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Free Online Test
Online Test 1 (Ratio and Proportion) Number of questions : 20 | Time : 30 minutes
Important Notes and Previous Year Questions :
Ratio and Proportion:
Ratio compares two... |
# An Easier Way to Solve Quadratic Equations
The Greek mathematician Heron (100? B.C.) is credited by some as the first (historically known) person who studied quadratic equations. He considered questions like: “There is a square. The sum of its area and circumference is 896. What is its length (or width)?” But some s... |
# Graphs Using Slope-Intercept Form
## Key Questions
• If your line goes through two distinct points of the equation, then your line is correct.
I hope that this was helpful.
• You can choose any nonzero value ${x}_{2}$ for $x$ and plug it into the equation of the line you are working on to find the corresponding $... |
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These 5 Elementary Math Problems Are So Hard That You Will Probably Get Them Wrong
Have you ever wondered why is it always a math problem that goes viral? The reason is that math problem is such a tricky thing. You may think that you have nailed a problem in a few simple steps, but the answer just might surprise you.
... |
# How do you find the square root of 81?
It is ##pm9##.
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##81=9*9## then the square root of ##sqrt(81)=9##.
Because the double multiplication for the same sign is always positive, the square root is also... |
# Factors of 140: Prime Factorization, Methods, Tree, and Examples
Factors of 140 are the numbers that evenly divide 140, leaving zero as the remainder. Factors can also be defined as whole numbers that produce the required result when multiplied with another whole number. Algebraic equations can also be factorized.
... |
# Solving problems using trigonometry - slope angle
In this class of problems, we are given a slope or ramp with some dimensions known, and we are asked to find the angle of the slope or ramp.
### Problem:
A ramp has been built to make a stage wheelchair accessible. The building inspector needs to find the angle of ... |
## Engineering Mathematics SEM – 1Concept
Mathematics Notes for Polytechnic SEM – 1 is Designed by the ” Basics in Maths” team. Here we can learn Concepts in Basic Engineering mathematics Polytechnic Sem – I.
This Material is very Useful for Basic Engineering Mathematics Polytechnic Sem – I Students.
By learning The... |
Surface Area of 3 – Dimensional Figures
Presentation on theme: "Surface Area of 3 – Dimensional Figures"— Presentation transcript:
Surface Area of 3 – Dimensional Figures
Cubes and Rectangular Prisms
Definition Surface area is the sum of the areas of all the surfaces of a 3 – Dimensional figure. It is basically the ... |
# When Adding and Multiplying are the Same
David A. Wheeler
This is another little essay is an exercise in mathematical recreations; I hope you find it amusing!
When is addition the same as multiplication? In other words, when is the following true?
``` x + y = x * y
```
A bit of thinking will help you realize th... |
# Is f(x)=(1-e^(2x))/(2x-4) increasing or decreasing at x=-1?
Jan 5, 2016
Increasing.
#### Explanation:
Find the sign of the derivative at $x = - 1$.
To find $f ' \left(x\right)$, use the quotient rule.
$f ' \left(x\right) = \frac{\left(2 x - 4\right) \frac{d}{\mathrm{dx}} \left(1 - {e}^{2 x}\right) - \left(1 - {... |
We explain what multiples and factors are and also how kids are teach to recognise multiples indigenous Year 1 and factors indigenous Year 5, with instances of the types of problem they can be asked come solve.
You are watching: Explain the difference between a factor and a multiple
A multiple is a number that deserv... |
Problem
Given a number N, determine if it is a prime.
What is a Prime Number?
A prime number is a positive number greater than 1 which has no positive divisor except for 1 and itself. For example, 2, 3, 5, 11 are prime numbers. Whereas 4, 6 are non-prime or composite numbers.
O(N) Solution
From the definition, we ... |
How do you factor (4x^2+16x+15)/(2x^2+x-3)?
Mar 30, 2016
(2x + 5)/(2(x - 1)
Explanation:
Call $f \left(x\right) = \frac{g \left(x\right)}{h \left(x\right)} .$
Factor g(x) by the new AC Method to factor trinomials (Socratic)
$g \left(x\right) = 4 {x}^{2} + 16 x + 15 =$ 4(x + p)(x + q)
Converted trinomial g'(x) = x^2... |
What is the NO-SHORTCUT approach for learning great Mathematics?
