Mathematics College

Shay's net pay is $575.50 biweekly. If her gross annual income is$17,500, how much is deducted from each paycheck?a. $153.67b. $2,537c. $97.58d. $3,688

Answers

Answer 1

a. $157.67

Explanation:

>> net income (total amount without the taxes etc...)

. biweekly = $575.50

. per month = $575.50 * 2 = $1,151 (~since it happens 2 times per month)

. per year = $1,151 * 12 = $13,812

>> gross income (total amount with the taxes etc...)

. per year = $17,500

>> amount deducted (~going to taxes etc...)

. per year = $17,500 - $13,812 = $3,688

. per month = $3,688 / 12 =~ $307.33

. per paycheck = $307.33 / 2 =~ $153.67

Related Questions

Composition of Functions and Inverses:Question 7Which expression represents f(f(x)) if f(x) = x2 – 1? A. 2x ^2-2 B. X^4-2x^2+1C. XD. X^4-2x^2

Answers

To solve the question, we will follow the steps below:

[tex]f(x)=x^2-1[/tex]

To find f(f(x)), we will simply replace x by x² - 1 in the function x² - 1

That is:

f((fx)) = (x²-1)² - 1

Then we open the parenthesis

f(f(x)) = (x² - 1)(x² -1) - 1

=x²(x²-1)-1(x²-1) - 1

= x⁴ - x² - x² + 1 - 1

= x⁴ - 2x²

So the correct option is option D. which is x⁴ - 2x²

I need help figuring out the measures of the missing sides

Answers

Given:

• c = 20

• h = 15

• j = 12

• k = 16

Let's find the measures of the mssing sides if triangle ABC is similar to triangle JKH.

Here, the missing sides are:

Side a and Side b

Since both triangles are similar, the corresponding sides will be proportional.

To solve for the length of side a, apply the proportionality equation:

[tex]\frac{c}{h}=\frac{a}{j}[/tex]

Plug in values and solve for a:

[tex]\begin{gathered} \frac{20}{15}=\frac{a}{12} \\ \\ \text{ Cross multiply:} \\ 15a=20*12 \\ \\ 15a=240 \\ \text{ } \\ \text{ Divide both sides by 15:} \\ \frac{15a}{15}=\frac{240}{15} \\ \\ a=16 \end{gathered}[/tex]

Thereofore, the length of side a = 16

To solve for the length of side b, apply the equation:

[tex]\frac{c}{h}=\frac{b}{k}[/tex]

Plug in the values for the variables and solve for b:

[tex]\begin{gathered} \frac{20}{15}=\frac{b}{16} \\ \\ 15b=20*16 \\ \\ 15b=320 \\ \\ b=\frac{320}{15} \\ \\ b=21.3 \end{gathered}[/tex]

The length of b is 21.3

ANSWER:

• a = 16

• b = 21.3

Explain how knowing the linear factor establishes that f(10) multiple of 12.

Answers

f(10) is a multiple of 12 because f(x) has a linear factor of x+2 and x+2 = 12, when x = 10

f(10) multiple of 12 is given as:

The first-degree equations that make up a polynomial's linear factors serve as the foundation stone for higher-order and more complicated polynomials. The formula for a linear factor is ax + b, and it cannot be factored further. When paired with other linear factors, each linear factor represents a separate line, resulting in several sorts of functions with progressively more intricate graphical representations.

f(10) = (10+2)(100+20+2)

= (12)(122)

= 1220+244

= 1464

Hence, f(10) is a multiple of 12

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The Lawrence family needed to cut expenses on their cell and landline phone service, cable television service, and Internet service. Here are the best prices they found forbasic service, using different service providers: Cell Phone Service: $36.45 per month Landline Phone Service: $30.11 per month Cable TV Service: $57.43 per monthInternet Service: $37.32 per month They found a company with a package deal with all 4 services for $131.59. What is the percentage decrease by purchasing the packagedeal?15.8%16.5%17.7%18.4%None of these choices are correct

Answers

Given:

Cell Phone Service, x=$36.45 per month

Landline Phone Service, y= $30.11 per month

Cable TV Service, z=$57.43 per month

Internet Service, p= $37.32 per month

The price for a package of all services, P=$131.59.

The total price of services before purchasing the package is,

[tex]T=36.45+30.11+57.43+37.32=161.31[/tex]

Now, the percentage decrease by purchasing the package is,

[tex]\begin{gathered} \text{Percentage}=\frac{T-P}{T}\times100 \\ =\frac{161.31-131.59}{161.31}\times100 \\ =18.4 \end{gathered}[/tex]

Therefore, the percentage decrease by purchasing the package is 18.4%.

