Agrocery store carries the same 8 flavors of 4 brands of yogurt. every flavor for each brand is sold in single-serving and quart-sized containers. how many different brand/flavor/size combinations of yogurt does the store sell?
a.14

b.24

c.64

d.144

Option 'c' is correct.

Step-by-step explanation:

Since we have given that

Number of flavors = 8

Number of brands = 4

Number of containers = 2

1) Single serving

2) Quart sized

According to question, Every flavor for each brand is sold in single-serving and quart-sized containers.

So, Number of different brand flavor size combinations of yogurt would be

Hence, Option 'c' is correct.

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