 2
## You’ve see the equations, but have you thought about how those elements work together? Part 2: Adding integral and derivative to the mix.
05/13/2013
Last week we started with proportional. (Read Part 1) Now let’s look at the next part of the equation, the integral component:
The mo... | HuggingFaceTB/finemath | |
# Math Help- Gr12
The relation between the # of time in days, D, it takes for a planet to revolve around the Sun is related to the planer's average distance from the Sun, k, in millions of kilometres is defined by log D= 3/2logk-0.7 .
How much longer does it take Mars than
Venus to orbit the Sun if Mars is 207 millio... | HuggingFaceTB/finemath | |
# Basic Sampling Concepts
## Presentation on theme: "Basic Sampling Concepts"— Presentation transcript:
Basic Sampling Concepts
SADC Course in Statistics Basic Sampling Concepts (Session 02)
Learning Objectives By the end of this session, you will be able to
describe what is meant by sample, target population, sampl... | HuggingFaceTB/finemath | |
Earth's Rotational Speed ```Name: Lori Status: Student Age: 40s Location: N/A Country: N/A Date: N/A ``` Question: What is the earth's rotational speed at different points on the globe? What formula can I use to determine it? Replies: To answer the question you are asking is trivially easy. The question I think you mea... | HuggingFaceTB/finemath | |
0
# What is 8x2 y x3 y2 5y?
Updated: 12/19/2022
Wiki User
11y ago
Assumption 8x2 = eight times x squared
Assumption: x3 is x to the third
Assumption: y2 is y squared
Answer 40 y to the fourth x to the fifth = 40 y4 x5
Wiki User
11y ago | HuggingFaceTB/finemath | |
# 74.17 kg to lbs - 74.17 kilograms to pounds
Do you want to learn how much is 74.17 kg equal to lbs and how to convert 74.17 kg to lbs? Here it is. This whole article is dedicated to kilogram to pound conversion - theoretical and also practical. It is also needed/We also want to emphasize that whole this article is d... | HuggingFaceTB/finemath | |
Surfstat.australia: an online text in introductory Statistics
# SUMMARISING AND PRESENTING DATA
## MEASURES OF CENTRAL TENDENCY ("Averages")
A measure of central tendency is a number which indicates the middle of the distribution of data values. The three main measures are the median, the mode and the mean.
### Med... | HuggingFaceTB/finemath | |
Free Algebra Tutorials!
Try the Free Math Solver or Scroll down to Tutorials!
Depdendent Variable
Number of equations to solve: 23456789
Equ. #1:
Equ. #2:
Equ. #3:
Equ. #4:
Equ. #5:
Equ. #6:
Equ. #7:
Equ. #8:
Equ. #9:
Solve for:
Dependent Variable
Number of inequalities to solve: 23456789
In... | HuggingFaceTB/finemath | |
# Can You Write An Equation In Standard Form For A Line Passing Through The Pair Of Points: (5,-4) And (0,-7)?
The 2-point form of the equation for a line is
(y - y1) = ((y2 - y1)/(x2 - x1))*(x - x1)
Let (x1, y1) = (5, -4); (x2, y2) = (0, -7). Then we have
y -(-4) = ((-7 - (-4))/(0 - 5))*(x - 5) (plug in the numbe... | HuggingFaceTB/finemath | |
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# Resistance of a wire
Extracts from this document...
Introduction
## Resistance of a wire
Background Information
What is resistance?
Resistance is anything that c... | HuggingFaceTB/finemath | |
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# A 1.80-kg connecting rod from a car engine is pivoted IS... | HuggingFaceTB/finemath | |
#### Eulia
##### New Member
I'm struggling with these two problems, i'll really appreciate any help, thanks in advance = )
1) Obtain the probablility, by counting, of each possible sample if a random sample of size 2 is taken from
a. a finite population of size 3
b. a finite population of size 4
2) The mean of a rand... | HuggingFaceTB/finemath | |
How is hyperconjugation into antibonding orbitals stabilizing?
