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Aliun [14]
2 years ago
11

Your gross pay is $2,759.00. your involuntary deductions are fica (7.65%), federal withholding (12%), and state withholding (7%)

. how much are you allowed for housing and fixed expenses? a. $772.52 b. $993.24 c. $728.54 d. $566.64
Mathematics
2 answers:
Alexxandr [17]2 years ago
8 0
728.54 is the correct answer in this particular situation.
max2010maxim [7]2 years ago
6 0
Gross pay = $2,759.00
Total deductions = 7.65%+12%+7% = 26.65% = 0.2665

By thumb rule, rent and other fixed expenses ≤ 28% of Monthly gross salary

Therefore,
Allowed housing and fixed expenses = 0.28*2,759 = $772.52

Then, a. is the correct answer.
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F(x)=3x 2 +9f, left parenthesis, x, right parenthesis, equals, 3, x, squared, plus, 9 and g(x)=\dfrac{1}{3}x^2-9g(x)= 3 1 ​ x 2
34kurt

Answer:

f(g(x)) = \frac{1}{3}x^4 - 18x^2 + 252

g(f(x)) = 3x^4 + 18x^2 + 18

<em>f(x) and g(x) and not inverse functions</em>

Step-by-step explanation:

Given

f(x) = 3x^2 + 9

g(x) = \dfrac{1}{3}x^2 - 9

Required

Determine f(g(x))

Determine g(f(x))

Determine if both functions are inverse:

Calculating f(g(x))

f(x) = 3x^2 + 9

f(g(x)) = 3(\frac{1}{3}x^2 - 9)^2 + 9

f(g(x)) = 3(\frac{1}{3}x^2 - 9)(\frac{1}{3}x^2 - 9) + 9

Expand Brackets

f(g(x)) = (x^2 - 27)(\frac{1}{3}x^2 - 9) + 9

f(g(x)) = x^2(\frac{1}{3}x^2 - 9) - 27(\frac{1}{3}x^2 - 9) + 9

f(g(x)) = \frac{1}{3}x^4 - 9x^2 - 9x^2 + 243 + 9

f(g(x)) = \frac{1}{3}x^4 - 18x^2 + 252

Calculating g(f(x))

g(x) = \dfrac{1}{3}x^2 - 9

g(f(x)) = \frac{1}{3}(3x^2 + 9)^2 - 9

g(f(x)) = \frac{1}{3}(3x^2 + 9)(3x^2 + 9) - 9

g(f(x)) = (x^2 + 3)(3x^2 + 9) - 9

Expand Brackets

g(f(x)) = x^2(3x^2 + 9) + 3(3x^2 + 9) - 9

g(f(x)) = 3x^4 + 9x^2 + 9x^2 + 27 - 9

g(f(x)) = 3x^4 + 18x^2 + 18

Checking for inverse functions

f(x) = 3x^2 + 9

Represent f(x) with y

y = 3x^2 + 9

Swap positions of x and y

x = 3y^2 + 9

Subtract 9 from both sides

x - 9 = 3y^2 + 9 - 9

x - 9 = 3y^2

3y^2 = x - 9

Divide through by 3

\frac{3y^2}{3} = \frac{x}{3} - \frac{9}{3}

y^2 = \frac{x}{3} - 3

Take square root of both sides

\sqrt{y^2} = \sqrt{\frac{x}{3} - 3}

y = \sqrt{\frac{x}{3} - 3}

Represent y with g(x)

g(x) = \sqrt{\frac{x}{3} - 3}

Note that the resulting value of g(x) is not the same as g(x) = \dfrac{1}{3}x^2 - 9

<em>Hence, f(x) and g(x) and not inverse functions</em>

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2 years ago
The distribution of the amount of money spent by students for textbooks in a semester is approximately normal in shape with a me
kkurt [141]

The final part of the question is asking;

How much did all (99.7%) of the students spend on textbooks in a semester

Answer:

almost all (99.7%) of the students spent between $165 and $315 on textbooks in a semester.

Step-by-step explanation:

The standard deviation rule describes to us that for distributions that have the normal shape, approximately 99.7% of the observations fall within 3 standard deviations of the mean.

In this question, we are given that; Mean = 240 and Standard deviation= 25

So, 3 standard deviation below the mean = Mean - 3(standard deviation)

= 240 - (3 × 25)

= 240 - 75 = 165

Now, 3 standard deviation above the mean = Mean + 3 standard deviation = 240 + (3 × 25)

= 240 + 75 = 315

So, almost all (99.7%) of the students spent between $165 and $315 on textbooks in a semester.

7 0
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PLEASE ANSWER FAST!!!!
xz_007 [3.2K]

Answer:

The answer is 24.

Step-by-step explanation:

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6 pints of a 20 percent solution of alcohol in water are mixed with 4 pints of a 10 percent alcohol in water solution. The perce
andreev551 [17]
Total Volume would be 6 + 4 = 10 pints
Let's calculate the volume of alcohol in final solution:
20% * 6 = 1.2 pints
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2 years ago
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Doss [256]

Answer:

d = \sqrt{2}\cdot \sqrt {1-\cos t - \sin t}

Step-by-step explanation:

Let suppose that one of the radii meets the circle at the point (1,0). The straight line distance formula is:

d = \sqrt{(\cos t - 1)^{2}+(\sin t - 1)^{2}}

d = \sqrt{(\cos^{2}t - 2\cdot \cos t + 1)+(\sin^{2}t - 2\cdot \sin t + 1)}

d = \sqrt{2-2\cdot (\cos t + \sin t )}

d = \sqrt{2}\cdot \sqrt {1-\cos t - \sin t}

5 0
2 years ago
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