1Margot, the manager of a coffee shop, is planning to order aprons for each of her employees. The cloth aprons cost $4 each, while the leather aprons cost $12 each. There are 15 employees at the shop, so she needs to order at least 15 aprons. Margot determines that $120 is the maximum amount that can be spent on all of the aprons. Assume x represent the cloth aprons and y represent the leather aprons,

Part A Which inequalities represent the cost constraints? Select two.

a. 4x + 12y = 120
b. 4x + 12y 120
C. 4x + 12y 15
d. x+y< 120
e. x + y = 15
f. x+y 15

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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