Evaluate and simplify the expression
when x = 5 and z = 3.
2x - 3(x-z)
z - 1
=
[?]

Answer:

The given function f(x) is:

f(x) = { 1, -π < x < 0

{ -1, 0 < x < π

Since the function is odd and has period 2π, the Fourier series will only have sine terms. The Fourier series of f(x) can be written as:

f(x) = Σ[b_n sin(n x)], where n >= 1

where b_n is the n-th Fourier coefficient, given by:

b_n = (1/π) ∫[0,π] f(x) sin(n x) dx

We can evaluate the integral to find the Fourier coefficients:

b_n = (1/π) ∫[0,π] f(x) sin(n x) dx

= (1/π) [ ∫[0,π/2] sin(n x) dx - ∫[π/2,π] sin(n x) dx ]

= (1/π) [ -cos(n x)/n |[0,π/2] + cos(n x)/n |[π/2,π] ]

= (1/π) [ (-cos(n π/2)/n + 1/n) - (cos(n π) - cos(n π/2))/n ]

= (1/π) [ (1 - (-1)^n) / n ]

Therefore, the Fourier series of f(x) is:

f(x) = Σ[(1 - (-1)^n)/(n π) sin(n x)]

Where the sum is taken over all odd integers n.

The payback period for Product A is 2.21 years and the payback period for Product B is 1.85 years, NPV of A = $21,215 and NPV of B = -$50,256. Product A: IRR = 28.28%, Product B: IRR = 29.58%, A: PI = 1.00, B: PI = 0.91, A: SRR = 0.49 or 49%, B: SRR = 0.44 or 44%.

Payback period is a financial metric used to evaluate the time required to recover the initial investment made in a project or investment opportunity.

To calculate the payback period, we need to find out how long it takes for the initial investment to be recovered by the annual cash inflows. We calculate the cumulative cash inflows for each year and determine in which year the cumulative cash inflows exceed the initial investment.

Product A:

Year 1: $380,000 - $170,000 - $68,000 - $86,000 = $56,000

Year 2: $380,000 - $170,000 - $68,000 - $86,000 = $56,000 + $56,000 = $112,000

Year 3: $380,000 - $170,000 - $68,000 - $86,000 = $56,000 + $112,000 = $168,000

Year 4: $380,000 - $170,000 - $68,000 - $86,000 = $56,000 + $168,000 = $224,000

Year 5: $380,000 - $170,000 - $68,000 - $86,000 = $56,000 + $224,000 = $280,000

The payback period for Product A is 2.21 years (rounded to two decimal places).

Product B:

Year 1: $460,000 - $206,000 - $108,000 - $66,000 = $80,000

Year 2: $460,000 - $206,000 - $108,000 - $66,000 = $80,000 + $80,000 = $160,000

Year 3: $460,000 - $206,000 - $108,000 - $66,000 = $80,000 + $160,000 = $240,000

Year 4: $460,000 - $206,000 - $108,000 - $66,000 = $80,000 + $240,000 = $320,000

Year 5: $460,000 - $206,000 - $108,000 - $66,000 = $80,000 + $320,000 = $400,000

The payback period for Product B is 1.85 years (rounded to two decimal places).

To calculate the net present value (NPV), we need to discount the cash inflows and outflows using the company’s discount rate of 20% and then subtract the initial investment.

Product A:

[tex]NPV = -$340,000 + ($56,000/(1+0.20)^1) + ($112,000/(1+0.20)^2) + ($168,000/(1+0.20)^3) + ($224,000/(1+0.20)^4) + ($280,000/(1+0.20)^5)[/tex]

NPV = -$340,000 + $38,611 + $64,357 + $79,396 + $81,193 + $77,658

NPV = $21,215

Product B:

[tex]NPV = -$540,000 + ($80,000/(1+0.20)^1) + ($160,000/(1+0.20)^2) + ($240,000/(1+0.20)^3) + ($320,000/(1+0.20)^4) + ($400,000/(1+0.20)^5)[/tex]

NPV = -$540,000 + $66,667 + $111,111 + $114,882 + $99,425 + $97,659

NPV = -$50,256

To calculate the internal rate of return (IRR), we need to find the discount rate that makes the NPV of the cash inflows and outflows equal to zero. We can use a financial calculator or spreadsheet software to solve for the IRR.

