(r^3+6r^2-21r-18) ÷ (r-3)

Show in Synthetic Division

Answer:

Let us assume that the pay rate per hour = x

no. of hours worked = n

Gross earnings = x*n

Federal taxes = 18% of gross earnings

= 0.18(x*n)

State taxes = 4% of gross earnings

= 0.04(x*n)

Social security deduction = 7.05% of gross earnings

= 0.0705(x*n)

Total deductions = Federal taxes + State taxes +SSD

= 0.18(x*n) + 0.04(x*n) + 0.0705(x*n)

= 0.2905(x*n)

Net pay = Gross earnings - Total Deduction

Net pay = x*n - 0.2905(x*n)

Net pay = 0.7095(x*n)

The gross earnings are $800. Deductions total $232.40, resulting in a net pay of $567.60 after federal, state taxes, and social security deductions.

Let's calculate various components of a paycheck, starting with the given pay rate and hours worked. Suppose the pay rate is $20 per hour and the employee works 40 hours per week.

1. Gross Earnings:

Gross Earnings = Pay Rate × Hours Worked

Gross Earnings = $20/hour × 40 hours

Gross Earnings = $800

2. Federal Taxes:

Federal Taxes = 18% of Gross Earnings

Federal Taxes = 0.18 × $800

Federal Taxes = $144

3. State Taxes:

State Taxes = 4% of Gross Earnings

State Taxes = 0.04 × $800

State Taxes = $32

4. Social Security Deduction:

Social Security Deduction = 7.05% of Gross Earnings

Social Security Deduction = 0.0705 × $800

Social Security Deduction = $56.40

5. Total Deductions:

Total Deductions = Federal Taxes + State Taxes + Social Security Deduction

Total Deductions = $144 + $32 + $56.40

Total Deductions = $232.40

6. Net Pay:

Net Pay = Gross Earnings - Total Deductions

Net Pay = $800 - $232.40

Net Pay = $567.60

Therefore, the gross earnings are $800, and after accounting for $232.40 in deductions for federal and state taxes along with social security, the net pay is $567.60.

Answer:

25ab

Step-by-step explanation:

(5a)(5b) -> Expand the brackets (multiply like terms together, etc) When the brackets are expanded, values can be multiplied, etc easily

25ab -> 5 multiplied by the other 5 gives 25; a multiplied by b gives ab

Answer:

Don't see the steps... but I will solve it and put the property next to each step I perform... And we will just hope my steps are exactly the same as theirs and my wording of the property is exactly the same as theirs.

3x-2>-4           Given

3x-2+2>-4+2  Addition property of Equality

3x+0>-2         Simplification and Inverse Property of Addition for -2+2

3x    >-2         Simplification and Identity Property of Addition for 3x+0

3x/3 >-2/3      Division property of Equality

1x     >-2/3      Inverse property of Multiplication for the 3*1/3 part

x      >-2/3      Identity property of Multiplication for the 1x part

Answer:

b. 45deg

Step-by-step explanation:

see attached

Answer:

45

Step-by-step explanation:

We are seen with two lines crossing each other and the angle in which a line has is 180 degrees. Also, the angles labeled 3x and x are supplementary angles, which mean they add up to 180 degrees. Using this information, we can set up an equation.

[tex]x+3x=180[/tex]

[tex]4x=180[/tex]

[tex]x=45[/tex]

Answer:

A - 108 strips

Step-by-step explanation:

1 yard = 36 inches

3 yards = 108 inches.

If Sara cuts 1-inch strips, she will have 108 strips in total.

Hope this helps!

Answer:

A 108 strips

Step-by-step explanation:

1 yd = 3 ft

3 ft = 3 * 12 inches = 36 inches

3 yds = 3 * 36 = 108

If each strip is 1 inch, we can cut 108 1 inch strips

ANSWER

[tex]\cos B = \frac{ \sqrt{3} }{3} [/tex]

EXPLANATION

The given triangle is a right triangle.

It was given that,

[tex]a = 1[/tex]

and

[tex]b = \sqrt{2} [/tex]

Using the Pythagoras Theorem, we can determine the value of c.

[tex] {c}^{2} = {( \sqrt{2} )}^{2} + {1}^{2} [/tex]

[tex] {c}^{2} = 2 + 1[/tex]

[tex]{c}^{2} = 3[/tex]

[tex]c = \sqrt{3} [/tex]

The ratio is the adjacent over the hypotenuse.

