The lengths of some caterpillars are shown below.
How many caterpillar lengths measured 4 3/4?

2

Step-by-step explanation:

This problem is fairly simple. I almost made the mistake of overthinking it (:

Anyway, looking at the number line we can see whole numbers (i.e., 1, 2,5,6...) and little ticks.

The little ticks are representing each fraction.

For example, the first tick after 4 is representing 1/4. The second 1/2 (2/4 simplified.)

Therefore the next tick (number 3) will be our desired place.

Good. Now that we've found it, all we have to do is count each dot. That represents how many lengths are each. Since there are, 2 dots, there must be 2 caterpillars with length 4 3/4 inches.

Thus, our desired answer is 2.

Hope this helps!

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