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3 years ago

13

Jane is paid 14.85 an hour for regular 40 hour work week. her overtime pay for any hours over 40 per week is 1.5 times her regul

ar hourly rate. this past week and Jane earned $727.65 in total pay. how many hours of overtime did she work this past week?

1 answer:

klasskru [66]3 years ago

4 0

Around 6 hours (exact decimal would be 5.99865). I did this by multiplying 14.85*40 (getting 594). After that, I subtracted 594 from 727.65 (getting 133.65), then multiplying 14.85 by 1.5, getting 22.28, and then, I did 133.65/22.28, getting 5.99865, which I rounded to 6.

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I know you want to answer this question.

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Step-by-step explanation:

$\frac{1}{2} ^{x-4}$ - 3 = $4^{x-3}$ - 2

First, convert $4^{x-3}$ to base 2:

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$\frac{1}{2} ^{x-4}$ - 3 = $(2^{2})^{x-3}$ - 2

Next, convert $\frac{1}{2} ^{x-4}$ to base 2:

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Apply exponent rule: $(a^{b})^{c}$ = $a^{bc}$ :

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Apply exponent rule: $(a^{b})^{c}$ = $a^{bc}$ :

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Apply exponent rule: $a^{b+c}$ = $a^{b}$ $a^{c}$ :

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Apply exponent rule: $(a^{b})^{c}$ = $a^{bc}$ :

$2^{-1x}$ = $(2^{x})^{-1}$ , $2^{2x}$ = $(2^{x})^{2}$

$(2^{x})^{-1}$ * $2^{4}$ - 3 = $(2^{x})^{2}$ * $2^{-6}$ - 2

Rewrite the equation with $2^{x} = u$ :

$(u)^{-1}$ * $2^{4}$ - 3 = $(u)^{2}$ * $2^{-6}$ - 2

Solve $u^{-1}$ * $2^{4}$ - 3 = $u^{2}$ * $2^{-6}$ - 2:

$u^{-1}$ * $2^{4}$ - 3 = $u^{2}$ * $2^{-6}$ - 2

Refine:

$\frac{16}{u}$ - 3 = $\frac{1}{64}$ $u^{2}$ - 2

Add 3 to both sides:

$\frac{16}{u}$ - 3 + 3 = $\frac{1}{64}$ $u^{2}$ - 2 + 3

Simplify:

$\frac{16}{u}$ = $\frac{1}{64}$ $u^{2}$ + 1

Multiply by the Least Common Multiplier (64u):

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Simplify:

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Substitute back u = $2^{x}$ :

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