7(9+3) using the distributive property

Deductions this Week: Federal Tax $52.02, FICA $33.02, State $5.33. Find the annual Federal Tax deduction

Leya [2.2K]

Answer:

The annual federal tax deduction is $2705.04 .

Step-by-step explanation:

As given deduction in a week

Federal Tax $52.02

As there are 52 weeks in a week.

Thus

Annual Federal Tax deduction = Total number of weeks in a year × Federal Tax deduction in week

= 52 × 52.02

= $ 2705.04

Therefore the annual federal tax deduction is $2705.04 .

3 0

3 years ago

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If <img src="https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20x%20%3D%20log_%7Ba%7D%28bc%29" id="TexFormula1" title="\rm \: x = log_{a}(

timama [110]

Use the change-of-basis identity,

$\log_x(y) = \dfrac{\ln(y)}{\ln(x)}$

to write

$xyz = \log_a(bc) \log_b(ac) \log_c(ab) = \dfrac{\ln(bc) \ln(ac) \ln(ab)}{\ln(a) \ln(b) \ln(c)}$

Use the product-to-sum identity,

$\log_x(yz) = \log_x(y) + \log_x(z)$

to write

$xyz = \dfrac{(\ln(b) + \ln(c)) (\ln(a) + \ln(c)) (\ln(a) + \ln(b))}{\ln(a) \ln(b) \ln(c)}$

Redistribute the factors on the left side as

$xyz = \dfrac{\ln(b) + \ln(c)}{\ln(b)} \times \dfrac{\ln(a) + \ln(c)}{\ln(c)} \times \dfrac{\ln(a) + \ln(b)}{\ln(a)}$

and simplify to

$xyz = \left(1 + \dfrac{\ln(c)}{\ln(b)}\right) \left(1 + \dfrac{\ln(a)}{\ln(c)}\right) \left(1 + \dfrac{\ln(b)}{\ln(a)}\right)$

Now expand the right side:

$xyz = 1 + \dfrac{\ln(c)}{\ln(b)} + \dfrac{\ln(a)}{\ln(c)} + \dfrac{\ln(b)}{\ln(a)} \\\\ ~~~~~~~~~~~~+ \dfrac{\ln(c)\ln(a)}{\ln(b)\ln(c)} + \dfrac{\ln(c)\ln(b)}{\ln(b)\ln(a)} + \dfrac{\ln(a)\ln(b)}{\ln(c)\ln(a)} \\\\ ~~~~~~~~~~~~ + \dfrac{\ln(c)\ln(a)\ln(b)}{\ln(b)\ln(c)\ln(a)}$

Simplify and rewrite using the logarithm properties mentioned earlier.

$xyz = 1 + \dfrac{\ln(c)}{\ln(b)} + \dfrac{\ln(a)}{\ln(c)} + \dfrac{\ln(b)}{\ln(a)} + \dfrac{\ln(a)}{\ln(b)} + \dfrac{\ln(c)}{\ln(a)} + \dfrac{\ln(b)}{\ln(c)} + 1$

$xyz = 2 + \dfrac{\ln(c)+\ln(a)}{\ln(b)} + \dfrac{\ln(a)+\ln(b)}{\ln(c)} + \dfrac{\ln(b)+\ln(c)}{\ln(a)}$

$xyz = 2 + \dfrac{\ln(ac)}{\ln(b)} + \dfrac{\ln(ab)}{\ln(c)} + \dfrac{\ln(bc)}{\ln(a)}$

$xyz = 2 + \log_b(ac) + \log_c(ab) + \log_a(bc)$

$\implies \boxed{xyz = x + y + z + 2}$

(C)

6 0

2 years ago

Solve the system:

marysya [2.9K]

Answer:

390

Step-by-step explanation:

4 0

3 years ago

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If sin x = .52 and cos x = .85, what is cot x?

lozanna [386]

Hi there

That's easy

All you have to know is that : cot x = cos x / sin x

cot x = .85 / .52 = 1.6346

I hope that's help:)

Any questions ? let me know

5 0

3 years ago

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An immigration agent sampled cars going from country M to country N. In his report, he indicated that of the 85 cars sampled,

amid [387]

Answer:

the numbers of women drivers are inconsistent

Step-by-step explanation:

Let W, C, P stand for the conditions that the drivers were women, the drivers were citizens, and the car had passengers, respectively.

We are told the number of WCP cars is 13, the number of WC cars is 23, and the number of WP cars is 22. The total of WC and WP cars counts WCP cars twice, so the total of cars in these three categories combined is ...

WC +WP -WCP = 23 +22 -13 = 32

This number (32) is more than the total number of cars with women driving (27), so there is obviously a mistake.

5 0

3 years ago