So I learned that hyperconjugation is electron delocalization from a $\ce{C-H}$ $\unicode[Times]{x3C3}$ bond into an empty p orbital (on a carbocation for example) or an antibonding orbital. I get how it's stabilizing in the case of an empty p orbital, but... | open-web-math/open-web-math | |
# The Rule of 72
The rule of 72 is an arithmetic trick that helps you understand compound growth. It will not make you intuitive but it will help you to understand when to look deeper.
Here’s how it works. The time until money doubles under a constant rate of interest (growth) is approximately 72 divided by the int... | HuggingFaceTB/finemath | |
How to derive consumer expenditures in EMEA 14.2.5
I am working on a problem 14.2.5 from EMEA by Sydsaeter, Hammond and Strom.
Consider the consumer demand problem: $$\max_{x,y} U(x,y) = \alpha \ln(x-a) + \beta \ln(y-b) \text{ s.t. } px+qy=m \tag{*}$$ where $$\alpha, \beta, a, b, p, q$$ and $$m$$ are positive constan... | HuggingFaceTB/finemath | |
# Trig
posted by .
cos45cos25 - sin 45sin25 = ??
a. cos70
b. sin70
c. cos 20
d. sin 20
• Trig -
cos a cos b - sin a sin b = cos(a+b)
= cos 70
## Similar Questions
1. ### trig
Reduce the following to the sine or cosine of one angle: (i) sin145*cos75 - cos145*sin75 (ii) cos35*cos15 - sin35*sin15 Use the formulae: ... | HuggingFaceTB/finemath | |
# Physics Course/Oscillation/Oscillation Up and Down
## The Oscillation up and down of a Spring ]]
When apply a force on an object of mass attach to a spring . The spring will move a distance y above and below the equilibrium point and this movement keeps on repeating itself for a period of time . The movement up and... | HuggingFaceTB/finemath | |
# You asked: What is the mole of 18 gm of water molecule?
Contents
To calculate the number of molecules we first have to calculate, the number of moles. And one mole consists of about 6.02×1023 molecules. – We can say that 18 grams of water means same as 1 mole of water , and in this NA Avogadro number of water molec... | HuggingFaceTB/finemath | |
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Pictorial Representation of Data
Poly... | HuggingFaceTB/finemath | |
Engineering Mechanics: Statics & Dynamics (14th Edition)
$\omega_A=32 rad/s$
We can determine the required angular velocity as follows: We know that $\vec{v_B}=\vec{v_E}+\vec{\omega_A}\times \vec{r_{B/E}}~~$[eq(1)] The velocity of $E$ is given as $\vec{v_E}=\vec{\omega_{B}}\times \vec{r_E}$ $\implies \vec{v_E}=2\hat k... | open-web-math/open-web-math | |
A small strip of plane mirror A is set with its plane normal to the principal axis of a convex mirror B and placed 15 cm in front of B which it partly covers. An object is placed 30 cm from A and the two virtual images formed by reflection in A and B concide without parallax. Find the radius of curvature of B. : K... | HuggingFaceTB/finemath | |
# Kindergarten Printables - Subtraction
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Kindergarten Printables, Worksheets, and games to practice Subtraction in a FUN way!
This pack is available at a discount in the Kindergarten Printables - Endles... | HuggingFaceTB/finemath | |
### Leetcode: 202. Happy Number
Determining Happy Numbers in C++
# Determining Happy Numbers in C++
Introduction: In this blog post, we'll explore a C++ solution to determine whether a given number is happy or not. A happy number is a positive integer that, when repeatedly replaced by the sum of the squares of its d... | HuggingFaceTB/finemath | |
GMAT Tutor Blog
# Rate Problems
## Mind the Gap: Part III
Posted by
We recently introduced a method for solving problems in which people or objects are moving in the same direction. We recommend that you simplify such problems by focusing only on the relative speed of the objects, rather than their individual rates... | HuggingFaceTB/finemath | |
UNIT-3. Ans: Arrays of two point sources with equal amplitude and opposite phase:
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1 `` UNIT-3 1. Derive the field components and draw the field pattern for two point source with... | HuggingFaceTB/finemath | |
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Hints (Greetings fr... | HuggingFaceTB/finemath | |
# How to Obtain Predicted Values and Residuals in Stata
Linear regression is a method we can use to understand the relationship between one or more explanatory variables and a response variable.
