Aflorist is creating centerpieces for an upcoming event later this evening. she has already been working for two hours and has budgeted only 6 hours to create the centerpieces. each centerpiece takes 15 minutes to make. if x represents the number of centerpieces she makes from now until the event, which inequality represents this situation?
120x - 15 ≤ 360
120 + 15x ≤ 360
15 + 120x < 360
120 - 15x < 360

Since, she has already been working for two hours (120 minutes) and has budgeted only 6 hours (360 minutes) to create the centerpieces.

Since, each centerpiece takes 15 minutes to make, the time it takes her to make x centerpieces is given by 15x.

Therefore, the correct inequality representing the situation is given by 120 + 15x ≤ 360.

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a. geometricb. g[h] = (3/4)·g[h-1]; g[1] = 384c. g[h] = 384·(3/4)^(h-1)d. g[12] ≈ 16.2183 gallonse. g[12] ≈ 64.8732 quarts

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