Question 1: a. Suppose that f(x)=2 x^{2}-5 x-8, g(x)=9-x and ( k(x)=2 x+4 ) Perform the following combination functions, then simplify your results as much as you can: (I Mark) 1. ( 4(f+k){x}

Without further clarification on the terms and the relationship between the variables and the given information, it is difficult to provide a complete and accurate answer to the problem.

It seems that there are several typos and irrelevant parts in the question, making it difficult to understand the problem and provide a clear and accurate answer. However, I will do my best to answer the question based on the information given.

In terms of "wmaller" and "aAy.", it is unclear what these terms are referring to or how they relate to the problem. It is also unclear what "peints" is referring to. Without further clarification on these terms, it is difficult to provide a complete answer.

Based on the given information, it seems that the problem is asking to solve for the unknown variables A2, x, and B2 in a triangle with sides b=49, c=46, and angle C=26 degrees. However, without knowing the relationship between these variables and the given information, it is difficult to provide a step-by-step explanation for solving the problem.

In conclusion, without further clarification on the terms and the relationship between the variables and the given information, it is difficult to provide a complete and accurate answer to the problem.

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The original amount borrowed was approximately $34,211.1.

To compute the first sum acquired, we can involve the recipe for the current worth of a customary annuity, which addresses a progression of equivalent installments made toward the finish of every period. The recipe is:

PV = [tex]PMT * (1 - (1 + r)^{(-n)}) / r[/tex]

where PV is the present value, PMT is the payment amount, r is the interest rate per period, and n is the total number of periods.

In this case, we have monthly payments, so we need to convert the APR to a monthly interest rate by dividing it by 12. We also have a 4-year loan, which means 48 monthly payments.

APR = 9.25%

Monthly interest rate = APR / 12 = 0.0925 / 12 = 0.00771 (rounded to five decimal places)

Total number of payments = 48

Total amount of payments = $4,200.0

Substituting these values into the formula, we get:

PV =[tex]PMT * (1 - (1 + r)^{(-n)}) / r[/tex]

PV = [tex]$4,200.0 * (1 - (1 + 0.00771)^{(-48)}) / 0.00771[/tex]

PV = $4,200.0 x (1 - 0.5180) / 0.00771

PV = $34,211.1 (rounded to the nearest tenth)

Therefore, the original amount borrowed was approximately $34,211.1.

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The probability of no oranges is 125/216.

The expected value of this experiment can be calculated by multiplying the probability of selecting each coin by its value, and then adding these products together.

First, let's find the probability of selecting each type of coin:

- The probability of selecting a quarter is 10/29 (since there are 10 quarters out of 29 total coins).
- The probability of selecting a dime is 10/29 (since there are 10 dimes out of 29 total coins).
- The probability of selecting a nickel is 2/29 (since there are 2 nickels out of 29 total coins).
- The probability of selecting a penny is 7/29 (since there are 7 pennies out of 29 total coins).

Next, let's multiply each probability by the value of the corresponding coin:

- The expected value from selecting a quarter is (10/29) * $0.25 = $0.0862
- The expected value from selecting a dime is (10/29) * $0.10 = $0.0345
- The expected value from selecting a nickel is (2/29) * $0.05 = $0.0034
- The expected value from selecting a penny is (7/29) * $0.01 = $0.0024

Finally, let's add these expected values together to find the overall expected value of the experiment:

$0.0862 + $0.0345 + $0.0034 + $0.0024 = $0.1265

So the expected value of this experiment is $0.1265, or $0.13 when rounded to the nearest cent.

As for the second part of the question, we can find the probability of three oranges by multiplying the probability of getting an orange on each dial:

(1/6) * (1/6) * (1/6) = 1/216

So the probability of three oranges is 1/216.

To find the probability of no oranges, we can multiply the probability of not getting an orange on each dial:

(5/6) * (5/6) * (5/6) = 125/216

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The expression for Jack's brother's age is x = 3 + w

It is important that we know algebraic expressions are defined as expressions which are composed of variables, coefficients, constants, factors and terms.

