Thuy rolls a number cube 7 times. Which expression represents the probability of rolling a 4 exactly 2 times? P (k successes) = Subscript n Baseline C Subscript k Baseline p Superscript k Baseline (1 minus p) Superscript n minus k. Subscript n Baseline C Subscript k Baseline = StartFraction n factorial Over (n minus k) factorial times k factorial EndFraction Subscript 7 Baseline C Subscript 5 Baseline (one-sixth) squared (one-sixth) Superscript 5 Subscript 7 Baseline C Subscript 5 Baseline (one-sixth) Superscript 5 Baseline (five-sixths) squared Subscript 7 Baseline C Subscript 2 Baseline (one-sixth) squared (five-eighths) Superscript 5 Subscript 7 Baseline C Subscript 2 Baseline (two-sixths) squared (four-sixths) Superscript 5

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

i’ll just s take the points thxs