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4 years ago

I'm so confused how do you expand brackets and ?

Mathematics

1 answer:

Bogdan [553]4 years ago

7 0

Expanding brackets is just your book's way of saying to use the distributive property and then simplify to solve each equation.

I'll show the work for a and b and then the answers for the rest.

a.

4(g + 5) - 4g

Multiply each part inside the parentheses by 4

4g + 4(5) - 4g
4g + 20 - 4g

Now combine like terms to simplify the equation. In this case, the 4g and - 4g cancel each other out.

4g - 4g + 20
0 + 20
20

20 is your answer.

b.

6(p + 4) + 2(p - 12)

Multiply each part of the first set of parentheses by 6 and the second set by 2

6p + 6(4) + 2p + 2(- 12)
6p + 24 + 2p - 24

Combine like terms

6p + 2p + 24 - 24
8p + 0
8p

8p is your answer

c. 6z

d. 3a + 8

e. 8a + 16 which simplifies 8(a + 2)

f. 32w + 16 which simplifies 16(2w + 1)

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3 years ago

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Answer:

0.2348 = 23.48% probability that four will have used the e-ticket check-in kiosk to obtain boarding passes.

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:

Population of 280, which means that $N = 280$

112 use e-ticket check-in kiosk, which means that $k = 112$

Sample of eight passengers means that $n = 8$

Find the approximate hypergeometric probability that four will have used the e-ticket check-in kiosk to obtain boarding passes.

This is P(X = 4). So

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

$P(X = 4) = h(4,280,8,112) = \frac{C_{112,4}*C_{168,4}}{C_{280,4}} = 0.2348$

0.2348 = 23.48% probability that four will have used the e-ticket check-in kiosk to obtain boarding passes.

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