Quigley Inc. is considering two financial plans for the coming year. Management expects sales to be $300,000, operating costs to be $265,000, assets (which is equal to its total invested capital) to be $200,000, and its tax rate to be 25%. Under Plan A it would finance the firm using 25% debt and 75% common equity. The interest rate on the debt would be 8.8%, but under a contract with existing bondholders the TIE ratio would have to be maintained at or above 3.2. Under Plan B, the maximum debt that met the TIE constraint would be employed. Assuming that sales, operating costs, assets, total invested capital, the interest rate, and the tax rate would all remain constant, by how much would the ROE change in response to the change in the capital structure? Do not round your intermediate calculations.

Answer:

The chord length x is growing at a rate of 1 m/min after 2π minutes.

Step-by-step explanation:

The formula for chord length x in terms of radius r is:

[tex]\boxed{x &= 2r\sin\left(\dfrac{\theta}{2}\right)}[/tex]

where θ is the central angle subtended by the chord.

The formula for arc length s in terms of radius r is:

[tex]\boxed{s=r\theta}[/tex]

where θ is the central angle subtended by the chord.

Rearrange the formula for arc length to isolate θ, then substitute this into the the formula for chord length to create an equation for x in terms of s:

[tex]\begin{aligned}\theta=\dfrac{s}{r} \implies x &= 2r\sin\left(\dfrac{\frac{s}{r}}{2}\right)\\x&= 2r\sin\left(\dfrac{s}{2r}\right)\end{aligned}[/tex]

Given the radius is 6 m, substitute r = 6 into the equation for x:

[tex]\implies x &= 12\sin\left(\dfrac{s}{12}\right)[/tex]

Differentiate with respect to s:

[tex]\begin{aligned}\implies \dfrac{\text{d}x}{\text{d}s} &= \dfrac{1}{12} \cdot 12\cos\left(\dfrac{s}{12}\right)\\\\&=\cos\left(\dfrac{s}{12}\right)\end{aligned}[/tex]

Given the arc length s is growing at a rate of 2 m/min:

[tex]\implies \dfrac{\text{d}s}{\text{d}t}=2[/tex]

Use the chain rule to create an equation for the rate of change of the chord x:

[tex]\begin{aligned}\implies \dfrac{\text{d}x}{\text{d}t}&=\dfrac{\text{d}x}{\text{d}s}\times \dfrac{\text{d}s}{\text{d}t}\\\\&=\cos\left(\dfrac{s}{12}\right) \times 2\\\\&=2\cos\left(\dfrac{s}{12}\right) \end{aligned}[/tex]

Given the arc length is growing at a rate of 2 m/min:

[tex]\implies \dfrac{\text{d}s}{\text{d}t}=2[/tex]

Integrate to create an equation for s in terms of t:

[tex]\begin{aligned}\displaystyle \int 1 \; \text{d}s&=\int 2\; \text{d}t}\\\\ s&=2t+\text{C}\end{aligned}[/tex]

Given s = 0 when t = 0, this means that C = 0. Therefore:

[tex]\implies s=2t[/tex]

If t = 2π then:

[tex]\implies s=2 \cdot 2\pi = 4\pi[/tex]

Finally, substitute s = 4π into the equation to calculate the rate of change of the chord at 2π minutes:

[tex]\begin{aligned}\implies \dfrac{\text{d}x}{\text{d}t}&=2\cos\left(\dfrac{4\pi}{12}\right) \\\\&=2 \cos \left(\dfrac{\pi}{3}\right)\\\\&=2 \cdot \dfrac{1}{2}\\\\&=1\end{aligned}[/tex]

Therefore, the chord length x is growing at a rate of 1 m/min after 2π minutes.

Answer: it is A  (The mean is about 57.4, and it represents the average number of students who left school early.)

Step-by-step explanation:

first you add all of the numbers then you get 689. then divide by 12 and you get 57.4

The value of the given function at f(-6) is -14.

A function in mathematics is a relationship between a set of inputs (the domain) and a set of outputs (the range), where each input corresponds to one specific outcome. Equations, tables, diagrams, and verbal descriptions can all be used to depict functions. They are frequently represented by the notation f(x), where x is the input variable and f is the name of the function. In many branches of mathematics, science, and engineering, functions are fundamental ideas that are used to simulate real-world occurrences and address issues in a variety of applications.

