Peter and Parker work for a cleaning crew. Peter can clean a room in 15 minutes less time than it takes Parker to do the same job. Working together,
they can clean two rooms in 110 minutes. Approximately how long does it take Peter to clean a room by himself?

Answer:

450

Step-by-step explanation:

You can easily calculate 337.5 is 75 percent of what number by using any regular calculator, simply enter 337.5 × 100 ÷ 75 and you will get your answer which is 450

If the temperatures on Earth continue to increase, the change in the pie graph would be C. Less than 2% of the Earth's water will be in polar ice caps.

The temperature of Earth has risen significantly in the last century as a result of human activity. This had led to the loss of polar ice caps due to them having melted into the oceans from the high temperatures.

This means that if the temperature of the planet should continue to increase, the polar ice caps we have will further be depleted. This would lead to less than 2% of the Earth comprising polar ice caps as is the case now.

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If  the total amount of period costs incurred to sell 9,000 units is closest to: D) $49,500.

First step is to find the variable selling and administrative expense per unit

Sales commissions $ 0.50

Add variable administrative expense 0.50

Variable selling and administrative expense per unit $ 1.00

Now let find the total amount of period costs

Total variable selling and administrative expense $9,000

($1.00 per unit × 9,000 unit)

Add total fixed selling and administrative expense 40,500

Total period cost $ 49,500

Therefore the correct option is D.

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The complete question is:

Shelp Corporation has provided the following information:

Cost per Unit Cost per Period

Direct materials $ 7.15

Direct labor $ 3.35

Variable manufacturing overhead $ 1.40

Fixed manufacturing overhead $ 81,000

Sales commissions $ 0.50

Variable administrative expense $ 0.50

Fixed selling and administrative expense $ 40,500

For financial reporting purposes, the total amount of period costs incurred to sell 9,000 units is closest to:

A) $33,000

B) $9,000

C) $40,500

D) $49,500

The real​ after-tax interest​ rate is -0.0096%, if the inflation rate rises to 4%

The real interest rate is the interest rate received by an investor, saver, or lender after adjusting for inflation. The Fisher equation, which indicates that the real interest rate is roughly the nominal interest rate minus the inflation rate, can be used to define it more explicitly.

For example, if an investor could lock in a 5% interest rate for the future year and expected a 2% increase in prices, they would receive a 3% real interest rate.

Because different investors forecast different levels of future inflation, the expected real interest rate is not a single number. Because the inflation rate during the life of a loan is unknown at the outset, inflation volatility represents a risk.

Given,

The income tax rate is 50%

After tax rate=Nominal return×(1- tax rate)

=0.06(1-0.5)

=0.03=3%

Inflation rate raises to 4% then,

=(1+ rate interest)/(1+Inflation rate)-1

=(1+0.03)/(1+0.04)-1

=-0.0096%

The real​ after-tax interest​ rate is -0.0096%.

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The value of x=20, according to the given question.

What is meant by equation?

A mathematical statement with two expressions that have the same value and the sign "equal to" between them is called an equation. Take the example of 3x + 5 = 15. Equations can be of several sorts, including linear, quadratic, cubic, and others.

According to the given data in the question,

We know that y varies directly with x like that,

y=kx..................(1)

y=12 when x=15.

Now, we have to find the value of x when y=16.

Then, putting the given values of x & y in the eq. (1), and determine the value of k.

12=k(15)

[tex]k=12/15\\k=4/5\\[/tex]

Now, putting the value of k in the second statement in eq.(1), where only y's value is given.

[tex]16=\frac{4}{5}x\\ x=16*\frac{5}{4} \\x=20[/tex]

Hence, the value of x=20.

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Answer:

The difference is the what the sum of 2+x is

Step-by-step explanation:

suppose x=3 2+3 = 5

the difference between 5 and 2 is 3

Answer The answer is 96 but as a fraction 96 8/13

Step-by-step explanation: There are 1256 rubber bands and 13 games to distribute them according to the problem; therefore, to divide to give an equal amount per each group for each game, you would give out 96 rubber bands each time, so 96 is the answer or 96 8/13.

