Demonstrate how to use algebraic equations to write the decimal 0.0&4&1&&7& as a fraction with a
whole number numerator and denominator. (Notice the line is over just the numbers 4,1&7)

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

answer: graph 2

step-by-step explanation:

answer: the answer is 100 x 12,500, which is 1,250,000.

step-by-step explanation: emily solved for a part when she should have solved for the whole.  

875,000 should be the numerator of the equivalent ratio.  

70 x 12,500 is 875,000.