Choose the multiplication equation that is related to the division equation eight divided by one fourth.

1. one twelfth multiplied by one fourth equals eight
2. one thirty second multiplied by one fourth equals eight
3. twelve multiplied by one fourth equals eight
4. thirty two multiplied by one fourth equals eight

4. thirty two multiplied by one fourth equals eight

Step-by-step explanation:

statement equal to  8/(1/4)

                                = 8 ÷ 1/4

                                = 8 × 4/1

                                = 32

1)

one twelfth multiplied by one fourth equals eight

1/12 x 1/4 = 8

1/(12 x 4) = 8

1/48 ≠ 8

2)

one thirty second multiplied by one fourth equals eight

1/32 x 1/4 = 8

1/(32*4) = 8

1/128 ≠ 8

3)

twelve multiplied by one fourth equals eight

12 x 1/4 = 8

12/4 = 8

3 ≠ 8

4)

thirty two multiplied by one fourth equals eight

32 x 1/4 = 8

32/4 = 8

8 = 8

answer:

sometimes

*i think

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