The height of the building, using similar triangles, is given by:

36 feet.

Similar triangles are two triangles that share these two features, which are listed as follows:

The second bullet point, regarding proportional side lengths, is especially relevant in the context of this problem, as a proportional relationship is built to find the height h of the building.

From the similar triangles, the equivalent side lengths are presented as follows:

Hence the proportional relationship that models this situation is presented as follows:

3/18 = 6/h.

Applying cross multiplication, the height of the building is obtained as follows:

3h = 18 x 6

h = 6 x 6 (simplifying by 3)

h = 36 feet.

The diagram is given by the image shown at the end of the answer.

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A total of 9 workers are needed to finish the same task in 4 days

From the question, we understand that:

3 workers can complete a certain task in 12 days

This means that

3 workers = 12 days

The proportionality constant is then calculated as

Proportionality constant = Number of workers x Number of days

Substitute the known values in the above equation So, we have the following equation

Proportionality constant = 3 * 12

Evaluate

Proportionality constant = 36

When the number of days is 4, we have

Days = 4

So, we have

Proportionality constant = Number of workers x Number of days

This gives

36 = Number of workers x 4

Divide both sides by 4

Number of workers = 9

Hence, the number of workers is 9

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The equation of the parabola which passes through the point (-3, -8) as described and has x-intercepts -7 and -4 as described is; y = -2 (x + 4) (x + 7).

It follows from the task content that the equation of the parabola whose x-intercepts are -7 and -4 and has the point, (-3, -8) on it be determined.

Since the equation of a parabola in the factored form usually takes the form;

y = a (x - f) (x - g) in which case when f and g are x-intercepts of the parabola.

Therefore, we have; y = a (x - (-4)) (x - (-7))

y = a (x + 4) (x + 7)

Hence, to find the value of a, we set y = -8 and x = -3 so that we have;

-8 = a (-3 + 4) (-3 + 7)

-8 = 4a

a = -2.

Therefore, the equation of the parabola is; y = -2 (x + 4) (x + 7).

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The required value of the land after 20 years is $53,163.95.

Given that,
A piece of land was purchased for $65,000. The value of the land has slowly been decreasing by 1% annually, the land worth in 20 years is to be determined.

Here,
As the function decreases by 1% annually,
The expression for the decrease,
y = 65000(1-0.01)ˣ
y = 65000(0.99)ˣ
Put x = 20
y = 65000(0.99)²⁰
y = $53,163

Thus, the required value of the land after 20 years is $53,163.95.

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Using elimination method in the equation 2x+y=7 and 2x*3y=3, x is 3 and y is 1.

Two equations are given solving it by using rule of elimination,

2x+y=7....(1) and 2x*3y=3. (2)

Multiply equation (1) by three to get 6x+3y=21. (3)

Add equations (2) and (3) together to get

8x=24

x=24/8

x= 3

Replace this number in equation (1):

2(3)+y=7

6+y=7

y=7-6

y= 1

Consequently, the answer is x=3,y=1.

To create an equation in one variable using the elimination approach, you can either add or subtract the equations. To eliminate a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are in equality.

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The solutions to these system of equations are given as follows:

1. x = 1, y = 7.

2. x = 0.5, y = 2.

3. x = 6, y = -2.

4. x = 3, y = 3.

A system of equations is a set of equations involving multiple variables that are related, and then operations are made to solve these equations and identify the numeric value of each variable in the context of a problem.

For item 1, it is already stated that the solution for x is x = 1, hence the solution for y is obtained as follows:

y = 2(1) + 5 = 7.

For item 2, we are given two equations for y, hence the solution for x is obtained as follows:

2x + 1 = 6x - 1

4x = 2

x = 2/4

x = 0.5.

Hence the solution for y is:

y = 2(0.5) + 1 = 1 + 1 = 2.

For item 3, from the second equation, we have that:

y = 4 - x.

Then the solution for x will be of:

2(x - 7) = 4 - x

2x - 14 = 4 - x

3x = 18

x = 18/3

x = 6.

The solution for y is:

y = 4 - 6 = -2.

