Answer:
the ratio would be 6.75:4.5:3:2
Step-by-step explanation:
replace d and c with
d=2 and c=3
Then using proportion multiplication, you will find that b is 4.5
now replace all b with 4.5.
Then again using proportion multiplication, you will get a is 6.75.
Plug in a, b, c, d in the ratio and you get 6.75:4.5:3:2
<span>x + y = 0 hope this helps </span>
Answer:
(2,√21)
Step-by-step explanation:
The circle centered at the origin has equation:

Any point that satisfies this equation lie on this circle.
When x=2, we substitute and solve for y.

Take square root to get:

Therefore (2,-√21) and (2,√21) are on this circle.
From the options, (2,√21) is the correct answer
Answer:
The final position is 5 feet below the back of the truck
Step-by-step explanation:
* Lets explain how to solve the problem
- A crane lifts a pallet of concrete blocks 8 feet from the back of
a truck
- The crane lowers the pallet 13 feet after the truck drives away
- Assume that the zero level of the position of the ballet of concrete
blocks is the back of the truck
∵ The crane lifts the pallet of concrete blocks 8 feet from the back
of the truck
- That means it take the pallet from zero to 8
∴ The height of the pallet of concrete blocks is 8 feet over
the starting position
∵ The crane lowers the pallet of concrete blocks 13 feet
- That means the crane lower the pallet from the height 8 and
lift it down 13 feet, so we must to take out from the 8 feet the
13 feet to find the final position of the pallet of concrete blocks
∴ The pallet position is ⇒ 8 - 13 = -5
∴ The position of the pallet of concrete blocks is 5 feet below the
starting position which is the back of the truck
* The final position is 5 feet below the back of the truck
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.

b. You get the marginal density
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.
![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.
- Compute the marginal density of
, 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
, 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
, 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)