Question 1 OT TU A taste test asks people from Texas and California which pasta they prefer,
brand A or brand B. This table shows the results.
Brand A
Brand B
Total
Texas
80
125
California
90
60
150
Total
170
105
275
A person is randomly selected from those tested.
What is the probability that the person is from California, given that the
person prefers brand A? Round your answer to two decimal places.
A. 0.55
O B. 0,60
oc. 0.62
D. 0:53

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

well in order to answer the question, you have to give us the dimensions of the prism first.