For item 4, from the first equation, we have that:

y = 3x - 6.

Then, replacing on the second equation, the solution for x is obtained as follows:

x + 3(3x - 6) = 12

x + 9x - 18 = 12

10x = 30

x = 3.

Then the solution for y is:

y = 3x - 6 = 3(3) - 6 = 9 - 6 = 3.

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Answer:

Step-by-step explanation:

whats the difference between first, second degree murder

The ball thrown vertically upward, the ball hits the ground after 6.719 seconds.

Quadratic equation :

To solve the quadratic equation:

h(t) = 0 = -5t² +33t+ 4

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

[tex]t = \frac{-33 \pm\sqrt{(33)^2 - 4(-5)(4)}}{2(-5)}[/tex]

t = {(-33) ±√(1169)}/(-10)

t = -0.1190

t = 6.719

neglecting the negative term we get :

t = 6.719 seconds

This represents that the ball hits the ground after 6.719 seconds.

The ball thrown vertically upward, the ball hits the ground after 6.719 seconds.

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Using the double-declining-balance method of depreciation, the completion of the table as shown is as follows:

Year Cost   Accumulated   Book Value  Depreciation Accumulated  Book

                  Depreciation        B.O.Y             Expense   Depreciation  Value

                       B.O.Y                                                               E.O.Y       E.O.Y

1    $30,000           $0           $30,000        $12,000          $12,000  $18,000

2   $30,000   $12,000          $18,000          $7,200         $19,200  $10,800

3   $30,000   $19,200          $10,800          $4,320         $23,520   $6,480

The double-declining-balance method is a depreciation method that allocates more cost to the earlier years of the asset's life.

The double-declining-balance method uses twice the straight-line rate and is computed as the product of 100/estimated useful life multiplied by 2.

The double rate is applied at the end of the year's balance for each year's depreciation expense.

The difference between the previous year's ending balance and the residual value is taken as the depreciation expense for the last year.

Auto = $30,000

Estimated life = 5 years

Residual value = $800

Depreciable amount = $29,200 ($30,000 - $800)

Straight-line depreciation rate = 20% (100/5)

Double-declining depreciation rate = 40% (20% x 2)

1st year = $12,000 ($30,000 x 40%)

2nd year = $7,200 ($18,000 x 40%)

3rd year =  $4,320 ($10,800 x 40%)

4th year = $2,592 ($6,480  x 40%)

5th year = $3,088 ($3,888 - $800)

Year Cost   Accumulated   Book Value  Depreciation Accumulated  Book

                  Depreciation        B.O.Y             Expense   Depreciation  Value

                       B.O.Y                                                               E.O.Y       E.O.Y

1    $30,000           $0           $30,000        $12,000          $12,000  $18,000

2   $30,000   $12,000          $18,000          $7,200         $19,200  $10,800

3   $30,000   $19,200          $10,800          $4,320         $23,520   $6,480

4   $30,000  $23,520           $6,480          $2,592           $26,112   $3,888

5  $30,000    $26,112           $3,888           $3,088          $29,200     $800

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The value of x is 33 and y is 39.

The fundamental characteristics listed below make it simple to recognise parallel lines.

As, (7x- 7) = 3x+ 45 (corresponding angles)

4x = 52

x= 13

Now, 7x- 7 + w + 63 = 180 (linear pair)

w= 180- 147

w= 33 degree.

y-6 = 33 (Alternate interior angle)

y= 39

Hence, the value of x is 33 and y is 39.

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Answer:

$145

Step-by-step explanation:

The revenue - the cost is the profit.

14x - (1708 + 7x)  Distribute what is in the parentheses by -1

14x -1(1780) -1(7x)  Simplify

14x - 1780 -7x  Combine like tersm

7x - 1780  Plug in 275 for x

7(275) - 1780

1925 - 1780

145

By using the fact that the angles are supplementary, we can write and solve a linear equation to find that x = 62.

In the image, we can see two supplementary angles, where by definition, two angles are supplementary if their addition is equal to a plane angle (an angle of 180°).

With that in mind, we can write the linear equation:

x + 118 = 180

So we just need to isolate x in that simple linear equation.