These algebraic expressions are also identified with mathematical operations, such as;

From the information given, we have that;

Jack is w years old

His brother is 3 years old than him

His brother's age is also x

This is represented as;

x = 3 + w

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If a patient takes 25 mg of medication twice a day, he will take 0.7 grams in 14 days.

To find out how many grams a patient will take in 14 days, we can follow these steps:

25mg × 2 = 50mg

50mg × 14 days = 700mg

700mg ÷ 1000 = 0.7 grams

Therefore, the patient will take 0.7 grams of medication in 14 days.

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the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

to get the slope of any straight line, we simply need two points off of it, let's use those above

[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{-6}~,~\stackrel{y_2}{2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{2}-\stackrel{y1}{(-6)}}}{\underset{\textit{\large run}} {\underset{x_2}{-6}-\underset{x_1}{1}}} \implies \cfrac{2 +6}{-7} \implies \cfrac{ 8 }{ -7 } \implies - \cfrac{8 }{ 7 }[/tex]

If (z³⁴)(z¹⁹)⁴ is equivalent to (zᵃ), The value of a is 110.

we can solve it by the rules of exponential :

To find the value of a, we need to use the laws of exponents. Specifically, we need to use the law that states (x^(y))(x^(z)) = x^(y+z) and the law that states (x^(y))^(z) = x^(y*z).

So, let's apply these laws to the given expression:

(z³⁴)(z¹⁹))⁴ = z³⁴ * z^(19*4) = z³⁴* z⁷⁶ = z^(34+76) = z¹¹⁰

Therefore, the value of a is 110.

So, the expression If (z³⁴)(z¹⁹)⁴ is equivalent to (z¹¹⁰).

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To solve this problem, we can use the formula for work rate:
Work rate = (Number of workers) × (Time taken) / (Number of houses built)

We can plug in the given values to find the work rate for the 12 builders:
Work rate = (12 builders) × (7 days) / (2 houses) = 42 builder-days / house

Now we can use this work rate to find the time taken for 15 builders to build the same amount of houses:
42 builder-days / house = (15 builders) × (Time taken) / (2 houses)
Solving for Time taken, we get:
Time taken = (42 builder-days / house) × (2 houses) / (15 builders) = 5.6 days

Therefore, it will take 15 builders 5.6 days to build the same amount of houses.
To convert this to days and hours, we can multiply the decimal part of the answer by 24 (since there are 24 hours in a day):
0.6 days × 24 hours/day = 14.4 hours

So the final answer is 5 days and 14.4 hours, or 5 days and 14 hours and 24 minutes.

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Answer:

C) 100

Step-by-step explanation:

[tex]3.5c - 1.5d > 50[/tex]

[tex]3.5c - 1.5(200) > 50[/tex]

[tex]3.5c - 300 > 50[/tex]

[tex]3.5c > 350[/tex]

[tex]c > 100[/tex]

Answer:

181.74

Step-by-step explanation:

I hope you meant the paycheck was $1398.. if not then this is wrong.

So you take 1398 and multiply it by 0.13 and then you get 181.74. So Jim donated 181.74 this month.

Answer:

The pattern described in the question follows the rule that each consecutive line has a number that is one less than twice the previous line. Starting with 2 as the first line, the pattern can be written as follows:

1st line: 2

2nd line: 2(2) - 1 = 3

3rd line: 2(3) - 1 = 5

4th line: 2(5) - 1 = 9

5th line: 2(9) - 1 = 17

6th line: 2(x) - 1 (unknown)

To find the number of marbles in the 6th line, we can use the rule of the pattern and solve for x:

2(x) - 1 = 2(17) - 1 (substitute 17 for the number in the 5th line)

2x - 1 = 33

2x = 34

x = 17

Therefore, the 6th line of the pattern would have 17 marbles

Step-by-step explanation:

The pattern is described as having a number in each line that is one less than twice the previous line.

