Rainforest data: mean = 7  σ2 = 12.405  σ ≈ 3.522 when using the formula zx = x − μ σ for the z-score for the 11.7 data point: x = ; μ =

Mean B =μ= 7

Standard Deviation =A=σ ≈ 3.522

Variance =σ²=12.405

X=Score=Data Point=11.7

z-score for the Score 11.7

b. 153 students do not participate in sports and seventy-five 12th graders were surveyed

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