Product A: IRR = 28.28%

Product B: IRR = 29.58%

To calculate the profitability index (PI), we divide the present value of the future cash inflows by the initial investment.

Product A:

PV of future cash inflows = $38,611 + $64,357 + $79,396 + $81,193 + $77,658 = $341,215

PI = $341,215/$340,000

PI = 1.00

Product B:

PV of future cash inflows = $66,667 + $111,111 + $114,882 + $99,425 + $97,659 = $489,744

PI = $489,744/$540,000

PI = 0.91

To calculate the simple rate of return (SRR), we divide the average annual cash inflow by the initial investment.

Product A:

Average annual cash inflow = ($56,000 + $112,000 + $168,000 + $224,000 + $280,000)/5 = $168,000

SRR = $168,000/$340,000

SRR = 0.49 or 49%

Product B:

Average annual cash inflow = ($80,000 + $160,000 + $240,000 + $320,000 + $400,000)/5 = $240,000

SRR = $240,000/$540,000

SRR = 0.44 or 44%

6a.

Based on the payback period, Product B is preferred because it has a shorter payback period of 1.85 years compared to Product A’s payback period of 2.21 years.

Based on the net present value, Product A is preferred because it has a positive NPV of $21,215 compared to Product B’s negative NPV of -$50,256.

Based on the internal rate of return, Product B is preferred because it has a higher IRR of 29.58% compared to Product A’s IRR of 28.28%.

Based on the profitability index, Product A is preferred because it has a PI of 1.00, indicating that for every dollar invested, we receive one dollar in return. Product B has a PI of 0.91, indicating that for every dollar invested, we receive only $0.91 in return.

Based on the simple rate of return, Product A is preferred because it has a higher SRR of 49% compared to Product B’s SRR of 44%.

6b. Based on the simple rate of return, Lou’s division should accept Product A because it has a higher SRR of 49% compared to Product B’s SRR of 44%. However, other measures such as the net present value and internal rate of return suggest that Product A may not be the best choice.

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The volume of shipping container is calculated as:

c. 3000116 in³ 3000 and 1 sixteenth, in³

The shipping container in this problem has a shape of rectangular prism. To find it's volume, we will apply the formula for the volume of a rectangular prism which is given as:

Volume = length × width × height.

Given the parameters of the shipping container as:

Length = 1512 inches

Width = 1014 inches

height = 2012 inches

Plug in the values:

volume of shipping container = 1512 × 1014 × 2012

= 3.08473402e9 cubic inches.

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Answer: 1256.63706

Step-by-step explanation: A=(π20)2

The approximate area of the circle segment bounded by arc DE and chord DE is approximately 17.72 square units.

To approximate the area of the circle segment bounded by arc DE and chord DE, you can use the following formula:

Area = (1/2) * r^2 * (θ - sinθ)

Where:

r is the radius of the circle (r = 20 in your case).

θ is the central angle in radians (47° converted to radians is approximately 0.8203 radians).

Let's calculate it:

θ = 47° * (π / 180) ≈ 0.8203 radians

Now, plug these values into the formula:

Area = (1/2) * (20^2) * (0.8203 - sin(0.8203))

Area ≈ (1/2) * 400 * (0.8203 - 0.7317)

Area ≈ (1/2) * 400 * 0.0886

Area ≈ 17.72 square units

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Answer: The answer is C

Answer:

  C.  (2x+3)/(x+2)

Step-by-step explanation:

You want the expression representing f(x)/g(x) where f(x) = 2x² -x -6 and g(x) = x² -4.

The ratio of the functions can be simplified by canceling common factors.

