Data on the number of hours per week of television viewing was collected on a sample of Americans. The graphs below summarize this data for two age groups. Hours Watching Television 12-17 Year-Old 18-24 Year-Old 10 12 14 16 18 20 22 24 26 28 30 32 Based on the graphs, which of the following statements is true? The Interquartile Range for the 12-17 year-old age group is greater than the 18-24 year-old age group The Interquartile Range for the 18-24 year-old age group is less than the 12-17 year-old age group o The Interquartile Range is the same for the 12-17 and 18-24 year-old age group. O The Interquartile Range for the 18-24 year-old age group is greater than the 12-17 year-old age group.​

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