Is this number prime or composite 70

2 1/4 X 3 1/3 What is the answer?

Alex

Answer:

The answer to 2 1/4 X 3 1/3 is 7 1/2

6 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

2 years ago

What is the length of D. 8ft

KengaRu [80]

Answer:

96 inches

Step-by-step explanation:

8 ft is 8(12) inches, which is 96 inches

6 0

2 years ago

Pls help math work bleh

Rina8888 [55]

Answer:

j = 8
j = 3
j = 6

I hope this helps!

8 0

2 years ago

Jessica is 5 years older than her sister Jenna. Jenna tells her sister that in 5 years, she will be as old as Jessica was 5 year

vlabodo [156]

Answer:

x + 5 = (x + 5) - 5, which has no solution ⇒ answer C

Step-by-step explanation:

* Lets study the situation in the problem

- Jessica is 5 years older than her sister Jenna

- After five years Jenna's age will be as old as Jessica was five years ago

- Jenna's age now is x

* Lets change all information above to equation

∵ Janna's age now is x

∵ Jessica is 5 years old than Janna

∴ The age of Jessica now is x + 5

- After 5 years Janna's age will be add by 5 years

∵ Her age now is x

∴ Her age after 5 years will be x + 5

- From 5 years ago Jessica's age was her age now mins 5 years

∵ Her age now is x + 5

∴ Her age from 5 years ago is (x + 5) - 5

∵ Janna's age after 5 years = Jessica age from 5 years ago

∴ x + 5 = (x + 5) - 5

- Lets solve the equation to know how many solution

∵ x + 5 = x + 5 - 5 ⇒ add the like terms

∴ x + 5 = x ⇒ subtract x from both sides

∴ 5 = 0

- But 5 ≠ 0, the two sides of the equation not equal each other

∴ There is no solution for this equation

* The equation is x + 5 = (x + 5) - 5, which has no solution

8 0

3 years ago

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