Net Present Value Method, Internal Rate of Return Method, and Analysis
The management of Advanced Alternative Power Inc. is considering two capital investment projects. The estimated net cash flows from each project are as follows:
Year Wind Turbines Biofuel Equipment
1 $420,000 $880,000
2 420,000 880,000
3 420,000 880,000
4 420,000 880,000

Present Value of an Annuity of $1 at Compound Interest
Year 6% 10% 12% 15% 20%
1 0.943 0.909 0.893 0.870 0.833
2 1.833 1.736 1.690 1.626 1.528
3 2.673 2.487 2.402 2.283 2.106
4 3.465 3.170 3.037 2.855 2.589
5 4.212 3.791 3.605 3.352 2.991
6 4.917 4.355 4.111 3.784 3.326
7 5.582 4.868 4.564 4.160 3.605
8 6.210 5.335 4.968 4.487 3.837
9 6.802 5.759 5.328 4.772 4.031
10 7.360 6.145 5.650 5.019 4.192
The wind turbines require an investment of $1,199,100, while the biofuel equipment requires an investment of $2,278,320. No residual value is expected from either project.
Required:
1a. Compute the net present value for each project. Use a rate of 10% and the present value of an annuity of $1 in the table above. If required, use the minus sign to indicate a negative net present value. If required, round to the nearest whole dollar.
Wind Turbines Biofuel Equipment
Present value of annual net cash flows $fill in the blank 1 $fill in the blank 2
Less amount to be invested $fill in the blank 3 $fill in the blank 4
Net present value $fill in the blank 5 $fill in the blank 6

1b. Compute a present value index for each project. If required, round your answers to two decimal places.
Present Value Index
Wind Turbines fill in the blank 7
Biofuel Equipment fill in the blank 8
2. Determine the internal rate of return for each project by (a) computing a present value factor for an annuity of $1 and (b) using the present value of an annuity of $1 in the table above. If required, round your present value factor answers to three decimal places and internal rate of return to the nearest whole percent.
Wind Turbines Biofuel Equipment
Present value factor for an annuity of $1 fill in the blank 9 fill in the blank 10
Internal rate of return fill in the blank 11 % fill in the blank 12 %
3. The net present value, present value index, and internal rate of return all indicate that the
is a better financial opportunity compared to the
, although both investments meet the minimum return criterion of 10%.

Answer:

x intercept : -1

y intercept : 3

Step-by-step explanation:

We have 3x - y = -3 ---eq(1)

The x intercept is the value of x when y = 0 in eq(1),

⇒ 3x - 0 = -3

⇒ x = -3/3

⇒ x = -1

The y intercept is the value of y when x = 0 in eq(1),

⇒ 3(0) - y = -3

⇒ -y = -3

⇒ y = 3

Answer:

Step-by-step explanation:

Converting between Fraction, Decimal, and Percent:

Fraction to Decimal: Divide the numerator by the denominator. The result is the decimal form.

Example: 1/4 = 1 ÷ 4 = 0.25

Decimal to Fraction: Write the decimal as a fraction by placing the decimal value over the appropriate power of 10.

Example: 0.75 = 75/100 = 3/4

Fraction to Percent: Divide the numerator by the denominator and multiply by 100.

Example: 1/3 = (1 ÷ 3) × 100 = 33.33...%

Percent to Fraction: Write the percent as a fraction with a denominator of 100 and simplify if necessary.

Example: 40% = 40/100 = 2/5

Decimal to Percent: Multiply the decimal by 100 and add the percent symbol (%).

Example: 0.75 = 0.75 × 100 = 75%

Percent to Decimal: Divide the percent by 100.

Example: 40% = 40 ÷ 100 = 0.4

The solution to the given equation is x = -1/4.To solve the equation, let's break down the steps as outlined by Deepak:

Combine like terms: Starting with the left side of the equation, combine the x terms and the constant terms separately. On the left side, we have -3x and 4x, which can be combined to give x. Similarly, we have -5 and 5, which cancel each other out, leaving us with zero.

Simplify both sides: Now, the equation becomes x = -7/4 - 3x.

