Convert 330 litres per hour into millilitres per minute (ml/min).

hodyreva [135]

Answer:a

Step-by-step explanation:

7 0

3 years ago

The probability that your call to a service line is answered in less than 30 seconds is 0.85. Assume that your calls are indepen

aev [14]

Answer:

a) 0.1720

b) 0.8298

c) 19

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:

$p = 0.85$

(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

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

$P(X = 9) = C_{12,9}.(0.85)^{9}.(0.15)^{3} = 0.1720$

(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

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

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

$P(X = 16) = C_{20,16}.(0.85)^{16}.(0.15)^{4} = 0.1821$

$P(X = 17) = C_{20,17}.(0.85)^{17}.(0.15)^{3} = 0.2428$

$P(X = 18) = C_{20,18}.(0.85)^{18}.(0.15)^{2} = 0.2293$

$P(X = 19) = C_{20,19}.(0.85)^{19}.(0.15)^{1} = 0.1368$

$P(X = 20) = C_{20,20}.(0.85)^{20}.(0.15)^{0} = 0.0388$

So

$P(X \geq 16) = P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20) = 0.1821 + 0.2428 + 0.2293 + 0.1368 + 0.0388 = 0.8298$

(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

$E(X) = 22*0.85 = 18.7$

The nearest integer to 18.7 is 19.

7 0

3 years ago

Find the number C(10,6)

EastWind [94]

Answer:

210.

Step-by-step explanation:

Combination formula is

$nCr = \frac{n!}{r!(n-r)!}$

Then, we have that n = 10 and r=6:

$C(10,6) = \frac{10!}{6!(10-6)!}$

$C(10,6) = \frac{10!}{6!4!}$

To simplify calculus, we are going to use that n! = (n-1)!n = (n-2)!(n-1)n and so on.

$C(10,6) = \frac{6!*7*8*9*10}{6!4!}$

$C(10,6) = \frac{7*8*9*10}{4!}$

$C(10,6) = \frac{5040}{4*3*2*1}$

$C(10,6) = \frac{5040}{24}$

$C(10,6) = 210.$

5 0

2 years ago

I need help!

Naddik [55]

Answer: Estimate: 36 ? units ? miles per hour ? feet per second?

Exact: 35.32142857 but if you are supposed to use significant digits, 35.32 is probably good.

Step-by-step explanation: For the estimate, round off the fractions to whole numbers, so multiply 6 x 6 to get 36

For exact I converted the mixed numbers to improper fractions, 5 3/4 = 23/4 and 6 1/7 = 43/7. Then multiplied the numerators 23 x 43= 989. And denominators, 4x7=28.

Divide numerator by denominator 989/28= 35.321428571

7 0

3 years ago

What is the range of the function y=e^x+1 graphed below

REY [17]

The range of y=e^x+1 is y>1.

5 0

3 years ago

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