Answer:
The expected cost is 152
Step-by-step explanation:
Recall that since Y is uniformly distributed over the interval [1,5] we have the following probability density function for Y
if 
and 0 othewise. (To check this is the pdf, check the definition of an uniform random variable)
Recall that, by definition
Also, we are given that 
. Recall the following properties of the expected value. If X,Y are random variables, then
Then, using this property we have that ![E[C] = 50+3E[Y]+ 9E[Y^2]](https://tex.z-dn.net/?f=E%5BC%5D%20%3D%2050%2B3E%5BY%5D%2B%209E%5BY%5E2%5D)
.
Thus, we must calculate E[Y] and E[Y^2].
Using the definition, we get that
![E[Y] = \int_{1}^{5}\frac{y}{4} dy =\frac{1}{4}\left\frac{y^2}{2}\right|_{1}^{5} = \frac{25}{8}-\frac{1}{8} = 3](https://tex.z-dn.net/?f=E%5BY%5D%20%3D%20%5Cint_%7B1%7D%5E%7B5%7D%5Cfrac%7By%7D%7B4%7D%20dy%20%3D%5Cfrac%7B1%7D%7B4%7D%5Cleft%5Cfrac%7By%5E2%7D%7B2%7D%5Cright%7C_%7B1%7D%5E%7B5%7D%20%3D%20%5Cfrac%7B25%7D%7B8%7D-%5Cfrac%7B1%7D%7B8%7D%20%3D%203)
![E[Y^2] = \int_{1}^{5}\frac{y^2}{4} dy =\frac{1}{4}\left\frac{y^3}{3}\right|_{1}^{5} = \frac{125}{12}-\frac{1}{12} = \frac{31}{3}](https://tex.z-dn.net/?f=E%5BY%5E2%5D%20%3D%20%5Cint_%7B1%7D%5E%7B5%7D%5Cfrac%7By%5E2%7D%7B4%7D%20dy%20%3D%5Cfrac%7B1%7D%7B4%7D%5Cleft%5Cfrac%7By%5E3%7D%7B3%7D%5Cright%7C_%7B1%7D%5E%7B5%7D%20%3D%20%5Cfrac%7B125%7D%7B12%7D-%5Cfrac%7B1%7D%7B12%7D%20%3D%20%5Cfrac%7B31%7D%7B3%7D)
Then
3*10^6
Three * 10 to the power of 6
From what I remember it is -x-31y
Answer:
x = 25
<B = 120 degrees
<C = 30 degrees
Step-by-step explanation:
Total angle measure of a triangle - 180 degrees
Add all the angles together to find the value of x
30 + 4x + 20 + x + 5 = 180
55 + 5x = 180
55 - 55 + 5x = 180 - 55
5x = 125
x = 25
<B = 4(25) + 20
<B = 100 + 20
<B = 120
<C = 25 + 5
<C = 30
Answer:
10 kilometers
Step-by-step explanation:
4 kilometers north plus 6 kilometers east makes 10 kilometers. This is the right answer.
