The ratio of sam's age to Hank's age is 5 to 3.if the sum of their ages is 24, how old is Hank? a. 21
b. 9
c. 19
d. 15

c is the answer if this question

9

Step-by-step explanation:

So for this it's kinda guessing.

Just do

5 × 1 = 5 and 3 × 1 = 3

Now add 5 + 3 = 8, that's not 24

5 × 2 = 10 and 3 × 2 = 6

10 + 6 = 16, again 16 isn't equivalent to 24

5 × 3 = 15 and 3 × 3 = 9

15 + 9 = 24, and since they're asking for hank's age, it would be 9.

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im with everythinglos so yeahhhhh

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