Consider the set n of positive integers to be the universal set. sets h, t, e, and p are defined to the right. determine whether or not the sets upper e prime font size decreased by 10 and upper p prime are disjoint. h equals startset n is an element of upper n vertical line n greater than 100 endset t equals startset n is an element of upper n vertical line n less than 900 endset e equals startset n is an element of upper n vertical line n is even endset p equals startset n is an element of upper n vertical line n is prime endset

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step-by-step explanation:

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answer: 4 (:

step-by-step explanation:

answer:

c) the x-coordinate of the center of the circle increases by 3

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