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1) f(x) = 1/(x - 2)^3 - 8

2)f(x) from x = 1 to x = 3 is 15.5.

1) Sketch the function f(x) = 1/(x - 2)^3 - 8 and calculate its x-intercepts, y-intercepts, horizontal and vertical asymptotes.To sketch the function f(x) = 1/(x - 2)^3 - 8, we need to find the x-intercepts, y-intercepts, horizontal and vertical asymptotes. First, let's find the x-intercept. It's a point on the graph where the function intersects the x-axis, so y-coordinate should be zero.f(x) = 1/(x - 2)^3 - 8y = 0 = 1/(x - 2)^3 - 8⇒ 1/(x - 2)^3 = 8⇒ (x - 2)^3 = 1/8⇒ x - 2 = 1/2⇒ x = 2 + 1/2 = 5/2So, the x-intercept is (5/2, 0).Next, let's find the y-intercept. It's a point on the graph where the function intersects the y-axis, so x-coordinate should be zero.f(x) = 1/(x - 2)^3 - 8x = 0 = 1/(0 - 2)^3 - 8⇒ 1/(-2)^3 - 8 = -1/8 - 8 = -8 1/8So, the y-intercept is (0, -8 1/8).Next, let's find the horizontal asymptote. As x approaches infinity or negative infinity, the function approaches a certain value, which is the horizontal asymptote.To find the horizontal asymptote, we need to find the limit of f(x) as x approaches infinity.f(x) = 1/(x - 2)^3 - 8∴ as x → ∞, (x - 2)^3 → ∞⇒ 1/(x - 2)^3 → 0So, the horizontal asymptote is y = -8. To find the vertical asymptotes, we need to find the values of x that make the denominator of the fraction zero.f(x) = 1/(x - 2)^3 - 8x - 2 = 0 = (x - 2)^3⇒ x = 2So, the vertical asymptote is x = 2.Now, we can sketch the function as shown below. f(x) = 1/(x - 2)^3 - 8Answer:2) Calculate the average rate of change of f(x) = 2x^3 - 3x^2 - 4x from x = 1 to x = 3.To find the average rate of change of a function, we need to divide the change in the function by the change in the variable. In this case, the change in the variable is Δx = 3 - 1 = 2.f(x) = 2x^3 - 3x^2 - 4xf(1) = 2(1)^3 - 3(1)^2 - 4(1) = -5f(3) = 2(3)^3 - 3(3)^2 - 4(3) = 26So, the change in the function is Δf = f(3) - f(1) = 26 - (-5) = 31.Now, the average rate of change is given by,Δf/Δx = 31/2 = 15.5Therefore, the average rate of change of f(x) from x = 1 to x = 3 is 15.5.

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Answer:

y = x/3 - 8/3 (OR) 3y = x - 8

Both of the above solutions are the same

Step-by-step explanation:

Using the form 'y=mx+c',

Since m = 1/3,

y = 1/3x + c

Substituting (5, -1) into the above equation:

-1  = 5/3 + c

c = -1 - 5/3

= -8/3

Hence,

y = x/3 - 8/3

(which is also the same as)

3y = x - 8

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7 times 5 shows the number of students in the four-square match. The solution has been obtained by using arithmetic operations.

What are arithmetic operations?

It is stated that the four fundamental operations, often known as "arithmetic operations," can explain all real numbers. Quotient, product, sum, and difference are the next four mathematical operations after division, multiplication, addition, and subtraction.

We are given that there were 7 teams in the four-square match and each team was made of 5 third-graders.

Now, in order to find the total students, we will use the multiplication operation.

From this, we get 7 times 5 which represents the total students.

Hence, 7 times 5 shows the number of students in the four-square match.

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The Answer is approximately equal to 942.48 or 300π

(π=pi)

The expected value for Darryl's sister is -$0.31. This means that on average, she can expect to lose 31 cents per game played with the 52 card deck.

The expected value for Darryl's sister can be calculated by multiplying the probability of each outcome by the value of that outcome and then summing those products.

Probability of choosing the 4 of hearts: 1/52

Probability of choosing any spade: 13/52

Probability of choosing any other card: 38/52

Expected value = (1/52)($10) + (13/52)(-$2) + (38/52)($0)

Expected value = $0.19 - $0.50 + $0

Expected value = -$0.31

Therefore, the expected value for Darryl's sister is -$0.31. This means that on average, she can expect to lose 31 cents per game played with the 52 card deck.

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There are approximately 2425 of those intervals that will contain the population means.