# Maximum area | PRMO-2019 | Problem 23
Try this beautiful problem from PRMO, 2019 based on Maximum area
## Maximum area | PRMO-2019 | Problem-23
Let $\mathrm{ABCD}$ be a convex cyclic quadrilateral. Suppose $\mathrm{P}$ is a point in the plane of the... |
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# What Is The Cube Root Of 1?
• Cube root ∛1 cannot be reduced, because it already is in its simplest form.
• All radicals are now simplified. The radicand no longer has any cubed factors.
• The simplified root of ∛1 is number 1
• All radicals are now simplified. The... |
In mathematics, a dyadic product of two vectors is a third vector product next to dot product and cross product. The dyadic product is a square matrix that represents a tensor with respect to the same system of axes as to which the components of the vectors are defined that constitute the dyadic product. Thus, if
$\ma... |
Range
Lesson
Range
The range is a measure of spread in a quantitative (numerical) data set. In other words, it describes whether the scores in a data set are very similar and clustered together, or whether there is a lot of variation in the scores and they are very spread out.
If we looked at the range of ages of s... |
# Fraction- A Portion Or Section Of A Whole
The fractions are nothing but the parts of a whole figure or number. The representation of the whole number can be a cluster of objects or a single object as a whole. Fraction is the word that originated from a Latin word, ‘Fractus’ which means, ‘broken’ in the English langu... |
# Fraction Equivalence and Ordering
## Objective
Recognize and generate equivalent fractions with smaller units using area models.
## Common Core Standards
### Core Standards
?
• 4.NF.A.1 — Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to ho... |
# 1993 AIME Problems/Problem 7
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
## Problem
Three numbers, $a_1\,$, $a_2\,$, $a_3\,$, are drawn randomly and without replacement from the set $\{1, 2, 3, \dots, 1000\}\,$. Three other numbers, $b_1\,$, $b_2\,$, $b_3\,$, are then drawn randomly ... |
# R S Aggarwal Solutions for Class 11 Maths Chapter 29 Mathematical Reasoning
R S Aggarwal Class 11 Solutions of Chapter 29 consist of various concepts on Mathematical Reasoning, explained step by step for an easy understanding. In Mathematical language, there are two kinds of reasoning, namely inductive and deductive... |
# AP Statistics Curriculum 2007 StudentsT
(Difference between revisions)
Revision as of 02:52, 4 February 2008 (view source)IvoDinov (Talk | contribs) (→Example)← Older edit Current revision as of 00:18, 11 March 2011 (view source)IvoDinov (Talk | contribs) m (→Approach III (Approximate)) (17 intermediate revisions n... |
Education
# What Is Midpoint In Mathematics?
If you are fond of securing a good career in the mathematical field, keep in mind that you must have a hands-on grip on certain important concepts. Among these concepts is the midpoint, which is going to be our today’s topic of discussion. Not only this, but we will also l... |
# Transforming the graph of a function
Alignments to Content Standards: F-BF.B.3
The figure shows the graph of a function $f$ whose domain is the interval $-2 \leq x \leq 2$.
1. In (i)–(iii), sketch the graph of the given function and compare with the graph of $f$. Explain what you see.
1. $g(x) = f(x) + 2$
2. $h(... |
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# Let $$a, b, c$$ be the lengths of the sides of a triangle and let $$\theta$$ be the angle opposite the side of length $$c$$. Find the differential do and approximate c when $$\mathrm{a}=6.20, \mathrm{~b}=5.90$$, and $$0=58^{\circ}$$.
Expert verified
In con... |
##### Child pages
• Production of Tables
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# Production of Tables
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## Production of Tables
###### Third Grade Lessons
1. Candy Boxes - This class centers on the possible amounts of candies ... |
# When an Apparent Solution Does Not Satisfy the Original Equation It Is Called
When an Apparent Solution Does Not Satisfy the Original Equation It Is Called
In the world of mathematics, equations play a crucial role in problem-solving and understanding various phenomena. Solving equations involves finding values tha... |
# Pappus Chain
Pappus Chain
Pappus chain consists of all the black circles in the pink region.
