If, while training for a marathon, you ran 68 miles in 2 2/3 months, how many miles did you run each month? (assume you ran the same amount each month) write your answer as a whole number, proper fraction, or mixed number in simplest form.

25 1/2

Step-by-step explanation:

You need to divide 68 miles by 2 2/3 months.

68/(2 2/3) =

= 68/(8/3)

= 68 * 3/8

= 68/1 * 3/8

= 204/8

= 102/4

= 51/2

= 25 1/2

25½ mi/mo  

Step-by-step explanation:

Distance = rate × time

d = rt     Divide each side by t

r = d/t

Data:

d = 68 mi

t = 2⅔ mo

Calculation:

r = 68/(2⅔)        Convert denominator to improper fraction

  = 68/(⁸/₃)         Invert the denominator and multiply

  = ⁶⁸/₁ × ³/₈       Multiply the numerators and denominators

  = ²⁰⁴/₈             Reduce to simplest terms

  = ⁵¹/₂               Convert to mixed number

  = 25½ mi/mo

On average, you ran 25½ miles each month.

£56

step-by-step explanation:

u divide 24 by 3 and u get 8 so if u do 8 time 7 or 8+8+8+8+8+8+8 u get 56 and 56 divided by 7 is 8.

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