Hi there!
If cross sections were made perpendicular to the base, they would assume the shape of the lateral sides.
Thus, the cross sections would be rectangles. The correction answer is C.
I assume c, because usually to get to the opposite you reflect the line or figure on the x axis
Answer:
4 ml of the 63% milk drink
Step-by-step explanation:
Multiplying 15 ml by 0.15 results in 2.25 ml, the amount of whole milk in the drink. Let m represent the number of ml of a drink that is 63% milk.
The final amount of milk drink that is to be 45% milk will be 15 ml + m, and the amount of whole milk contained in this drink will be 0.45(15 + m).
Then:
0.15(15 ml) + 0.63(m) = 0.45(15 + m), where m is to be in milliliters.
2.25 + 0.63m = 6.75 + 0.45m
First: consolidate the m terms on the left. 0.63m less 0.45m yields 18 m; then we have:
2.25 + 18m = 6.75, or
18 m = 4.50, or m = 4 ml.
In conclusion: adding 4 ml of that 63% milk drink to the initial 15 ml of 15% milk will result in (15 ml + 4 ml) of a 45% milk drink.
a. 
is a joint density function if its integral over the given support is 1:
so the answer is yes.
b. We should first find the density of the marginal distribution, 
:
Then
or about 0.2019.
For the other probability, we can use the joint PDF directly:
which is about 0.7326.
c. We already know the PDF for 
, so we just integrate:
![E[Y]=\displaystyle\int_{-\infty}^\infty y\,f_Y(y)\,\mathrm dy=\frac15\int_0^\infty ye^{-y/5}\,\mathrm dy=\boxed5](https://tex.z-dn.net/?f=E%5BY%5D%3D%5Cdisplaystyle%5Cint_%7B-%5Cinfty%7D%5E%5Cinfty%20y%5C%2Cf_Y%28y%29%5C%2C%5Cmathrm%20dy%3D%5Cfrac15%5Cint_0%5E%5Cinfty%20ye%5E%7B-y%2F5%7D%5C%2C%5Cmathrm%20dy%3D%5Cboxed5)
