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3 years ago

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Given the pay rate and hours worked, determine the gross earnings, Federal taxes (assuming 20% of gross earnings), state taxes (

assuming 6% of gross earnings), social security deduction (assuming 6.45% of gross earnings), total deductions, and net pay.

1 answer:

qaws [65]3 years ago

8 0

Answer: Total deductions= 0.3245ab and Net pay= 0.6755ab

Step-by-step explanation:

Suppose, the pay rate= a dollar per hour

And hours worked= b hours

Gross earning= the pay rate x hours worked

Gross earning= ab

Deductions are:

Federal taxes= 20% of gross earnings= 20/100 x ab= 0.2ab dollars

State taxes= 6% of gross earning= 6/100 x ab= 0.06ab dollars

Social security deduction= 6.45% of gross earning= 6.45/100 x ab= 0.0645ab

So,

The total deduction= federal taxes + state taxes + social security deduction

The total deduction= 0.2ab + 0.06ab + 0.0645ab= 0.3245ab dollars

And

Net pay= gross earning – total deduction

Net pay= ab – 0.3245ab= 0.6755ab dollars

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PLEASE!!! NEED HELP ASAP!!! 50 PTS AND BRAINLIEST!!!

noname [10]

1) Inverse function: $f^{-1}(x)=g(x)=\frac{x+4}{3}$

2) $f(1) = -1, g(-1) = 1$

3) $f(g(x))=g(f(x))=x$

Step-by-step explanation:

1)

In this first method, we want to find the inverse function of $f(x)$ .

The original function is:

$f(x) = 3x-4$

We rewrite it as

$y=3x-4$

We swap the name of the variables:

$x=3y-4$

Adding +4 on both sides:

$x+4=3y-4+4\\x+4=3y$

And dividing by 3 on both sides:

$y=\frac{x+4}{3}$

which is identical to $g(x)$ :

$g(x)=\frac{x+4}{3}$

2)

In this second method, we want to use the output of one function as input to the other function, and show that the output value is equal to the imput value.

We start using the function

$f(x)=3x-4$

We choose $x=1$ . We find:

$f(1)=3(1)-4=3-4=-1$

Now we use this output value as input in the function

$g(x)=\frac{x+4}{3}$

Substituting $x=-1$ ,

$g(-1)=\frac{-1+4}{3}=\frac{3}{3}=1$

So, the final output value (1) is equal to the input value (1).

3)

Here we want to verify that the two are inverse functions by showing that

$f(g(x))=x$

We have

$f(x)=3x-4\\g(x)=\frac{x+4}{3}$

Substituting g(x) into f(x),

$f(g(x))=3g(x)-4 = 3(\frac{x+4}{3})-4=(x+4)-4=x$

Viceversa, we want to show that

$g(f(x))=x$

Substituting g(x) into f(x), we get

$g(f(x))=\frac{f(x)+4}{3}=\frac{(3x-4)+4}{3}=\frac{3x-4+4}{3}=\frac{3x}{3}=x$

So, the two functions are one the inverse of the other.

Learn more about inverse functions:

brainly.com/question/1632445

brainly.com/question/2456302

brainly.com/question/3225044

#LearnwithBrainly

6 0

3 years ago

1.1<br>Solve the following equations:<br>1.1.1 (x+5)(x-3)=33

schepotkina [342]

Step-by-step explanation:

x²-3x +5x -15=33

x²-3x+5x=33+15

x²-3x+5x=48

x²+2x=48

divide both sides by 2

x²+x =24

x²= 24

x= ✓24

dunno from here

8 0

3 years ago

A. 5<br> B. 5.5<br> C. 6<br> D. 5[2

34kurt

Answer is D 5]2 that's wut I know

8 0

3 years ago

POSSIBLE POINTS: 10

Nadusha1986 [10]

Answer:

5 + 3t

Step-by-step explanation:

t = amount Tanya has

Lucy = $5 more than 3x of what Tanya has

5 0

3 years ago

Solve using the method of elimination and determine if the system has 1 solution, no solutions, or infinite solutions

Minchanka [31]

$\begin{array}{rrrrr} 10x&-&18y&=&2\\ -5x&+&9y&=&-1 \end{array}~\hfill \implies ~\hfill \stackrel{\textit{second equation }\times 2}{ \begin{array}{rrrrr} 10x&-&18y&=&2\\ 2(-5x&+&9y&)=&2(-1) \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{rrrrr} 10x&-&18y&=&2\\ -10x&+&18y&=&-2\\\cline{1-5} 0&+&0&=&0 \end{array}\qquad \impliedby \textit{another way of saying \underline{infinite solutions}}$

if we were to solve both equations for "y", we'd get

$10x-18y=2\implies 10x-2=18y\implies \cfrac{10x-2}{18}=y\implies \cfrac{5}{9}x-\cfrac{1}{9}=y \\\\\\ -5x+9y=-1\implies 9y=5x-1\implies y=\cfrac{5x-1}{9}\implies y = \cfrac{5}{9}x-\cfrac{1}{9}$

notice, the 1st equation is really the 2nd in disguise, since both lines are just pancaked on top of each other, every point in the lines is a solution or an intersection, and since both go to infinity, well, there you have it.

8 0

2 years ago