When we perform linear regression on a dataset, we end up with a regression equation which can be used to predict the value... | HuggingFaceTB/finemath | |
# Prove that $f$ is discontinuous on $\mathbb{R}$ [closed]
$$f(x)=\begin{cases} x+1, & \text{if x is irrational} \\ x, & \text{if x is rational} \end{cases}$$
Show that $f$ is discontinuous on $\mathbb{R}$
edit: It would be preferable if this could be proved without the use of sequences or epsilon-delta
## closed a... | HuggingFaceTB/finemath | |
# 2003 AMC 10B Problems/Problem 8
## Problem
The second and fourth terms of a geometric sequence are $2$ and $6$. Which of the following is a possible first term? $\textbf{(A) } -\sqrt{3} \qquad\textbf{(B) } -\frac{2\sqrt{3}}{3} \qquad\textbf{(C) } -\frac{\sqrt{3}}{3} \qquad\textbf{(D) } \sqrt{3} \qquad\textbf{(E) } ... | HuggingFaceTB/finemath | |
# Number Sense Worksheets – Number Activity Worksheets
Grab this set of free printable number sense worksheets and give the kids a fun way to learn numbers, number formation, counting and more!
## Number Sense Worksheets
Learning numbers is very important, but it can be time consuming to find engaging resources for ... | HuggingFaceTB/finemath | |
# Quick Answer: What Is 2×3 Matrix?
## Is square matrix invertible?
A square matrix that is not invertible is called singular or degenerate.
A square matrix is singular if and only if its determinant is zero.
Non-square matrices (m-by-n matrices for which m ≠ n) do not have an inverse.
However, in some cases such ... | HuggingFaceTB/finemath | |
# Problems: Table 1: Labor Hours needed to make one
Problems:
Table 1:
Labor Hours needed to make one
Quilt
Dress
Helen
50
10
Carolyn
90
45
Amount produced in 90 hours:
Quilts
Dresses
1.8
9
1
2
1. Refer to Table 1. For Carolyn, the opportunity cost of 1 quilt is
a. 0.5 dresses.
b. 1 dress.
c. 2 dresses.
d. 3 dresses.
... | HuggingFaceTB/finemath | |
# 11.03 Frequency histograms and polygons
Lesson
### Histograms
The histogram is a graph that represents the value of a data type using a column. The label underneath the column tells us what data type the column refers to while the height of the column tells us the value.
In addition to this, a histogram also has ... | HuggingFaceTB/finemath | |
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# The radius $R_h$ and mass $M_h$ of a black hole are related by $R_h = 2 GM_h/c^2$, where c is the speed of light. Assume that the gravitational acceleration $a_g$ of an object at a distance $r_o = 1.001 R_h$ from the center of a black hole is given (it is, for large ... | HuggingFaceTB/finemath | |
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# The area bounded by the y-axis, y = cos xand y = sin x when 0lt=xlt=pi/2is(A) 2(sqrt(2-1)) (B) sqrt(2)-1 (C) sqrt(2)+1 (D) sqrt(2)
Khareedo DN Pro and dekho sari videos bina kisi ad ki rukaavat ke!
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Question
A theater charges $8 for an adult ticket, and$6 for a children’s ticket. on a certain day, a total of 255 tickets were sold for a total cost of $1,850. how many more children’s tickets were sold than adult tickets? Answers 1. quangkhai Answer: BRO ?WHAT ARE THE QUESTIONS? Step-by-step explanation: Reply 2. Th... | HuggingFaceTB/finemath | |
, 24.04.2023 20:45 Dailyn
# A figure is located at (2, 0), (2, −2), and (6, 0) on a coordinate plane. What kind of 3-D shape would be created if the figure was rotated around the x-axis? Provide an explanation and proof of your answer to receive full credit. Include the dimensions of the 3-D shape in your explanation... | HuggingFaceTB/finemath | |
# Chapter 15 : Vapour Liquid Equilibrium¶
### Example 15.1 Page Number : 503¶
In [1]:
# Variables
T = 90+ 273.15; #[K] - Temperature
P = 1; #[atm] - Pressure
x_1 = 0.5748; # Equilibrium composition of liquid phase
y_1 = 0.7725; # Equilibrium composition of vapour phase
# We start with 1 mol of mixture of co... | HuggingFaceTB/finemath | |
# Portal:Mathematics
## The Mathematics Portal
Mathematics is the study of numbers, quantity, space, pattern, structure, and change. Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. Applied mathematics, the branch ... | HuggingFaceTB/finemath | |
# Split mind - VAT
Registered Posts: 45 Regular contributor ⭐
Hi all,
me and my brother are having a discussion and ive got to the stage where im so confused i dont know which answer is right.
for example... (forget roundings)
He is saying..