The give function is f(x) = 3x + 4.

Substitute the value of x = -6 to obtain the value of f(-6):

f(-6) = 3(-6) + 4

f(-6) = -18 + 4

f(-6) = -14

Hence, the value of the given function at f(-6) is -14.

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The total cost with 4 snacks is $59.

The total cost with x snacks is $29 + $5x.

The first step is to determine the total number of people going to the movies. There are 3 people going to the movies.

The total cost spent by Ellie is the sum of the tickets and the total cost of the snacks.

Total cost = total cost of the tickets + total cost of the snacks

= (cost of one ticket x number of people going to the movie) + (number of snacks bought x price of one snack)

= (13 x 3) + ($5 x 4)

$39 + $20 = $59

Total cost if x snacks is bought: (13 x 3) + ($5 x x) = $39  + $5x

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Answer:

B.2/3

Step-by-step explanation:

Let's work backwards from the information we have to determine which diagram Ronald drew.

We know that after Ronald ate on Tuesday, there was 1/2 of the pizza remaining. This means that he ate 1/2 of the pizza on Tuesday, since he had eaten 1/3 of the pizza on Monday.

So, if we add 1/2 and 1/3, we get:

1/2 + 1/3 = 5/6

This means that Ronald ate 5/6 of the pizza in total. We also know that he ate 1/2 of the pizza on Tuesday, so the fraction he ate on Monday was:

5/6 - 1/2 = 1/3

This confirms that Ronald ate 1/3 of the pizza on Monday.

Now, let's look at the answer choices. We need to find a diagram that represents Ronald eating 1/2 of the pizza, since that's what he ate on Tuesday. The only answer choice that represents 1/2 of the pizza shaded is B. 2/3.

Therefore, Ronald drew diagram B. 2/3.

Answer:

Step-by-step explanation:

Interest is a fee charged by a lender to a borrower for the use of money or credit, usually expressed as a percentage of the amount borrowed or invested over a period of time. Brandon invested $[tex]4700[/tex] at 3% interest and $[tex]1100[/tex] at [tex]8[/tex]% interest.  The total interest earned after one year is $229

How much was in each account?

Let x be the amount invested in the first account that pays 3% interest, and let y be the amount invested in the second account that pays 8% interest. Since the total amount invested is $5800, we have:

[tex]x + y = 5800[/tex]

The amount of interest earned on the first account is 0.03x, and the amount of interest earned on the second account is 0.08y. Since the total interest earned after one year is $229, we have:

[tex]0.03x + 0.08y = 229[/tex]

We now have two equations with two unknowns:

[tex]x + y = 5800[/tex]

[tex]0.03x + 0.08y = 229[/tex]

We can solve for x and y by using elimination or substitution method. Here, we will use the substitution method.

Solve the first equation for x:

[tex]x = 5800 - y[/tex]

Substitute this expression for x into the second equation and solve for y:

[tex]0.03(5800 - y) + 0.08y = 229[/tex]

[tex]174 - 0.03y + 0.08y = 229[/tex]

[tex]0.05y = 55[/tex]

[tex]y = 1100[/tex]

Now substitute this value of y into either equation to solve for x:

[tex]x + 1100 = 5800[/tex]

[tex]x = 4700[/tex]

Therefore, Brandon invested $[tex]4700[/tex] at 3% interest and $[tex]1100[/tex] at [tex]8[/tex]% interest.

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The midpoint of the interval is 60.

To find the midpoint of an interval, we take the average of its endpoints.

The endpoints of the interval 50 < x < 70 are 50 and 70.

Therefore, the midpoint of the interval is:

(midpoint) = (50 + 70) / 2

= 120 / 2

= 60

Hence, the midpoint of the interval is 60.

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There are 48 ways to order this model of car. The correct option is A

We need to multiply the number of options for each feature to get the total number of ways to order this particular car:

   4 color choices

   2 options (manual or automatic) for the transmission

   Audio system: 6 choices

We can multiply these figures in order to find the total number of ways by applying the counting principle to multiplication:

4 × 2 × 6 = 48

Therefore, there are 48 ways to order this model of car.