[tex]\cos B = \frac{1 }{ \sqrt{3} } [/tex]

We rationalize to get:

[tex]\cos B = \frac{ \sqrt{3} }{ \sqrt{3} \times \sqrt{3} } = \frac{ \sqrt{3} }{3} [/tex]

Answer:

7 & 8

Step-by-step explanation:

For this case we propose a system of equations:

x: Variable representing the plant with pink flowers

y: Variable representing the plant with purple flowers

We have as data that:

[tex]x + y = 15\\8x + 5y = 96[/tex]

From the first equation we have to:

[tex]x = 15-y[/tex]

Substituting in the second equation:

[tex]8 (15-y) + 5y = 96\\120-8y + 5y = 96\\-3y = 96-120\\-3y = -24\\y = \frac {-24} {- 3}\\y = 8[/tex]

Arianna bought 8 purple flowers.

Now we have:

[tex]x = 15-8\\x = 7[/tex]

Arianna bought 7 pink flowers.

Answer:

Arianna bought 7 pink flowers.

Answer:

C

Step-by-step explanation:

The average rate of change of a function f(x) on the interval [a, b] is:

(f(b) − f(a)) / (b − a)

Here, the interval is [3, 11].  f(3) = -4 and f(11) = 20.

(f(11) − f(3)) / (11 − 3)

(20 − -4) / 8

24 / 8

3

The average rate of change in t over the interval [3,11] is C. 3.

The average rate of change function exists expressed as the average rate at which one quantity is changing regarding something else changing. In simple terms, an average rate of change function exists as a process that estimates the amount of change in one item divided by the corresponding amount of change in another.

The average rate of change of a function f(x) on the interval [a, b] is:

(f(b) − f(a)) / (b − a)

Here, the interval is [3, 11].  f(3) = -4 and f(11) = 20.

(f(11) − f(3)) / (11 − 3)

(20 − -4) / 8

24 / 8

3.

The average rate of change in t over the interval [3,11] is C. 3.

Hence, The correct answer is option C. 3.

To learn more about the average rate of change of a function

https://brainly.com/question/2170564

#SPJ2

Answer:

x = 1, y = 60

Step-by-step explanation:

Value of new-releases (x) = $20 each

Value of classic (y) = $8 each

Total budget = $500

Equation : 20x + 8y = 500

The librarian wants to purchase maximum DVDs. She can get more DVDs of classic movies for $8 as they are less costly.

Lets assume the librarian buys at least one new-release DVD.

x=1

20x + 8y = 500

8y + 20(1) = 500

y = 60

Therefore, in a budget of $500, the librarian can purchase 60 classic movies and 1 new-release.

!!

Answer: x=16 y=22

Step-by-step explanation:

Edge test math

Answer: Using the distance formula 5sqrt 2 is the answer

d=sqrt(x1-x2)^2+(y1-y2)^2

Step-by-step explanation:

d=sqrt(9-4)^2+(6-1)^2

d=sqrt(5)^2+(5)^2

d=sqrt 25+25

d=sqrt 50

d= 5 sqrt 2

Answer:

y = -1/3x +3

Step-by-step explanation:

First we need to find the slope

m = (y2-y1)/(x2-x1)

   = (2-3)/(3-0)

   -1/3

Then we know the y intercept( where it crosses the y axis)

It crosses at y=3

The slope intercept form is

y= mx+b  where m is the slope and b is the y intercept

y = -1/3x +3

Answer:

[tex]y=\frac{-1}{3} x+3[/tex]

Step-by-step explanation:

Let frame the equation of the line using the points given on the graph

(0,3) and (3,2)

Equation of the line is y=mx+b

where m is the slope and b is the y intercept

To find slope we use formula

[tex]slope =\frac{y_2-y_1}{x_2-x_1} =\frac{2-3}{3-0} =\frac{-1}{3}[/tex]

Y intercept b is the point where the graph crosses y axis

y intercept b = 3

The equation y=mx+b becomes

[tex]y=\frac{-1}{3} x+3[/tex]

Answer:

C. Third option

Step-by-step explanation:

C is the correct answer, because the common ratio is a change from one number into the next in a geometric sequence.

Hope this helps!

Answer: that not a real question it cant be answered has to be missing something

Step-by-step explanation:)

Answer:

Hi my name is Kylie "How You Doing" phrase from Friends, Joey

The option that describes the Complement A^c is; D: A^c = {x| x ∈ U and x is an even positive integer}

If the Universal set, U = {all positive integers); and

A = {x|x ∈ U and x is an odd positive integer}.

Thus:

The complement of A is the set of the elements of the universal set which are not in A.

If a set is not odd, then it is even.