# Basic Description
A chain of inscribed circles is called a Pappus Chain when its first circle $C_1$ is tangent to the three semicircles forming the Arbelos, and all the subsequent circles $C_n$ are tangent to one anothe... |
Factoring Day 2 of 2
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Objective
SWBAT factor quadratic equations when appropriate. SWBAT connect the solutions of quadratic equations to x-intercepts. SWBAT distinguish between quadratic equations that are not factorable and still have x-intercepts with those that do not have ... |
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Introduction to the Rule of Pythagoras.
This topic is part of the TCS FREE high school mathematics 'How-to Library'. It introduces you to the rule of Pythagoras for right triangles, as well as Pythagorian triples. (See the index page for a list of all available topics in the library.)Â To make best use of... |
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# Octal and Hexadecimal Number Systems
OCTAL or BASE-8 numbers uses eight symbols: 0, 1, 2, 3, 4, 5, 6, and 7 (count them!) and position plays
a major role in expressing their meaning. For example 53,7028 means 5 x 84 + 3 x 83 + 7 x 82 + 0 x 81 + 1 x 80
4096s 512s Sixty-fours Eights Ones (Un... |
# Discovering Pick’s Formula
Finding the area of polygons is pretty easy if the shapes are familiar to you like rectangles, triangles, circles, etc. Those shapes have nice formulas we can learn that will give us the area of the figure without much hassle.
But what about unusual shapes like this?
Sure we could find t... |
## Intermediate Algebra: Connecting Concepts through Application
$\color{blue}{\left\{-4, 1\right\}}$
Recall The solutions of the quadratic equation $ax^2+bx+c=0$ can be found using the quadratic formula: $$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$$ The given quadratic equation has $a=3, b=9, \text{ and } c= -125$. Substitut... |
# SAT Math : How to find the perimeter of an acute / obtuse triangle
## Example Questions
### Example Question #1 : Acute / Obtuse Triangles
If a = 7 and b = 4, which of the following could be the perimeter of the triangle?
I. 11
II. 15
III. 25
II and III Only
II Only
I and II Only
I Only
I, II and III
II O... |
Factors
# Factors of 152 | Prime Factorization of 152 | Factor Tree of 152
Written by Prerit Jain
Updated on: 15 Feb 2023
## Factors of 152
Calculate Factors of
The Factors are
https://wiingy.com/learn/math/factors-of-152/
## What are the factors of 152
To find the factors of 152, we can use either division or... |
Lesson 6
How Much is 10,000?
Lesson Purpose
The purpose of this lesson is to develop a relative sense of ten-thousand and understand it as a unit consisting of 10 units of one-thousand.
Lesson Narrative
In this lesson, students build on their understanding of the base-ten structure to develop a sense of the magnit... |
# How do you find final velocity with distance?
Contents
## How do you find final velocity with distance?
Provided an object traveled 500 meters in 3 minutes , to calculate the average velocity you should take the following steps:
1. Change minutes into seconds (so that the final result would be in meters per secon... |
FutureStarr
11 Out of 14 Percentage
## 11 Out of 14 Percentage
In standard form, the percentage is usually expressed in decimal form, whereas in scientific notation it is expressed as a power of "10".
### Decimal
via GIPHY
When you are working in a role where you might deal frequently with taxes (for example in a... |
# How do I convert 3427 into scientific notation?
Oct 11, 2014
A number in scientific notation is in the form
$a \cdot {10}^{b}$
Generally,
$1 \le a < 10$
For $3427$, the decimal point is on the right of 7
$3427.0$
We need to move the decimal such that $1 \le a < 10$ will be satisfied.
However, we also need to... |
# Inverse of a Matrix
An n x n matrix A is said to have an inverse provided there exists an n x n matrix B such that AB = BA = In. We call B the inverse of A and denote it as A-1. Thus, AA-1 = A-1A = In. In this case, A is also called nonsingular.
Example.
$A = \left(\begin{array}{cccc}4&3\\3&2\end{array}\right)$
$A... |
# Reciprocal Calculator
Created by Hanna Pamuła, PhD
Reviewed by Steven Wooding and Jack Bowater
Last updated: Feb 02, 2023
If you're wondering how to find the reciprocal, we're here to help with this easy-to-use reciprocal calculator.
