For a tax rate of 8.25%, find the amount of tax that will be paid on an automobile tube-up costing $76. Find the total price of the tune-up with tax.

The answer is 842500.

Answer:

w = no solutions

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

-8 - 3(w + 13) = 4(w + 11) - 7w

Step 2: Solve for w

Here we see that -47 does not equal 44.

∴ w = no solutions.

There is no solution to the equation -8-3(w+13)=4(w+11)-7w, as it simplifies to an untrue statement.

Here is the step-by-step solution:

Distribute the constants through the parentheses:

-8 - 3w - 39 = 4w + 44 - 7w

Combine like terms:

-47 - 3w = -3w + 44

Since -3w on both sides cancels out, we are left with just the constants:

-47 ≠ 44

There is no value for w that will make this equation true, hence there is no solution.

[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill&19000\\ P=\textit{original amount deposited}\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &5 \end{cases}[/tex]

[tex]\bf 19000=P\left(1+\frac{0.08}{2}\right)^{2\cdot 5}\implies 19000=P(1.04)^{10} \\\\\\ \cfrac{19000}{1.04^{10}}=P\implies 12835.72\approx P[/tex]

To have $19,000 in 5 years with an 8% interest rate compounded semiannually, you should deposit approximately $12,840.72 now.

The question is about calculating the present value of an investment to reach a future sum of money with a given interest rate, compounded semiannually. To find out how much you should deposit now to have $19,000 in the future, we can use the formula for the present value of an investment for compound interest:

PV = FV / (1 + r/n)(nt)

FV = $19,000

r = 8% or 0.08

n = 2 (because interest is compounded semiannually)

t = 5 years

We can substitute these values into our formula:

PV = $19,000 / (1 + 0.08/2)(2*5)

Doing the math:

PV = $19,000 / (1 + 0.04)10

PV = $19,000 / 1.48024

PV = $12,840.72

So, you would need to deposit approximately $12,840.72 now in order to have $19,000 in 5 years, given an 8% interest rate compounded semiannually.

Answer:

The answer is 2.

2 + 6 = 8, 16/8 = 2.

For x -

180 = 4x + 6 + 11x - 6

180 = 15x

[tex]\frac{180}{15}[/tex] = x

x = 12

For m∠ABD -

4(12) + 6

48 + 6

m∠ABD = 54

For m∠DBC -

11(12) - 6

132 - 6

m∠DBC = 126

Answer:

x = 12° ; m∠ABD= 54°    ; m∠DBC=126°

Step-by-step explanation:

∠ABD + ∠DBC = ∠ABC

Here ,

∠ABC is a straight line .

We know,

A straight angle is 180 degrees.

So,

∠ABD + ∠DBC = 180°

⇒(4x+6)° + (11x-6)° =180°                        [given]

⇒15x =180°

⇒x = (180/15)°      [divide both sides by 15]

∴ x = 12°

Now,

∠ABD = (4x+6)°         [given]

           ={(4 . 12) + 6 }°    

            =(48+6)°

            =54°  

And,

∠DBC = (11x-6)°                       [given]

           ={(11 .12)-6}°

           =(132 - 6)°

           =126°  

Answer:

[tex]\sin\theta=\dfrac{15}{17}[/tex]

[tex]?=15[/tex]

Step-by-step explanation:

Use the trigonometry formula

[tex]\cos^2\theta+\sin^2\theta=1[/tex]

You are given that

[tex]\cos \theta=\dfrac{8}{17}[/tex]

Substitute into the first formula

[tex]\left(\dfrac{8}{17}\right)^2+\sin^2\theta=1\\ \\\dfrac{64}{289}+\sin^2\theta=1\\ \\\sin^2\theta=1-\dfrac{64}{289}=\dfrac{289-64}{289}=\dfrac{225}{289}\\ \\\sin \theta=\pm \dfrac{15}{17}[/tex]

Angle [tex]\theta[/tex] is acute angle, then the sine of this angle is positive and

[tex]\sin\theta=\dfrac{15}{17}[/tex]

Answer:

55.75

Step-by-step explanation:

First you start by doing what is in the parenthesis. so we divide 6 by 24 which gets us 0.25. Then we follow the rest of PEMDAS. Addition is next so we add 8 to 0.25 to get 8.25. Now we finally get to the fun part. 4 to the third power which is 64, then we subtract 8.25 to get 55.75. Hope that helps.