Move all the x terms to one side: To isolate the x term on one side, we can add 3x to both sides of the equation. This gives us 4x + 3x = -7/4.

Combine like terms: On the left side, we have 4x and 3x, which can be added to give 7x. The equation now becomes 7x = -7/4.

Solve for x: To solve for x, we divide both sides of the equation by 7. This yields x = -1/4.

Therefore, the solution to the given equation is x = -1/4.

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Answer:

A''(-1, 1), B''(-4, 2), C''(-2, 4)

Step-by-step explanation:

When rotated 180°, the symbol of the coordinames change

i.e., if x = 2 it becomes x = -2 and if y = -4, it becomes y = 4

so the coordinates A(1, -1), B(4, -2), C(2, -4)

change to A''(-1, 1), B''(-4, 2), C''(-2, 4)

Answer:

Let's denote:

- A as the event "student is accepted at FSU"

- B as the event "student is accepted at UF"

We have the following probabilities given:

- P(A) = 0.4 (probability of being accepted at FSU)

- P(B|A) = 0.6 (probability of being accepted at UF given acceptance at FSU)

- P(B'|A') = 0.9 (probability of not being accepted at UF given non-acceptance at FSU), where B' is the complement of B (not being accepted at UF) and A' is the complement of A (not being accepted at FSU).

We want to find P(A|B'), or the probability of being accepted at FSU given non-acceptance at UF.

To calculate this, we can use Bayes' Theorem, which states that:

P(A|B') = P(B'|A) * P(A) / P(B')

We can calculate P(B'|A), the probability of non-acceptance at UF given acceptance at FSU, by using the fact that the sum of probabilities of complementary events equals 1:

P(B'|A) = 1 - P(B|A) = 1 - 0.6 = 0.4

Next, we need to find P(B'), the total probability of non-acceptance at UF. We can use the law of total probability to calculate this:

P(B') = P(B'|A) * P(A) + P(B'|A') * P(A')

P(B') = 0.4 * 0.4 + 0.9 * 0.6 = 0.16 + 0.54 = 0.7

Finally, we can substitute these values into Bayes' theorem:

P(A|B') = P(B'|A) * P(A) / P(B') = 0.4 * 0.4 / 0.7 ≈ 0.229

Therefore, the probability that a student is accepted at FSU given that they are not accepted at UF is approximately 22.9%.

The function for which f(x) is equal to f⁻¹(x) is: C. [tex]f(x) = \frac{x+1}{x-1}[/tex]

In this exercise, you are required to determine the inverse of the function f(x) with an equivalent inverse function f⁻¹(x). This ultimately implies that, we would have to swap (interchange) both the independent value (x-value) and dependent value (y-value) as follows;

[tex]f(x) = y = \frac{x+6}{x-6} \\\\x=\frac{y+6}{y-6}[/tex]

x(y - 6) = y + 6

y = xy - 6x - 6

f⁻¹(x) = (-6x - 6)/(x - 1) ⇒ Not equal.

Option B.

[tex]f(x) = y = \frac{x+2}{x-2} \\\\x=\frac{y+2}{y-2}[/tex]

x(y - 2) = y + 2

y = xy - 2x - 2

f⁻¹(x) = (-2x - 2)/(x - 1) ⇒ Not equal.

Option C.

[tex]f(x) = y = \frac{x+1}{x-1} \\\\x=\frac{y+1}{y-1}[/tex]

x(y - 1) = y + 1

y - xy = x + 1

f⁻¹(x) = (x + 1)/(x - 1) ⇒ equal.

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Answer: -27

Step-by-step explanation: Use inductive reasoning to predict the most probable next number in the list.

3, 9, -3, 3, -9, -3, -15, -9, -21, ?

We can start by looking at the differences between consecutive terms in the list:

9 - 3 = 6 -3 - 9 = -12 3 - (-3) = 6 -9 - 3 = -12 -3 - (-9) = 6 -15 - (-3) = -12 -9 - (-15) = 6 -21 - (-9) = -12

Notice that the differences alternate between positive 6 and negative 12. This suggests that the pattern involves adding 6, then subtracting 12, and then adding 6 again. Applying this pattern to the last term in the list (-21), we get:

-21 + 6 = -15 -15 - 12 = -27 -27 + 6 = -21

Therefore, we predict that the most probable next number in the list is -27.

