Find all the values of b that will make the trinomial 3x^(2)-bx+12 factorable? Choose one value of b and factor the resulting trinomial.

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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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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The table of values is added below and and the graph is attached

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

y < |4x + 1| - 3

To create a table of values for y < |4x + 1| - 3, we can choose different values of x and substitute them into the expression to find the corresponding values of y.

Let's choose some values of x: -2, -1, 0, 1, 2.

When x = -2, we have:

y < |4(-2) + 1| - 3

y < 4

When x = -1, we have:

y < |4(-1) + 1| - 3

y < 0

When x = 0, we have:

y < |4(0) + 1| - 3

y < |1| - 3

y < -2

When x = 1, we have:

y < |4(1) + 1| - 3

y < 2

When x = 2, we have:

y < |4(2) + 1| - 3

y < 6

Putting it all together, we have the following table:

x y values

-2 y < 4

-1 y < 0

0 y < -2

1 y < 2

2 y < 6

The graph is attached

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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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The cafeteria earned $945 from all of the lunches sold on Friday.

percentage, a relative value indicating hundredth parts of any quantity.

Let us calculate the number of students who bought each pizza.

Number of students who bought cheese pizza = 50% of 270 = 0.5 x 270 = 135

Number of students who bought pepperoni pizza = 40% of 270 = 0.4 x 270 = 108

Total lunches sold = Number of cheese pizzas sold + Number of pepperoni pizzas sold + Number of fried chicken sold

= 135 + 108 + 27

= 270

Therefore, a total of 270 lunches were sold on Friday.

To calculate how much money the cafeteria earned from all of the lunches, we can multiply the total number of lunches sold by the cost of each lunch:

Total earnings = Total lunches sold x Cost per lunch

= 270 x $3.50

= $945

Therefore, the cafeteria earned $945 from all of the lunches sold on Friday.

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The area of the rug is A = 1/2 × 7/6 and the area is 7/12

The space enclosed by the boundary of a plane figure is called its area. The area of a figure is the number of unit squares that cover the surface of a closed figure. Area is measured in square units like cm² and m². Area of a shape is a two dimensional quantity.

The area of a rectangle = l× w

The length = 7/6

The width = 1/2

Therefore the area = 7/6 × 1/2

= 7/12

therefore the area of the rug is 7/12

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Answer: C and D

Step-by-step explanation:

∠AFD measures 150°, not 130° and ∠AFB & ∠CFD are complementary, not supplementary.

Answer:

Step-by-step explanation:

I am definitely willing to help anyone with algebra!

It seems you need explanations on mode, median and mean. First, let's remember that these terms are related to data sets.

Example: I have a list of grades in Algebra 2, which list off as 94, 94, 95, 96, 98, 99, 99, 99, 99, 100.

I want the mode, median and mean. The mode is the number that appears the most in a data set, the median is the number in the exact middle of a data set, and the mean is the average value of the data set.

Mode: The number that appears most in this list of grades is 99. My mode is 99, and usually people use this to represent the whole of a data set, especially when the mode appears in the majority of the data set, at least 80% of the data set.

Median: My median is basically the number in the middle of the list. Since I have an even number of 10 grades, I need to find the two numbers closest to the middle, which is 98 and 99, the fifth and sixth term. I find the average of these two numbers- (98+99)/2 = 98.5. This is my median grade. This is usually used to represent data sets when describing demographics.

Mean: This is the average of the whole data set, which means we add up all the numbers and divide them by the number of items there are. Since we have ten grades in the data set, I add (94+94+95+96+98+99+99+99+99+100)/10 = 97.3

This is my mean, which represents my average grade. The mean is used a lot when teachers create our report cards! Hope this helps, but if you need anything else, feel free to comment back on this. If you want, my electronic mail account is my username and I use g mail dot com. Feel free to each out, and Happy Birthday!

The factored form of the given polynomial is 5(x-9)(x-2).

To factor the given polynomial, 5x^(2)-55x+90, we first need to factor out the greatest common factor (GCF) which is 5. Factoring out the GCF will make the polynomial easier to factor completely.

