Answer:
The number of unique rhombuses that can be constructed is one.
Step-by-step explanation:
A rhombus is a 2D shape with 4 straight sides that are all equal length. Also opposite sides are parallel and opposite angles are equal.
The addition of the 4 angles in a rhombus is equal to 360°. We know that one angle is 40°, its opposite angle is also 40°, then the addition of the other 2 angles (which are equal) is 360° - 2*40° = 280°. The other 2 congruent angles measure 140°.
If you have the length of one side (8 cm in this case), you have the length of all sides.
In conclusion, with one side and one angle a rhombus is completely defined and it's unique.
Answer:
a) 
b) 
And replacing we got:
![P(X \geq 3) = 1- [0.2+0.3+0.1]= 0.4](https://tex.z-dn.net/?f=%20P%28X%20%5Cgeq%203%29%20%3D%201-%20%5B0.2%2B0.3%2B0.1%5D%3D%200.4)
c) 
d) 
e) 
f) 
And replacing we got:

And the variance would be:
![Var(X0 =E(X^2)- [E(X)]^2 = 6.4 -(2^2)= 2.4](https://tex.z-dn.net/?f=%20Var%28X0%20%3DE%28X%5E2%29-%20%5BE%28X%29%5D%5E2%20%3D%206.4%20-%282%5E2%29%3D%202.4)
And the deviation:

Step-by-step explanation:
We have the following distribution
x 0 1 2 3 4
P(x) 0.2 0.3 0.1 0.1 0.3
Part a
For this case:

Part b
We want this probability:

And replacing we got:
![P(X \geq 3) = 1- [0.2+0.3+0.1]= 0.4](https://tex.z-dn.net/?f=%20P%28X%20%5Cgeq%203%29%20%3D%201-%20%5B0.2%2B0.3%2B0.1%5D%3D%200.4)
Part c
For this case we want this probability:

Part d

Part e
We can find the mean with this formula:

And replacing we got:

Part f
We can find the second moment with this formula

And replacing we got:

And the variance would be:
![Var(X0 =E(X^2)- [E(X)]^2 = 6.4 -(2^2)= 2.4](https://tex.z-dn.net/?f=%20Var%28X0%20%3DE%28X%5E2%29-%20%5BE%28X%29%5D%5E2%20%3D%206.4%20-%282%5E2%29%3D%202.4)
And the deviation:

It isn't different, it is very much the same
1-1 = 0
.1-.1 = 0
5.25 - 3.75 = 1.50
1.0005 +1.005 = 2.0055
just make sure to line the decimal places on top of each other <span />