Asmall town surveys 250 adults, 180 of which are parents, about whether or not a park should be expanded. the results showed that 150 of the adults with children and 40 of those without thought the park should be expanded. use this information to complete the two-way table below. enter the correct values in the boxes.

yes no
parents |
|
not parents |

250 adults and 180 of which are parents, so 250 -180 = 70 are not parents. The results showed that 150 of the adults with children and 40 of those without thought the park should be expanded. So there are 180 – 150 = 30 parents who answered no. and 70 – 40 = 30 not parents who answered no.    
                    yes | no
parents       150 | 30
not parents   40 | 30

D.

a. geometricb. g[h] = (3/4)·g[h-1]; g[1] = 384c. g[h] = 384·(3/4)^(h-1)d. g[12] ≈ 16.2183 gallonse. g[12] ≈ 64.8732 quarts

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