In each of the following scenarios, determine whether the data is paired or not paired. Part A: Compare pre- (beginning of semester) and post-test (end of semester) scores of students.
Part B: Assess gender-related salary gap by comparing salaries of randomly sampled men and women.
Part C: Compare artery thicknesses at the beginning of a study and after 2 years of taking Vitamin E for the same group of patients.
Part D: Assess effectiveness of a diet regimen by comparing the before and after weights of subjects.

the radius is 2 times the diameter.

step-by-step explanation:

$119.20

step-by-step explanation:

$372.50 - 60% off is $149. $149-20% off is $119.20

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt