All categories

3 years ago

Which table shows a proportional relationship between x and y?

Mathematics

2 answers:

Alexxandr [17]3 years ago

7 0

Your answer is correct.

Serjik [45]3 years ago

7 0

The bottom choice is correct. Every y is 1/2 of every x

You might be interested in

I really need help please

antoniya [11.8K]

B. 30% is the better deal

.3x12=3.6

(:

4 0

3 years ago

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

What is f(g(x)) if f(x)= 4x²+3x-4 and g(x)=2x

S_A_V [24]

Answer:

f(g(x))=16x^2+6x-4

Step-by-step explanation:

f(g(x))=4(2x)^2 +3(2x)-4

f(g(x))=16x^2+6x-4

8 0

3 years ago

Determine the value of each variable in the figure below. Keep answers in simplest<br> radical form.

Tanzania [10]

Answer:

a = 21

b = 63

c = 42√3

d = 21√3

Step-by-step explanation:

The sides of a 30°-60°-90° triangle have the ratios 1 : √3 : 2. The given side (42) is the longest side of the smallest triangle, and the shortest side of the largest triangle.

That means the other sides of the smallest triangle will be ...

a = 42/2 = 21

a+b = 2(42) = 84

b = (a+b) -a = 84 -21 = 63

d = 21√3 . . . . middle-length side of the smallest triangle

c = 42√3 . . . . middle-length side of the largest triangle

The values of the variables are ...

a = 21
b = 63
c = 42√3
d = 21√3

7 0

2 years ago

How should I choose stocks?

Art [367]

One way to choose stocks is by customers demand

4 0

3 years ago