2. Ashley's older brother, Jamaal, is planning to ride his bicycle from Los Angeles to Washington D. C., a distance of 2,668 miles, in two months. Jamaal has decided that he will ride for three days and then rest on the fourth day. If he maintains this plan, and rides on 45 of the 60 days, what
is the minimum number of miles that Jamaal must ride each day with his new plan?
A. 55 miles
B. 60 miles
O
C. 65 miles
O
D. 70 miles

The correct answer is B. 60

Explanation:

To cover the distance between Los Angeles and Washington, Jamaal needs to travel 2668 miles in 45 days considering he will rest every fourth day and therefore there are 15 days in which he will not ride his bike (60 ÷ 4 =15). Now, to find the minimum distance he needs to travel every day, simply divide the total distance into the total days he will travel 2688 ÷ 45 = 59.7333 which can be rounded as 60 miles per day. According to this, the correct answer is B.

you didn't give me the choices, so i will just give you the graph so you can look at your choices and choose the right one.

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