  [tex]\dfrac{f(x)}{g(x)}=\dfrac{2x^2-x-6}{x^2-4}=\dfrac{(x-2)(2x+3)}{(x-2)(x+2)}=\boxed{\dfrac{2x+3}{x+2}}\qquad\text{matches choice C}[/tex]

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Answer:

b.59

Step-by-step explanation:

this is the answer of whats you want

We may still infer something about their connection, though: the mean function and standard deviation both rise as p approaches 0.5, peaking at their highest levels at p = 0.5.

Mathematics is concerned with numbers and their variations, equations and related structures, shapes and their places, and possible placements for them. The relationship between a collection of inputs, each of which has an associated output, is referred to as a "function". An relationship between inputs and outputs, where each input yields a single, distinct output, is called a function. Each function has a domain and a codomain, often known as a scope. The letter f is frequently used to represent functions (x). X is the input. The four main types of functions that are offered are on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

A binomial distribution's mean or anticipated value is determined by the formula = np, where n is the number of trials and p is the success probability. The mean is = 8p in this instance since n = 8 and p is a parameter.

The formula for a binomial distribution's standard deviation is = sqrt(np(1-p)). We obtain = sqrt(8p(1-p)) using the same numbers as previously.

So, for this particular issue, we have:

Mean: μ = 8p

[tex]\Sqrt(8p(1-p))[/tex] is the standard deviation.

Since p is unknown, we are unable to determine the actual mean and standard deviation. We may still infer something about their connection, though: the mean and standard deviation both rise as p approaches 0.5, peaking at their highest levels at p = 0.5.

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Answer :

a) It is given that

Everyday a machine makes 500000 staples and puts them into the boxes.

The machine need 170 staples to fill a box

One box contans = 170 staples.

Total number of staples = 500000

Number of box required to fill 500000 staples = Total number of staples/No. of staples 1 box contains.

[tex] \: :\implies [/tex] 500000 /170

[tex] :\implies \: [/tex] 2941 (approx)

Therefore, 2941 boxes are required to fill with 500000 staples.

b) It is given that,

Each staple is made of 0.21 g of metal .

Total weight of metal = 1 kg = 1000 g

1 staple = 0.21 g

Number of staples = weight of metal/ Weight of 1 staple.

[tex] \: :\implies [/tex] 1000/0.21

[tex] \: :\implies [/tex] 4761 (approximately)

Therefore, 4761 staples can be made from 1 kg of the metal.

The percentage of females that do not satisfy the requirement is given as follows:

55.17%.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given as follows:

[tex]\mu = 998, \sigma = 202[/tex]

The proportion that does not satisfy the requirement is the p-value of Z when X = 1025(proportion less than 1025), hence:

Z = (1025 - 998)/202

Z = 0.13

Z = 0.13 has a p-value of 0.5517.

Hence the percentage is given as follows:

0.5517 x 100% = 55.17%.

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At the end, Antonio has 4 cups of milk leftover.

We know that Antonio has 1 gallon of mil, and he needs to use 3 quarts of milk for the recipe.

Then we need to perform a change of units, we know that:

1 gallon = 4 quarts.

Then after he uses 3 quarts, he will have 1 quart remaining, and now we want to know how many cups is that, we know that:

1 quart = 4 cups.

So Antonio has 4 cups leftover.

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To reach her home in half an hour, she needs to double her speed twice, which is equivalent to a 200% increase in speed. Therefore, the correct answer is 200%.

Speed is a measure of how quickly an object or person moves from one point to another. It is usually expressed in terms of distance traveled over time, for example, miles per hour or kilometers per hour.

To calculate this, we need to find the time taken for her to reach her home if her speed is doubled.

If her initial speed is 40 km/hr, then by doubling her speed, she will be travelling at a speed of 80 km/hr.

By travelling at this speed, she can reach her home in half an hour i.e. 30 minutes.

Therefore, the time taken to reach her destination by doubling her speed is 30 minutes.

The time taken to reach her destination while travelling at her initial speed is 2 hours.

To calculate the percentage increase in speed, we have to find the ratio of the time taken to reach her destination when the speed is doubled to the time taken to reach her destination when the speed is not doubled.

Therefore, the percentage increase in speed

= (30/120) x 100

= 25%.

Since she needs to double her speed to reach her home in half an hour, the percentage increase in speed required is 100%.

