Answer:
1) -0.669
2) -0.669
3) 0.669
Step-by-step explanation:
Since we are subtracting or adding multipled of pi, we will either obtain 0.669 or -0.669 as our answer for each of the three different questions.
Cosine is the x-coordinate in our orderes pairs. If our point ends up on the right side of the y-axis, the cosine will be positive. If our point ends up on left side, it will be negative.
Choose a thetha (I'm going to choose it in degrees) in the first quadrant to help with a visual.
If theta=70:
1) then 180-70=110 which is in second quadrant, so our cosines will be opposite in value.
2) then 180+70=250 which is in third quadrant, so our cosines will be opposite in value.
3) then 4×180-70=720-70=650 =1(360)+290 which ends up in the 4th quadrant which means the consines will have the same value.
It will be 14.
i’ll attach an image to show work
Answer:
a) 
And replacing we got:

b) ![E(80Y^2) =80[ 0^2*0.45 +1^2*0.2 +2^2*0.3 +3^2*0.05]= 148](https://tex.z-dn.net/?f=%20E%2880Y%5E2%29%20%3D80%5B%200%5E2%2A0.45%20%2B1%5E2%2A0.2%20%2B2%5E2%2A0.3%20%2B3%5E2%2A0.05%5D%3D%20148)
Step-by-step explanation:
Previous concepts
In statistics and probability analysis, the expected value "is calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur and then summing all of those values".
The variance of a random variable Var(X) is the expected value of the squared deviation from the mean of X, E(X).
And the standard deviation of a random variable X is just the square root of the variance.
Solution to the problem
Part a
We have the following distribution function:
Y 0 1 2 3
P(Y) 0.45 0.2 0.3 0.05
And we can calculate the expected value with the following formula:

And replacing we got:

Part b
For this case the new expected value would be given by:

And replacing we got
![E(80Y^2) =80[ 0^2*0.45 +1^2*0.2 +2^2*0.3 +3^2*0.05]= 148](https://tex.z-dn.net/?f=%20E%2880Y%5E2%29%20%3D80%5B%200%5E2%2A0.45%20%2B1%5E2%2A0.2%20%2B2%5E2%2A0.3%20%2B3%5E2%2A0.05%5D%3D%20148)
Answer:
QN = 43
Step-by-step explanation:
3x-5 = 2x+8+3
3x-5 = 2x+11
x-5 = 11
x = 16
MP = 3x-5
MP = 3(16)-5
MP = 48-5
MP = 43
MP and QN are ≅ so QN = 43