One way to tell if a relation is a function is by using something called the vertical line test. In other words, if we can draw a vertical that passes through more than one point on a graph, then the relation does not represent a function. Another way to tell if a relation represents a function is by looking at the X coordinates of each ordered pair. If any of the ordered pairs have the same X coordinate, then the relation is not a function.

Answer:

3/16 cups

Step-by-step explanation:

Well, you see that 3/4 of a cup is 1 batch --->

3/4 cup  :  1 batch

to get 1/4 of a batch, you can just multiply both sides of the ratio by 1/4

3/4 * 1/4 cups : 1 * 1/4 batches

3/16 cups : 1/4 batches

Answer: answer is D and F

Step-by-step explanation:

Answer:

2.13

Step-by-step explanation:

because 2.1349 is closer to 2.13 than 2.14 because the number 4 is less than 5 so it's closer to 0

When round a number to the nearest hundredth, digit in the thousandths place should be focused.

To round the number 2.1349 to the nearest hundredth, look at the digit in the thousandths place, which is 4 in this case.

When rounding to the nearest hundredth, consider the digit immediately to the right of the hundredth place, which is the digit in the thousandths place. In this case, 4 is less than 5.

1. Start with the number 2.1349 on a number line.

2. Look at the digit in the thousandths place (4). Since it's less than 5, we do not need to round up.

3. Therefore, 2.1349 rounded to the nearest hundredth is 2.13.

If it's 5 or greater, you round up; if it's less than 5, you leave the hundredths place unchanged. In this case, 4 is less than 5, so we round down to 2.13.

Learn more about Rounding off here:

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Answer:

Because the sum of the measures of a pair of same-side interior angles

is equal to one-half the number of degrees in a parallelogram ⇒ B

Step-by-step explanation:

* Lets explain how to solve the problem

- In a parallelogram every two opposite sides are parallel

- In a parallelogram every tow opposite angles are equal

∵ The parallelogram is a quadrilateral

∵ The sum of the measures of the interior angles in any quadrilateral

   is 360°

∵ In parallelogram each two opposite angles are equal

∴ The sum of the measures of every two adjacent angles

   equal 360° ÷ 2 = 180°

* Lets solve the problem

- When parallel lines are cut by a transversal

∵ It is a fact that the parallel lines and their transversal can form a

  parallelogram

∵ The sum of the measures of the adjacent angles of the

   parallelogram is 180°

∵ The sum of the measures of the supplementary angles is 180°

∴ The same side-interior angles are supplementary, because

   they are two adjacent angles in a parallelogram

* Lets find the true statement

∵ The sum of the measures of every two adjacent interior angles

  in the parallelogram = 360° ÷ 2 = 180°

∵ 180° is half the sum of the measures of interior angles in the

  parallelogram

∴ Because the sum of the measures of a pair of same-side interior

  angles is equal to one-half the number of degrees in a

  parallelogram

The solution to the absolute value equation 5[2x-4] + 1 = 11 is the solution set {1, 3}.

To solve the absolute value equation 5[2x-4] + 1 = 11, we first isolate the absolute value expression by subtracting 1 from both sides of the equation, resulting in 5[2x-4] = 10. Then we divide both sides by 5, yielding |2x - 4| = 2. Next, we consider the two cases where 2x - 4 equals 2 and where 2x - 4 equals -2.

For the first case, 2x - 4 = 2, we add 4 to both sides to get 2x = 6, and then divide by 2 to find that x = 3. For the second case, 2x - 4 = -2, we add 4 to both sides to get 2x = 2, and then divide by 2 to find that x = 1.

Thus, the solution set to the original equation is {1, 3}, and we can verify these solutions by substituting them back into the equation to check that they satisfy the initial condition.

Answer:

d

Step-by-step explanation:

the expression cant be factored because there is no number that multiplies to get 16 but adds up to 9. ex; 8*2 is 16 but add to 10, 16 and 1 equals 17, and 4*4 is 16 but adds up to 8.