Below, you can find an explanation of what a reciprocal is and examples of how to ... |
# Illustrative Mathematics Unit 6.3, Lesson 16: Finding the Percentage
Learning Targets:
• I can solve different problems like “60 is what percentage of 40?” by dividing and multiplying.
Related Pages
Illustrative Math
### Lesson 16: Finding the Percentage
Let’s find percentages in general.
Illustrative Math Unit... |
# Introduction to Rate of Change
We have already learned how to find the derivative of composite functions, inverse trigonometric functions, implicit functions, exponential functions and logarithmic functions. Here, we learn how derivatives can be used to determine rate of change of quantities.
## Rate of change of ... |
# Lesson 9
Mismo dígito, distinto valor
## Warm-up: Verdadero o falso: Expresiones desarrolladas (10 minutes)
### Narrative
The purpose of this True or False is for students to consider the value of the same digit in different places. This reasoning will also be helpful later in this lesson when students describe t... |
Standards and Practice Problem(s)
Note: Click on the to open the mathcast and to close it.
6NS.1.0:
Students compare and order positive and negative fractions, decimals, and mixed numbers. Students solve problems involving fractions, ratios, proportions, and percentages.
6NS.1.1 Compare and order positive and nega... |
# What is 51/205 as a decimal?
## Solution and how to convert 51 / 205 into a decimal
51 / 205 = 0.249
Convert 51/205 to 0.249 decimal form by understanding when to use each form of the number. Both are used to handle numbers less than one or between whole numbers, known as integers. Choosing which to use starts wit... |
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# Word Problems Involving Geometric Shapes Help
based on 2 ratings
By — McGraw-Hill Professional
Updated on Sep 27, 2011
## Introduction to Geometry Word Problems
To solve word problems involving geometric shapes, write down the formula or formulas referred to in the problem. For ... |
### Posts under category statistics homework help
Constructing a Confidence Interval for the Difference between Two Population Proportions
In order to determine if a new instructional technology improves students' scores, a professor wants to know if a larger percentage of students using the instructional technology p... |
Ray is a licensed technician in the Philippines. The loves to write about mathematics and also civil engineering.
You are watching: Converse of the triangle proportionality theorem
## What Is the Triangle Proportionality Theorem?
The triangle proportionality theorem says that if a heat parallel to one side of a tria... |
```College Algebra: Lesson 5.1 Introduction to Polynomial Equations and Graphs
1. A polynomial function can be written in the form p( x) a n x n a n 1 x n 1 .... a1 x a 0 , where n is a whole
number.
2. The largest power of a polynomial is called the degree of the polynomial.
3. A coefficient is the number ... |
Multiplying and Dividing Complex Numbers Topic Index | Algebra2/Trig Index | Regents Exam Prep Center
Multiplication:
Multiplying two complex numbers is accomplished in a manner similar to multiplying two binomials. You can use the FOIL process of multiplication, distributive multiplication, or your personal favori... |
Truth values
## Equality and other comparisons
In the last chapter, we used the equals sign to define variables and functions in Haskell as in the following code:
r = 5
That means that the evaluation of the program replaces all occurrences of r with 5 (within the scope of the definition). Similarly, evaluating the... |
# Printable Multiplication Table Up To 100
Learning multiplication right after counting, addition, and subtraction is perfect. Children learn arithmetic using a organic progression. This progress of discovering arithmetic is truly the following: counting, addition, subtraction, multiplication, lastly section. This sta... |
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# If y is directly proportional to the square of x, when x=4 y = 25, how do you find an expression for y in terms of x?
Last updated date: 12th Jul 2024
Total views: 381.3k
Views today: 7.81k
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381.3k+ views
Hint: First try to get an equat... |
# Lesson 5Common SenseSolidify Understanding
## Learning Focus
Use logarithms to solve exponential equations.
Solve systems of equations that contain exponential functions.
How can we use logarithms and algebraic reasoning to help us solve exponential equations?
## Open Up the Math: Launch, Explore, Discuss
You a... |
HSC Science (Electronics) 12th Board ExamMaharashtra State Board
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# Maxima and Minima
#### definition
Let f be a function defined on an interval I. Then
(a) f is said to have a maximum value in I, if there exists a point c in I such that f(c )>f (x), for all x ∈ I.