5x^(2)-55x+90 = 5(x^(2)-11x+18)

Now, we need to factor the polynomial inside the parentheses completely. We can do this by finding two numbers that multiply to give us the constant term (18) and add to give us the coefficient of the x term (-11).

The two numbers that fit these criteria are -9 and -2. So, we can factor the polynomial inside the parentheses as follows:

x^(2)-11x+18 = (x-9)(x-2)

Putting it all together, we get the completely factored form of the given polynomial:

5x^(2)-55x+90 = 5(x-9)(x-2)

Therefore, the factored form of the given polynomial is 5(x-9)(x-2).

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The measure of the arc of the ferris wheel in which the lines of sight intersect is approximately 320.1 degrees.

An arc is a segment of a curved line or curve that forms part of a circle or other curved shape. In geometry, an arc is defined as a part of a curve that is contained between two endpoints, known as the arc's endpoints.

Let's draw a diagram to help us visualize the problem:

                      B

                      / \

                     /    \

               18 /        \

                  /            \

               /                  \

             /    O                \

           /                           \

        /  40°                         \

     /                                      \

    A----------------------------------C

Here, the ride operator is standing at point A, and the ferris wheel is centered at point O. Points B and C represent the top and bottom of the ferris wheel, respectively.

We want to find the measure of the arc BC that is intercepted by the lines of sight of the ride operator.

First, we can use trigonometry to find the height of the ferris wheel. We know that angle AOB (the complement of angle AOC) is 50° (since the angles in a triangle add up to 180°). Using trigonometry, we have:

tan(50°) = height / 18

height = 18 * tan(50°) ≈ 22.6

So the height of the ferris wheel is approximately 22.6 meters.

Next, we can use the height to find the distance between points B and C. Since the ferris wheel is a circle, we know that the distance between B and C is twice the height:

BC = 2 * height ≈ 45.2

So the distance between points B and C is approximately 45.2 meters.

Finally, we can use the distance between points A and O (which is 18 meters) and the distance between points B and O to find the angle that the lines of sight make with each other. Let's call this angle x. Using trigonometry again, we have:

tan(x) = height / (18 - r)

where r is the radius of the ferris wheel. Since we know that the distance between A and O is 18 meters and the height is approximately 22.6 meters, we can solve for r:

tan(x) = 22.6 / (18 - r)

(18 - r) * tan(x) = 22.6

18 - r = 22.6 / tan(x)

r = 18 - 22.6 / tan(x)

We also know that the distance between B and O is equal to the radius, so we have:

r = BC / 2 ≈ 22.6

Now we can solve for x:

18 - 22.6 / tan(x) ≈ 22.6

tan(x) ≈ 22.6 / (18 - 22.6)

tan(x) ≈ -5.65

x ≈ -79.9° (using arctan on a calculator)

Note that we get a negative angle because the lines of sight are intersecting below the horizontal line passing through the ferris wheel.

Finally, we can find the measure of the arc BC by using the central angle formula:

arc BC = x + 40° ≈ -39.9°

Again, we get a negative value because the arc is measured clockwise from point B. To get the positive measure of the arc, we can subtract this value from 360°:

arc BC ≈ 320.1°

So the measure of the arc of the ferris wheel in which the lines of sight intersect is approximately 320.1 degrees.

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D. No, not similar

ΔFNY: 8<10<12 ⇔ FN<NY<FY

ΔWRY: 14 <18<21 ⇔ WR<YW<YR

[tex]\dfrac{FN}{WR} = \dfrac{8}{14} = \dfrac{4}{7}[/tex]

[tex]\dfrac{NY}{YW} = \dfrac{10}{18} = \dfrac{5}{9}[/tex]

[tex]\dfrac{FY}{YR} = \dfrac{12}{21} = \dfrac{4}{7}[/tex]

[tex]\dfrac{FN}{WR} = \dfrac{FY}{YR} \bf \neq \dfrac{NY}{YW}[/tex]

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 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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The total cost for the dinner date including sales tax and tip is $88.44.

