Match the situations with the equations: 1:Mai slept for x hours, and Kiran slept for 1/10 less than that
2:Kiran practice the piano for x hours and my practice for two and a half less than that.
3: my drink x oz of juice and Karen drink 4/3 more than that.
4: Kiran spent x dollars and Mai spent 1/4 less than that
5: my ate x grams of almonds and Karen ate 1.5 times more than that
6: Kiran collected x pounds of recycling in my collected 3/10 less than that.
7: Mai walked x kilometers and Kiran walked 3/8
8:Kiran completed x puzzles and Mai completed 3/5 more than that
Please help!!!

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

d. you cannot tell because there are no values shown.

the football players are volunteering for the test.

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