For a collection of numbers to be considered a sequence, it is essential that they have a law of formation, are ordered in a specific manner, and can be either finite or infinite.

B: They have a law of formation:

A sequence is a set of numbers arranged in a specific order according to a rule or pattern. The numbers in a sequence are not random but follow a specific law of formation.

This law can be a mathematical formula, a recursive relationship, or any other systematic pattern that determines the values of the sequence. Without a well-defined law of formation, a collection of numbers cannot be considered a sequence.

C: They are ordered:

In a sequence, the numbers are arranged in a specific order or sequence. The order of the numbers is crucial and defines the pattern and structure of the sequence.

Each number in the sequence has a unique position or index that determines its place in the sequence. The order of the numbers allows us to identify the next number or predict the pattern of the sequence. Without the concept of order, the numbers would simply be a set of unrelated elements and not a sequence.

A: They may or may not be infinite:

Sequences can be finite or infinite. A finite sequence has a specific number of terms, and once the pattern or rule is established, the sequence ends.

On the other hand, an infinite sequence continues indefinitely, and its terms extend infinitely in one direction or both directions. Whether a sequence is finite or infinite depends on the context and the specific rule or pattern that governs its formation.

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Note: the translated question is:

To have a sequence it is essential that the numbers that form it:

A: be infinite

B: they have a law of formation C: they are ordered

Answer:

Step-by-step explanation:

Let's represent the number of people that Ms. Hernandez can bring to the zoo as "x". Each person will require an admission ticket, which costs $10.40 per person. Additionally, there is a parking fee of $3.

The total cost of admission tickets and parking is given as $150. We can set up the equation as follows:

10.40x + 3 = 150

To solve for x, we need to isolate the variable:

10.40x = 150 - 3

10.40x = 147

Now, divide both sides of the equation by 10.40 to solve for x:

x = 147 / 10.40

Using a calculator, we find:

x ≈ 14.13

Since we can't have a fractional number of people, we need to round down to the nearest whole number since we can't bring a fraction of a person. Therefore, Ms. Hernandez can bring 14 people to the zoo, including herself.

The average speed of a car is calculated by dividing the total distance traveled by the total time taken. In this case, the car travels 50+ miles in "of an hour".

To calculate the average speed in miles per hour, we need to determine the value of "of an hour". If the value is given as a fraction, we need to convert it to a decimal.

Assuming "of an hour" is 1/2 (0.5), the average speed can be calculated as:

Average speed = Total distance / Total time

Average speed = 50+ miles / (1/2) hour

To divide by a fraction, we can multiply by its reciprocal:

Average speed = 50+ miles * (2/1) hour

Average speed = 100+ miles per hour

Therefore, the average speed of the car is 100+ miles per hour.

Answer: 2,2

Step-by-step explanation:

trust me

El movimiento en línea recta se refiere al desplazamiento de un objeto en una trayectoria rectilínea, es decir, sin cambios de dirección.

En este tipo de movimiento, la velocidad y la aceleración del objeto pueden variar, pero su dirección se mantiene constante a lo largo del recorrido.

El movimiento en línea recta puede ser uniforme o no uniforme. En el caso del movimiento uniforme, la velocidad del objeto es constante, lo que implica que el desplazamiento realizado en intervalos iguales de tiempo es también constante.

Por otro lado, en el movimiento no uniforme, la velocidad cambia a lo largo del tiempo, resultando en diferentes desplazamientos en intervalos de tiempo iguales.

La descripción matemática del movimiento en línea recta se basa en conceptos como la posición, la velocidad y la aceleración. La posición se refiere a la ubicación del objeto en relación a un punto de referencia, la velocidad representa la tasa de cambio de la posición y la aceleración indica la tasa de cambio de la velocidad.

El estudio del movimiento en línea recta es fundamental en la física y tiene aplicaciones en diversas áreas, como la mecánica, la cinemática, la dinámica y la física de partículas.

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The completed sequence would then be: 2, 4, 7, 9, 16, 19, 29.

