(1) how many meters are in 4,250 centimeters?

(2) maria determined that the length of her driveway from the main road is 35.25 meters.
which number sentence will tell how long maria’s driveway is, measured in kilometers?

a.

35.25 × 100

b.

35.25 ÷ 1,000

c.

35.25 ÷ 100

d.

35.25 × 1,000

(3) a large spool holds 78.5 meters of steel cable.
how many centimeters of cable does the spool hold?

(4) manny ran 562.5 meters and his brother ran 75 fewer meters.
how many centimeters did manny’s brother run?

(5)the mass of a large adult male hippo is about 1,850,000 grams and the mass of a large adult female is about 1,525,000 grams.
what is the difference, in kilograms, between the masses of the adult male and female hippos?

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

step-by-step explanation: