long division setup showing an incomplete calculation. 15 is in the divisor, 6396 is in the dividend, and 4 hundreds and 2 tens is written in the quotient. 6000 is subtracted from 6396 to give 396. An unknown value represented by a box is being subtracted from 396.

The unknown is 300

Step-by-step explanation:

Given the question :

long division setup showing an incomplete calculation. 15 is in the divisor, 6396 is in the dividend, and 4 hundreds and 2 tens is written in the quotient. 6000 is subtracted from 6396 to give 396. An unknown value represented by a box is being subtracted from 396

The unknown is derived by multiplying the obtained quotient by the divisor, then subtracting it from the remaining Dividend.

Since the remaining Dividend is 396, and the obtained quotient is 2 tens (20). Then (divisor × quotient) = (15 × 20) = 300.

The steps can be found in the explanation attached below

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