Corinne buys a craft kit that has 10 different colors of beads. There are 10 beads of each color. She uses 5 of the 10 blue beads for a project. To complete the project, she uses 43 more beads from the kit.

The kit has 10 different colors of beads.

There are 10 beads of each color.

This means that we have 10*10 = 100 beads in total.

We know that she uses 5 beads in a project, and then to complete it she uses other 43 beads.

Then the total number of beads used is:

43 + 5 = 48 beads.

Then the remaining number of beads is:

100 - 48 = 52

answer: b

step-by-step explanation:

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