1. Find the range of the function rule y = 5x – 2 for the domain. (-5, -1, 0, 2, 10)

Refer to Exercise 3.122. If it takes approximately ten minutes to serve each customer, find the mean and variance of the total s

garri49 [273]

Answer

a. The expected total service time for customers = 70 minutes

b. The variance for the total service time = 700 minutes

c. It is not likely that the total service time will exceed 2.5 hours

Step-by-step explanation:

This question is incomplete. I will give the complete version below and proceed with my solution.

Refer to Exercise 3.122. If it takes approximately ten minutes to serve each customer, find the mean and variance of the total service time for customers arriving during a 1-hour period. (Assume that a sufficient number of servers are available so that no customer must wait for service.) Is it likely that the total service time will exceed 2.5 hours?

Reference

Customers arrive at a checkout counter in a department store according to a Poisson distribution at an average of seven per hour.

From the information supplied, we denote that

$X=$ Customers that arrive within the hour

and since $X$ follows a Poisson distribution with mean $\alpha$ = 7

Therefore,

$E(X)= 7$

$& V(X)=7$

Let $Y =$ the total service time for customers arriving during the 1 hour period.

Now, since it takes approximately ten minutes to serve each customer,

$Y=10X$

For a random variable $X$ and a constant $c$ ,

$E(cX)=cE(X)\\V(cX)=c^2V(X)$

Thus,

$E(Y)=E(10X)=10E(X)=10*7=70\\V(Y)=V(10X)=100V(X)=100*7=700$

Therefore the expected total service time for customers = 70 minutes

and the variance for serving time = 700 minutes

Also, the probability of the distribution $Y$ is,

$p_Y(y)=p_x(\frac{y}{10} )\frac{dx}{dy} =\frac{\alpha^{\frac{y}{10} } }{(\frac{y}{10})! }e^{-\alpha } \frac{1}{10}\\ =\frac{7^{\frac{y}{10} } }{(\frac{y}{10})! }e^{-7 } \frac{1}{10}$

So the probability that the total service time exceeds 2.5 hrs or 150 minutes is,

$P(Y>150)=\sum^{\infty}_{k=150} {p_Y} (k) =\sum^{\infty}_{k=150} \frac{7^{\frac{k}{10} }}{(\frac{k}{10})! }.e^{-7} .\frac{1}{10} \\=\frac{7^{\frac{150}{10} }}{(\frac{150}{10})! } .e^{-7}.\frac{1}{10} =0.002$

0.002 is small enough, and the function $\frac{7^{\frac{k}{10} }}{(\frac{k}{10} )!} .e^{-7}.\frac{1}{10}$ gets even smaller when $k$ increases. Hence the probability that the total service time exceeds 2.5 hours is not likely to happen.

3 0

3 years ago

Translate the statement into an algebraic expression or equation.

Alexandra [31]

We want to translate the given statement into an algebraic expression.

The expression is:

d = 0.45*L

---------------------------------

When we have a discount of an X% on a given value V, that discount will be:

D = (X%/100%)*V.

Here we have:

"A discount of a 45% on the list price L"

The discount will be given by:

d = (45%/100%)*L = 0.45*L

d = 0.45*L

This is the expression we wanted to get.

If you want to learn more, you can read:

brainly.com/question/2736271

4 0

2 years ago

Please help me with this question

mihalych1998 [28]

Answer:

John and Pam are paid $8.5 for each hour worked. John's share of the money is $29.75.

Step-by-step explanation:

Let x = the hourly salary. John worked for 3.5 hrs, and Pam for two. We can represent this using the equation:

3.5x + 2x = 46.75, where the coefficients equals the amount of hours.

Let's solve for x!

5.5x=46.75

x = 46.75/5.5 = 17/2 = 8.5

John and Pam are paid 8.5 dollars per each hour worked.

To figure out John's share of the money, we will multiply the wage by the hours he worked.

8.5 x 3.5 = 29.75

8 0

3 years ago

The second of two numbers is 3 less than twice the first. Their sum is 36. Find the numbers.

o-na [289]

Answer:

13 and 23

Step-by-step explanation:

create an equation to solve:

(2x-3) + x = 36

3x - 3 = 36 combine like terms

+3 +3 add 3 to both sides

3x = 39

3 3 divide both sides by 3

x = 13

13 is the first number

the 2nd number is 3 let than twice the first so we create and solve a new equation:

2x - 3 = ?

2(13) = ? substitute 13 from the

smaller number to solve

23 = the 2nd number

3 0

3 years ago

Help pleaseee will mark brainliest

STatiana [176]

Ais the answer I’m pretty sure

4 0

3 years ago