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3 years ago

8

The length of a rectangle is 12 in. and the perimeter is 56 in. find the width of the rectangle

1 answer:

pentagon [3]3 years ago

8 0

The perimeter p of the rectangle with length l and width w is:
p = 2l + 2w
that is, two times its length and two times its width, lets solve for the width w and substitute known data:
<span>p = 2l + 2w
</span>2w = p - 2l
w = (<span>p - 2l</span>)/2
w = (56 - (2*12))/2
w = (56 - 24)/2
w = 32/2
w = 16
therefore the width of the rectangle is 16 in

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What do each of these numbers have in common?

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So, divide each one of these by 9x⁷

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10. A random sample of 10 fibers is taken from a collection of 92 fibers that consists of 43 fibers of polymer A, 17 fibers of p

vazorg [7]

Answer:

0.1150 = 11.50% probability that the sample does not contain any fibers of polymer B

Step-by-step explanation:

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this question:

Fibers are chosen without replacement, which means that we use the hypergeometric distribution.

92 fibers means that $N = 92$

Sample of 10 means that $n = 10$

No polymeter B which means that $x = 0$

17 fibers of polymeter B which means that $k = 17$

a. What is the probability that the sample does not contain any fibers of polymer B

This is P(X = 0).

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

$P(X = 0) = h(0,92,10,17) = \frac{C_{17,0}*C_{75,10}}{C_{92,10}} = 0.1150$

0.1150 = 11.50% probability that the sample does not contain any fibers of polymer B

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2 years ago

Answer this please (9)

Alja [10]

Answer:

The answer is C 10.

Step-by-step explanation:

Since there is a parentheses around 2⁴, we know that we are multiplying the exponent in (2⁴) by 3. This will give us a product of 2¹².

Since 2¹² is set equal to 2² x 2^n, we know that whatever n equals will be added to the exponent of 2 to get 12.

We know this because since there are no parentheses, when we see the x (multiplication sign) we know that we are adding and not multiplying.

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2 years ago