Help ASAP please and thanks Problems 9 and 10 concern the following situation.
Vera's gross weekly pay is $976.42. From each
(weekly) paycheck $135.32 is deducted for federal
tax, $50.27 for state tax, 6.5% for Social Security,
and 1.5% for Medicare. Also, her weekly living
expenses are $465.27.
9) What is Vera's weekly disposable income?
A) $281.09
B) $270.18
C) $269.27
D) $258.36
E) $247.45
10) If Vera commits to saving 65% of her
disposable income, how much will she save in
a year?
A) $8630.32
B) $8541.41
C) S8452.50
D) $8363.69
E) $8274.78

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