To complete the given number sequence, let's analyze the pattern and identify the missing terms.

Looking at the given sequence 2, 4, 7, __, 16, __, 29, __, we can observe the following pattern:

The difference between consecutive terms in the sequence is increasing by 1. In other words, the sequence is formed by adding 2 to the previous term, then adding 3, then adding 4, and so on.

Using this pattern, we can determine the missing terms as follows:

To obtain the third term, we add 2 to the second term:

7 + 2 = 9

To find the fifth term, we add 3 to the fourth term:

16 + 3 = 19

To determine the seventh term, we add 4 to the sixth term:

__ + 4 = 23

Therefore, the missing terms in the sequence are 9, 19, and 23.

By identifying the pattern of increasing differences, we can extend the sequence and fill in the missing terms accordingly.

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Answer:

64 and 65

Step-by-step explanation:

Let the two lockers be x and (x+1) since they are consecutive

The sum is 129 so,

x + (x+1) = 129

2x + 1 = 129

2x = 128

x = 64

x + 1 = 65

The locker numbers are 64 and 65

The number line inequality that represents x > -7 is: Option D

In number line inequalities we know that:

A closed circle indicates "greater than or equal to" or "less than or equal to" .

Meanwhile an open circle indicates "greater than" or "less than".

A closed circle pointing to the right indicates  "greater than or equal to" while a closed circle pointing to the left indicates "less than or equal to,"

Similarly:

An open circle pointing to the right indicates "greater than" while An open circle pointing to the left indicates  "less than".

Thus , the correct number line that shows x > -7 is: Option D

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The vertex of point A' in the dilated triangle A'B'C' is (6, 4.5).

1. Start by calculating the distance between the vertices of the original triangle ABC:

  - Distance between A(4, 3) and B(3, -2):

    Δx = 3 - 4 = -1

    Δy = -2 - 3 = -5

    Distance = √((-[tex]1)^2[/tex] + (-[tex]5)^2[/tex]) = √26

  - Distance between B(3, -2) and C(-3, 1):

    Δx = -3 - 3 = -6

    Δy = 1 - (-2) = 3

    Distance = √((-6)² + 3²) = √45 = 3√5

  - Distance between C(-3, 1) and A(4, 3):

    Δx = 4 - (-3) = 7

    Δy = 3 - 1 = 2

    Distance = √(7² + 2²) = √53

2. Apply the scale factor of 1.5 to the distances calculated above:

  - Distance between A' and B' = 1.5 * √26

  - Distance between B' and C' = 1.5 * 3√5

  - Distance between C' and A' = 1.5 * √53

3. Determine the coordinates of A' by using the distance formula and the given coordinates of A(4, 3):

  - A' is located Δx units horizontally and Δy units vertically from A.

  - Δx = 1.5 * (-1) = -1.5

  - Δy = 1.5 * (-5) = -7.5

  - Coordinates of A':

    x-coordinate: 4 + (-1.5) = 2.5

    y-coordinate: 3 + (-7.5) = -4.5

4. Thus, the vertex of point A' in the dilated triangle A'B'C' is (2.5, -4.5).

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Answer: D. 145°

Step-by-step explanation:

Since it is a parallelogram given by the symbol, then angle B is equal to angle D which is 145°.

Answer:

Step-by-step explanation:

Let's calculate the expression step by step:

93 - (15 × 10) + (160 ÷ 16)

First, we perform the multiplication:

93 - 150 + (160 ÷ 16)

Next, we perform the division:

93 - 150 + 10

Finally, we perform the subtraction and addition:

-57 + 10

The result is:

-47

Therefore, 93 - (15 × 10) + (160 ÷ 16) equals -47.

Answer:

R = {(0, 8), (0, -8), (8, 0), (-8, 0), (6, ±2), (-6, ±2), (2, ±6), (-2, ±6)}

Step-by-step explanation:

Since [tex](\pm8)^2+0^2=64[/tex], [tex]0^2+(\pm 8)^2=64[/tex], [tex](\pm 6)^2+2^2=64[/tex], and [tex]6^2+(\pm 2)^2=64[/tex], then those are your integer solutions to find R.