182.82 - VAT at 17.5% = £150.83 on a calculator
150.83 + VAT at 17.5% = ... | HuggingFaceTB/finemath | |
# Common Core Grade 5 Math 5-nf-5b
Back
Number And Operations - Fractions: Apply And Extend Previous Understandings Of Multiplication And Division To Multiply And Divide Fractions.
Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing m... | HuggingFaceTB/finemath | |
0
# When A number is less than but more than 40 . it is divisible by 4 and when added to 19 what will be the resulting answer?
Updated: 4/28/2022
Wiki User
6y ago
A number cannot be "less than but more than 40".
Wiki User
6y ago
Study guides
20 cards
## A number a power of a variable or a product of the two is... | HuggingFaceTB/finemath | |
# Why Doesn't the Limit of $$xe^{-\frac{1}{x}}$$ Exist as $$x \to 0$$?
• MHB
• Vali
In summary, the limit of $xe^{-\frac{1}{x}}$ as x approaches 0 does not exist because the limits from below and above are not equal. The limit from below is 0, while the limit from above is $-\infty$.
Vali
Why the following limit doesn... | HuggingFaceTB/finemath | |
#### Archived
This topic is now archived and is closed to further replies.
# uniform particles on a polygon
This topic is 5954 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.
## Recommended Posts
Anyone know of a good technique to uniformly distribute an arbitra... | HuggingFaceTB/finemath | |
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# Exercises and problems in Physics January 1998
## New experimental problem:
m. 194. Observe how a candle floating on water with a ballast attached to its bottom burns down. Measure the distance between the ballast a... | HuggingFaceTB/finemath | |
# Concepts 7: Compare How Different Areas of Your Casino are doing using an Independent T-Test!
What if you wanted to compare different areas with different numbers of machines on your gaming floor? What if you wanted to know if a certain area was receiving more profit than another?
In a previous post, we looked at h... | HuggingFaceTB/finemath | |
# Thread: Negative number in the denominator
1. ## Negative number in the denominator
Is that right?
$\frac{3-x}{-10} = -\frac{3-x}{10}$
2. Yes.
This is also correct.
$\dfrac{3-x}{-10}=\dfrac{x-3}{10}$.
Do you understand why?
3. Yes. Thanks
4. Another question.
Is this right?
$(\dfrac{x-1}{2})^{2} = \dfrac{x-1}... | HuggingFaceTB/finemath | |
Main Content
## Rectangular Coordinates
### Definitions of Coordinates
Construct a rectangular, or Cartesian, coordinate system for three-dimensional space by specifying three mutually orthogonal coordinate axes. The following figure shows one possible specification of the coordinate axes.
Rectangular coordinates s... | HuggingFaceTB/finemath | |
# Why do we use Riemann approximations when we can find actual area by using integrals
I am a calculus 1 student. I was wondering that if Riemann sums only give us an approximation(either over-estimate or under-estimate) the area under the curve, Why do we celebrate Riemann sums(considering it came out in the 19th cen... | HuggingFaceTB/finemath | |
# What Is The Purpose Of Using A Histogram?
## Why would you use a histogram?
A histogram is used to summarize discrete or continuous data.
In other words, it provides a visual interpretation.