The number f(c) is called the maximum value ... |
# 30 Standard Deviation
You probably won’t need a calculator for this module.
This topic requires a leap of faith. It is one of the rare times when this textbook will say “don’t worry about why it’s true; just accept it.” 😂
# Normal Distributions & Standard Deviation
A normal distribution, often referred to as a b... |
University Physics Volume 1
# 9.3Conservation of Linear Momentum
University Physics Volume 19.3 Conservation of Linear Momentum
## Learning Objectives
By the end of this section, you will be able to:
• Explain the meaning of “conservation of momentum”
• Correctly identify if a system is, or is not, closed
• Define... |
# Test 1
4 dx − 2x2
Name:
Evaluate each of the following integrals: 1. x3
Solution. The denominator factors as x2 (x − 2), so try the partial fraction decomposition A B 4 C = + 2+ − 2) x x x−2
x2 (x
(The first term is needed because of the repeated root.) Clearing denominators, we have
4 = 0x2 + 0x + 4 = Ax(x − 2... |
Mathematics » Introducing Numbers » Divide Whole Numbers
# Properties of Division
## Divide Whole Numbers
We said that addition and subtraction are inverse operations because one undoes the other. Similarly, division is the inverse operation of multiplication. We know $$12÷4=3$$ because $$3·4=12.$$ Knowing all the m... |
# Compound interest formula explained in detail
Learn and know what is compound interest formula which we will study in comparing quantities chapter which comes in class 8 mathematics.
Regarding interest we have two types; they are simple interest and compound interest. Both of these have lot of difference and both o... |
# Video: GCSE Mathematics Foundation Tier Pack 1 • Paper 1 • Question 1
GCSE Mathematics Foundation Tier Pack 1 • Paper 1 • Question 1
04:03
### Video Transcript
Shown are four numbers. Three, negative three, eight, negative eight. Use two of these numbers to finish the calculation. Something plus something equals ... |
# Video: Evaluating Trigonometric Functions Using Pythagorean Identities
In this video, we will learn how to use the Pythagorean identities to find the values of trigonometric functions.
15:16
### Video Transcript
In this video, we will learn how to use the Pythagorean identities to find the values of trigonometric... |
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# Venika can embroider a saree in 3 days. What portion of the saree will she be able to embroider in (i) 1 day (ii) 2 days?
Last updated date: 21st Jul 2024
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Hint: Assume that the saree... |
# 2020 CIME II Problems/Problem 10
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
First suppose that $c=1$. Then $a+b+1=ab\Rightarrow (a-1)(b-1)=2$ from whence we have $(a,b,c)\in\{(2,3,1),(3,2,1)\}$.
Now suppose that $c\geq 2$. Since $a$ is a positive integer, from the equation we have $... |
# Definition:Trigonometric Function
## Definition
There are six basic trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.
## Sine
### Definition from Triangle
In the above right triangle, we are concerned about the angle $\theta$.
The sine of $\angle \theta$ is defined as being $\dfra... |
Polynomial elements Variable X at which we find values of a derivative
Given function
Consider one of the simple and undeservedly forgotten on the Internet Internet methods for determining the derivative of a polynomial, an arbitrary (positive) degree.
Until recently, I was sure that if a polynomial of the form
$f(... |
# Average Vs Mean
Mean vs. average!
In mathematics or statistics, you are very likely to come across two terms, average and mean. They are often used interchangeably, and many people aren’t sure whether these two words refer to the same thing or not. If you feel confused as well, don’t feel bad.
After reading this p... |
# SSC CGL solved question paper Tier-I exam held on 7 September 2016: Quantitative Aptitude
Find all solved questions of Aptitude section asked in SSC CGL tier-1 exam held on 7thSeptember, 2016 (Morning shift).Please go through these questions-
Created On: Jul 4, 2018 18:04 IST
SSC CGL solved paper
In this article, ... |
# 9.7 Solving systems with inverses (Page 6/8)
Page 6 / 8
## Algebraic
In the following exercises, show that matrix $\text{\hspace{0.17em}}A\text{\hspace{0.17em}}$ is the inverse of matrix $\text{\hspace{0.17em}}B.$
$A=\left[\begin{array}{cc}1& 0\\ -1& 1\end{array}\right],\text{\hspace{0.17em}}B=\left[\begin{arra... |
# SAT Math : Arithmetic Sequences
## Example Questions
### Example Question #1 : How To Find The Answer To An Arithmetic Sequence
-27, -24, -21, -18…
In the sequence above, each term after the first is 3 greater than the preceding term. Which of the following could not be a value in the sequence?