Answer:

(90°/360°)π(3^2) = (1/4)(9π) = 9π/4 m²

Answer:

Step-by-step explanation:

Let's break down the given information step by step to solve the problem:

The sum of three numbers x, y, and z is 165: x + y + z = 165.

When the smallest number x is multiplied by 7, the result is n: 7x = n.

The value n is obtained by subtracting 9 from the largest number y: y - 9 = n.

The value n is also obtained by adding 9 to the third number z: z + 9 = n.

We can use this information to form a system of equations:

Equation 1: x + y + z = 165

Equation 2: 7x = n

Equation 3: y - 9 = n

Equation 4: z + 9 = n

To find the product of the three numbers, we need to determine the values of x, y, z, and n.

First, let's solve for n using Equation 2:

7x = n

Now, let's substitute the value of n into Equations 3 and 4:

Equation 3: y - 9 = 7x

Equation 4: z + 9 = 7x

We can rearrange Equation 3 to express y in terms of x:

y = 7x + 9

Now, we can substitute the value of y in Equation 1:

x + (7x + 9) + z = 165

Simplifying:

8x + z = 156

Now, we have two equations:

Equation 4: z + 9 = 7x

8x + z = 156

We can solve this system of equations to find the values of x and z:

From Equation 4, we have z = 7x - 9.

Substituting z in Equation 8x + z = 156:

8x + (7x - 9) = 156

15x - 9 = 156

15x = 165

x = 11

Substituting x = 11 in Equation 4:

z + 9 = 7(11)

z + 9 = 77

z = 68

Now, we have the values of x = 11, y = 7x + 9 = 7(11) + 9 = 86, and z = 68.

The product of the three numbers x, y, and z is:

Product = x * y * z = 11 * 86 * 68 = 64648.

Therefore, the product of the three numbers is 64648.

The value of x is 5625 when √x + √y=138 and x-y=1656.

To solve for x using the given equations, we will use the method of substitution. Let's go through the steps:

Start with the equation √x + √y = 138.

We want to express y in terms of x, so solve for y in terms of x by isolating √y:

√y = 138 - √x

Square both sides of the equation to eliminate the square root:

(√y)² = (138 - √x)²

y = (138 - √x)²

Now, substitute the expression for y in the second equation x - y = 1656:

x - (138 - √x)² = 1656

Expand the squared term:

x - (138² - 2 * 138 * √x + (√x)²) = 1656

Simplify the equation further:

x - (19044 - 276 * √x + x) = 1656

Combine like terms and rearrange the equation:

-19044 + 276 * √x = 1656

Move the constant term to the other side:

276 * √x = 20700

Divide both sides of the equation by 276 to solve for √x:

√x = 20700 / 276

√x = 75

Square both sides to solve for x:

x = (√x)²

x = 75²

x = 5625

Therefore, the value of x is 5625.

By substituting this value of x back into the original equations, we can verify that √x + √y = 138 and x - y = 1656 hold true.

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Remember to use the appropriate units for measurements when calculating surface area.

To find the surface area of an object, you need to calculate the total area of all its exposed surfaces. The method for finding the surface area will vary depending on the shape of the object. Here are some common shapes and their respective formulas:

1. Cube: The surface area of a cube can be found by multiplying the length of one side by itself and then multiplying by 6 since a cube has six equal faces. The formula is: SA = 6s^2, where s is the length of a side.

2. Rectangular Prism: A rectangular prism has six faces, each of which is a rectangle. To find the surface area, calculate the area of each face and add them up. The formula is: SA = 2lw + 2lh + 2wh, where l, w, and h represent the length, width, and height of the prism.

3. Cylinder: The surface area of a cylinder includes the area of two circular bases and the area of the curved side. The formula is: SA = 2πr^2 + 2πrh, where r is the radius and h is the height.

4. Sphere: The surface area of a sphere can be found using the formula: SA = 4πr^2, where r is the radius.

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Answer:

Relative maximum at x=0; Relative minimum at x=8/3

Step-by-step explanation:

To find the relative maximums and the relative minimums, you must first find the first derivative of the function. The first derivative of this function is 6x^2-16x. Simply it and you get 2x(3x-8). X would be equal to 0 and 8/3. Next, make a number line where you put 0 and 8/3 have a value of zero.