Answer:

your answer is d

Step-by-step explanation:

Answer:

i think ur right or letter b butu not c

Step-by-step explanation:

Answer:

no solution

Step-by-step explanation:

Given

27x + 14 = 3(9x - 7) ← distribute right side

27x + 14 = 27x - 21 ( subtract 27x from both sides )

0 + 14 = - 21 ( subtract 14 from both sides )

0 = - 35 ← not possible

Thus the equation has no solution

Answer and Step-by-step explanation :

There is no answer for this question.

Step 1: Simplify both sides of the equation :

[tex]27x+14=(3)(9x)+(3)(-7)[/tex]  [tex]Distribute[/tex]

[tex]27x+14=27x+-21[/tex]

[tex]27x+14=27x-21[/tex]

Step 2 : Subtract [tex]27x[/tex] from both the side :

[tex]27x+14-27x=27x-21-27x[/tex]

[tex]14=-21[/tex]

Step 3 : Subtract [tex]14[/tex] from both the sides :

[tex]14-14=-21-14[/tex]

[tex]0=-35[/tex]

Hence there is no solution to this answer.

Answer:

x= -7/8

Step-by-step explanation:

8x + 7 = 0

8x + 7-7 = 0-7

8x=-7

8x/8x = -7/8

Answer:

no solution

Step-by-step explanation:

use the box method to find out the factors

                 |         7      

     x^2      |

the top left and top right must multiply to 7x^2 and add up to 6x.

7 is multiplied together by 7 and 1, but only 7 and -1 can add up to 6x, so therefore there is no solution to this equation

another way is the quadratic equation

for an equation in form ax^2 +bx + c,

the quadratic equation states x = (-b + square root(b^2-4ac))/2a

in this case : x = -6 + (6^2 -28)^1/2 = -6+ (some negative root that doesn't exist)

so x = no solution

Answer:

18

Step-by-step explanation:

There are

So,

Hence, 3 + 5 + 4 + 1 + 1 + 2 + 2 = 18 played one or more of the three sports

Answer: There are 18 players who played one or more of the three sports.

Step-by-step explanation:

Since we have given that

Number of students played basketball = 7

Number of students played volleyball = 9

Number of students played soccer = 10

Number of students played basketball and volleyball = 1

Number of students played volleyball and soccer = 2

Number of students played volleyball, basketball and soccer = 2

Number of students who played basketball only is given by

[tex]7-1-1-2=3[/tex]

Number of students who played volleyball only is given by

[tex]9-1-2-2\\\\=4[/tex]

Number of students who played soccer only is given by

[tex]10-1-2-2\\\\=5[/tex]

So, Number of students one or more of the three sports is given by

[tex]3+4+5+1+1+2+2\\\\=18[/tex]

Hence, there are 18 players who played one or more of the three sports.

Answer:

see explanation

Step-by-step explanation:

x = r cosΘ

y = r sinΘ

with r = 54 and Θ = 69°, thus

x = 54cos69° ≈ 19.4

y = 54sin69° ≈ 50.4

Thus (54, 69° ) as an ordered pair

= [tex]\left[\begin{array}{ccc}19.4\\50.4\\\end{array}\right][/tex]

[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2977\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &13 \end{cases} \\\\\\ A=2977\left(1+\frac{0.06}{4}\right)^{4\cdot 13}\implies A=2977(1.015)^{52}\implies A\approx 6456.74[/tex]

To calculate the account balance after 13 years, we can use the formula for compound interest. Plugging in the given values, the account balance will be approximately $5,646.98.

To calculate the account balance after 13 years, we can use the formula for compound interest: A = P(1+(r/n))^(nt), where A is the final account balance, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, P = $2,977, r = 6% or 0.06, n = 4 (quarterly compounding), and t = 13 years. Plugging these values into the formula, we get:

A = $2,977(1+(0.06/4))^(4*13)

Simplifying further, we have:

A = $2,977(1.015)^52

Using a calculator, we find that A ≈ $5,646.98. Therefore, the account balance will be approximately $5,646.98 after 13 years.

