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Ksju [112]
3 years ago
8

Pigeon Hole Principle :

Mathematics
1 answer:
yaroslaw [1]3 years ago
5 0

Answer:

A proof can be as follows:

Step-by-step explanation:

Let S=\{a_{1},a_{2},...,a_{n},a_{n+1}\} be a set of n+1 integers. By the division algorithm the possible remainders when we divide by n are 0,1,2,....,n-1. Then, each integer a_{i}\in S can be written as:

a_{i}=np_{i}+r_{i},\,\,0\leq r_{i}

Observe that the set of remainders \{r_{1},r_{2},...,r_{n+1}\} has n+1 elements and each element has n possible values. By the Pigenhole principle at least two remainders have the same value. Suppose that this two elements are a_{i}, a_{j}. Then,

\begin{array}{c}a_{i}=np_{i}+r\\a_{j}=np_{j}+r\end{array}

Where r_{i}=r_{j}=r. Then,  a_{i}-a_{j}=np_{i}-np_{i}=n(p_{i}-p_{j}). Then we have that n divides a_{i}-a_{j}.

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If h = 9 units and r = 5 units, then what is the volume of the cone shown above?
dexar [7]

Answer:

Answer = 235.5

Step-by-step explanation:

Cone volume formula is V = 1/3 * pi * r^2 * h

V = 1/3 * 3.14 * 5^2 * 9

V = 235.5

6 0
3 years ago
An important application of regression analysis in accounting is in the estimation of cost. By collecting data on volume and cos
Amanda [17]

Answer:

Y = 7.60X + 1246.67

Step-by-step explanation:

Given the data:

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400 4000

450 5000

550 5400

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Using technology, the linear regression calculator, the regression model obtained by fitting the data is :

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6 0
3 years ago
A singles tennis court is a rectangle 27 feet wide and 78 feet long. Suppose a player at corner A hits the ball to her opponent
Sav [38]
Basically, you just have to find the length of the rectangle that is 27 x 78 feet.
The equation for the diagonal: 
d = sqrt(l^2+w^2)
l = 27
w = 78
plug them in and solve
d = sqrt ( (27^2) + (78^2) )
d = sqrt ( 729 + 6084 )
d = sqrt ( 6813 )
d <span>≈ 82.5

The ball traveled approximately 82.5 feet from one corner of the rectangular 27 x 78 foot field, diagonally to the other side.

Hope this helps</span>

6 0
3 years ago
Find the area. <br> (Please let me know soon if you can, it’s a test.) thanks!!
cricket20 [7]

Answer:

60sq ft

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
POINTS, AND BRAINLIEST
Andru [333]

The identification of parts A,B andC is illustrated below with their various reasons given.

<h3>What is an equilateral triangle?</h3>

An equilateral triangle is the triangle that has all its sides equal in length and each angle is made up of angle 60°.

Part A = The similar triangle are RGE and PBE

Part B = The triangles selected are similar because it was formed by an interception of the parallel lines of the rectangle GCPR.

Part C= All the sides of the equilateral triangle are the same therefore the distance from B to E and from P to E is the same with BP which is 225ft.

Learn more about triangles here:

brainly.com/question/2217700

#SPJ1

3 0
2 years ago
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