An insurance company offers a discount to home-owners who install smoke detectors in their homes. a company representative claims that 80% or more of policyholders have smoke detectors. you draw a random sample of eight policyholders. let x be the number of policyholders in the sample who have smoke detectors. a. if exactly 80% of the policyholders have smoke detectors ( so the representative's claim is true, but just barely), what is p( x ≤ 1)? b. based on the answer to part (a), if 80% of the policyholders have somke detectors, would one policyholder with a smoke detectors in a sample of size 8 be an unusually small number? c. if you found that exactly one of the eight sample policyholders had a smoke detector, would this be convincing evidence that the claim is false? explain d. if exactly 80% of the policyholders have smoke detectors, what is p(x≤ 6)? e. based on the answer to part (d), if 80% of the policyholders have smoke detectors, would six policyholders with smoke detectors in a sample of size 8 be an unusually small number? f. if you found that exactly six of the eight sample policyholders had smoke detectors, would this be convincing evidence that the claim is false? explain.

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

139 divided by a number

step-by-step explanation:

convert the answer to millimeters there are 25.4 millimeters in an inch and 12 inches in a foot so just divide the 5280 feet into a fraction of the numbers till you get to the simplest form you need so (5280 x 12=63360 inches) (63360 x 25.4=1609344 millimeters) (5280/12=440 feet) its as simple as that just break it down to it's simplest form.

can you attach the image again? it’s not working