461
501
126
65... |
# Multiply numbers with decimals by double digit numbers
Lesson
## Multiplication strategies
When we perform multiplication problems with whole numbers, we can use some strategies to help us. These strategies, including doubling, partitioning and multiplying by powers of 10, can help us when solving decimal multip... |
Set Operations : Intersection And Difference Of Two Sets
Intersection and difference of two sets are two different set operations. In set theory, we perform different types of set operations. Such as intersection of sets, a difference of sets, the complement of set and union of sets. It is very easy to differentiate b... |
# 1.5: Logarithms and Exponential Functions
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$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$
$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$
( \newcommand{\kernel}{\mathrm{nu... |
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### CAGIS Clubhouse
Search
By CAGIS
This year it’s our 30th birthday, so what better topic to talk about than the birthday paradox!
With 23 people in a room, there is a 50% chance that at least two people will have the same birthday. With 75 people in a room, there is a 99% chance that at least two people w... |
# Handshake Lemma
## Theorem
Let $G$ be a $\tuple {p, q}$-undirected graph, which may be a multigraph or a loop-graph, or both.
Let $V = \set {v_1, v_2, \ldots, v_p}$ be the vertex set of $G$.
Then:
$\ds \sum_{i \mathop = 1}^p \map {\deg_G} {v_i} = 2 q$
where $\map {\deg_G} {v_i}$ is the degree of vertex $v_i$.
... |
# Perimeter and Area - PowerPoint PPT Presentation
1 / 7
Perimeter and Area. Lesson 10-1. Area. Area is the amount of space inside a figure. We use square units to describe area. For rectangles, the area formula is A= lw (area equals length times width).
I am the owner, or an agent authorized to act on behalf of the... |
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# Lesson 17
## Pearson’s Correlation Coefficient
Outline
Measures of Relationships
Pearson’s Correlation Coefficient (r)
-types of data
-scatter plots
-measure of direction
-measure of strength
Computation
-covariation of X and Y
-unique variation in X and Y
-measuring variability
Ex... |
+0
# How do we find the area of an overlapping object?
0
428
15
How do we find the area of an overlapping object?
Guest Jun 18, 2014
#1
+59
+10
I'm afraid I don't know exactly what you mean, but I assume you mean a shape that overlaps another shape like so:
To find the combined area of a shape and another shape ... |
# Difference between revisions of "2020 AIME II Problems/Problem 7"
## Problem
Two congruent right circular cones each with base radius $3$ and height $8$ have the axes of symmetry that intersect at right angles at a point in the interior of the cones a distance $3$ from the base of each cone. A sphere with radius $r... |
# How do you find the horizontal asymptote for g(x) = (3x^2) / (x^2 - 9)?
Nov 14, 2015
Solve for ${x}^{2} - 9 = 0$
#### Explanation:
In order to find the horizontal asymptote of a function, you have to solve it's denominator, while in order to find the vertical asymptote, you'll have to solve $y = \frac{a}{c}$, su... |
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# Solve for Polynomials: A Comprehensive Guide
## What is a Polynomial?
A polynomial is an expression that consists of variables and coefficients, with only the operations of addition, subtraction, multiplication, and exponentiation of non-negative integers.
Ex... |
# Find relationships between the stair total and the position of the stair shape on the grid for a three step stair.
Introduction
In this investigation I am going to see if I can find relationships between the stair total and the position of the stair shape on the grid for a three step stair. I will then try to work ... |
# Natural Numbers
Natural numbers are a part of the number system which includes all the positive integers from 1 till infinity and are also used for counting purpose. It does not include zero (0). In fact, 1,2,3,4,5,6,7,8,9…., are also called counting numbers.
Natural numbers are part of real numbers, that include o... |
# 2.10 Practical problems with inequalities
Lesson
We have now looked at solving inequalities that involve one step or two steps to solve. We're now going to take a look at how we can use inequalities to solve problems given a written description.
