Answer:
The probability that you get zero questions correct is 0.4096
The probability that you get one questions correct is 0.4096
The probability that you get three questions correct is 0.0256
Step-by-step explanation:
These probability can be describe with a Binomial Distribution. These distribution can be used when we have n identical and independent situations in which there is a probability p or probability of success and a probability q or probability of fail. Additionally q is equal to 1 - p. The probability of x for a situation in which we can apply binomial distribution is:

Where x is the variable that says the number of success in the n situations
And nCx is calculate as:

From the question we can identify that:
- n is equal to 4 multiple choice question
- p is 1/5 or 0.2, the probability of get one question correct
- q is 4/5 or 0.8, the probability of get one question incorrect
Then the probability of get zero questions correct of 4 questions is:

The probability of get one question correct of 4 questions is:

The probability of get three questions correct of 4 questions is:

It increases then decreases then becomes constant
Answer:
112
Step-by-step explanation:
Given that in a study of the stability of IQ scores, a large group of individuals is tested once at age 18 and again at age 35.
Age 18: average score = 100, SD = 15
Age 35: average score = 100, SD = 15, r = 0.80
Let us obtain regression equation of y on x.
Let y be the scores at age 35 and x at age 18
Slope = 
The line passes through (100,100) being average of x and y
Hence regression line would be

a) Here given that x =115
Hence 
the average score at age 35 for all the individuals who scored 115 at age 18, would be 112.
b) Prediction also would be the same 112.
Y+4= x blue bikes
G-2= x yellow bikes
4y+4= 8 blue bikes
4y+2= 6 green bikes
4y= 4 yellow bikes
8 blue bikes
+
6 green bikes
+
4 yellow bikes
=
18 bikes total
Answer:
The answer is a. cos2x - sin2x - sin x. Use the rule: cos2x = (cos^2)x - (sin^2)x. So, substitute cos2x in the expression: cos2x - sinx = ((cos^2)x - (sin^2)x) - sinx = (cos^2)x - (sin^2)x - sinx. Therefore, choice a. is correct choice.