This requires focusing on the main points, factsof numerical data by showing the number of data points that fall within a s... | HuggingFaceTB/finemath | |
8th Grade NYSE Math FREE Sample Practice Questions
Preparing your student for the 8th Grade NYSE Math test? To succeed on the NYSE Math test, students need to practice as many real NYSE Math questions as possible. There’s nothing like working on NYSE Math sample questions to measure your student’s exam readiness and ... | HuggingFaceTB/finemath | |
# A man 2 m tall is walking from a lampost that is 6 m tall at a rate pf 1.5 m/s. Find the rate of change of the angle of depression when he is 8 m away.
justaguide | College Teacher | (Level 2) Distinguished Educator
Posted on
A man that is 2 m tall is walking away from a lamp post that is 6 m tall at a rate of 1.5... | HuggingFaceTB/finemath | |
## 559872
559,872 (five hundred fifty-nine thousand eight hundred seventy-two) is an even six-digits composite number following 559871 and preceding 559873. In scientific notation, it is written as 5.59872 × 105. The sum of its digits is 36. It has a total of 15 prime factors and 72 positive divisors. There are 186,62... | HuggingFaceTB/finemath | |
# Addition of Vectors Lab Report
Topics: Force, Euclidean vector, Technical drawing Pages: 2 (378 words) Published: May 6, 2013
Addition of Vectors
Objectives:
The purpose of this experiment is to show that the magnitude and direction of the resultant of several forces acting on a particle may be determined by drawin... | HuggingFaceTB/finemath | |
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Tommy: "How old are you, Mamma?"
Mamma: "Let me think, Tommy. Well, our three ages add up to e... | HuggingFaceTB/finemath | |
# Quiz-1
Question 1
Time: 00:00:00
Find the parameters a and b included in the linear function f(x) = a x + b so that f -1 (2) = 3 and f -1 (-3) = 6, where f -1 (x) is the inverse of function f.
a = - 5 / 3 and b = 7
a = - 5 / 3 and b = 7
a = 5 / 3 and b = 7
a = 5 / 3 and b = 7
a = -3 / 5 and b = 7
a = -3 / 5 a... | HuggingFaceTB/finemath | |
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#### Online Quiz (WorksheetABCD)
Questions Per Quiz = 2 4 6 8 10
### Grade 5 - Mathematics2.2 Decimal Vocabulary
The places to the right of a decimal point are called decimal places. The decimal places starting from t... | HuggingFaceTB/finemath | |
+0
# Hard Problem
0
200
3
For what value of the constant $a$ does the system of equations below have infinitely many solutions?\begin{align*} 2x + 5y &= -8,\\ 6x &= 16 + a - 15y \end{align*}
Jul 9, 2022
#1
0
In order for a system to have infinitely many solutions, the equations must represent the same coefficient... | HuggingFaceTB/finemath | |
+0
Kindly help, thanks!
0
58
1
Peter read the same number of pages of his storybook each day. At the end of the
7th day, he was left with $${1\over 4}$$ of the total number of pages. After another 2 days, he
was left with 10 pages. How many pages are there in Peter's storybook?
Oct 20, 2021
#1
0
Let the numbe... | HuggingFaceTB/finemath | |
MATH
posted by .
a library shelf is 9 ft wide. a set of books fills 1/6 of the shelf space.each book in the set is 3/5 inch thick. how many books are in the set?
I have tried working this fraction problem and I am stuck
• MATH -
The total shelf space is 9 feet wide.
But the set of books uses only 1/6 of the space.... | HuggingFaceTB/finemath | |
v do not blindly compute tan × where a × ) v where B B 1 The Characteristic Equation always features polynomials which can have complex as well as real roots, then so can the eigenvalues & eigenvectors of matrices be complex as well as real. 1 0. I . However, when complex eigenvalues are encountered, they always occur ... | HuggingFaceTB/finemath | |
1. ## two series questions
Hi all,
1. $\displaystyle \sum ^{\infty}_{i=1} \frac{1}{\left(i-1\right)!} \frac{d}{d\lambda} \left(\lambda^{i}\right)= \frac{d}{d\lambda} \sum ^{\infty}_{i=1} \frac{1}{\left(i-1\right)!} \lambda^{i}$
2. $\displaystyle \sum^{\infty}_{x=1} x r^{x} = \frac{r}{\left(1-r\right)^{2}}$
why are ... | HuggingFaceTB/finemath | |
# Projectile Motion Problem of a ship
• kdf8
In summary, an enemy ship can fire projectiles that will land at a distance of 400 m from the western shoreline if the firing angle is between -18 and 18 degrees.
kdf8
Okay, I'm in a rut. We got a pack of physics problems from our teacher and no one knows how to go about do... | HuggingFaceTB/finemath | |
ABC News
Can You Figure Out How To Beat Roger Federer At Wimbledon?