To reach her home in half an hour, she needs to double her speed twice, which is equivalent to a 200% increase in speed.

Therefore, the correct answer is 200%.

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The solution of the logarithmic equation is v = 0.00137

Here we want to solve the logarithmic equation:

log₃(v) = -6

Remember that:

logₐ(x) = ln(c)/ln(a)

Then we can rewrite the equation as follows:

log₃(v) = -6

ln(v)/ln(3) = -6

ln(v) = -6*ln(3)

Now we can apply the exponential equation in both sides, we will get.

exp(ln(v)) = exp(-6*ln(3))

v =  exp(-6*ln(3))

v = 0.00137

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The number line that shows the position of each country is added as an attachment

From the question, we have the following parameters to create the number line

See attachment for the label of each tick as a multiple of the power of 10⁷

Next, we represent each country on the number line

See attachment for the completed number line

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The cross product of (a - b) and (a + b) is: [-8, -8, -2].

Given the vectors a = (3, 4, -7) and b = (4, 5, 8), you want to compute the cross product of (a - b) and (a + b).

First, let's compute the vectors (a - b) and (a + b):

a - b = (3 - 4, 4 - 5, -7 - 8) = (-1, -1, -15)

a + b = (3 + 4, 4 + 5, -7 + 8) = (7, 9, 1)

Now, let's compute the cross product of the two vectors:

(-1, -1, -15) × (7, 9, 1) = [(-1)(9) - (-1)(1), (-15)(1) - (-1)(7), (-1)(7) - (-1)(9)] = [-8, -8, -2]

So, the cross product of (a - b) and (a + b) is: [-8, -8, -2].

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Answer:

63 cm²

Concept used:

Area of a parallelogram = b · h

(b: base and h: height of the parallelogram)

Step-by-step explanation:

The given figure is a parallelogram.

Required Area = 9 * 7

= 63 cm²

Answer:

The area of a square is given by the formula A = s^2, where s is the side length. If Doug has 8 square pieces of wood, each with a side length of s centimeters, the total area of all the pieces can be expressed as:

8s^2 = 200

To solve for s, we can simplify the equation by dividing both sides by 8:

s^2 = 25

Now we can create a quadratic equation by subtracting 25 from both sides:

s^2 - 25 = 0

This is a quadratic equation in standard form, where the coefficient of the squared term is 1, the coefficient of the linear term is 0, and the constant term is -25. Doug can use this equation to find the side length of each piece of wood by solving for s using methods such as factoring, completing the square, or using the quadratic formula.

The answer of the given question based on the the sentence into an equation is , 2x - 3 = 4.

In mathematics, equation is statement that asserts equality of the two mathematical expressions. It typically contains variables, constants, and mathematical operations like  addition, subtraction, multiplication, division, exponentiation, and logarithm. An equation usually consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=). The values of the variables that satisfy the equation are called its solutions.

The sentence be translated into equation are as  follows:

2x - 3 = 4

where x is the unknown number.

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Answer: 1. the probability of both balls being red is 3/8 or 0.375. 2.unlikely to occur

Step-by-step explanation:

Answer:

62.50

Step-by-step explanation:

The event is more likely to occur because there are 4 more red balls than white balls. The probability of 2 white balls selected are 37.50, which means that the probability of 2 red balls selected are 62.50.

Esta es la pendiente de la recta tangente a la curva f(x) en el punto x = a.

La tangente de una derivada no es una operación matemática bien definida. Supongo que lo que se quiere encontrar es la pendiente de la recta tangente a la curva representada por la función f(x) cuya derivada es f'(x) = 6x^2 - 6x - 12 en algún punto x = a.

La pendiente de la recta tangente a la curva f(x) en el punto x = a está dada por la derivada de f(x) evaluada en ese punto, es decir:

m = f'(a)

Entonces, para encontrar la pendiente de la recta tangente a la curva de la función f(x) en el punto x = a, tenemos que evaluar f'(x) en x = a:

m = f'(a) = 6a^2 - 6a - 12

donde f(a) es el valor de la función en el punto x = a.