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Answer:

± 13

Step-by-step explanation:

[tex]\sqrt{169}[/tex] = ± 13, since

13 × 13 = 169 and - 13 × - 13 = 169

[tex]\text{Hello there!}\\\\\text{Lets see if the rate of change for the two functions are the same}\\\\\text{We know that the rate of change for the first function is -2/3}\\\text{Lets find the rate of change for the second function}\\\\\text{We will use}\,\,\frac{y2-y1}{x2-x1}\,\,\text{to find the rate of change}\\\\\text{Plug in the coordinates:}\\\\\frac{3-5}{3-0}\\\\\text{Solve:}\\\\\frac{3-5}{3-0}\\\\\frac{-2}{3} = \text{rate of change for function 2}\\[/tex]

[tex]\text{The rate of change is the same for both functions}\\\\\text{This means that:}\\\\\large\boxed{\text{Answer: C. Function 1 and Function 2 have the same rate of change.}}[/tex]

Answer:

The new coordinates of the points of the line segment are p'(2,1) and q'(3,4)

Step-by-step explanation:

we know that

When you reflect a point across the line y= x, the x-coordinate and y-coordinate change places.

so

The rule of the reflection of a point across the line y=x is

(x,y) -----> (y,x)

we have

Points p(1,2) and q(4,3)

Applying the rule of the reflection across the line y=x

p(1,2) ------> p'(2,1)

q(4,3) -----> q'(3,4)

therefore

The new coordinates of the points of the line segment are p'(2,1) and q'(3,4)

Answer:

Step-by-step explanation:

Because they are like terms, you can just subtract them.

9 - 2 = 7

So:

9x - 2x = 7x

Let me know if you have any questions about this.

Answer:

9x-2x=7x that means 9-2=7

Answer:

California has the largest population out of the three.

Step-by-step explanation:

We would first start by showing the proportions.

California: 3/25

New York: 3/50

Texas: 2/25

You would have to find the least common denominator (in this case, 50) to accurately compare it.

So, if we wanted to convert California's ratio to one with a denominator of 50, we would multiply both sides by 2.

(3*2)/(25*2)

= 6/50.

Now, we can do the same with Texas' population.

(2*2)/(25*2)

= 4/50

Seeing that 3/50 < 4/50 < 6/50, the population of New York would be less than the population of Texas, which is in turn less than the population of California.

Therefore, California has the largest population.

Answer:

m∠R

Step-by-step explanation:

Q is the inscribed angle formed by the interception of segments TQ and SQ

R is the inscribed angle formed by the interception of segments TR and SR

The inscribed angle theorem states that an angle inscribed in a circle is half of the central angle that subtends the same arc on the circle; then, both angles Q and R are half of the central angle and equal between them. Therefore, the angle does not change as its vertex is moved to different positions on the circle.

Final answer:

To determine how many times 5/9 is greater than 4/15, we find a common denominator and compare the equivalent fractions. The fraction 5/9 is approximately 2.0833 times greater than 4/15.

Explanation:

The question is asking to find out how many times 5/9 is greater than 4/15. To compare these two fractions, we must find a common denominator or convert them to decimal form for easier comparison.

To find a common denominator, we can multiply the denominators 9 and 15 to get 135. Converting 5/9 to a fraction with 135 as the denominator, we get 75/135. Converting 4/15 to a fraction with 135 as the denominator, we get 36/135. Now, we compare the numerators 75 and 36, and we see that 75 is greater than 36.

Therefore, to find out how many times 5/9 is greater than 4/15, we divide 75 by 36, which gives us approximately 2.0833. Thus, 5/9 is about 2.0833 times greater than 4/15.

Answer:

D no solution

Step-by-step explanation:

4 + 2y = 9 + 2y

-2y -2y

4=9

Answer:

Addition.

Step-by-step explanation:

Multiplication is a faster way to do repeated addition.

For example, lets say you would add 10 fifteen's together. Addition would make it:

15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15

= 30 + 30 + 30 + 30 + 30

   = 60 + 60 + 30

      = 120 + 30

          = 150

However, when multiplying:

15 x 10 = 150

As you can tell, multiplication makes it so there are less steps, and is less time consuming.

~

Answer:

Additions.

Step-by-step explanation:

Multiplication is equivalent to repeated additions and is faster, especially if the numbers are large.

A simple example is 2 * 3 = 2 + 2 + 2.