If we subtract 118 in both sides, we will get:

x + 118 - 118 = 180 - 118

x = 62

So the unknown angle has a measure of 62°.

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Answer: -52

Step-by-step explanation: multiply by breaking apart a factor (-13) x 4

Answer:

28561

Step-by-step explanation:

Find the Exact Value:

Raise -13 to the power of 4.

28561 is the answer.

The image of of (0,-4) After the dilation by the scale factor of 2 at the center is (0,-8)

What is the scale factor?

A scale factor is Scaling the shape of an object. it means the shape of the object remains the same but the size of the object is either increased or decreased. A scale factor greater than 1 means size is increased and less than one means size is decreased

We are given a point (0,-4)

Which is to be scaled by the factor of 2 at the center position

As the value is greater than 1 the size increase

We multiply the coordinate to find the new coordinates

We get (0,-8)

Hence, The image of of (0,-4) After the dilation by the scale factor of 2 at the center is (0,-8)

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Using the probability of adults of having tattoo, critical value is 1.76 and margin of error is 0.0353 and a 95% confidence interval for the proportion of all adults that have a tattoo is (0.2347, 0.3053)

In the given question,

In a poll of 489 adults, 132 of then said they have a tattoo.

We have to find critical value and margin of error, and then construct a 95% confidence interval for the proportion of all adults that have a tattoo.

From the question

Total number of adults = 489

The adults that have tattoo = 132

So the proportion in the sample is

p = 132/489

p = 0.269

p ≈ 0.27

Now finding the proportion of adults not having tattoo.

q = 1−p

q = 1−0.27

q = 0.73

Now finding the critical value(z).

The value of z from the standard table for 95% confidence interval.

We can write 95% as 0.95

Z = [tex]z_{\alpha /2}[/tex]

Z = [tex]z_{0.95 /2}[/tex]

Z = [tex]z_{0.475}[/tex]

From the standard table of z

Z = 1.96.

Now finding the margin error.

Margin Error(E) = [tex]Z\times\sqrt{\frac{pq}{n}}[/tex]

As we know that Z = 1.96, p = 0.27, q = 0.73, n = 489

Now putting the value

E = [tex]1.76\times\sqrt{\frac{0.27\times0.73}{489}}[/tex]

Simplifying

E = [tex]1.76\times\sqrt{\frac{0.1971}{489}}[/tex]

E = [tex]1.76\times\sqrt{0.000403}[/tex]

E = 1.76×0.0201

E = 0.0353

Now finding a 95% confidence interval for the proportion of all adults that have a tattoo.

Confidence Interval = p−E< P < p+E

Confidence Interval = 0.27−0.0353< P < 0.27+0.0353

Confidence Interval = 0.2347< P < 0.3053

Hence, critical value is 1.76 and margin of error is 0.0353 and a 95% confidence interval for the proportion of all adults that have a tattoo is (0.2347, 0.3053)

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The intercept reveals that the first loan amount was $1,560.00.

Every month, Michael's debt to his father drops by 290.

acc to our question-

The amount Michael owes is given by :

y = - 290x +18,560

x = number of months ; y = amount owed

Amount owed after 3 months :

Put x = 3 in the equation :

y= - 290(3) +18,560

y = - 870 + 18560

y = 17690

According to the general form of a linear equation :

y = mx + c

Where, m = slope ; c = intercept

The slope = - 290 ; Intercept = 18560

Slope is the change in y per unit change in x ; The slope means that amount owed, y decreases by 290 per month

The intercept shows that the original amount borrowed is 18560.

Hence,The intercept reveals that the first loan amount was $1,560.00.

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Answer: A scale factor of 1/2 was applied to the first triangle to get the resulting image.

Step-by-step explanation: The initial side length of 3.4 is twice as long as 1.7, the initial triangle was reduced to half of the initial size.

Answer:

The triangle is still an equilateral triangle as before, and the only difference is that the side length is halved from 3.4 to 1.7 (3.4/2=1.7). Therefore, the scale factor is 1.7/3.4=0.5. A scale factor <1 means that the original shape is reduced. The scale factor would be a reduction.