A confidence interval is a range of values that includes a parameter estimate with a certain degree of certainty. A confidence interval is a measure of uncertainty about an estimation procedure, rather than a statement about a parameter. A confidence interval is a specific value or a range of values in statistics that is used to estimate population characteristics.

This is because a 97% confidence interval means that if we were to repeat the sampling process many times, about 97% of the resulting intervals would contain the population mean. In other words, we would expect 97% of the intervals to be "correct" in the long run, while about 3% of them would not contain the population mean.

Therefore, out of the 2500 intervals we compute, we would expect approximately 0.97 x 2500 = 2425 intervals to contain the population mean, and about 0.03 x 2500 = 75 intervals not to contain the population mean. However, it's important to note that the actual number of intervals that contain the population means may vary from this expected value due to random sampling variability.

Where, [tex]\[\bar{x}\][/tex] is the sample mean

[tex]\[\frac{s}{\sqrt{n}}\][/tex] is the standard error of the mean

zα/2 is the z-score that covers α/2 in the tails of a normal distribution.

As we draw 2500 samples of size 100 from a population and compute a 97% confidence interval for each sample, the proportion of the sample will contain the population means.

Therefore, the number of intervals that will contain the population mean is approximately 2425.

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Answer: 450

Step-by-step explanation:

9x10x5

Answer:

The formula for the volume of a triangular prism is given by:

V = (1/2)bhL

where b is the base length of the triangle, h is the height of the triangle, and L is the length of the prism (i.e., the distance between the two triangular faces).

We are given the area of the rectangular surface of the prism, which is the product of the lengths of two adjacent sides of the rectangle, and we know that this area is equal to 864 cm^2. Therefore, we can use the Pythagorean theorem to find the length of the third side of the rectangle, which is also the base length of the triangular face:

17^2 = 9^2 + 10^2

289 = 81 + 100

289 = 181

So, the base length of the triangular face is 8 cm. Now we can plug in the known values into the formula for the volume of the prism:

864 = (1/2)(8 cm)(h)(L)

We are not given the length of the prism, L, but we know that it is equal to the base length of the triangle, which is 8 cm. Therefore, we can simplify the equation to:

864 = 32h

Solving for h, we get:

h = 864/32

h = 27

So the height of the prism is 27 cm.

The correct response is (f) 26 ft. The radius of the cylinder is approximately 26 ft.

To solve for the radius, we can use the formula for the volume of a cylinder, V = πr²h, where V is the volume, r is the radius, and h is the height. We can plug in the given values to get:

63,679 = πr²(30)

Dividing both sides by 30π gives:

r² = 676

Taking the square root of both sides gives:

r ≈ 26

Rounding to the nearest whole number gives the answer of 26 ft. Therefore, the correct response is (f) 26 ft.

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Complete Question:

A cylinder has a height of 30 ft and a volume of 63,679 ft³. what is the radius of the cylinder? round your answer to the nearest whole number. responses

a) 676 ft

b) 676 ft  

c)338 ft

d) 338 ft

e) 52 ft

f) 26 ft.  

Using the perimeter formula of a rectangle we can write an equation describing the values of x and y is as follows:

2y + 2x = 52 inches

The perimeter of a rectangle is the total length of its edges. It is expressed in linear units like centimetres, inches, and the like and can be taken to mean the total measurement of the rectangle's length and width. For instance, you may rapidly calculate how much ribbon you'd need if you needed to decorate the edge of your rectangular notebook. Similar to how calculating the perimeter will help you determine how much wire you'll need to erect a fence around your garden.

The formula P = 2(l + w), where l is the length and w is the width, determines the perimeter of a rectangle. Since we are aware that this rectangle's perimeter is 52 inches, we can write the following equation: 2l + 2w = 52 inches.

We can express the equation in terms of x and y to discover the potential values for x and y. We may substitute the width (x) and the length (y) into the equation to get 52 inches: 2y + 2x.

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The correct equations that form a system of equations to determine the number of boxes of pens, x, and the number of boxes of pencils, y, that Mr. Kelly buys are:

A. x+y = 40 (since he buys a total of 40 boxes)

E. 5x + 2y = 131 (since he spends a total of $131)

Therefore, the correct answers are A and E.

1. Linear function: n(p) = -40p + 800

2. r(p) = P. n(p)

3. Total revenue = $4000

There are numerous formulas for deriving a line's equation using linear functions, depending on the available data.

With the exception of vertical lines, which are not functions, any line may have its equation found using a formula for a linear function.