Therefore, The correct option is A

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The minimum cost is achieved when we use 14 pounds of deluxe coffee and 35 pounds of regular coffee.

Let x be the number of pounds of deluxe coffee to be used in the blend, and let y be the number of pounds of regular coffee to be used in the blend.

We are told that the blend must contain at least 14 pounds of deluxe coffee, so we have the inequality:

We are also told that the total amount of blend must be at least 49 pounds, so we have the inequality:

To minimize costs, we need to minimize the cost function C(x,y), which is the total cost of the blend. The cost of deluxe coffee is $6 per pound, and the cost of regular coffee is $4 per pound, so we have:

Now we can use the method of Lagrange multipliers to find the minimum value of C(x,y) subject to the two constraints above. We define the Lagrange function L as follows:

where λ and μ are Lagrange multipliers. We need to find the values of x, y, λ, and μ that minimize L.

Taking partial derivatives of L with respect to x, y, λ, and μ, and setting them equal to zero, we get the following system of equations:

From the second equation, we get λ = 4. Substituting this into the first equation, we get μ = 2. Substituting these values into the third equation, we get y = 35. Substituting μ = 2 into the fourth equation, we get x = 14.

Therefore, the minimum cost is achieved when we use 14 pounds of deluxe coffee and 35 pounds of regular coffee.

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The interest on $279,811.47 for the second payment is $933.04.

The payment to principal for the second payment is $403.11

The new balance after the second payment is $279,408.36.

Interest = $279,811.47 x 0.04 / 12 = $933.04

Payment to principal = Payment amount - Interest

Payment to principal = $1,336.15 - $933.04 = $403.11

New balance = Previous balance - Payment to principal

New balance = $279,811.47 - $403.11 = $279,408.36

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Answer:

y = (5/7)x + (75/7)

Step-by-step explanation:

If you ever find yourself in a math class where you have to write the equation of a line that goes through a certain point and has a certain slope, don't panic. There is a simple formula that can help you out. It's called the point-slope form and it looks like this:

y - y1 = m (x - x1)

It may look scary, but it's actually pretty easy to use. All you have to do is plug in the values that you know and solve for the ones that you don't. For example, let's say you have a line that passes through the point (-1, 10) and has a slope of 5/7. You can use the point-slope form to write the equation of the line like this:

y - 10 = (5/7) (x - (-1))

See? That wasn't so bad. Now you can simplify the equation by distributing the 5/7 and adding 10 to both sides. You get:

y = (5/7)x + (75/7)

And that's it! You have written the equation of the line in slope-intercept form, which is another way of writing the equation of a line. You can check your answer by plugging in the values of x and y from the original point and seeing if they make the equation true. If they do, you're good to go. If not, you made a mistake somewhere and you should go back and fix it.

Congratulations! You have learned how to use the point-slope form to write the equation of a line. Now you can impress your math teacher and your friends with your skills.  Remember, with great power comes great responsibility.

✧☆*: .｡. That's all folks, have fun with math! (✧ω✧) .｡.:*☆✧

Answer:

x= √2

(or)

x = [tex]\frac{-3\sqrt{2}}{5}[/tex]

Step-by-step explanation:

If I assume your equation was like this,

5x²-2[tex]\sqrt{2x}[/tex] - 6 = 0

([tex]x - \sqrt{2}[/tex]) ([tex]5x + 3\sqrt{2}[/tex]) = 0

[tex]x - \sqrt{2}[/tex] = 0  (or)    [tex]5x + 3\sqrt{2}[/tex] =0

x = [tex]\sqrt{2}[/tex]  (or) 5x = [tex]-3\sqrt{2}[/tex]

x = [tex]\sqrt{2}[/tex]  (or)  x = [tex]\frac{-3\sqrt{2}}{5}[/tex]

The quadratic equation can be solved to give the value of x1 = √2 and x2 = -3√2 / 5.

To solve the quadratic equation 5x² - 2√2x - 6 = 0, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

Now we have two solutions, one for the positive value and one for the negative value:

x1 = (2√2 + 8√2) / 10

x2 = (2√2 - 8√2) / 10

Simplify the solutions:

x1 = (10√2) / 10 = √2

x2 = (-6√2) / 10 = -3√2 / 5

So the solutions for the equation 5x² - 2√2x - 6 = 0 are x1 = √2 and x2 = -3√2 / 5.

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The dimension of the rectangular of a norman window will be 1.6803*3.3606.

What is the area of Rectangle?

In any quadrilateral which have equal and parallel opposite sides is considered to be a rectangle. It is also called as a polygon with four sides and the four angles that are all 90 degrees each. A rectangle is a shape with only two dimensions. The product of the length and the breadth calculates its area. The length of the diagonals of any rectangle are equal in length. Thus, the length of the diagonals can be calculated easily using the Pythagoras theorem where, the diagonal is considered to be the hypotenuse.

Let r represents the radius, and b be the breadth.

Then, perimeter = 3.14*r+2r+2b = 12

For the dimension needed for the most light to enter we need to maximize the area.

Hence, area of the window : area of the semicircle + area of the rectangle

= [tex]\frac{3.14*r^2}{2} + 2rb[/tex]

= [tex]12r - (\frac{3.14+4}{2}) r^2[/tex]

A'(r) = 0

Therefore, [tex]r=\frac{12}{3.14+4}[/tex] which is nearly equal to 1.6803m

From this value of r we can calculate the value of b to be;

b= 1.6803m

Thus, a= 3.606m

Thus the required dimension is : 1.6803*33606

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Answer:

length = 9 feet

Step-by-step explanation:

We know that the formula for perimeter (P) is P = 2w + 2l

Because we're told that the length (l) is 4 feet more than the width (w), our formula for length is l = w + 4

We can now substitute w + 4 for l in the perimeter formula and 28 for P.  This will allows us to first solve for the width:

[tex]28 = 2(w+4)+2w\\28=2w+8+2w\\28=4w+8\\20=4w\\5=w[/tex]

Now we can plug in 5 for w in our length formula to find the length:

[tex]l = 5 + 4\\l = 9[/tex]

We can check our solutions by plugging in 5 for w and 9 for l in the perimeter formula and check whether we get 28 as an answer:

[tex]2(9) + 2(5)=28\\18+10=28\\28=28[/tex]

Answer:262144

Step-by-step explanation:4^9

4^3=

64^3=262144

its is our required answer

hope it will help you!

The triangle with the sides 8, 11 and 12 is an acute triangle

From the question, we have the following parameters that can be used in our computation:

8, 11 and 12

Using the pythagoras theorem, we have

12² = 11² + 8²

Evaluate the exponent on the left hand side and the sum of exponents on the right hand side

144 = 185

The above equation is false

This is because 144 and 185 are not equal

However, 144 is less than 185

This means that the triangle is an acute triangle

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1. The policy has a $3,000 deductible clause, which means that Jasper must pay the first $3,000 of his expenses before the insurance company begins to cover the remaining expenses.

2. Jasper should expect to receive $13,270 from the insurance company.

His total out of pocket expense will be $5,730.

3. Other policies may have offered Jasper additional protection, such as disability income benefits. This would have helped him while he was unable to work due to his injury.

4. Based on the information given, the health care insurance coverage that Jasper had appears to be adequate, given his circumstances.

The deductible clause is used by insurance companies to reduce the risk of paying out large amounts of money for small claims and to spread out the cost of insurance among policyholders.

1. The policy provisions as they relate to deductibles, co-insurance, and internal limits are as follows: The policy has a $3,000 deductible clause, which means that Jasper must pay the first $3,000 of his expenses before the insurance company begins to cover the remaining expenses. The co-insurance clause means that the insurance company will cover 80% of the remaining expenses and Jasper will be responsible for the remaining 20%.

The internal limits for hospital room and board and surgical fees are $180 and $1,500, respectively. This means that the insurance company will only cover up to $180 per day for hospital room and board and up to $1,500 for surgical fees.

2. Jasper should expect to receive $13,270 from the insurance company. He must pay $3,000 out of his own pocket to meet the deductible, and he will also be responsible for the remaining 20% of the expenses not covered by the insurance company, which amounts to $2,730.

This means that his total out of pocket expense will be $5,730.

3. Other policies may have offered Jasper additional protection, such as disability income benefits. This would have helped him while he was unable to work due to his injury.

4. Based on the information given, the health care insurance coverage that Jasper had appears to be adequate, given his circumstances.

The policy provides enough coverage to cover the majority of his medical expenses and the deductible and co-insurance amounts are reasonable. In addition, the internal limits for hospital room and board and surgical fees are within reasonable limits.

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The expected value of the distribution is 1 and the probability that a randomly selected student completes fewer than 2 bonus assignments is 0.75

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

a. To compute the expected value of the distribution, we need to multiply each possible number of completed bonus assignments by its probability and then add up the results. That is:

Expected value = (0 x 0.55) + (1 x 0.2) + (2 x 0.15) + (3 x 0.1) = 0 + 0.2 + 0.3 + 0.3 = 1.0

Therefore, the expected value of the distribution is 1.0.

b. To find the probability that a randomly selected student completes fewer than 2 bonus assignments, we need to add up the probabilities for the cases where x is 0 or 1. That is:

P(x < 2) = P(x=0) + P(x=1) = 0.55 + 0.2 = 0.75

Therefore, the probability that a randomly selected student completes fewer than 2 bonus assignments is 0.75 or 75%.

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Answer:

6

Step-by-step explanation:

he needs 6 points to score over the last nine holes

Kevin needs to score 8.5 strokes per hole for the last nine holes to get back to an even par.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

We can find the total number of strokes Kevin needs to score over 18 holes to reach an even par.

If the par score for 18 holes is 72,

and Kevin scored 4 over par on the first nine holes

= 9 × 4 = 36 extra strokes.

Now, if the par score for the last nine holes is x, then we have:

4 + x + x + x + x + x + x + x + x = 72

4 + 8x = 72

8x = 68

x = 8.5

Therefore, Kevin needs to score 8.5 strokes per hole for the last nine holes to get back to an even par.

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Answer:

100 grandparents

200 parents

100 children

Step-by-step explanation:

Define the variables: Let g be the number of grandparents, p be the number of parents, and c be the number of children.

Use the total number of people to set up an equation: g + p + c = 400

Use the information that there were twice as many parents as grandparents to set up another equation: p = 2g

Use the information that there were 50 more children than parents to set up a third equation: c = p + 50

Substitute the second equation into the third equation to eliminate p: c = 2g + 50

Substitute the second equation into the first equation to get an equation in terms of g only: g + 2g + c = 400

Substitute the third equation into the first equation to get another equation in terms of g only: g + 2(1/2 c - 50) + c = 400

Simplify the equations and solve for g: g = 100

Use the second equation to solve for p: p = 2g = 200

Use the third equation to solve for c: c = p + 50 = 250

Therefore, there were 100 grandparents, 200 parents, and 100 children in attendance at the family reunion! :DDDD

Answer:

the coordinates of point P are (15, 19 + 3 sqrt(3)).

Step-by-step explanation:

Let's first find the center of the circle, which is (h, k). From the given information, we know that h = 12 and k = 16.

Next, we need to find the coordinates of the point P. We can do this using the formula for finding a point on a circle given its center and angle:

x = h + r cos(theta)

y = k + r sin(theta)

where r is the radius of the circle and theta is the angle between the horizontal axis and the line connecting the center of the circle to the point P.

Substituting the given values, we have:

x = 12 + 6 cos(pi/3)

y = 16 + 6 sin(pi/3)

Evaluating the trigonometric functions, we get:

x = 12 + 6 (1/2) = 15

y = 16 + 6 (sqrt(3)/2) = 19 + 3 sqrt(3)

Therefore, the coordinates of point P are (15, 19 + 3 sqrt(3)).

The scale ratio is therefore 1:5 miles per inch

The connection between distances on the map and their equivalent distances on the ground is expressed by the scale ratio. Here, one inch on the chart corresponds to five miles on the Earth. We must represent this connection as a fraction using the same units in order to calculate the scale ratio:

5 miles per inch.

By reducing both the numerator and denominator by one inch, we may simplify the following fraction:

1/5 of a mile per inch

The scale ratio is therefore 1:5 miles per inch. This implies that the comparable distance on the ground is 5 units long for every 1 unit of distance indicated on the map (1 inch) (5 miles).

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Find x, so that 7x + 2, 5x + 7 and 2x - 1 form an arithmatic sequence

The total number of possible outcomes when flipping a coin three times is 8, since there are two possible outcomes for each flip (heads or tails).

Combination is a way of selecting items from a set where order does not matter. Combinations are written as a set of n distinct objects taken r at a time, where n is the total number of objects and r is the number of objects taken.

Of these 8 outcomes, 3 include exactly one head. These are the outcomes HHT, HTH, and THH.

The total number of possible outcomes is calculated using the formula 2ⁿ, where n represents the number of flips. In this case, n = 3, so the total number of outcomes is 2³ = 8.

To find the number of outcomes with exactly one head, we can use the formula nCr, which stands for n choose r.

This formula is used to calculate the number of combinations of r elements that can be chosen from a set of n elements.

In this case, n = 3 (the number of flips) and r = 1 (the number of heads).

This gives us 3C1 = 3, which is the number of outcomes with exactly one head.

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The deduction that is optional is C. Retirement plan deductions.

When contributing to a retirement plan like a 401(k) or an Individual Retirement Account (IRA), you receive deductions from your taxable income. Essentially, whatever amount of money contributed towards the retirement fund can be subtracted from your total annual income.

Consequently, the entire amount cannot then be seized for taxation purposes. Let's say, for instance that you earn $50,000 annually and contribute $5,000 into your account; this would imply your taxable revenue reduces to $45,000.

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Options for this question are:

In interval notation, we can write this as:

(-∞, -1) ∪ (19, ∞)

An inequality is a comparison between two numbers or expressions that are not equal to one another. Indicating which value is less or greater than the other, or simply different, are symbols like, >,,, or.

We are given the compound inequality:

x - 9 < -10 or x - 9 > 10

We can simplify each inequality separately:

x - 9 < -10 --> x < -1 (by adding 9 to both sides)

x - 9 > 10 --> x > 19 (by adding 9 to both sides)

So the solution to the compound inequality is:

x < -1 or x > 19

In interval notation, we can write this as:

(-∞, -1) ∪ (19, ∞)

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Triangles QNR and RMQ are congruent

PQR is an isosceles triangle, by extension PQ = PR.

Considering the triangles QNR and RMQ:

Given that angle MRQ = angle NQR.

Likewise, angle RQM = angle RQN (since they are vertically opposite angles).

Consequently, angle MRQ = angle RQM + angle NQR = angle RQN + angle NQR = angle RNQ.

Hence, two pairs of angles that are equal:

angle MRQ = angle RNQ

angle RMQ = angle RQN

Also, PQ = PR, and for M and N are on PQ and PR at the same time, then, MQ = NR.

Through the angle-side-angle (ASA) congruence criterion, we can conclude that triangles QNR and RMQ are congruent.

Therefore, we have proved that triangles QNR and RMQ are congruent.

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The additional cost incurred in dollars when production is increased from 12 units to 15 units is -$2.28.

To find the additional cost incurred in dollars when production is increased from 12 units to 15 units, we need to calculate the difference in the marginal cost between these two production levels.

Given the marginal cost function: C′(x) = 0.12x^2 − 4x + 140

We can substitute x = 12 into the marginal cost function to find the marginal cost at 12 units:

C′(12) = 0.12(12)^2 − 4(12) + 140

C′(12) = 0.12(144) − 48 + 140

C′(12) = 17.28 − 48 + 140

C′(12) = 109.28

Similarly, we can substitute x = 15 into the marginal cost function to find the marginal cost at 15 units:

C′(15) = 0.12(15)^2 − 4(15) + 140

C′(15) = 0.12(225) − 60 + 140

C′(15) = 27 − 60 + 140

C′(15) = 107

Now, we can calculate the difference in marginal cost between 15 units and 12 units. The Additional cost wil be:

= C′(15) - C′(12)

= 107 - 109.28

= -2.28.

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