Alvin is planning to be out of town for the day, so he asks a friend to dog-sit his 3 dogs. Each dog eats 0.5 pounds of food every day. If dog food is sold in 12-ounce cans, how many cans should Alvin leave for the time he is away?

2 cans

Step-by-step explanation:

He has 3 dogs and each eats .5 lbs

per day 3 * .5 = 1.5 lbs

He is gone for 1 day, so they will need 1.5 lbs

1 pound is 16 ounces

1.5 lbs * 16 ounces/1 lb =24 ounces

Each can is 12 ounces

24/12 = 2 cans

2 cans

Step-by-step explanation:

There are 16 oz. in a lb.

3 x .5 lb = 1.5 lb x 16 oz/lb = 24 oz / 12 oz cans = 2 cans

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