Welcome to The Riddler. Every week, I offer up a problem related to the things we hold dear around here: math, logic and probability. These problems, puzzles and riddles come from lots of top-notch puzzle folks around the world — including you! You’ll... | HuggingFaceTB/finemath | |
Lee asked in Science & MathematicsMathematics · 4 months ago
# Is 3/8 a half of 6/8?
Relevance
• 4 months ago
Yes. Do want to know another fact? 1 + 3 + 3 equals you’re a moron.
• 4 months ago
yes, but 6/8 would be reduced to 3/4.
• 4 months ago
1/2 * 6/8 = 6/16
6/16 = (2/2) * 3/8 = 3/8
So YES it's true
or...... | HuggingFaceTB/finemath | |
# Transformations of Variables
When a residual plot reveals a data set to be nonlinear, it is often possible to "transform" the raw data to make it more linear. This allows us to use linear regression techniques more effectively with nonlinear data.
## What is a Transformation to Achieve Linearity?
Transforming a va... | HuggingFaceTB/finemath | |
# How do you solve 5y + 9- 2( - 4y - 2) = 5( y - 1)?
Sep 16, 2017
$y = - \frac{18}{8}$
#### Explanation:
$5 y + 9 - 2 \left(- 4 y - 2\right) = 5 \left(y - 1\right)$
To simplify the eqaution,we need to solve the brackets,we need to multiply $- 2$ with $\left(- 4 y - 2\right)$ and also $5$ with $\left(y - 1\right)$
... | HuggingFaceTB/finemath | |
# Colloquium Details
## IBM Research NYU/Columbia Theory Day
Speaker:
Location: Warren Weaver Hall 109
Date: April 19, 2002, 9:30 a.m.
Host: Yevgeniy Dodis
Synopsis:
### Learning a Hidden Matching
Prof. Noga Alon
Tel Aviv University and IAS Princeton
### Abstract
We consider the problem of learning a matching... | open-web-math/open-web-math | |
```Question 154741
One morning, John drove 5 hours before stopping to eat. After lunch, he
increased his speed by 10 mph. If he completed a 430-mile trip in 8 hours of
driving time, how fast did he drive in the morning?
:
Let s = his speed in the morning
then
(s+10) = his speed in the afternoon
;
A total of 8 hrs drivi... | HuggingFaceTB/finemath | |
# Interest Rate
What are Interest Rates?
Interest rate can be defined as the amount a bank or a lender charges to the borrower for the use of its assets or money. The rate a bank pays to its depositors for keeping money in a savings account, recurring deposit or fixed deposit is also termed as an interest rate.
Inte... | HuggingFaceTB/finemath | |
Question
# A concave mirror produces three times magnified (enlarged) real image of an object placed at $10cm$ in front of it. Where is the image located?
Open in App
Solution
## Step 1: Given dataMagnification ($m$)= $-3$ (negative because image is real)Object distance ($u$)= $-10cm$ (negative because it is on the ... | HuggingFaceTB/finemath | |
# What Is the Formula for Daily Compound Interest?
The interest generated on your savings account balance each day after the interest from the previous day has been applied is known as daily compound interest. The interest you earn on your savings account is added back to the balance each day as daily compound interes... | HuggingFaceTB/finemath | |
# Multiplication on a Number Line
Multiplication on a number line is performing the multiplication operation on a set of numbers and finding the result using a number line.
Since multiplication is also known as repeated addition, the result is obtained after performing addition for the required number of times.
Usin... | HuggingFaceTB/finemath | |
# Quick Answer: What Is A Conjugate In Math?
## What is the conjugate of 5?
The conjugate of 5 is 5 ..