Let's calculate the cost of each item first:

Now, let's calculate the subtotal by adding up the costs of all the items:

Next, let's calculate the sales tax by multiplying the subtotal by the tax rate:

Sales Tax = 8% x $68.00

Sales Tax = $5.44

Now, let's calculate the total cost by adding the subtotal and the sales tax:

Total Cost = Subtotal + Sales Tax

Total Cost = $68.00 + $5.44

Total Cost = $73.44

Finally, let's add the tip to get the final cost:

Final Cost = Total Cost + Tip

Final Cost = $73.44 + $15.00

Final Cost = $88.44

Therefore, the total cost for the dinner date including sales tax and tip is $88.44.

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In A parallelogram MNPQ with MN=12cm, MQ = 10 cm

a) The length of side PQ is equals to the 12 cm.

b) The measure of angle Q is equals to the 155°.

In a geometry, a parallelogram is a simple quadrilateral with

We have a parallelogram MNPQ, with

Side length, MN = 12cm

Other side length, MQ = 10 cm

Measure of angle M is = 25°

Also, MN|| PQ and MQ||NP

a) From the definition of parallelogram, the length of side MN is parallel to PQ and are of equal length. So, PQ = MN

= 12 cm

b) By the definition of parallelogram, opposite angles of a parallelogram are of equal measure. So, the measure of angle P = measure of angle M = 25°

Also, measure of angle N = measure of angle Q = x

Sum of all interior angles of quadrilateral

= 360°

=> m∠P + m∠N + m∠M + m∠Q = 360°

=> 25° + x + 25° + x = 360°

=> 2x + 50° = 360°

=> 2x = 310°

=> x = (310/2)° = 155°

Hence, required value of measure of angle Q is 155°.

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Complete question:

In A parallelogram MNPQ if MN=12cm , MQ = 10 cm and mZM = 25°. What is a)PQ

b) measure of angle Q

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 solution to the system of equations using the substitution method is (7,2).

No, the substitution approach cannot be used to solve every system of equations. It can be challenging to replace one equation with another in some systems because they feature equations that are challenging or impossible to solve for one variable in terms of the other. Other approaches, such graphing or elimination, could be more useful in such circumstances.

Given that, the two equations are:

x= 4y - 1

3x + 2y = 25

Substitute x = 4y - 1 into the second equation:

3(4y - 1) + 2y = 25

12y - 3 + 2y = 25

14y - 3 = 25

14y = 28

y = 2

Substitute the value of y in equation:

x = 4y - 1

x = 4(2) - 1

x = 7

Hence, the solution to the system of equations using the substitution method is (7,2)

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Answer:

its 0183

Step-by-step explanation:

jfirst queal then u have to divided then zjs

Answer: It is a minimum

Step-by-step explanation:

It is a minimum because the coefficient (5) is positive.

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?

Answer: -14.9 and 2.1

Step-by-step explanation:

If you take -6.4 - 8.5 in one direction you get -14.9 .

And if you add them together (-6.4 + 8.5) you get 2.1,

those are two possible values depending on if you add or subtract the 8.5 .

The solutions to this 3x^(2)-4x=-2  are x=(2/3)+i*√(2/9) or x=(2/3)-i*√(2/9).

To solve this equation by completing the square, we need to first rearrange the equation and then complete the square for the x terms. Here are the steps:

1. Rearrange the equation:
3x^(2)-4x=-2 becomes 3x^(2)-4x+2=0

2. Divide the entire equation by the coefficient of the x^(2) term:
(3x^(2)-4x+2)/3=0/3 becomes x^(2)-(4/3)x+(2/3)=0

3. Complete the square by adding the square of half the coefficient of the x term to both sides of the equation:
x^(2)-(4/3)x+(2/3)+(4/3)^(2)/4=(4/3)^(2)/4 becomes x^(2)-(4/3)x+(4/9)=(4/3)^(2)/4-(2/3)