Write out the first few lines of the pattern, starting with 2 as the first line:

1st line: 2

2nd line: 2(2) - 1 = 3

3rd line: 2(3) - 1 = 5

4th line: 2(5) - 1 = 9

5th line: 2(9) - 1 = 17

To find the number of marbles in the 6th line, use the pattern rule and substitute the value for the 5th line:

6th line: 2(x) - 1

Substitute 17 for x (the value in the 5th line):

2(x) - 1 = 2(17) - 1

Simplify the right-hand side:

2(x) - 1 = 33

Add 1 to both sides:

2(x) = 34

Divide both sides by 2:

x = 17

Therefore, the 6th line of the pattern would have 17 marbles.

The complete pattern in the given question is: 2, 3, 5, 9, 17, 33.

To solve this problem, we need to apply the given rule to generate the numbers in the sequence and then find the sixth number.

Starting with two, we can apply the rule to generate the next few numbers:

First line: 2

Second line: 2(2) - 1 = 3

Third line: 2(3) - 1 = 5

Fourth line: 2(5) - 1 = 9

Fifth line: 2(9) - 1 = 17

Now we can apply the rule again to find the sixth number:

Sixth line: 2(17) - 1 = 33

Therefore, the sixth line must have 33 marbles.

The pattern starts with two, which is the first line.

The second line follows the given rule: "every consecutive line has a number that is one less than twice the previous line". We can apply this rule to the first line by multiplying it by 2 and subtracting 1: 2(2) - 1 = 3. Therefore, the second line has 3 marbles.

To find the third line, we can apply the same rule to the second line: 2(3) - 1 = 5. Therefore, the third line has 5 marbles.

Similarly, we can find the fourth line by applying the rule to the third line: 2(5) - 1 = 9. Therefore, the fourth line has 9 marbles.

We can find the fifth line by applying the rule to the fourth line: 2(9) - 1 = 17. Therefore, the fifth line has 17 marbles.

Finally, to find the sixth line, we apply the rule again to the fifth line: 2(17) - 1 = 33. Therefore, the sixth line has 33 marbles.

So, the complete pattern is: 2, 3, 5, 9, 17, 33.

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The probability that at least 3 of the selected human resource managers say job applicants should follow up within two weeks is 0.55.

From the question, we are to determine the probability that at least 3 of the managers say job applicants should follow up within two weeks

This problem requires the use of the binomial probability distribution. We are given that the probability of success (a human resource manager saying that job applicants should follow up within two weeks) is p = 0.57. The number of trials is n = 6.

To find the probability that at least 3 of the selected human resource managers say job applicants should follow up within two weeks, we need to find the sum of the probabilities of 3, 4, 5, and 6 successes. We can use the binomial probability formula to find these individual probabilities and add them up:

P(X ≥ 3) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)

Where X is the number of successes.

Using the binomial probability formula, we get:

P(X = k) = (n Ck) * p^k * (1-p)^(n-k)

Where (n Ck) = n! / (k! * (n-k)!)

So,

P(X = 3) = (6 C3) * 0.57^3 * (1-0.57)^(6-3) = 0.307

P(X = 4) = (6 C4) * 0.57^4 * (1-0.57)^(6-4) = 0.185

P(X = 5) = (6 C 5) * 0.57^5 * (1-0.57)^(6-5) = 0.051

P(X = 6) = (6 C6) * 0.57^6 * (1-0.57)^(6-6) = 0.007

So,

P(X ≥ 3) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) = 0.307 + 0.185 + 0.051 + 0.007 = 0.55

Hence, the probability is 0.55.

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The y-intercept of the given function is 0.

A y-intercept is the place where a line or curve crosses, or touches, the y-axis the vertical, often darkened line in the center of a graph.

Given is a function f(x) = 3(12)x, we need to find the y-intercept.