Ward is planning to install a new counter top in kitchen, as shown in the figure. Determine the area of the countertop.

Answers

[tex]\begin{gathered} A=\frac{a+b}{2}\cdot h \\ A=\frac{6+8}{2}\cdot2 \\ A=14ft^2 \end{gathered}[/tex][tex]\begin{gathered} A=h\cdot l \\ A=2\cdot3 \\ A=6ft^2 \end{gathered}[/tex][tex]\begin{gathered} \text{Total area:} \\ A_T=6ft^2+14ft^2+6ft^2=26ft^2 \end{gathered}[/tex]

result step by step of this simple but yet hard for me exercise

Answers

Answer:

The anser is

Step-by-step explanation:

DO IT YOURSELF BRO GO LEARN AND STOP USING BRAINLY PU_$$y

Use the square root property to solve the equation.x² = 36Select one:O A. (18)O B. {16}O C. {±6i}O D. {6}

Answers

Given the equation

[tex]x^2=36[/tex][tex]x=\sqrt{36}[/tex][tex]x=\pm6[/tex]

Then

The Correct answer is

Option D 6

A triangle can be formed by drawing line segments on a map of Texas connecting the cities of Dallas, Houston, and San Antonio (see figure).
If the actual distance from San Antonio to Houston is approximately 192 miles, use the lengths of the line segments indicated in the figure along with similar triangles to approximate
a. the actual distance from Dallas to Houston.
b. the actual distance from Dallas to San Antonio.

Answers

a. The actual distance from Dallas to Houston is 0.058 mi. b. The actual distance from Dallas to San Antonio is 0.064 mi

What is the scale factor?

The ratio between comparable measurements of an item and a representation of that thing is known as a scale factor in arithmetic.

Given that the actual distance from San Antonio to Houston is approximately 192 miles.

The scale factor from the map to the real world is;

(actual)/( map) = (192mi)/(3 in) = 64 mi/in

Then the actual distance from Dallas to Houston will be;

(3.75 in)(64 mi/in) = 0.058 mi

And from Dallas to San Antonio, the distance will be;

(4.125 in)(64 mi/in) = 0.064 mi

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given AC=XZ and AB=XY prove BC=YZ

Answers

119 that is it because Ac = 19 then Xz is 50 and AB = 54 and Xy is 6

which three ordered pairs represents an input value of the function with the corresponding output value? select three answer.A.(-1,0)B.(0,1)C.(2,1)D.(2,4)E.(3,8)F.(4,2)

Answers

In order to determine the ordered pairs, look if the given points are on the curve.

Based on the graph, you can identify that the points are:

B. (0,1)

D. (2,4)

E. (3,8)

The value of a baseball player's rookie card began to increase once the player retired. When he retired in 1997 his card was worth $6.36. The value has increased by $1.93 each year since then. Express the relationship relating the value of the card y in dollars and the number of years x the player has been in retirement with an equation. Is the relationship between x and y proportional? What was the value of the card in 2007
?

Answers

Part a: The relationship between x and y can be represented as y = 6.36 + 1.93x

Part b: The relationship between x and y is proportional

Part c: The value of the card in 2007 will be $25.66

Worth of the card in 1997 = $6.36

Increase in value each year = $1.93

Let x be the number of years the player has been in retirement and y be the value of the cards in dollars

Formulating the equations we get the following:

Value of the card = Worth of the card in 1997 + Increase in value each year*Number of years the player has been in retirement

Part a:

y = 6.36 + 1.93x

Part b:

The relationship between x and y is proportional as the increase in the value each year leads to an increase in the worth of the card

Part c:

Value of the card in 2007:

The number of years the player has been retired will be 10 years in this case

Formulating the equation we get the following:

y = 6.36 + 1.93(10)

= 25.66

So, the value will be $25.66

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Find the simple interest on $50,000 for 2 years at 7%

Answers

Answer:

$7,000

Explanation:

To find the simple interest on any principal, we use the formula:

[tex]Simple\: Interest=\frac{Principal\times Rate\times Time}{100}[/tex]

From the given question:

• Principal = $50,000

• Rate= 7%

• Time = 2 years

Therefore:

[tex]\begin{gathered} \text{Interest}=\frac{50,000\times7\times2}{100} \\ =\$7,000 \end{gathered}[/tex]

The simple interest is $7,000.

