Cathy found a part time job for the summer. Each week , when she works up to 10 hours she earns a regular hourly wage if she works more than 10 hours each week , she earns more money per hour for overtime hours. She worked 14.5 hour during the first week. Her paycheck before taxes and deduction was $93.75. The second week she worked 12 hours and her paycheck before taxes and deduction was $75.00. Cathy boo had told her what her hourly and overtime rates were but cathy was so excited to get the job that she couldn't remember what she was told. Write a system of equations for Cathys hourly and overtime pay rates.

hit or miss i guess they never miss huh

step-by-step explanation:

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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

49/6 is going to equal 8 1/6