The general equation of a line is given by

y = mx+c

Where m is the slope and the c is the y-intercept,

But in our equation, the y-intercept is not available that means it is zero,

We can write the equation as ;-

f(x) = 3(12)x + 0

Hence, the y-intercept of the given function is 0.

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Answer:

If sin = 1⁄2 and lies in the second quadrant, the remaining five trigonometric values are cos = √3/2, tan = 1/√3, cot = √3, sec = 2/√3, and csc = 2. These values can be derived from the basic trigonometric identities and the given value of sin. For example, the cosine of an angle in the second quadrant is the same as the sine of the same angle in the first quadrant, and vice versa. Therefore, since sin = 1⁄2 in the second quadrant, cos = √3/2 in the first quadrant. The other values can be derived in a similar manner

Step-by-step explanation:

The temperature of the Carbon (IV) Oxide surrounding the thermometer is approximately -46.83 °C (226.32 K).

We can use Charles's Law and Boyle's Law to relate the pressure of the gas in the thermometer to the temperature of the surrounding Carbon (IV) Oxide. Since the volume of the gas in the thermometer is constant, we can assume that the pressure is directly proportional to the absolute temperature.

Therefore, we can use the following equation:

P₁/T₁ = P₂/T₂

where;

Solving for T₂, we get:

T₂ = (P₂/P₁) * T₁

T₂ = (105.2/82) * 273.15 K

T₂ = 348.85 K

Similarly, we can use the pressure at the third measurement (68.4 cm) and the temperature we just calculated (348.85 K) to find the temperature of the surrounding Carbon (IV) Oxide using the same equation:

T₃ = (P₃/P₁) * T₁

T₃ = (68.4/82) * 273.15 K

T₃ = 226.32 K

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Answer:14

Step-by-step explanation:

The correct answer is d)C(x)=4x+60. This is because an equation should have an equal sign to show that both sides of the equation are equal.

Additionally, the variable "x" should be on one side of the equation and the constants should be on the other side. In this case, the variable "x" is multiplied by 4 and the constant is 60, making the equation C(x)=4x+60. This equation shows the relationship between the variable "x" and the function "C(x)".

It is important to note that the other options are not correct because they do not have an equal sign or the variable and constants are not on the correct sides of the equation. Option a)C(x)−60x+4 does not have an equal sign, option b)C(x)=−60x+4 has the variable and constants on the wrong sides of the equation, option c)C(x)−−4x+60 does not have an equal sign, and option e)C(x)−4x+4 does not have an equal sign.

Therefore, the correct answer is d)C(x)=4x+60.

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Answer:

We can solve for p by isolating it on one side of the inequality symbol. First, we'll subtract 7 from both sides:

55 - 7 < -12p

48 < -12p

Next, we'll divide both sides by -12. Since we're dividing by a negative number, we'll need to flip the direction of the inequality:

48/-12 > p

-4 > p

Therefore, p is greater than -4. Written in interval notation, this solution is p ∈ (-∞, -4).

√(9 + 25) is real; π - 4 is negative irrational ; √-27 is a non-real ; 3 3/2 is a rational that is not an integer.

√138 lies between 11 and 12; 0.26 as fraction = 13/50

A number is an arithmetic value which is used to represent the quantity of an object. There are different types of numbers as natural numbers, whole numbers, integers, real numbers, rational numbers, irrational numbers, complex numbers and imaginary numbers.

Given numbers,

a) √(9 + 25)

= √34

square root of a real number is real number.

b) π - 4

∵π is irrational and less than four,

∴π - 4 is negative irrational number

c) √-27

Square root of -27 is not possible,

√-27 is a non-real number

d) 3 3/2

= 9/2

= 4.5

3 3/2 is a rational number that is not an integer.

e) √138 = 11.747

∴ two consecutive integers between which √138 lies are 11 and 12

f) 0.26

multiplying and dividing with 100

= 26/100

Simplifying

= 13/50

Hence,

√(9 + 25) is real number; π - 4 is negative irrational number;

√-27 is a non-real number; 3 3/2 is a rational number that is not an integer.

