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4 years ago

13

The volume of a triangular prism is 84 cubic inches. What is the volume of a similar prism that is smaller by a scale 1/2

1 answer:

wariber [46]4 years ago

3 0

I'm not entirely sure but since the proportions are halved, the volume may be (84/2) = 42

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3 years ago

Lindsay is checking out books at the library, and she is primarily interested in mysteries and nonfiction. She has narrowed her

Ratling [72]

Answer:

0.0677 = 6.77% probability that they will all be nonfiction

Step-by-step explanation:

The books are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes 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 successes.

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:

10 + 12 = 22 books.

She chooses 4 books, which means that $n = 4$

12 nonfiction, which meas that $k = 12$

What’s the probability that they will all be nonfiction?

This is P(X = 4). So

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

$P(X = 4) = h(4,22,4,12) = \frac{C_{12,4}*C_{10,0}}{C_{22,4}} = 0.0677$

0.0677 = 6.77% probability that they will all be nonfiction

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3 years ago