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Answer:

Step-by-step explanation:

The equation 12x + 15y = 120 represents the total number of t-shirts and sweatshirts bought if spend $120What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.The price for t-shirts = $12 eachThe price for the sweatshirt = $15 eachLet's suppose x number of t-shirts and y number of sweatshirts bought.Then,12x + 15y = 120The equation represents the total number of t-shirts and sweatshirts bought if spend $120Thus, the equation 12x + 15y = 120 represents the total number of t-shirts and sweatshirts bought if spend $120

Answer:A quart contains 4 cups or 2 pints while a gallon contains 16 cups or 8 pints. Hence, a liquid gallon is equal to 4 liquid quarts.

Step-by-step    please give me brainiest and have a nice day :)

Answer:

z = 23

Step-by-step explanation:

62 + 95 = 157

180 - 157 = 23

The graphs of functions f(x) and g(x) compare as -

Option B: They have the same y-intercept, but the graph of g(x) rises more quickly over time.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The function f(x) is given as [tex]f(x)=500(1.015)^x[/tex].

The function f(x) is given as [tex]g(x)=500(1.021)^x[/tex].

The y-intercept of both functions is 500, which represents the initial amount in the savings accounts.

To compare the rates at which the functions rise over time, we need to compare their growth factors, which are 1.015 and 1.021 for f(x) and g(x), respectively.

Since 1.021 is greater than 1.015, the function g(x) grows at a faster rate than f(x).

Therefore, the correct answer is -

Option B: They have the same y-intercept, but the graph of g(x) rises more quickly over time.

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Answer:

y = 12x - 73

Step-by-step explanation:

We are given the line y=4(3x+2).

We want to find the equation of line G, which contains the point (7,11), and is parallel to y=4(3x+2) in the form y=mx+c. m is the slope, and c is the value of y at the y-intercept.

Parallel lines have the same slopes. So, we should start by finding the slope of y=4(3x+2).

We can do the distributive property to distribute the 4 to both terms on the right side.

y=4(3x+2) => y=12x + 8

Notice how this equation is written in the form y=mx+c. As 12 is written in the place where m is, the slope of this line is 12.

It is also the slope of line G.

We can replace m in y=mx+c with 12 for line G. We'll get:

y=12x + c

Now, we need to find c.

We can use the point (7,11) to help us find c.

Substitute 7 for x and 11 for y.

11 = 12(7) + c

Multiply.

11 = 84 + c

Subtract 84 from both sides

-73 = c

Substitute -73 as c.

y = 12x - 73

Answer:

Step-by-step explanation:

Product means multiply.

-300

Answer:g=23/16

Step-by-step explanation: The negative number adds up.

Answer:

Therefore, the value of the truck 12 years after it was purchased is approximately $1,624.

Step-by-step explanation:

To find the value of the truck after 12 years, we need to apply the seven-eighths decrease to the original value each year. Let's set up an equation:

Value after 12 years = $58,000 x (7/8)^12

Simplifying, we get:

Value after 12 years = $58,000 x 0.028

Value after 12 years = $1,624

Therefore, the value of the truck 12 years after it was purchased is approximately $1,624.

The speed of the boat in still water (x) is 12 mph, and the speed of the current (y) is 9 mph.

To find the speed of the boat in still water and the speed of the current, let's follow these steps:

Step 1: Let x represent the speed of the boat in still water, and y represent the speed of the current. The speed downstream is (x + y) and the speed upstream is (x - y).

Step 2: Use the formula distance = time × speed to write two equations based on the given information.

Downstream: 9(x + y) = 189

Upstream: 63(x - y) = 189

Step 3: Simplify both equations:

Downstream: x + y = 21 (divide both sides by 9)

Upstream: x - y = 3 (divide both sides by 63)

Step 4: Solve the system of equations by adding the two simplified equations:

2x = 24

x = 12

Step 5: Plug the value of x back into either equation to solve for y:

12 + y = 21

y = 9

So, the speed of the boat in still water (x) is 12 mph, and the speed of the current (y) is 9 mph.

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