Two consecutive integers between which √138 lies are 11 and 12

0.26 as fraction = 13/50

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If Allegiant Airlines charges a mean base fare of $89. The population mean cost per flight is $128.

As given in the problem, the population mean base fare is $89 and the population mean additional fare per person is $39.

To find the population mean cost per flight, we need to add the population mean base fare to the population mean additional fare per person,

Population mean cost per flight =  (Population mean base fare + Population mean additional fare per person)

Population mean cost per flight =  ($89 + $39)

Population mean cost per flight = 128

Therefore the population mean cost per flight is $128.

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The complete question is:

Allegiant Airlines charges a mean base fare of $89. In addition, the airline charges for making a reservation on its website, checking bags, and inflight beverages. These additional charges average $39 per passenger (Bloomberg Businessweek, October 8 � 14, 2012). Suppose a random sample of 60 passengers is taken to determine the total cost of their flight on Allegiant Airlines. The population standard deviation of total flight cost is known to be $40.

Allegiant Airline reports a population mean base fare of $89 and a population mean additional fare of $39 per person. What is the population mean cost per flight?

Therefore , the solution of the given problem of unitary method  comes out to be the height of the table in the scale model because we lack any measurements to base our calculations on.

Divide the measures of just this microsecond portion by two in order to complete the task using the unitary variable technique. Briefly stated, the characterised by a group and colour subgroups are both removed from the unit method when a wanted item is present. For example, 40 pens subset with a changeable price would cost Rupees ($1.01). It's possible that one country will have total influence over the approach taken to accomplish this. Almost every living creature has a distinctive quality.

Here,

We could use the scale factor to determine the height of the table in the scale model if we knew the measurements of the actual table and the scale model. The scale factor is the ratio of the actual object's dimensions to the scale model's dimensions. For instance, if the scale factor is 1:12 and the actual table is 48 inches tall, the scale model table would be 12 inches tall.

12 times 48 inches, or 4 inches,

However, we are unable to calculate the height of the table in the scale model because we lack any measurements to base our calculations on.

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The area of the shaded region is 176.5 square centimeters rounded up to one decimal place.

To get the area of the shaded region, we subtract the area of the sector from the area of the triangle as follows:

The angle m∠AOB = 180° - (34 + 90) {sum of interior angles of a triangle}

m∠AOB = 56°

area of sector = 56/360 × 22/7 × 26 cm × 26 cm

area of sector =14872/45 cm²

area of sector = 330.4888 cm²

area of the triangle = 1/2 × 26 cm × 39 cm

area of the triangle = 507 cm²

area of the shaded region = 507 cm² - 330.4888 cm²

area of the shaded region = 176.5111 cm²

Therefore, the area of the shaded region is 176.5 square centimeters rounded up to one decimal place.

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Answer:

Proof:

Draw circle C with center at point A and radius AD = CD = DE.

Draw point P outside the circle C.

Draw segment AP and extend it to intersect the circle at point B.

Draw segment BD.

Draw segment CP.

Note that triangle BCD is isosceles, since CD = BD. Therefore, angle BDC = angle CBD.

Since angle BDC is an inscribed angle that intercepts arc BC, and angle CBD is an angle that intercepts the same arc, then angle BDC = angle CBD = 1/2(arc BC).

Since CD = DE, then angle CED = angle CDE. Therefore, angle DCE = 1/2(arc BC).

Since angles BDC and DCE are equal, then angles BDC and CBD are also equal, and triangle BPC is isosceles. Therefore, segment BP = segment PC.

Since BP = PC, then segment CP is perpendicular to segment BD, by the Converse of the Perpendicular Bisector Theorem.

Therefore, segment CP is a tangent to circle C at point B.

Hence, the proof is complete.

