Ask question

Ask question

All categories

3 years ago

12

Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9}. n distinct integers will be chosen from A. How big does n have to be

1 answer:

Hitman42 [59]3 years ago

7 0

Partition the set A into 4 subsets: {1, 8}, {2, 7}, {3, 6}, and {4, 5}, each consisting of two integers whose sum is 9. If 5 integers are selected from A, then by the Pigeonhole Principle at least two must be from the same subset. But then the sum of these two integers is 9.

You might be interested in

Zayn puts garland around a square window. He

mojhsa [17]

2 meters because 8/4 is 2

8 0

3 years ago

Are the following two expressions equivalent? 7+7x ; 7 (x+ 1/7 )

love history [14]

Answer:

no 7(x+1/7) is not equivalent to 7+7x

Step-by-step explanation:

6 0

2 years ago

How can csc^2-cot^2 = 1?

Softa [21]

ANSWER

By simplifying the left hand side using the Pythagorean Identity.

EXPLANATION

The given identity is

$\csc^{2} (x) - \cot^{2} (x) = 1$

Take the left hand side and simplify to get the right hand side.

$\csc^{2} (x) - \cot^{2} (x) = \frac{1}{\sin^{2} (x)} - \frac{ \cos^{2} (x)}{\sin^{2} (x)}$

Collect LCM for the denominators.

$\csc^{2} (x) - \cot^{2} (x) = \frac{1 - \cos^{2} (x)}{\sin^{2} (x)}$

Recall the Pythagorean Identity.

$\cos^{2} (x) + \sin^{2} (x) = 1$

This implies that:

$1 - \cos^{2} (x) = \sin^{2} (x)$

We substitute this to get,

$\csc^{2} (x) - \cot^{2} (x) = \frac{\sin^{2} (x)}{\sin^{2} (x)}$

$\csc^{2} (x) - \cot^{2} (x) = 1$

6 0

2 years ago

Marty’s water bottle holds 4 cups of liquid. He has 24 fl oz of water to put into the bottle. Will all 24 fl oz fit in the bottl

alexgriva [62]

Answer:

yes all fl oz will fit in the bottle

Step-by-step explanation:

1 cup = 8 fl oz

4 cups = 32 fl oz

you have still space 8 fl oz

5 0

3 years ago

You put $5,000 in a simple interest account at a bank. You will earn $1,200 in just 4 years. What is the annual interest rate fo

Sav [38]

<span>1200 = 5000*4r
1200/20000 = r = .06 0r 6%</span>

4 0

3 years ago