In the question,

We can assume, we have two points:

(5, 600) and (20,0)

The slope:

0-600/20-5

= -40

So, n(p) = -40 (p-20)

n(p) = -40p +800

Now solving,

r(p) = P. n(p)

= -40p² + 800p

Now to calculate the revenue,

r'(p) = -2 × 40p + 800

= -80p + 800

Order r'(p) = 0

⇒ P = 10

The highest price is: $10.

Revenue = -40 × ($10) ² + 800 × $10 = $4000

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The length of the edge of the cube with the given total surface area is 7.1 inches.

The region that includes the base(s) and the curved portion is referred to as the total surface area. It is the overall area that the object's surface occupies. The total area of a form with a curved base and surface is equal to the sum of the two areas.

Let us suppose the length of an edge of the cube = l.

The total surface are of the cube is given as:

TSA = 6l²

Substituting TSA = 302.46 we have:

302.46 = 6l²

l² = 50.41

l = 7.1 in.

Hence, the length of the edge of the cube with the given total surface area is 7.1 inches.

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Answer:

13 matches

Step-by-step explanation:

Notice 1st have 4 matches
then 2nd have 7 matches (since one is shared), this is 8-1

then 3rd have 10 matches (since two are shared) this is 12-2
Notice the pattern 4 matches per square minus one per aditional square from the first.
This give an equation
4n-1(n-1)= 3n+1
lets check
For n=1    matches= 3(1)+1=4

For n=2    matches= 3(2)+1=7

For n=3    matches= 3(3)+1=10
It works.
so

For n=4   matches= 3(4)+1=13

The value of the vehicle 5 years after purchase will be $12,500. After we predict the depreciation of car values as time progresses.

Due to use, wear, and tear, or becoming obsolete, an asset loses value over time. Depreciation is the measurement of this decrease.

Using the given linear model y = -1100x + 25,000, we can substitute x = 5 (since we want to find the value after 5 years of purchase) and solve for y:

y = -1100(5) + 25,000

y = -5500 + 25,000

y = 19,500

Therefore, the value of the vehicle 5 years after purchase will be $19,500.

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For the given quadrilateral the value of p is 8, UV = 70 and VW = 34. The property of parallelogram used is the opposite sides are parallel and equal.

A quadrilateral having two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Also, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.

The opposing sides are equal and parallel. Angles on either side are equal. The subsequent or neighbouring angles are additional. All of the angles will be at right angles if any one of them is a right angle.

We know that the opposite sides of a parallelogram are parallel and equal thus,

8p + 6 = 9p – 2

6 + 2 = 9p – 8p

8 = p

Now, the value of side is:

UV = 8(8) + 6 = 70

The value of side VW is:

VW = 5(8) – 6 = 34

Hence, for the given quadrilateral the value of p is 8, UV = 70 and VW = 34. The property of parallelogram used is the opposite sides are parallel and equal.

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The first 5 terms of the sequence, whose general term is an = -9n - 9, would be the following: -18, -27, -36, -45, -54.

In mathematics, a sequence is an ordered list of numbers, called terms, that follow a particular pattern or rule. Each term in a sequence is identified by its position in the sequence, which is usually represented by an integer index or subscript.

To find the first 5 terms of the sequence with the general term an = -9n - 9, we can simply substitute the values of n from 1 to 5 into the formula and simplify:

a1 = -9(1) - 9 = -18

a2 = -9(2) - 9 = -27

a3 = -9(3) - 9 = -36

a4 = -9(4) - 9 = -45

a5 = -9(5) - 9 = -54

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Answer:

The length of the hypotenuse is $x=\sqrt{2}$ units. ($x=\√2$)

Explanation:

If one of the angles of a right triangle is 45 degrees, then the other acute angle is also 45 degrees. Let's label the other leg of the triangle as $y$ units.

Using the Pythagorean Theorem, we have:

$1^2 + y^2 = x^2$

Simplifying:

$1 + y^2 = x^2$

We can also use the fact that the ratio of the sides of a 45-45-90 triangle is $1:1:\sqrt{2}$ to write:

$\frac{x}{1}=\sqrt{2}$

Simplifying:

$x=\sqrt{2}$

Now, substituting this value of $x$ into our equation $1 + y^2 = x^2$, we have:

$1 + y^2 = (\sqrt{2})^2$

Simplifying:

$1 + y^2 = 2$

$y^2 = 1$

$y = 1$ (since we're looking for a positive length)

Therefore, the length of the hypotenuse is $x=\sqrt{2}$ units.

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On a taxable income of $25,000, you must pay $3,358.75 in taxes.

To find how much tax you need to pay on a taxable income of $25,000, you will need to use the tax table given.