4. Simplify the right side of the equation:
(4/3)^(2)/4-(2/3)=(16/9)/4-(2/3)=(4/9)-(2/3)=(4/9)-(6/9)=-(2/9)

5. Factor the left side of the equation:
(x-(2/3))^(2)=-(2/9)

6. Take the square root of both sides of the equation:
x-(2/3)=+/-sqrt(-(2/9))

7. Solve for x:
x=(2/3)+/-sqrt(-(2/9)) becomes x=(2/3)+i*sqrt(2/9) or x=(2/3)-i*sqrt(2/9)

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The values of x that make the equation equals 0 are -3 and 3

The equation given from the question is represented as

(6x^2 - 54)/(5x^2 - 20) = 0

The format of the above equation is that of a radical equation

For the expression to equal to 0, the numerator must be 0

So, we have

6x^2 - 54 = 0

Evaluate the like terms

6x^2 = 54

Divide both sides by 6

x^2 = 9

take the square root of both sides

x = -3 and x = 3

Hence, the solutions are -3 and 3

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The difference in elevation for A and B is the difference in elevation for line AB minus the slope correction: D = 330.422m

The slope correction formula is:
C = L * (D^2 / (2 * R)), Where:
- C is the slope correction
- L is the horizontal length of the line
- D is the difference in elevation
- R is the Earth's radius

For line BC, we can plug in the given values to find the slope correction:
C = 660.97m * (10.85m^2 / (2 * 6371000m))
C = 0.059m

For line AB, we need to find the difference in elevation first. We can do this by subtracting the slope correction from the slope distance:
D = 330.49m - 0.059m
D = 330.431m

Now we can plug in the values for line AB into the slope correction formula: C = 330.431m * (330.431m^2 / (2 * 6371000m))  C = 0.009m

The difference in elevation for A and B is the difference in elevation for line AB minus the slope correction:
D = 330.431m - 0.009m
D = 330.422m

Therefore, the difference in elevation for A and B is 330.422m.

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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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Answer:

36.9

Step-by-step explanation:

sinJ=[tex]\frac{21}{35}[/tex]

    J= [tex]sin^{-1}[/tex][tex]\frac{21}{35}[/tex]

    J= 36.9

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).

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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The expense function consists of two parts: the monthly payment for the car loan and the monthly cost of depreciation. The monthly payment can be calculated using the following formula: P = (r(PV)) / (1 - (1+r)^(-n)) = $1,062.66 per month. The depreciation function will be a straight line from $54,000 to $0 over a period of 10 years (or 120 months).

A depreciation function is a mathematical model that explains how the worth of an object decreases over time. It denotes the pace at which the worth of an asset depreciates over time.

In the given question,

a. The expense function will consist of two parts: the monthly payment for the car loan and the monthly cost of depreciation. The monthly payment can be calculated using the following formula:

[tex]P = (r(PV)) / (1 - (1+r)^(-n))[/tex]

where P is the monthly payment, r is the monthly interest rate (4.875%/12 = 0.40625%), PV is the present value of the loan (54,000 - 8,000 = 46,000), and n is the total number of payments (4 years x 12 months per year = 48). Plugging these values into the formula, we get:

[tex]P = (0.0040625(46000)) / (1 - (1 + 0.0040625)^(-48)) = $1,062.66 per month[/tex]

The depreciation function will be a straight line from $54,000 to $0 over a period of 10 years (or 120 months), so the monthly depreciation can be calculated as:

d = (54000 - 0) / 120 = $450 per month

Therefore, the expense function E(x) and depreciation function D(x) are:

E(x) = 1062.66 + 450x

D(x) = 450x

where x is the number of months since the car was purchased.

b. The graph of the expense function and depreciation function on the same axes is attached.

c. At the intersection point (around 66 months), the monthly loan payment becomes greater than the monthly depreciation cost, meaning that Winnie is paying more each month than the car is depreciating. After 66 months, the expense function is increasing faster than the depreciation function, so the total value of the car is decreasing rapidly. By the end of 120 months, the car will have depreciated to a value of $0 and Winnie will have paid a total of $62,719.20 in loan payments.

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