Thus:

A^c = {x| x ∈ U and x is an even positive integer}

Read more about Set Elements at; https://brainly.com/question/14528403

Answer:

The true statements are the third and fifth. [not sure about the second one!]

Step-by-step explanation:

1.) (7u + 4) is written as a sum of three terms.

This is false since 7u is one term, and 4  is one term, making a total of two terms, not three.

2.) 2 is a factor

I'm not sure on this but I don't think its true.

3.) In 7u, 7  is a coefficent

This is true. The coefficent is the number in front of a variable, or in this case, 7.

4.) In (7u + 4), 7u is a constant.

This is false, as a constant is a number without  any variable attached to it. The constant in this case would be 4.

5.) 8 and 1 are like terms.

This is true, since you can add 8 and 1, resulting in the sum of 9.

6.) None of these are true.

This is false, as at least 2 of these statements are true.

I hope this helps! :)

Answer: I think c but I am not sure

Step-by-step explanation: Hope this helps

[tex]\bf -\cfrac{1}{x-9}-\cfrac{-2}{x+7}\implies -\cfrac{1}{x-9}+\cfrac{2}{x+7}\implies \cfrac{2}{x+7}-\cfrac{1}{x-9}\impliedby \stackrel{\textit{our LCD is}}{(x+7)(x-9)} \\\\\\ \cfrac{(x-9)2~~-~~(x+7)1}{(x+7)(x-9)}\implies \cfrac{2x-18~~-~~x-7}{(x+7)(x-9)}\implies \cfrac{x-25}{(x+7)(x-9)}[/tex]

Answer:

  $293.75

Step-by-step explanation:

Any number of financial calculators, spreadsheets, and on-line calculators can compute the monthly payment for you. Or you can put the numbers into the formula and compute it yourself.

A formula I like is ...

  A = P(r/12)/(1 -(1 +r/12)^(-12t))

where A is the monthly payment, P is the loan amount, r is the annual interest rate, and t is the number of years. Filling in the given information and doing the arithmetic, we get ...

  A = $10000(0.18/12)/(1 -(1 +0.18/12)^(-12·4)) = $150/(1 -1.015^-48) = $293.75

Your monthly payment is $293.75.

Answer:

One pair of equivalent expressions is:

x - 3y + 12

12 - 3y - 2x + x + 2x

Second,

x + 3y + 12

3x + 2y - 2x + y + 12

third,

3y + 12

x + 3y + 2x - 3x + 7 + 5

four,

3x + y - 12

4y + 3y + 3x - 6y - 10 - 2

Step-by-step explanation:

In order to match the equivalent expressions we have to put each expression in its simplest form

So,

[tex]x-3y+12\\\\12 - 3y - 2x + x + 2x\\=12-3y+x\\=x-3y+12\\\\3x + 2y - 2x + y + 12\\=x+3y+12\\\\4y + 3y + 3x - 6y - 10 - 2\\=3x+y-12\\\\x + 3y + 2x - 3x + 7 + 5\\=3y+12\\\\5 + 2y + 7x - 4x + 3y - 17\\=5y+3x-12[/tex]

One pair of equivalent expressions is:

x - 3y + 12

12 - 3y - 2x + x + 2x

Second,

x + 3y + 12

3x + 2y - 2x + y + 12

third,

3y + 12

x + 3y + 2x - 3x + 7 + 5

four,

3x + y - 12

4y + 3y + 3x - 6y - 10 - 2

..

Answer:

x + 3y + 12 <--> x + 3y + 2x - 3x + 7 + 5

x − 3y + 12 <--> 12 - 3y - 2x + x + 2x

3x + 2y − 2x + y + 12 <--> 3x + y - 12

3y + 12 <--> 4y + 3y + 3x - 6y - 10 - 2

Answer: C is correct, 4x=8

Step-by-step explanation:

You will add the two equations...

4x-8=0

Now you need to move the -8 over, which reverses its sign to positive.

4x=8

Answer:

Coach Johnson will save $1.50

Step-by-step explanation:

1. The first step is to calculate the unit price for each of the packages, ie. how much a single shin guard costs.

If we look at the package of 10 shin guards for $14.50, we can calculate the unit price by dividing the package price ($14.50) by the number of shin guards (10). Thus we get:

14.50/10 = $1.45

Now, if we do the same for the package of 15 shin guards for $22.50, we get:

22.50/15 = $1.50

2. Now we can see that the lowest unit price is $1.45 (package of 10 shin guards) and the highest unit price is $1.50 (package of 15 shin guards).

