Select the correct answer. A sample survey was taken of 100 customers to determine which brand of snack crackers they prefer. Brand A was selected by about 17% of the customers, brand B was selected by about 50% of the customers, and brand C was selected by the remaining customers. Which statistical model could be used to make predictions about the snack cracker brand a random customer may prefer? A. brand A: die roll is 3 brand B: die roll is even brand C: die roll is 1 or 5 B. brand A: die roll is 1 brand B: die roll is even brand C: die roll is odd C. brand A: die roll is 3 brand B: die roll is less than 3 brand C: die roll is greater than 3 D. brand A: die roll is 4 brand B: die roll is greater than 4 brand C: die roll less than 4

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see attached graph

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