Much as with solving equations from worded problems, there are certai... |
# Prove that a circle can be inscribed in the hexagon
Given a convex hexagon $ABCDEF$. All its sides are equal (it can be irregular). Furthermore, $AD = BE = CF$. How can I prove that a circle can be inscribed in this hexagon?
Let $O$ be the intersection point of diagonals $AD$ and $BE$ (see diagram below) and set $a... |
# ML Aggarwal Solutions for Class 8 Maths Chapter 10 Algebraic Expressions and Identities
ML Aggarwal Solutions for Class 8 Maths Chapter 10 Algebraic Expressions and Identities are given here to make the exam preparations of students easier. This chapter mainly deals with problems based on identifying and performing ... |
# What value of x makes the three terms x, x/(x + 1) , 3x/(x + 1)(x + 2) those of a geometric sequence?
justaguide | College Teacher | (Level 2) Distinguished Educator
Posted on
For the terms x , x/(x + 1) and 3x/(x + 1)(x + 2) to be those of a geometric progression we need the following to be satisfied:
[3x/(x + ... |
# BM8.1 – Finding Present and Future Value
Chapter 8, Lesson 1
In this lesson students will:
• calculate the future value of a general annuity due
• calculate the principle amount of a general annuity due
## Future Value – General Annuities Due
Recall from Lesson 7.1 the general annuity problem occurs when the com... |
Mister Exam
# Factor polynomial a^2+8*a+16
An expression to simplify:
### The solution
You have entered [src]
2
a + 8*a + 16
$$\left(a^{2} + 8 a\right) + 16$$
a^2 + 8*a + 16
Factorization [src]
a + 4
$$a + 4$$
a + 4
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(a^{2} + 8... |
Lesson 7.6 Ratios, Rates, and Percents
# Use Percent in the Real-World
#### Materials
• CCB Mathematics pages 242 - 245
#### Standards
• MP.1
• Analyze proportional relationships and use them to solve real-world and mathematical problems.
#### Objectives
• Understand the interest formula
• Use a formula to fin... |
How do you find the area of a pentagon with an 8cm radius? Let's say you have a trapezoid with bases that have a length of 6 and 8 and a height of 10. This problem has been solved! Another important part of a pentagon is the apothem and the area. Incircle radius of pentagon can be calculated by using the below formula:... |
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# Let’s assume a function $f\left( x \right)$ be a derivable function, $f'\left( x \right) > f\left( x \right)$ and $f\left( 0 \right) = 0$. Then?${\text{A}}{\text{. }}f\left( x \right) > 0$ for all $x > {\text{0}}... |
# Lesson 3: The Thousands Places
## Getting Started
### Questions to Explore
• How does place value work?
• How can we use place value to name, create, and compare numbers to a million?
• How do we write and speak in mathematical language?
### Facts and Definitions
• Base-10 number system: a commonly used number s... |
## The top of Mrs. Vonvilla’s coffee table has the dimensions shown. She wants to put a bumper around the edges of the table to protect her chi
Question
The top of Mrs. Vonvilla’s coffee table has the dimensions shown. She wants to put a bumper around the edges of the table to protect her child in case he falls. What... |
Trigonometry
# Trigonometric Equation
An equation involving one or more trigonometric functions of a variable is called a trigonometric equation. The equation may be true for one or more values, but not for every value of the variable. The values of the variable (angle) are known as the root(s) of the equation.
The ... |
# How to differentiate this function to find f'(7)?
## Suppose that f(x) is a differentiable function such that f(7+h)=2/(h+1) and that f(7)=2. Then f'(7) = ??? The answer is -2, I'm just not sure how to reach it.
May 16, 2018
See below
#### Explanation:
We use the definition of the derivative
${f}^{'} \left(x\ri... |
# 2013 USAJMO Problems/Problem 5
## Problem
Quadrilateral $XABY$ is inscribed in the semicircle $\omega$ with diameter $XY$. Segments $AY$ and $BX$ meet at $P$. Point $Z$ is the foot of the perpendicular from $P$ to line $XY$. Point $C$ lies on $\omega$ such that line $XC$ is perpendicular to line $AZ$. Let $Q$ be th... |
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