        +                           -                                 +      

-------------------0----------------------------8/3-----------------------

Plug in a value of x<0 to get the region left of 0. Say we use -1, we get -2(-3-8), which is positive, meaning that it is increasing there. From 0 to 8/3, if we use 1, we get 2(3-8), which is decreasing. If we use 3, we get 6(9-8), which is increasing. From this, we can see that when x=0, the graph has a relative maximum. When x=8/3, the graph has a relative minimum.

Answer:

PO = 12

Step-by-step explanation:

given a tangent and a secant from an external point to the circle then

the product of the measures of the secant's external part and the entire secant is equal to the square of the measure of the tangent , that is

OP × OQ = NO²

OP × 27 = 18² = 324 ( divide both sides by 27 )

OP = 12

The value of cos E in the triangle is √2/2

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. Trigonometric ratio is only applied in right triangles.

Some of the trigonometric functions are ;

sinθ = opp/hyp

cosθ = adj/hyp

tanθ = opp/adj

In the triangle taking reference from angle E, 5 is the opposite and 5 is the adjascent and 5√2 is the hypotenuse.

Therefore;

cos E = 5/5√2

cos E = 1/√2

rationalizing the value;

cos E = √2/2

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Answer:

  19 or 26

Step-by-step explanation:

You want the value of 3n² -8n -9, given that n(n -3) = 10.

We recognize that 10 = 5·2 and that these factors differ by 3. This means n(n -3) = 10 is equivalent to saying n ∈ {-2, 5}.

The value of 3n² -8n -9 will be one of ...

  (3n -8)n -9 = (3(-2) -8)(-2) -9 = (-14)(-2) -9 = 19 . . . . for n = -2

or

  (3(5) -8)(5) -9 = (7)(5) -9 = 26 . . . . . . . for n = 5

The expression 3n² -8n -9 will be either 19 or 26.

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Answer: the answer is -4

Step-by-step explanation: the reason why the answer is -4 becaue all of the option is in correct.

Answer:The present worth of the project for Bronson Building Inc is $6,389,137.

In order to calculate the present worth, follow these steps:

1. The given information is:

Initial cost (first cost) = $18,000,000

Annual revenue = $5,000,000

Annual expenses = $2,000,000

Net annual cash flow = Annual revenue - Annual expenses = $5,000,000 - $2,000,000 = $3,000,000

MARR = 11%

Project duration = 18 years

Sale price at the end of the project = $8,000,000

2. To calculate the present worth, we first need to find the present value of the net annual cash flows using the MARR as the discount rate. Then, we will add the present value of the sale price and subtract the initial cost.

Present value of net annual cash flows (PV_ACF) = Net annual cash flow * [(1 - (1 + MARR)^(-duration)) / MARR]

PV_ACF = $3,000,000 * [(1 - (1 + 0.11)^(-18)) / 0.11] = $3,000,000 * 7.696 = $23,088,000

3. Find the present value of the sale price at the end of the project.

Present value of sale price (PV_SP) = Sale price / (1 + MARR)^duration

PV_SP = $8,000,000 / (1 + 0.11)^18 = $8,000,000 / 6.146 = $1,301,137

4. Calculate the present worth of the project.

Present worth = PV_ACF + PV_SP - Initial cost

Present worth = $23,088,000 + $1,301,137 - $18,000,000 = $6,389,137

Step-by-step explanation:

a. The absolute maximum of g is 4.

The absolute minimum of g is -4.

b. The absolute maximum of h is 3.

The absolute minimum of h is -4.

In Mathematics and Geometry, the vertical asymptote of a function simply refers to the value of x (x-value) which makes its denominator equal to zero (0).

By critically observing the graph of the polynomial function g shown above, we can logically deduce that its vertical asymptote is at x = 3. Furthermore, the absolute maximum of the polynomial function g is 4 while the absolute minimum of g is -4.

In conclusion, the absolute maximum of the polynomial function h is 3 while the absolute minimum of h is -4.

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