For a celebration a town is going to pass out miniature replicas of the town's bell. The replicas are 9 in. tall. If the scale of the replica is l in. : 0.5 ft, how
tall is the actual bell?

The bell is 4.5 feet tall

Step-by-step explanation:

The ratio of the replicas are 1in : 0.5ft, so each inch of the model is 0.5 feet in real life.

The replicas are 9 inches tall, so you would multiply by the scale factor, 0.5 feet. You want the units to end up being feet, so you position the fractions to cancel out inches.

in x  

the inches cancel out and you are left with:

9 x 0.5 ft

Simplify.

4.5 ft

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

answer: answer is b.

[m < b = 120º]

step-by-step explanation: