evaluate the line integral ∫cf⋅d r where f=⟨−4sinx,3cosy,10xz⟩ and c is the path given by r(t)=(−3t3,t2,2t) for 0≤t≤1

Answer:

a. The company's profit function P(x, y, z) = 24x +12y +16z – 0.2x^2 – 0.1y^2 – 0.1z^2 – 26

b. The number of cars that must be sold in each market are 60 in America, also 60 in Europe and 80 in Asia.

Step-by-step explanation:

Note: This question is not complete and it has some errors in the figures used. The correct complete question is therefore provided before answering the question as follows:

An automobile manufacturer sells cars in America, Europe, and Asia, charging a different price in each of the three markets. The price function for cars sold in America is p = 27 − 0.2x  (for 0 ≤ x ≤ 135), the price function for cars sold in Europe is q = 15 − 0.1y  (for 0 ≤ y ≤ 150), and the price function for cars sold in Asia is r = 19 − 0.1z (for 0 ≤ z ≤ 190), all in thousands of dollars, where x, y, and z are the numbers of cars sold in America, Europe, and Asia, respectively. The company's cost function is C = 26 + 3(x + y + z) thousand dollars.

(a) Find the company's profit function P(x, y, z). [Hint: The profit will be revenue from America plus revenue from Europe plus revenue from Asia minus costs, where each revenue is price times quantity.]

P(x, y, z) =

(b) Find how many cars should be sold in each market to maximize profit. [Hint: Set the three partials Px, Py, and Pz equal to zero and solve. Assuming that the maximum exists, it must occur at this point.]

The explanation to the answers is now given as follows:

(a) Find the company's profit function P(x, y, z). [Hint: The profit will be revenue from America plus revenue from Europe plus revenue from Asia minus costs, where each revenue is price times quantity.]

p = price function for cars sold in America = p = 27 − 0.2x (for 0 ≤ x ≤ 135)

q = price function for cars sold in Europe = 15 − 0.1y (for 0 ≤ y ≤ 150)

r = price function for cars sold in Asia = 19 − 0.1z (for 0 ≤ z ≤ 190)

C = company's cost function = 26 + 3(x + y + z) = 26 + 3x + 3y + 3z

P(x, y, z) = profit function

x, y, and z are the numbers of cars sold in America, Europe, and Asia, respectively

Therefore, we have:

TR = Total revenue = px + qy + rz …………………………….. (1)

Substituting the relevant values into equation (1), we have:

TR = (27 − 0.2x)x + (15 − 0.1y)y + (19 − 0.1z)z

TR = 27x – 0.2x^2 + 15y – 0.1y^2 + 19z – 0.1z^2

Also,

P(x, y, z) = TR – C ……………………………………… (2)

Substituting the relevant values into equation (2), we have:

P(x, y, z) = 27x – 0.2x^2 + 15y – 0.1y^2 + 19z – 0.1z^2 – (26 + 3x + 3y + 3z)

P(x, y, z) = 27x – 0.2x^2 + 15y – 0.1y^2 + 19z – 0.1z^2 – 26 – 3x – 3y – 3z

P(x, y, z) = 27x – 3x +15y – 3y +19z – 3z – 0.2x^2 – 0.1y^2 – 0.1z^2 – 26

P(x, y, z) = 24x +12y +16z – 0.2x^2 – 0.1y^2 – 0.1z^2 – 26 ……………….. (3)

Therefore, the company's profit function P(x, y, z) = 24x +12y +16z – 0.2x^2 – 0.1y^2 – 0.1z^2 – 26.

(b) Find how many cars should be sold in each market to maximize profit. [Hint: Set the three partials Px, Py, and Pz equal to zero and solve. Assuming that the maximum exists, it must occur at this point.]

As indicated in the question, the number cars that should be sold in each market to maximize profit can be calculated by deriving the three partials Px, Py, and Pz from the profit function P(x, y, z), i.e. equation (3) in part a above, and set equal to zero and then solve as follows:

In America

From equation (3), we have:

Px = 24 – 0.4x = 0

Therefore, we have:

24 – 0.4x = 0

24 = 0.4x

x = 24 / 0.4

x = 60

In Europe

From equation (3), we have:

Py = 12 – 0.2y = 0

Therefore, we have:

12 – 0.2y = 0

12 = 0.2y

y = 12 / 0.2

y = 60

In Asia

From equation (3), we have:

Pz = 16 - 0.2z = 0

Therefore, we have:

16 - 0.2z = 0

16 = 0.2z

z = 16 / 0.2

z = 80

Based on the above calculations, the number of cars that must be sold in each market are 60 in America, also 60 in Europe and 80 in Asia.

In analyzing the performance of implementing the given methods over Singly Linked List and Doubly Linked List data structures, we consider the Big-O notation, which provides insight into the time complexity of these operations as the size of the list increases.

Add to Start of List:

Singly Linked List: O(1)

Doubly Linked List: O(1)

Both Singly Linked List and Doubly Linked List offer constant time complexity, O(1), for adding an element to the start of the list.

This is because the operation only involves updating the head pointer (for the Singly Linked List) or the head and previous pointers (for the Doubly Linked List). It does not require traversing the entire list, regardless of its size.

Add to End of List:

Singly Linked List: O(n)

Doubly Linked List: O(1)

Adding an element to the end of a Singly Linked List has a time complexity of O(n), where n is the number of elements in the list. This is because we need to traverse the entire list to reach the end before adding the new element.

In contrast, a Doubly Linked List offers a constant time complexity of O(1) for adding an element to the end.

This is possible because the list maintains a reference to both the tail and the previous node, allowing efficient insertion.

Add at Given Index:

Singly Linked List: O(n)

Doubly Linked List: O(n)

Adding an element at a given index in both Singly Linked List and Doubly Linked List has a time complexity of O(n), where n is the number of elements in the list.

This is because, in both cases, we need to traverse the list to the desired index, which takes linear time.

Additionally, for a Doubly Linked List, we need to update the previous and next pointers of the surrounding nodes to accommodate the new element.

In summary, Singly Linked List has a constant time complexity of O(1) for adding to the start and a linear time complexity of O(n) for adding to the end or at a given index.

On the other hand, Doubly Linked List offers constant time complexity of O(1) for adding to both the start and the end, but still requires linear time complexity of O(n) for adding at a given index due to the need for traversal.

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Answer:

3 8 + 3 7  divided by 8

Step-by-step explanation:

The capitalized cost for the solid waste treatment plant, based on a 6% MARR, is approximately $579 million.

To calculate the capitalized cost for the solid waste treatment plant, we need to determine the present value of all the costs over the project's lifespan.

The costs involved in the project are as follows:

Initial installation cost: $35 million.

Minor repair and renovation (R&R) after 10 years: $14 million.

Major R&R after 20 years: $18 million.

Operating and maintenance (O&M) costs each year, increasing at a compound rate of 6% per year.

First, let's calculate the present value of the O&M costs over the 20-year period: Using the TVM Factor Table calculator, the present value factor for a 6% MARR and 20 years is 10.206.

The total O&M costs over 20 years can be calculated as follows: O&M costs for the first year: $3 million. O&M costs for the subsequent years: $3 million * (1 + 0.06) + $3 million * (1 + 0.06)^2 + ... + $3 million * (1 + 0.06)^19.

Using the formula for the sum of a geometric series, the O&M costs over the 20-year period can be calculated as: O&M costs = $3 million * (1 - (1 + 0.06)^20) / (1 - (1 + 0.06)) = $3 million * (1 - 1.418519) / (-0.06) = $3 million * (-0.418519) / (-0.06) = $2.91038 million.

Now, let's calculate the present value of the costs: Present value of the initial installation cost: $35 million.

Present value of the minor R&R cost after 10 years: $14 million * 10.206 (present value factor for 6% MARR and 10 years) = $142.884 million. Present value of the major R&R cost after 20 years: $18 million * 10.206^2 (present value factor for 6% MARR and 20 years) = $371.001 million.

Present value of the O&M costs: $2.91038 million * 10.206 = $29.721 million. Finally, the capitalized cost of the solid waste treatment plant is the sum of all the present values: Capitalized cost = $35 million + $142.884 million + $371.001 million + $29.721 million = $578.606 million.

Rounding the final answer to the nearest whole number, the capitalized cost for the solid waste treatment plant is $579 million.

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The complete question is:

A new solid waste treatment plant is to be constructed in Washington County. The initial installation will cost $35 million (M). After 10 years, minor repair and renovation (R&R) will occur at a cost of $14M will be required; after 20 years, a major R&R costing $18M will be required. The investment pattern will repeat every 20 years. Each year during the 20 -year period, operating and maintenance (O\&M) costs will occur. The first year, O\&M costs will total $3M. Thereafter, O\&M costs will increase at a compound rate of 6% per year. Based on a 6% MARR, what is the capitalized cost for the solid waste treatment plant? Click here to access the TVM Factor Table calculator. $ Carry all interim calculations to 5 decimal places and then round your final answer to a whole number. The tolerance is ±25,000.

The probability of each outcome is 1/12 or 0.083.

The probability of each outcome in the sample space can be calculated using the formula for permutations. The formula for permutations is nPk = n!/(n-k)!. In this case n is the number of gift cards (4) and k is the number of gift cards to be selected (2).  In this example, the sample space consists of 16 possible outcomes, and each outcome is equally likely. Thus, the probability of each outcome is 1/16. To calculate this, divide 1 by the total number of outcomes (16). This results in the probability of each outcome being 1/16.Therefore, nPk = 4P2 = 4!/2! = 12. Since each outcome is equally likely, the probability of each outcome is 1/12 or 0.083. This can be written as a fraction as 1/12 or as a decimal as 0.083.

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Answer: I believe the answer is 88

~i hope that is answered your question correctly, have a gr8 day/night my friend!~

Step-by-step explanation:

Answer:

Yeah the answer would be 288

Step-by-step explanation:

A number that is .5 or up you always round up.

A minimum sample size of 121 individuals needs to be surveyed, ensuring a rounded-up value to estimate the proportion of non-graduates within the 25 to 30 age group with a 10% margin of error and 90% confidence.

To determine the sample size required to estimate the proportion of non-graduates within the 25 to 30 age group with a certain level of confidence and margin of error, we can use the formula:

n = (Z^2 * p * (1 - p)) / E^2

Where:

n is the required sample size

Z is the Z-score corresponding to the desired confidence level (90% confidence corresponds to a Z-score of approximately 1.645)

p is the estimated proportion of non-graduates (0.21 based on the information provided)

E is the desired margin of error (10% or 0.10)

Substituting the values into the formula:

n = (1.645^2 * 0.21 * (1 - 0.21)) / 0.10^2

n ≈ 120.41

Rounding up to the nearest integer, the required sample size is 121.

Therefore, you would need to survey at least 121 individuals in the 25 to 30 age group to estimate the proportion of non-graduates within 10% margin of error with 90% confidence.

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Answer:

When 2.7 is multiplied by 10 to the 2nd power, it becomes 270. The digit 7 is in the ones place, so the value of the digit 7 is 7.

Step-by-step explanation:

The equation which best shows the relationship between Davis' savings, y and the number of months passed, x is; y = 20 + 5x.

It follows from the task content that the equation which represents the relationship between Davis' savings and the number of months passed be determined.

According to the task content;

Davis has $20 in his savings account, and he adds $5 every month.

Therefore, we have;

y = 20 + 5x

This follows from the fact that the amount added after each month is $5.

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Answer:

(x+9) are the like terms so u just put 5x and -7 in brackets

the answer is

(5x-7) ( x+9)

Answer:

Step-by-step explanation:

74

We can see here that:

A cube is a three-dimensional geometric shape that has six square faces, all of which are congruent (equal in size) and perpendicular to each other. It is a special type of rectangular prism where all edges have the same length, and all angles are right angles (90 degrees).

Cubes are commonly encountered in everyday life, such as dice, boxes, and Rubik's Cube puzzles. They have precise and uniform geometry, making them useful in various mathematical and engineering applications.

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Answer:

4. x = 16.8

5. x = 35.98

Step-by-step explanation:

For both triangles that you need to work on, use the trigonometric function which is tan and you are dividing opposite by adjacent for the answers.

For number 4, the equation you are setting up is tan 35 = x/24.  Multiply 24 on both sides to get the answer which is 16.8 for the x side.

For number 5, the equation you are setting up is tan 17 = 11/x.  As a result on your calculator, you should get 35.98 for the x side.

To find the equation of the tangent line to the graph of a function at a specific point, we need to determine the slope of the tangent line at that point.

Let's begin by finding the derivative of the function f(x) = 3x³ - 2x.

f'(x) represents the derivative of f(x), so let's calculate it:

f'(x) = d/dx (3x³ - 2x)

To find the derivative, we differentiate each term of the function:

f'(x) = 9x² - 2

Now that we have the derivative, we can find the slope of the tangent line at the point (2, 20) by substituting x = 2 into f'(x):

m = f'(2) = 9(2)² - 2

= 9(4) - 2

= 36 - 2

= 34

Therefore, the slope of the tangent line at the point (2, 20) is 34.

Now that we know the slope of the tangent line, we can use the point-slope form of a linear equation to find the equation of the tangent line. The point-slope form is given by:

y - y₁ = m(x - x₁),

where (x₁, y₁) represents the coordinates of the point (2, 20), and m represents the slope.

Substituting the values, we get:

y - 20 = 34(x - 2).

Expanding the equation further:

y - 20 = 34x - 68.

Now, let's simplify and rewrite the equation in slope-intercept form (y = mx + b):

y = 34x - 68 + 20,

y = 34x - 48.

Therefore, the equation of the tangent line to the graph of f(x) = 3x³ - 2x at the point (2, 20) is y = 34x - 48.

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Not merely a cluster of random elements, a narrative presents an ordered series of events connected by the logic of cause and effect.

A narrative depicts an ordered set of events linked by the logic of cause and effect, not just a collection of random pieces. In tales, the sequence of events is linear, making it evident to the viewer the motivation behind and effects of character behavior.

The sequence of events in a story is referred to as the story. Simply put, sequencing a story is determining the beginning, middle, and end of the story as a first step toward retelling the events in a logical order.

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Answer:

hope it helps the answer

We know that, the trigonometric relationship -

sin(x) = C.O/ h

where,

C.O = opposite leg

h = hypotenuse

using these values in the equation we have -

sin(20) = 5/c

c = 5/sin(20)

c = 14.61

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Disclaimer : The diagram for the question is attached.

\( \to \sf6x - 3(2x - 1)\)

\( \\ \\ \)

\( \to \sf6x - 6x + 3\)

\( \\ \\ \)

\( \to \sf0 + 3\)

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\( \to \sf 3\)

The coefficient of variation for 2012 is 20 %. While the coefficient of variation for 2013 is 15%.Therefor the donations in 2012 shows more dispersed distribution.

Here

for 2012  x=245, s = 49

for 2013 X = 480 ,s=72

CV for 2012 is

CV =S /x* 100% =(49 / 245)*100

CV = 20 %.

of cv for 2013 is

CV= (S /x)*100= (72 /480)*100

CV = 15%

The coefficient of variation for 2012 is 20 %. While the coefficient of variation for 2013 is 15%.Therefor the donations in 2012 shows more dispersed distribution.

The coefficient of variation (CV) is a statistical measurement used to compare the amount of variation in a set of data to the mean of the data. It expresses the variation as a percentage of the mean. The formula for CV is the standard deviation divided by the mean, multiplied by 100. CV is used to determine whether the data has a large or small amount of variation relative to its mean. A low CV indicates that the data is relatively consistent, while a high CV means that the data is more spread out. The CV is useful for comparing data sets with different units of measurement or data sets with different means. CV is commonly used in fields such as finance, economics, and quality control.

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Answer:

56 is the answer

Step-by-step explanation:

bcz sum is equal to 90

hence 90-34 = 56

The value of p+q+r+s = 36 is the required answer.

In mathematics, integers are numbers without decimals or fractions. The set consists of 0, natural numbers and the additive inverses of the natural numbers  (the negative integers). Integer examples include -5, 0 and 7.

Integers can be Positive integers , zero and negative integers.

positive integers are also called natural number.

Here we are given an equation :-

(9-p)(9-q)(9-r)(9-s)=9

and here p, q, r, s are distinct positive integers.

we need to find the value of .

so here we know that RHS contain 9 and we know the multiple of 9 are 1,3,9.

therefore  must be equals to +1,-1,+3,-3,+9,-9

In pair (1,3) and (-1,-3) let equate the equation,

so by putting the value of p, q, r, s as 8,6,10,12 we will get

p=8

q=6

r=10

s=12

hence  

so option e ) 36 is our required answer.

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The probability of selecting a red marble first and then a blue marble, without replacement, is 4/15.

To find the probability of selecting a red marble first and then a blue marble without replacement, we need to consider the outcomes of both selections.

Given that the jar contains four blue marbles and two red marbles, let's calculate the probabilities for each event:

Event 1: Selecting a red marble

The probability of selecting a red marble on the first draw is given by:

P(red) = Number of red marbles / Total number of marbles

P(red) = 2 / 6 = 1/3

After the first draw, there are now five marbles left in the jar, with one red marble remaining.

Event 2: Selecting a blue marble

The probability of selecting a blue marble on the second draw, without replacement, is given by:

P(blue) = Number of blue marbles / Total number of marbles after the first draw

P(blue) = 4 / 5 = 4/5

To find the probability of both events occurring (selecting a red marble first and then a blue marble), we multiply the individual probabilities:

P(red and then blue) = P(red) * P(blue)

P(red and then blue) = (1/3) * (4/5)

P(red and then blue) = 4/15

Therefore, the probability of selecting a red marble first and then a blue marble, without replacement, is 4/15.

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Answer:

\(\frac{12}{25}\) ↔ sinD × cosD

\(\frac{3}{5}\)  ↔ sinC

\(\frac{16}{15}\) ↔ cosC × tanD

\(\frac{4}{5}\) ↔ sinD

Step-by-step explanation:

In the given triangle CBD

∵ ∠B is a right angle

∴ CD is the hypotenuse

→ We can use the trigonometry ratios

∵ sinC = opposite side of ∠C ÷ hypotenuse

∴ sinC = \(\frac{BD}{DC}\)

∵ BD = 3 and CD = 5

∴ sinC = \(\frac{3}{5}\)

∵ cosC = adjacent side of ∠C ÷ hypotenuse

∴ cosC = \(\frac{BC}{DC}\)

∵ BC = 4 and CD = 5

∴ cosC = \(\frac{4}{5}\)

∵ tanC = opposite side of ∠C ÷ adjacent side of ∠C

∴ tanC = \(\frac{BD}{BC}\)

∵ BD = 3 and BC = 4

∴ tanC = \(\frac{3}{4}\)

∵ sinD = opposite side of ∠D ÷ hypotenuse

∴ sinD = \(\frac{BC}{DC}\)

∵ BC = 4 and CD = 5

∴ sinD = \(\frac{4}{5}\)

∵ cosD = adjacent side of ∠D ÷ hypotenuse

∴ cosD = \(\frac{BD}{DC}\)

∵ BD = 3 and CD = 5

∴ cosD = \(\frac{3}{5}\)

∵ tanD = opposite side of ∠D ÷ adjacent side of ∠D

∴ tanD = \(\frac{BC}{BD}\)

∵ BD = 3 and BC = 4

∴ tanD = \(\frac{4}{3}\)

Let us find the answer to each tile

→ sinD = \(\frac{4}{5}\) ⇒ 4th answer

→ sinC = \(\frac{3}{5}\) ⇒ 2nd answer

→ sinD × cosD = ( \(\frac{4}{5}\)) × (\(\frac{3}{5}\)) = \(\frac{12}{25}\) ⇒ 1st answer

→ tanC × tanD = \(\frac{3}{4}\) × \(\frac{4}{3}\) = 1 ⇒ Not used

→ cosC × tanD = \(\frac{4}{5}\) × \(\frac{4}{3}\) = \(\frac{16}{15}\) ⇒ 3rd answer

Answer:  ↔ sinD × cosD

 ↔ sinC

↔ cosC × tanD

↔ sinD

Step-by-step explanation:

In the given triangle CBD

∵ ∠B is a right angle

∴ CD is the hypotenuse

→ We can use the trigonometry ratios

∵ sinC = opposite side of ∠C ÷ hypotenuse

∴ sinC =  

∵ BD = 3 and CD = 5

∴ sinC =  

∵ cosC = adjacent side of ∠C ÷ hypotenuse

∴ cosC =  

∵ BC = 4 and CD = 5

∴ cosC =  

∵ tanC = opposite side of ∠C ÷ adjacent side of ∠C

∴ tanC =  

∵ BD = 3 and BC = 4

∴ tanC =  

∵ sinD = opposite side of ∠D ÷ hypotenuse

∴ sinD =  

∵ BC = 4 and CD = 5

∴ sinD =  

∵ cosD = adjacent side of ∠D ÷ hypotenuse

∴ cosD =  

∵ BD = 3 and CD = 5

∴ cosD =  

∵ tanD = opposite side of ∠D ÷ adjacent side of ∠D

∴ tanD =  

∵ BD = 3 and BC = 4

∴ tanD =  

Let us find the answer to each tile

→ sinD =  ⇒ 4th answer

→ sinC =  ⇒ 2nd answer

→ sinD × cosD = ( ) × () =  ⇒ 1st answer

→ tanC × tanD =  ×  = 1 ⇒ Not used

→ cosC × tanD =  ×  =  ⇒ 3rd answer

Step-by-step explanation:

The probability that the total is bigger than or equal to 3 is given as follows:

35/36.

The two parameters that are needed to calculate a probability are listed as follows:

Then the probability is given as the division of the number of desired outcomes by the number of total outcomes.

The total number of outcomes when two dice are rolled is given as follows:

6² = 36.

There is only one outcome with a sum less than 3, which is given as follows:

(1,1).

Hence the probability that the total is bigger than or equal to 3 is given as follows:

1 - 1/36 = 36/36 - 1/36 = 35/36.

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The range for the strength of the concrete samples provided is 1110 psi, and the sample standard deviation is 456.7 psi.

In the given set of concrete strength values, the range is calculated by subtracting the lowest value from the highest value. In this case, the lowest value is 2950 psi and the highest value is 4060 psi. Thus, the range is obtained by subtracting 2950 from 4060, resulting in a range of 1110 psi.

To compute the sample standard deviation, we follow a two-step process. First, we calculate the mean (average) of the data set, which is found by summing up all the values and dividing by the total number of values. In this case, the mean is (3980 + 4060 + 3200 + 3100 + 2950 + 3830 + 4060 + 4060) / 8 = 3695 psi.

Next, we find the difference between each data point and the mean, square each difference, sum up the squared differences, divide by (n-1), and take the square root. Performing these calculations for the given data set, we obtain a sample standard deviation of approximately 456.7 psi.

In summary, the range for the concrete strength is 1110 psi, indicating the difference between the highest and lowest values. The sample standard deviation of 456.7 psi reflects the dispersion of the data points around the mean, providing a measure of the variability in concrete strength samples.

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Answer:

An exceptional answer to the question provided would be, y = 6x + 2

Answer: m = 1/3

Step-by-step explanation:

Answer:

Not much of a difference but the second bottle is the best buy

Step-by-step explanation:

1) Make sure that all corresponding units are the same.

Litres to millilitres

1.5 L x 1000 = 1500 ml

2) Find out how much you are paying for 1 ml for each bottle

a) First bottle

330 ml = $0.42

1 ml = x

330x = 0.42

x = 0.42/330

x = 0.0013

b) Second bottle

1500 ml = $1.65

1 ml = x

1500x = 1.65

x= 1.65/1500

x= 0.0011

Answer:

Number of Nickels is 12

Number of Dimes is 9

Number of Quarters is 15

Step-by-step explanation:

Given that there are a total of 36 coins, which consists of nickels, dimes, and quarters.

That is, when we sum the numbers of nickels, dimes, and quarters, we have 36.

Let number of nickels be N

Let number of dimes be D

Let number of quarters be Q

Then

N + D + Q = 36 .................................(1)

- There are three fewer quarters than nickels.

This implies that

N = Q - 3 ..............................................(2)

Or

Q = N + 3 .............................................(3)

- There are six more dimes than quarters.

This implies that

Q = D + 6 .............................................(4)

Comparing (3) with (4), we see that

N + 3 = D + 6

N - D = 6 - 3

N - D = 3 ................................................(5)

Using (3) in (1)

N + D + (N + 3) = 36

2N + D = 36 - 3

2N + D = 33 ..........................................(6)

Solving (5) and (6) simultaneously

From (5): D = N - 3

From (6): D = 33 - 2N

=> N - 3 = 33 - 2N

N + 2N = 33 + 3

3N = 36

N = 36/3 = 12..........................................(7)

Using (7) in (6)

2(12) + D = 33

24 + D = 33

D = 33 - 24

D = 9 ........................................................(8)

Using (7) and (8) in (1)

12 + 9 + Q = 36

21 + Q = 36

Q = 36 - 21 = 15.......................................(9)

Therefore,

Number of Nickels, N = 12

Number of Dimes, D = 9

Number of Quarters, Q = 15