I just need to make sure 1-9 are correct so if you could confirm please.9 b)

Answers

Given:

[tex]2x^2+3x+9=0[/tex]

To find:

The roots.

Explanation:

Here,

[tex]\begin{gathered} a=2 \\ b=3 \\ c=9 \end{gathered}[/tex]

Using the quadratic formula,

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

On substitution we get,

[tex]\begin{gathered} x=\frac{-3\pm\sqrt{(3)^2-4(2)(9)}}{2(2)} \\ =\frac{-3\pm\sqrt{9-72}}{4} \\ =\frac{-3\pm\sqrt{-63}}{4} \\ =\frac{-3\pm3i\sqrt{7}}{4} \end{gathered}[/tex]

Therefore, the solutions are,

[tex]x=\frac{-3+3\imaginaryI\sqrt{7}}{4},x=\frac{-3-3\imaginaryI\sqrt{7}}{4}[/tex]

Final answer:

The solutions are,

[tex]x=\frac{-3+3\imaginaryI\sqrt{7}}{4},x=\frac{-3-3\imaginaryI\sqrt{7}}{4}[/tex]

a line goes through the point (5, -7) and has slope m = -3. write the equation that represents the line.

Answers

We are given the following information

Slope of the line = m = -3

The line passes through the point (5, -7)

Recall that the equation of a line in the point-slope form is given by

[tex](y-y_1)=m(x_{}-x_1)[/tex]

Where m is the slope and (x₁, y₁) is a point on the line.

Let us substitute the given values into the above equation

[tex]\begin{gathered} (y-(-7)_{})=-3(x_{}-5_{}) \\ (y+7)=-3(x_{}-5_{}) \\ y+7=-3x+15 \\ y=-3x+15-7 \\ y=-3x+8 \end{gathered}[/tex]

Therefore, the equation of the line in slope-intercept form is

[tex]y=-3x+8[/tex]

Write the equation of the line with a slopeof -3 that passes through (-5,20)

Answers

The equation of the line which passes through point (-5,20), with a slope of -3 is y = -3x + 5.

How yo determine the equation of line from a point and slope?

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given the data in the question;

Slope m = -3

Point ( -5,20 )

x = -5y = 20

First, we find the y-intercept 'b', by plug the slope m ( -3 ) and point ( -5,20 ) into the equation of line formula and solving for b.

y = mx + b

20 = (-3)(-5) + b

20 = 15 + b

b = 20 - 15

b = 5

Now that both the slope m and y-intercept b is known, plug these into y = mx + b to determine the equation of the line.

y = (-3)x + 5

y = -3x + 5

Therefore, the linear equation of the line is y = -3x + 5.

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A square has an area of 144 ft^2 what is the length of each side

Answers

Answer: 12 feet

This is because [tex]12^2 = 12*12 = 144[/tex]

Squaring a number means you multiply it with itself.

The square root goes in reverse to have [tex]\sqrt{144} = 12[/tex]

Answer:

Each side is 12 ft long.

Step-by-step explanation:

So, you have a square, which means all of the sides are going to be the same length. So, you need something times itself that equals 144. Or, you need the square root of 144 (Because when something is squared, it is multiplied by itself). And the square root of 144 is 12.

9y-(2y-3)=5(y-2)+2
Should equal ‘no solution’

Answers

[tex]9y - 2y + 3 = 5y - 10 + 2 \\ 7y + 3 = 5y - 8 \\ 7y - 5y = - 8 - 3 \\ 2y = - 11 \\ \frac{2y}{2} = \frac{ - 11}{2} \\ y = \frac{ - 11}{2} [/tex]

ATTACHED IS THE SOLUTION OF Y

BE AWARE THERE IS A SOLUTION FOR THE PROBLEM.

What number would you add to both sides of x2 + 7x = 4 to complete the square?2²0 72이를즐이

Answers

To complete the square, we want a number such that:

[tex]\begin{gathered} 2\sqrt{a}=7 \\ a=(\frac{7}{2})^2 \end{gathered}[/tex]

because in this way we can writte the square as follows:

[tex]\begin{gathered} x^2+7x+(\frac{7}{2})^2=4+(\frac{7}{2})^2 \\ (x+\frac{7}{2})^2=4+(\frac{7}{2})^2 \end{gathered}[/tex]

Hence the answer is the last option:

[tex](\frac{7}{2})^2[/tex]

A clothing designer is selecting models to walk the runway for her fashion show.
The designer prefers models that are no more than 3 inches away from being 5'10".
Since 5'10" is the same as 70 inches, write an inequality - in terms of inches - that
could be used to determine if a model's height is within the designer's preferred height
range.

