The time in days from the beginning of each year when the first bud appears on a pumpkin plant follows a continuous random variable 50 F(d) = P(D≤d)= (d-50^2)/2500.
(a) What is the probability that the plant will bud within 80.0 days of the beginning of the year?
(b) What are the expected value and standard deviation of the time in days when the first bud appears?

the volume is the product of the area of the base, 3x(3x+4), and the height, 3x-1

step-by-step explanation:

what i would say the best answer is a. 40.5

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