Write and expression and determine which function. Please help with these questions.

Student A starts with $100 in the bank and makes $5 a day. Student B starts with $50 and makes $7 a day. Assuming the students s

nasty-shy [4]

Student A starts with $100 in the bank and makes $5 a day. Student B starts with $50 and makes $7 a day. Assuming the students save their money, when will they have the same amount of money ?

3 0

3 years ago

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The probability that your call to a service line is answered in less than 30 seconds is 0.75. Assume that your calls are indepen

vfiekz [6]

Answer:

a) 0.2581

b) 0.4148

c) 17

Step-by-step explanation:

For each call, there are only two possible outcomes. Either they are answered in less than 30 seconds. Or they are not. The probabilities for each call are independent. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

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

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

And p is the probability of X happening.

In this problem we have that:

$p = 0.75$

a. If you call 12 times, what is the probability that exactly 9 of your calls are answered within 30 seconds? Round your answer to four decimal places (e.g. 98.7654).

This is $P(X = 9)$ when $n = 12$ . So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 9) = C_{12,9}.(0.75)^{9}.(0.25)^{3} = 0.2581$

b. If you call 20 times, what is the probability that at least 16 calls are answered in less than 30 seconds? Round your answer to four decimal places (e.g. 98.7654).

This is $P(X \geq 16)$ when $n = 20$

So

$P(X \geq 16) = P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 16) = C_{20,16}.(0.75)^{16}.(0.25)^{4} = 0.1897$

$P(X = 17) = C_{20,17}.(0.75)^{17}.(0.25)^{3} = 0.1339$

$P(X = 18) = C_{20,18}.(0.75)^{18}.(0.25)^{2} = 0.0669$

$P(X = 19) = C_{20,19}.(0.75)^{19}.(0.25)^{1} = 0.0211$

$P(X = 20) = C_{20,20}.(0.75)^{20}.(0.25)^{0} = 0.0032$

So

$P(X \geq 16) = P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20) = 0.1897 + 0.1339 + 0.0669 + 0.0211 + 0.0032 = 0.4148$

c. If you call 22 times, what is the mean number of calls that are answered in less than 30 seconds? Round your answer to the nearest integer.

The expected value of the binomial distribution is:

$E(X) = np$

In this question, we have $n = 22$

So

$E(X) = 22*0.75 = 16.5$

The closest integer to 16.5 is 17.

7 0

3 years ago

G(x)=2x-2 <br> f(x)=x^2+3x <br> find (g of f)(2+x)

Bumek [7]

Answer:

Step-by-step explanation:

G(f(2+x))=g(2+x)^2+3(2+x)=2(2+x)^2+3(2+x)-2=2(4+4x+x^2)+6+3x=8+8x+2x^2+6+3x=2x^2+11x+14

6 0

3 years ago

Find the tax (7%) paid on $99 sneakers

anygoal [31]

$6.93
you just multiply $99 by .07 since that’s the percentage

5 0

3 years ago

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three apples and four bananas cost $4.85 . three apples and ten bananas cost $8.75.Find the cost of an apple.

konstantin123 [22]

8.75-4.85= 3.90= cost of 6 bananas
3.9/6=0.65= cost of one banana
.65*4=2.60= cost of 4 bananas
4.85-2.60= 2.25= cost of 3 apples
2.25/3=.75= cost of an apple

5 0

3 years ago

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