A number without denominator such is equal to number with denominator 1.
So, 24 is equal to 24/1
5/8 x 24
= 5/8 x 24/1
= (5x24) / (8x1)
= 120/8
= 15
36ft by 32ft. I didn't do any math to solve this, but you can tell by comparing the ratios.
9:8 (Nine is just larger than eight, so you need to find an answer where the first number is just larger than the second. None of the others come anywhere close to that besides 36:32)
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
