Answer:
You'd use grams because the strawberry is so small, and kilograms are emasuring bigger things.
Step-by-step explanation:
2.

(this is given in the first sentence)
3.

and

due to ...
7. ... the alternate interior angles theorem (which holds because

and

are parallel)
8. Because the above establishes that

, which means

, which in turn means

is a parallelogram.
Answer:
Equivalent
Step-by-step explanation:
The sets are not equal since computer science is not the same as algebra.
Equal means exactly the same
Equivalent means they have the same number of items in them
If they are equal, they are equivalent
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)
Answer:
One Triangle = 2.09 in²
Two Triangles = 4.18 in²
Rectangle = 17.48 in²
Total area of whole trapezoid = 21.66 in²
Step-by-step explanation:
Since it was not clarified which region is shaded we will just find the area of each individual part of the shape.
Let's start with the triangles.
1. To find the area of a triangle, the formula is
. It is given that the base of one triangle is equal to 1.1 in and the height is equal to 3.8 in., so in the equation, it would look like:
in²
2. So now that we know one triangle is equal to 2.09 in², we now know that the other triangle is equal to the same area. To find the total of the two triangles you need to multiply the area by 2:
in²
Moving on to the rectangle...
1. To find the area of the rectangle we need to use the formula base times height or b x h. It is given that the height is 3.8 in while the length is 4.6 in. So in the equation it would look like:
in²
Now to find the total area of all shapes combined...
1. To do this, we just need to add up all the areas we found, so...
17.48 + 4.18 = 21.66 in²