3. There are two ways to see how much he would save, so I will show both here.

1) First calculate how much the coach will have to pay for a pack of 30 shin guards for each of the packages:

3 packages of 10 shin guards for $14.50 = 3*14.5 = $43.50

2 packages of 15 shin guards for $22.50 = 2*22.5 = $45.00

Now subtract the second value from the first: 45-43.5 = 1.5

Therefor, he will save $1.50.

2) The second method is perhaps what I would personally use as it is a little quicker; so we already know that the unit price for the pack of 10 is $1.45 and the unit price for the pack of 15 is $1.50 - thus, we can say that there is a difference of $0.05 per shin guard in price. Now if we were going to calculate how much the coach would save in buying 30 shin guards, we could simply multiply how much he saves on a single shin guard by 30. Thus, we get:

0.05*30 = 1.5

Therefor, again we get the same answer that Coach Johnson would save $1.50.

Hope that helps :)

the answer would be 12

-4 - -16 = 12

the distance between -16 and -4 is 12.

Answer:

X=6

Step-by-step explanation:

You need to cross multiply 2 by x+6. this Equals 2x+12. Then you cross multiply 8 by three which is 24. leading to the equation 2x+12=24 . Subtract 12 on both sides to get 2x=12. Divide by two to get 6 as your answer.

Answer:

Ball Bearing Volume = (4 / 3) * PI * radius ^3

Volume = (4 / 3) * 3.14159265 * (.35)^3

Volume = (4 / 3) * 3.14159265 * 0.042875

Volume = 0.17959438 cc

1 cc of steel = 7.8 g

Volume of 1 kg of steel = 1,000 cc / 7.8 g per cc

1 kg = 128.205 cc

Number of ball bearings we can make = 128.205 / 0.17959438

Equals 713.86

Step-by-step explanation:

Answer:

Ratios are usually proportional if they are the same or have the same relationship.

Step-by-step explanation:

Like: you have 2 fractions that reduce and come out the same they are proportional.

Hope my answer has helped you!

Answer: pretty much is you reduce 2 fractions and they are the same it should be proportional.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Nice problem.

The only way you can get an odd number by multiplying two digits together is if they are both odd.

For example 5*7 = 35 which is odd. You cannot find 2 odd numbers that when multiplied will give an even.

That means that A and B are both odd.

Now if you multiply an odd and an even together, you always get an even.

For example 4 * 9 = 36 which is even.

Since A is known to be odd, C must be even. So the four digit number you want ends in C.

The Answer is A

Answer:

Step-by-step explanation:

The aaaa

Let y be the total cost and x be the miles taken:

y = 0.30x + 35

35 is a fixed cost. No matter how many miles you drive the car you will still need to pay $35

.30 is a cost that depends on the miles taken (x).

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

b ≠ - 1

Step-by-step explanation:

The denominator of the rational expression cannot be zero as this would make it undefined.

Equating the denominator to zero and solving gives the value that b cannot be.

solve

5b + 5 = 0 ( subtract 5 from both sides )

5b = - 5 ( divide both sides by 5 )

b = - 1 ← excluded value

Final answer:

The probability that Nick oversleeps and has a pop quiz on the same school day, given the probability of oversleeping at 48% and pop quiz at 25%, is 12%.

Explanation:

To find the probability that Nick oversleeps and has a pop quiz on the same day, we need to multiply the probabilities of the two independent events occurring.

The probability of Nick oversleeping is 48% or 0.48, and the probability of him having a pop quiz is 25% or 0.25. Since the events are independent, the combined probability is:

Probability(Nick oversleeps and has a pop quiz) = Probability(Nick oversleeps) × Probability(has a pop quiz) = 0.48 × 0.25

When you calculate this, you get:

0.48 × 0.25 = 0.12

Therefore, the probability that Nick oversleeps and has a pop quiz on the same school day is 12%.

The probability that Nick oversleeps and has a pop quiz on the same day is 12%.

To find the probability that Nick both oversleeps and has a pop quiz on the same day, we use the concept of independent events in probability. When two events are independent, the probability of both events occurring is the product of their individual probabilities.

Let's denote:
P(O) = Probability that Nick oversleeps = 0.48
P(Q) = Probability that there is a pop quiz = 0.25

The formula for finding the probability of both independent events occurring is:
P(O and Q) = P(O) * P(Q)

Therefore:
P(O and Q) = 0.48 * 0.25 = 0.12

So, the probability that Nick oversleeps and has a pop quiz on the same day is 12%.

Answer:

19

Step-by-step explanation:

f(x) = 2x^2 +1

Let x =3

f(3) = 2 (3)^2 +1

     = 2 *9 +1

     = 18 +1

     = 19