Answers

Using proportions, the inequality that could be used to determine if a model's height is within the designer's preferred height range is of:

67 inches ≤ Height ≤ 73 inches.

What is a proportion?

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using operations such as multiplication and division, from the unit rates in the context of the problem.

One example of application of proportions is for conversion of units, as there are rates for each unit.

In the context of this problem, the rate used is:

1 feet = 12 inches.

Hence the measure of 5'10" = 5 feet and 10 inches is given by:

5 x 12 + 10 = 60 + 10 = 70 inches.

The heights that are within 3 inches of 70 inches are given by:

70 - 3 = 67 inches.70 + 3 = 73 inches.

Hence the inequality that models the situation is:

67 inches ≤ Height ≤ 73 inches.

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PLEASE HELP! Sharel received a bank account statement report the recent changes to her account. The statement showed an overall increase in the account balance of $4,317.59. During the time shown on the statement, Sharel was paid three times and withdrew a total of $1,230.67 to cover all her bills and expenses. How much (x) is each of Sharel's paychecks? Write an equation to represent this situation.

Answers

I believe it is 4,317.59 + (x •3) - 1,230.67

Which two values of x are roots of the polynomial below?
4x² - 6x+1
A. x = -6-√52/16
B. x = 6+ √20/8
C. x = 6-√20/8
D. x = -8-√28/6
E. x = -8+ √28/6
F. x = -6 + √52/16

Answers

Roots are x = - 6 + √20/8 and x = - 6 - √20/8 of polynomial.

What in mathematics is a polynomial?

Sums of terms with the form kxn, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials. In this video, basic terms such terms, degrees, standard form, monomial, binomial, and trinomial are covered.

4x² - 6x+1 = 0

x = -b ± √b² - 4ac/2a

x = - (6) ± √(-6)² - 4 * 4 * 1/2 * 4

x = -( 6) ± √36 - 16/8

x = - 6 ± √20/8

So, roots are x = - 6 + √20/8 and x = - 6 - √20/8

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Your lunch in the hospital cafeteria cost $6.50. How much will you spend each week if you average spending $6.50 per meal every day for your five day work week?

Answers

$32.50 per week because you take $6.50 x 5 days a week

Keandre wants to buy a new pair of shoes that costs $220. In order to earn money for this, Keandre babysits his neighbor for $10 an hour. He also has saved up his monthly allowance which totals $50. What is the minimum number of hours he should babysit in order to be able to afford the shoes?

Answers

Answer:

Step-by-step explanation:

$220=$10x+$50

x= hours

subtract $50 from both sides making sure to cancel the right side

$220-$50=$10x

$170=$10x

Divide both sides by $10 to leaving x by itself on the right side

$170/$10=x

17hrs=x

The minimum number of hours is 17 hours to babysit in order to be able to afford the shoes.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Cost of new pair of shoes = $220

In order to earn money for this, Keandre babysits his neighbor for $10 an hour.

And, He also has saved up his monthly allowance which totals $50.

Now,

Let number of minimum hours = x hour

So, We can formulate;

⇒ $10x + $50 = $220

Solve for x as;

⇒ $10x + $50 = $220

Subtract 50 both side, we get;

⇒ $10x + $50 - $50 = $220 - $50

⇒ $10x = $170

Divide by 10 both side, we get;

⇒x = 17

Thus, The minimum number of hours is 17 hours to babysit in order to be able to afford the shoes.

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Bharat types 20 words/min. How many words can he type in each length of time? a) 5 min b) 30 min c) 23 min

Answers

Bharat can type words in lengths of time as 100 words, 600 words, and 460 words in 5 minutes, 30 minutes, and 23 minutes respectively.

What are Arithmetic operations?

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

* Multiplication operation: Multiplies values on either side of the operator

For example 12×2 = 24

Bharat types 20 words per minute which are given in the question.

To determine the number of words can he type in each length of time

We have to multiply the time by his typing speed.

The number of words that can be typed by Bharat in 5 minutes :

⇒ 20 × 5

⇒ 100

The number of words that can be typed by Bharat in 30 minutes :

⇒ 20 × 30

⇒ 600

The number of words that can be typed by Bharat in 23 minutes :

⇒ 20 × 23

⇒ 460

Therefore, He can type words in lengths of time as 100 words, 600 words, and 460 words in 5 minutes, 30 minutes, and 23 minutes respectively.

