Erika has 3 pieces of ribbon. Each piece is 25 yards long. She needs to cut pieces that are 22 inches long . What is the greatest number of 22-inch pieces that she can cut from the three ribbons? Why is this not 122 if 3*25 is 75, and 75*36 is 2700 since a yard is 36 inches, and 2700/22 rounded to the nearest whole number is about 122? If each piece of ribbon is 25yards, wouldn't 25 times 3 equal 75? Thanks!

40 pieces (for the first question)

Step-by-step explanation:

25 yards*3 pieces=75 yards

75 yards*12 inches=900 inches

900 inches/22 inches=40 sets of 22 inches

i believe the answer is c.

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