Answer:
f(x) = 25.50x      Roberto can buy 7 video games
Step-by-step explanation: 
Each game is $25.50 which in math means it has an "x"
So if x=1 then 25.50x says that 1 video game is $25.50
Set up the equation:
200 = 25.50x (divide both sides by 25.50 to isolate the x)
200/25.50 = 7.84
x = 7.84
You can't have 0.84 of a video game, so Roberto can only buy 7 of them.
 
        
                    
             
        
        
        
The x and y axis so that’s why it’s true
        
                    
             
        
        
        
Answer:
9(8+y)
Step-by-step explanation:
simple addition, plz answer my question posted on my profile under "questions asked" and click my recent one. it would mean a lot.... thanks!!
 
        
                    
             
        
        
        
I'm going to assume the joint density function is

a. In order for  to be a proper probability density function, the integral over its support must be 1.
 to be a proper probability density function, the integral over its support must be 1.

b. You get the marginal density  by integrating the joint density over all possible values of
 by integrating the joint density over all possible values of  :
:

c. We have

d. We have

and by definition of conditional probability,


e. We can find the expectation of  using the marginal distribution found earlier.
 using the marginal distribution found earlier.
![E[X]=\displaystyle\int_0^1xf_X(x)\,\mathrm dx=\frac67\int_0^1(2x^2+x)\,\mathrm dx=\boxed{\frac57}](https://tex.z-dn.net/?f=E%5BX%5D%3D%5Cdisplaystyle%5Cint_0%5E1xf_X%28x%29%5C%2C%5Cmathrm%20dx%3D%5Cfrac67%5Cint_0%5E1%282x%5E2%2Bx%29%5C%2C%5Cmathrm%20dx%3D%5Cboxed%7B%5Cfrac57%7D)
f. This part is cut off, but if you're supposed to find the expectation of  , there are several ways to do so.
, there are several ways to do so.
- Compute the marginal density of  , then directly compute the expected value. , then directly compute the expected value.

![\implies E[Y]=\displaystyle\int_0^2yf_Y(y)\,\mathrm dy=\frac87](https://tex.z-dn.net/?f=%5Cimplies%20E%5BY%5D%3D%5Cdisplaystyle%5Cint_0%5E2yf_Y%28y%29%5C%2C%5Cmathrm%20dy%3D%5Cfrac87)
- Compute the conditional density of  given given , then use the law of total expectation. , then use the law of total expectation.

The law of total expectation says
![E[Y]=E[E[Y\mid X]]](https://tex.z-dn.net/?f=E%5BY%5D%3DE%5BE%5BY%5Cmid%20X%5D%5D)
We have
![E[Y\mid X=x]=\displaystyle\int_0^2yf_{Y\mid X}(y\mid x)\,\mathrm dy=\frac{6x+4}{6x+3}=1+\frac1{6x+3}](https://tex.z-dn.net/?f=E%5BY%5Cmid%20X%3Dx%5D%3D%5Cdisplaystyle%5Cint_0%5E2yf_%7BY%5Cmid%20X%7D%28y%5Cmid%20x%29%5C%2C%5Cmathrm%20dy%3D%5Cfrac%7B6x%2B4%7D%7B6x%2B3%7D%3D1%2B%5Cfrac1%7B6x%2B3%7D)
![\implies E[Y\mid X]=1+\dfrac1{6X+3}](https://tex.z-dn.net/?f=%5Cimplies%20E%5BY%5Cmid%20X%5D%3D1%2B%5Cdfrac1%7B6X%2B3%7D)
This random variable is undefined only when  which is outside the support of
 which is outside the support of  , so we have
, so we have
![E[Y]=E\left[1+\dfrac1{6X+3}\right]=\displaystyle\int_0^1\left(1+\frac1{6x+3}\right)f_X(x)\,\mathrm dx=\frac87](https://tex.z-dn.net/?f=E%5BY%5D%3DE%5Cleft%5B1%2B%5Cdfrac1%7B6X%2B3%7D%5Cright%5D%3D%5Cdisplaystyle%5Cint_0%5E1%5Cleft%281%2B%5Cfrac1%7B6x%2B3%7D%5Cright%29f_X%28x%29%5C%2C%5Cmathrm%20dx%3D%5Cfrac87)
 
        
             
        
        
        
  &
 &  so ,
 so ,  .
 .
<u>Step-by-step explanation:</u>
Here we have , ab= 8 & a^2+b^2=16 i.e.  and
  and  .
 .
We need to find value of (a+b)^2 i.e.  :
 :
It's and identity and we know that 
⇒ 
⇒ 
⇒ 
⇒ 
⇒ 
∴  &
 &  so ,
 so ,  .
 .