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A square napkin has sides of length 8 inches. To the nearest inch, what is the length of the diagonal of the (1
napkin?
O8 inches
09 inches
O11 inches
O16 inches

Answers

The length of the diagonal of the napkin is 11 inches.

Here, we are given that a square napkin has a side of length 8 inches.

All the sides of a square are equal and the measure of angle formed by any two adjacent sides is also equal and 90°.

Thus, by using Pythagoras theorem, we can form the following equation-

[tex]side^{2} + side^{2} = diagonal^{2}[/tex]

Let the diagonal of the square be d. Then, we have-

[tex]8^{2} +8^{2} =d^{2}[/tex]

64 + 64 = [tex]d^{2}[/tex]

128 = [tex]d^{2}[/tex]

[tex]d^{2}[/tex] = 128

d = [tex]\sqrt{128}[/tex]

d = [tex]8\sqrt{2}[/tex]

the value of [tex]\sqrt{2}[/tex] is approximately 1.41. Thus,

d = 8 × 1.41

= 11.28

Thus, the length of the diagonal of the napkin to the nearest inch comes out to be 11.

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What type of chart did we use to build a tornado chart?

Answers

Bar chart

For 20 charterers

Translate the sentence into an equation. Use the variable w for the unknown number.Two times the sum of a number and 7 equals 6.

Answers

we have that

Two times the sum of a number and 7 -----> 2(w+7)

Two times the sum of a number and 7 equals 6 ----> 2(w+7)=6

the answer is

2(w+7)=6

Find the expected value of the winningsfrom a game that has the followingpayout probability distribution:Payout ($) 1 2 5 8 10Probability 0.35 0.2 0.1 0.2 0.15Expected Value = [?]Round to the nearest hundredth.

Answers

On the frequency table, you can see the payouts of the lottery and the corresponding probabilities for every payout. To determine the expected payout, you have to multiply each possible price by its corresponding probability and add the results, following the formula:

[tex]E(X)=\sum ^{10}_{n\mathop=1}x_i\cdot P(x_i)[/tex][tex]\begin{gathered} E(X)=(1\cdot0.35)+(2\cdot0.20)+(5\cdot0.10)+(8\cdot0.20)+(10\cdot0.15) \\ E(X)=0.35+0.4+0.5+1.6+1.5 \\ E(X)=4.35 \end{gathered}[/tex]

The expected payout for the lottery is $4.35

The apartment you want has a monthly rent of $585. What does your gross monthly income range need to be for you to be able to rent this apartment? Maximum spent on rent should be 25% - 35% of your gross monthly income

Answers

The gross monthly income range to be for you to be able to rent this apartment is $1671 - $2340.

How to calculate the value?

Let the monthly income be x.

Therefore, 25% of x = 585

0.25x = 585

Divide

x = 585/0.25

x = $2340

The maximum income is $2340.

The minimum income will be:

35% of x = 585

0.35x = 585

Divide.

x = 585 / 0.35

x = $1671

In this case, the minimum value is $1671 and the maximum value is $2340. This illustrates the concept for finding the range.

The range is $1671 - $2340.

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The drama club is selling tickets to its play. An adult ticket costs $15 and a student ticket costs $11. The auditorium will seat 300 ticket-holders. The drama club wants to collect at least $3630 from ticket sales.

a. Write and graph a system of four inequalities that describe how many of each type of ticket the club must sell to meet its goal.

b. List three different combinations of tickets sold that satisfy the inequalities.

Answers

The system of inequalities is x + y ≤ 300, 11x + 15y ≥ 3630, x ≥ 0 and y ≥ 0 while the three points are (70, 200), (150, 140) and (140, 150)

How to graph the system

From the question, we have the following parameters that can be used to determine system of inequalities

An adult ticket = $15Student ticket = $11. Auditorium capacity = 300 ticket-holdersAmount from sales = at least $3630 from ticket sales.

Represent the adult with y and the students with x

So, we have the following representations

x + y ≤ 300 ---- the ticket holders cannot exceed the capacity

11x + 15y ≥ 3630 --- the total sales cannot be less than $3630

x ≥ 0 -- the number of students cannot be negative

y ≥ 0 -- the number of students cannot be negative

Write out the inequalities

x + y ≤ 300

11x + 15y ≥ 3630

x ≥ 0

y ≥ 0

Next, we represent the inequalities on a graph

See attachment for the graph of the inequalities

The combinations from the graph

To get the combination, we make use of the coordinate points that are in the shaded region of the graph

Using the above as a guide, we have

(70, 200), (150, 140) and (140, 150)

There are other points too