## What are conjugate harmonic functions?
From Encyclopedia of Mathematics. harmonically-conjugate functions. A pair of real harmonic functions u and v which are the real and imaginary parts of some analytic funct... | HuggingFaceTB/finemath | |
# How do you simplify f(theta)=csc2theta-sec2theta-3cot2theta to trigonometric functions of a unit theta?
##### 1 Answer
Oct 14, 2017
$f \left(\theta\right) = \frac{1}{\sin \left(2 \theta\right)} = \frac{1}{2 \sin \theta \cos \theta} - \frac{1}{2 {\cos}^{2} \theta - 1} - \frac{2 - 1 {\tan}^{2} \theta}{2 \tan \theta}$... | HuggingFaceTB/finemath | |
## Precalculus (6th Edition) Blitzer
Domain of $f\left( x \right):\left( -\infty ,\infty \right)$ , Range of $f\left( x \right):\left( -\infty ,9 \right]$
The graph is a parabola. Since $f\left( x \right)$ is a polynomial, it exists for every value of $x$ on the real axis. Therefore, the domain of $f\left( x \right)=-... | HuggingFaceTB/finemath | |
# How parameters formulated for Simple Regression Model
I am reading Simple Regression Model from this book, Section 6.5 (page 267 in downloaded pdf, 276 if viewed online).
The author starts with below equation for a simple linear regression model,
$$Y_i = \alpha_1 + \beta x_i + \varepsilon_i$$
And then after few l... | HuggingFaceTB/finemath | |
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# Nota Fizik
1,058
Published on
Published in: Education, Technology... | HuggingFaceTB/finemath | |
WHAT YOU GET:
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This 3rd GRADE MOUNTAIN MATH CENTER EDITION is the DAILY REVIEW your students need to MASTER the concepts you have taught.
Research has proven that LONG-TERM MASTE... | HuggingFaceTB/finemath | |
# Force exerted by a magnetic field
## Homework Statement
a 10cm long straight wire is parallel with the z axis and carries a current of 4.0A in the +z direction. The force on this wire due to a uniform magnetic field B is -0.20N i+0.20N j. If this wire is rotated so that it is parallel with the x axis with the curre... | HuggingFaceTB/finemath | |
# How do you factor by grouping y^2 + 3y - 2y - 6?
May 22, 2015
${y}^{2} + 3 y - 2 y - 6$
We can make groups of two to factorise this expression:
color(blue)((y^2+3y) - color(red)((2y + 6)
color(blue)(y is common to both the terms in the first group, and color(red)(2 is common to both the terms in the second group:... | HuggingFaceTB/finemath | |
# Probability an honest node finds the next block vs. probability the attacker finds the next block
I am trying to understand Satoshi's paper . On page 6 of the paper, he calculates the probability that someone can attack the blockchain from z blocks behind. He begins by defining: My question: The mining of a block i.... | HuggingFaceTB/finemath | |
# Law of Coulomb (electrostatic)
In electrostatic, the law of Coulomb expresses the electric force $\ vec \left\{F\right\} _ \left\{1 \ rightarrow 2\right\} \,$ exerted by a electric Charge $q_1 \,$ placed in a point $M_1 \,$ on a load $q_2 \,$ placed in a point $M_2 \,$. This law is expressed in vectorial form by the... | HuggingFaceTB/finemath | |
# $62,856 in 1989 is worth$120,002.24 in 2014
$62,856 in 1989 has the same purchasing power as$120,002.24 in 2014. Over the 25 years this is a change of $57,146.24. The average inflation rate of the dollar between 1989 and 2014 was 2.71% per year. The cumulative price increase of the dollar over this time was 90.92%. ... | HuggingFaceTB/finemath | |
Force, Mass, Acceleration | Zona Land Education
# The Mighty F = ma This equation is one of the most useful in classical physics. It is a concise statement of Isaac Newton's Second Law of Motion, holding both the proportions and vectors of the Second Law. It translates as:
The net force on an object is equal to the... | HuggingFaceTB/finemath | |
Solutions by everydaycalculation.com
## Subtract 50/48 from 20/70
1st number: 20/70, 2nd number: 1 2/48
20/70 - 50/48 is -127/168.
#### Steps for subtracting fractions
1. Find the least common denominator or LCM of the two denominators:
LCM of 70 and 48 is 1680
2. For the 1st fraction, since 70 × 24 = 1680,
20/70 ... | HuggingFaceTB/finemath |
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