Answer:

I got a good grade on it yw ;)

The value of x, given the equation, can be found to be 2 .

We are given the equation:

( 5x + 4 ) / 2 = 7

The first step is to remove the denominator using cross - multiplication :

2 x ( 5x + 4 ) / 2 = 7 x 2

5 x + 4 = 14

Solving directly for x then gives:

5 x + 4 = 14

5 x = 14 - 4

x = 10 / 5

x = 2

In conclusion, the value of x in the equation which needed to be simplified to 5 x + 4 = 14 , and then solved, is 2.

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We can also plot the vertical asymptote at x = -1/3 and the horizontal asymptote at y = 0.

A rational function can be represented by a polynomial that has been divided by another polynomial. The set of all numbers omitting the zeros in the denominator makes up the domain of a rational function because polynomials are defined everywhere. First example: x = f(x) (x - 3).

A) Factor the denominator and numerator together:

w(x) = 3(x - 7)/(3x + 1) = (3x - 21)/(3x2 - 20x - 7) (x - 7)

B) Locate the discontinuity point, if one exists:

With x - 7 = 0 or 3x + 1 = 0, the denominator is 0. As a result, the function exhibits discontinuity points at x = -7 and x = -1/3.

C) Identify the vertical asymptote: For x = -1/3, the function has a vertical asymptote.

D) Locate the horizontal asymptote: The numerator and denominator each have degrees of 2 and 1, respectively. As a result, the horizontal asymptote is y = 0.

E) Visualize the function

Using the value table:

x y

-5 4.5

-2 -1.4

-0.4 -4.11

0 -7

1 -2.4

5 -0.5

7 undefined

The horizontal asymptote at y = 0 and the vertical asymptote at x = -1/3 can also be plotted.

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The axis οf symmetry fοr the functiοn f(x) = -(x - 7)² - 30 is the vertical line x = 7.

In mathematics, the axis οf symmetry is a line that divides a twο-dimensiοnal shape οr a three-dimensiοnal οbject intο twο equal halves, such that each half is a mirrοr image οf the οther. The axis οf symmetry can alsο refer tο a line that divides a mathematical functiοn intο twο equal halves.

The given quadratic functiοn is:

f(x) = -(x - 7)² - 30

We can see that the cοefficient οf x² is -1, which means that the parabοla οpens dοwnwards. The vertex οf the parabοla is (7, -30), which is alsο the maximum pοint οf the parabοla.

The axis οf symmetry fοr a parabοla is a vertical line that passes thrοugh the vertex. Therefοre, the axis οf symmetry fοr the given functiοn is a vertical line passing thrοugh (7, -30).

The equatiοn οf the axis οf symmetry is given by:

x = 7

Therefοre, the axis οf symmetry fοr the functiοn f(x) = -(x - 7)² - 30 is the vertical line x = 7.

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There are 60 f-words that can be made using all the letters of the word "AGAIN".

To find the number of f-words that can be made using all the letters of the word "AGAIN", we need to use the concept of permutations.

There are five letters in the word "AGAIN". To find the number of f-words that can be made using all these letters, we need to find the number of permutations of these letters.

The number of permutations of a set of n elements is given by n!. However, in this case, we have two "A"s in the word "AGAIN". This means that we cannot simply use n! to calculate the number of permutations.

Instead, we need to use the formula for permutations with repeated elements, which is:

[tex]$\frac{n!}{n_1!n_2!\cdots n_k!}$$[/tex]

where n is the total number of elements, and n1, n2, ..., nk are the number of times each element is repeated.

In this case, we have two "A"s and one of each of the other letters. Therefore, we can plug in the values into the formula:

[tex]$\frac{5!}{2!1!1!1!} = \frac{120}{2} = 60$$[/tex]

This means that there are 60 f-words that can be made using all the letters of the word "AGAIN".

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eli=e

Cecil=c

e+c=15

e=2c

2c+c=15

3c=15

c=5

e=10