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3 years ago

Prove this polynomial identity... (x − y)(x2 + 2xy + y2)

Mathematics

1 answer:

olga nikolaevna [1]3 years ago

6 0

Answer:

x³ + x²y - xy² - y³

Step-by-step explanation:

Hi there !

(x − y)(x² + 2xy + y²) =

= x(x² + 2xy + y²) - y(x² + 2xy + y²)

= x³ + 2x²y + xy² - x²y - 2xy² - y³

= x³ + x²y - xy² - y³

Good luck !

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A recent CBS News survey reported that 64% of adults felt the U.S. Treasury should continue making pennies. Suppose we select a

enyata [817]

Complete Question

A recent CBS News survey reported that 64% of adults felt the U.S. Treasury should continue making pennies. Suppose we select a sample of 18 adults.

a-1. How many of the 18 would we expect to indicate that the Treasury should continue making pennies

a-2) What is the standard deviation?

a-3) What is the likelihood that exactly 3 adults would indicate the Treasury should continue making pennies?

Answer:

a-1 $\= x = 11 .52$

a-2 $\sigma = 2.036$

a-3 $P(3) = 4.7*10^{-5}$

Step-by-step explanation:

From the question we are told that

The sample size is $n = 18$

The proportion of adult that felt the U.S. Treasury should continue making pennies is p = 0.64

The proportion of adult that feel otherwise is

$q = 1- p = 1-0.64 = 0.36$

The mean is mathematically evaluated as

$\= x = n * p$

substituting values

$\= x = 18 * 0.64$

$\= x = 11 .52$

The standard deviation is mathematically represented as

$\sigma = \sqrt{ npq}$

substituting values

$\sigma = \sqrt{18 * 0.64 * 0.36}$

$\sigma = 2.036$

The likelihood that 3 adult would indicate the Treasury should continue making pennies is mathematically evaluated as

$P(3) = \left n} \atop \right. C_3 (p)^{3} * (q)^{n-3}$

Now

$\left n} \atop \right. C_3 = \frac{n! }{[n-3] ! 3!}$

substituting values

$\left n} \atop \right. C_3 = \frac{18! }{[15] ! 3!}$

$\left n} \atop \right. C_3 = \frac{18 * 17 * 16 * 15! }{[15] ! (3 *2 *1 )}$

$\left n} \atop \right. C_3 = \frac{18 * 17 * 16 }{ (3 *2 *1 )}$

$\left n} \atop \right. C_3 = 816$

$P(3) = 816 * (0.64 )^3 * (0.36 )^{18-3}$

$P(3) = 4.7*10^{-5}$

8 0

3 years ago

Find the value of x. a) 90 b) 158 c) 180 d) 9

arsen [322]

Answer:

d) 9

Step-by-step explanation:

In a kite, the two shorter sides have to be equal.

Therefore

3x-5 = 22

Add 5 to each side

3x-5+5 = 22+5

3x = 27

Divide each side by 3

3x/3 = 27/3

x =9

4 0

3 years ago

The NCAA basketball tournament begins with 64 teams and consists of 6 rounds of play. The winners of the first round play again

fredd [130]

Y = 2^x
For a 64 team tounament, 64 = 2^6, so there will be six rounds of play.
For a 128 team tounarment, 128 = 2^7, so there will be 7 rounds of play.

Any number of teams which is not a power of 2 is an inappropriate number of team for tounament play.

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3 years ago

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Alekssandra [29.7K]

Just do 12 divided by 32 it well give the answer

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3 years ago

Fill in the blank to make the two fractions equivalent. /24 = 5/6

Digiron [165]

Answer:

20/24 = 5/6