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3 years ago

Help—

Mathematics

1 answer:

NikAS [45]3 years ago

5 0

Answer:

7.32 inches

Step-by-step explanation:

The circumference of the circle is 46 inches, and you just have to find the radius... you do the 2xpixr=C backwards. So 2xpixr=46 simplify the expression; 6.28xr=46 then divide... r=46/6.28... Which rounds to 7.32 inches as the radius.

(And yes you are finding the radius if you are finding a line from the middle of the circle to an edge)

I hope this helps :))

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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

In a bag of 50 marbles, 20 marbles are blue or pink.

Scorpion4ik [409]

Answer:

40%

Step-by-step explanation:

The ratio is 20:50, we can expand to 40:100, so 40%

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3 years ago

The height of the cylinder is 25 inches and the radius of its base is 5 inches. What is the surface area of this cylinder, in te

Vikentia [17]

ok you need formula for surface area.

SA = πrh+2πr^2

Plug in 25 and 5

SA = 2π(5)(25)+2π(5)^2

SA = 10pi*25 + 2pi(25)

SA = 250pi + 50pi

SA = 300pi

Hope this helps :)

Jeron

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2 years ago