Since $25,000 falls in the third row of the table, which is for taxable income over $7,825 but not over $31,850, we will need to use the formula for this row:

Tax = $782.50 + 15% of the amount over $7,825

To calculate the tax, we need to first find the amount over $7,825, which is:

25,000 - 7,825 = 17,175

Now we can substitute this into the formula to get:

Tax = 782.50 + 0.15 x 17,175

Tax = 782.50 + 2,576.25

Tax = 3,358.75

Therefore, the amount of tax you need to pay on a taxable income of $25,000 is $3,358.75.

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Answer: The volume of a cube is calculated by multiplying the edge length by itself three times, or V = l^3.

If the edge length of Jasmine's cube is doubled, the new edge length will be 4 inches x 2 = 8 inches.

Thus, the new volume of the cube would be V = 8^3 = 512 cubic inches.

Comparing this new volume to the original volume of the cube, V = 4^3 = 64 cubic inches, we can see that the new volume is multiplied by 8.

Therefore, the correct answer is D) The volume is multiplied by 8.

Step-by-step explanation:

Answer: -16

Step-by-step explanation:

First, we need to solve the parentheses by performing the operation inside them. (-7 + 3) equals -4, so we can substitute that in the expression to get:

(-7 + 3)4 = -4 × 4

Next, we can perform the multiplication operation:

-4 × 4 = -16

Therefore, (-7 + 3)4 = -16.

Answer:

-16

Step-by-step explanation:

First, you distribute 4 into the equation, basically multiplying, so 4 * 3 is 12, then 4 * -7 is -28. Add them together so -28 + 12 is -16

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Answer:

133,380

Step-by-step explanation:

Cost of house 575,000

Khomo paid 245,000

Peter paid 575,000 - 245,000 = 330,000

Ratio of Khomo to Peter = 245,000 : 330,000 = 49:66

Profit made = 234,500

Khomos share is 49/ 115 x 234,00 = 0.43 x 234,000 = 100,620

Peters share is 66/115 x 234,000 = =0.57 x 234,000 = 133,380

22=4 square root 2

Step-by-step explanation:

Using Pythagorean Theory

Answer:

1. To expand the polynomial f(x) = (x-3)(x+2)(x+3), we can use the FOIL method twice, where we first multiply (x-3) and (x+2) using FOIL, then multiply the resulting binomial by (x+3) using FOIL again.

2. To expand the polynomial g(x) = (x-3)(x+2)(x-2), we can also use the FOIL method twice, where we first multiply (x-3) and (x+2) using FOIL, then multiply the resulting binomial by (x-2) using FOIL again.

3. The polynomial f(x) has three linear factors, and so the degree of the polynomial will be 3, since we will have to multiply three binomials together. The polynomial g(x) has four linear factors, and so the degree of the polynomial will be 4.

If we were to expand a polynomial with five linear factors, the degree of the polynomial would be 5, since we would have to multiply five binomials together.

4. The degree of a polynomial is determined by the highest power of x in the polynomial, which is determined by the number of terms in the expanded polynomial expression.

(6 sentences to use):

1. To expand the polynomial (x-3)(x+2)(x+3), we use the distributive property and multiply each term of the first binomial by each term of the second binomial, then multiply the resulting trinomial by the third binomial.

2. To expand the polynomial (x-3)(x+2)(x-2), we use the same strategy as in the previous example, multiplying each term of the first binomial by each term of the second binomial, and then multiplying the resulting trinomial by the third binomial.

3. The polynomial f(x) has three linear factors, so its degree is 3, which means the highest exponent in the polynomial is 3.

4. The polynomial g(x) has four linear factors, so its degree is 4, which means the highest exponent in the polynomial is 4.

5. If we were to expand a polynomial using five linear factors, we would again use the distributive property to multiply each term of each binomial together, resulting in a polynomial with a degree of 5, which means the highest exponent in the polynomial would be 5.

6. This strategy for multiplying three binomials is a useful tool in algebraic manipulation, allowing us to expand and simplify polynomial expressions.

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Answer:

No

Step-by-step explanation:

14x + 2 ≠ 16x

Because 2 doesn't have an x variable, it can't be added with 14x!

The amount that Jessica will earns if she sells 34 books is 86 dollars.

An earning refers to the income that a person  get from wages and salaries, security and other government benefits, dividends and interest, business ownership, other sources etc.

Our Equation to solve for earnings is:

A = 52 + (1)B

A = 52 + B

A(34) = 52 +34

A(34) = $86

Therefore, the total earned in one week if she sold 34 books is $86.

Missing words' Write an equation relating A to B. Then use this equation to find the amount of money Lena earns if she sells 34 books. Equation:  Amount Jessica earns is she sells 34 books: ____ dollars".

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