Step-by-step explanation:

The image would be of a triangle.
Hope this helps! :))

The probability that a student's mark is more than 75 is 0.0947 and in a class of 50 students, 5 students should have a mark of more than 75.

In the given question,

The Mathematics marks of all the students in the class are normally distributed with mean mark 54 and standard deviation 16.

We have to find the probability that a student's mark is more than 75.

In a class of 50 students, we also have to find how many students should have a mark of more than 75.

From the question the mean = 54

Standard Deviation = 16

So the probability that a student's mark is more than 75.

Using the normal distribution

z = (x−mean)/Standard Deviation

P(x>75) = P(z>(x−mean)/Standard Deviation)

P(x>75) = 1−P(z<(75−54)/16)

Simplifying

P(x>75) = 1−P(z<21/16)

P(x>75) = 1−P(z<1.3125)

From the standard z table value

P(x>75) = 1−0.9053

P(x>75) = 0.0947

Hence, the probability that a student's mark is more than 75 is 0.0947.

Now finding in a class of 50 students, how many students should have a mark of more than 75.

Total student = 50

So the student having mark of more than 75 = Total student * probability that a student's mark is more than 75

The student having mark of more than 75 = 50 * 0.0947

The student having mark of more than 75 = 4.735

The student having mark of more than 75 ≈ 5

Hence, in a class of 50 students, 5 students should have a mark of more than 75.

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The doubling time will be 4.4 years for a city is population is growing by 17% per year.

It's time to double down on the time-doubling equation (pun intended). On the assumption that the growth in amount remains constant from one period to the next, the equation is as follows:

Doubling time = log 2 / log (1 + increase)

It has given that the population of the city is growing back 17% per year.

Doubling time = log 2 / log (1 + increase)

Doubling time = log 2 / log (1 + 17/100)

[tex]\mathrm{Apply\:log\:rule}:\quad \frac{\log _c\left(b\right)}{\log _c\left(a\right)}=\log _a\left(b\right)[/tex]

[tex]=\log _{1+\frac{17}{100}}\left(2\right)[/tex]

Doubling time = 4.41484

Round to the nearest tenth decimal.

Doubling time = 4.4

Thus, the doubling time will be 4.4 years for a city is population is growing by 17% per year.

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Answer:

Step-by-step explanation:

Correct answer is A 5

Answer:

If you let 'n' to represent a number then '-9 times a number' can be written as -9n

'less then' means subtraction:  12 less then -9 times a number  becomes -9n - 12 (the subtraction in the equation is written in the opposite way as written in words)

'8 minus 4 times the number ' becomes 8 - 4n

So, the equation is:  -9n - 12  =  8 - 4n

Get all the variables to one side. If you add  9n  to both sides:

   -9n + 9n - 12  =  8 - 4n + 9n

   -12  =  8 + 5n

Subtract 8 from both sides:

   -12 - 8  =  8 - 8 + 5n

   -20  =  5n

Divide both sides by 5:

   -20 ÷ 5  =  5n ÷ 5

   -4  =  n

Now, check the answer:   -9n - 12  =  8 - 4n

              -9(-4) - 12  =  36 - 12  = 24                 8 - 4(-4)  =  8 + 16  = 24        They check!

Step-by-step explanation:

Hope this helps! :)

x = [tex]x^{2}[/tex] - 20  is equivalent to  [tex]x^{2}[/tex] - x - 20 = 0 .

What do you mean by algebraic expression?

Algebraic expressions are mathematical expressions that result when you perform operations such as addition, subtraction, multiplication, and division on variables and constants. Algebraic expressions have different components. Variables, constants, terms, and coefficients in algebraic expressions. A symbol that does not have a fixed value is called a variable.

Given equation:

x = [tex]x^{2}[/tex] - 20

⇒ [tex]x^{2}[/tex] - 20 - x = 0

⇒ [tex]x^{2}[/tex] - x - 20 = 0

Therefore, x = [tex]x^{2}[/tex] - 20  is equivalent to  [tex]x^{2}[/tex] - x - 20 = 0 .

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