The surface area of a cylinder is 2,285.92 square inches. What is the height?

The solution is:

[tex]\int\limits^a_b {\frac{x^{3} }{x^{2} + x -2 } } \, dx[/tex] =[tex]ln|x| + \frac{2}{5} ln|x+2| + \frac{1}{3} ln|x-1| + C[/tex]

The partial fraction expansion of a rational fraction is  described as an operation that consists of expressing the fraction as a sum of a polynomial and one or several fractions with a simpler denominator.

To solve the above partial fraction decomposition,

[tex]x^3 + x^2 - 2x = x(x^2 + x - 2) = x(x+2)(x-1)[/tex]

we then write the fraction as a sum of partial fractions:

[tex]fx-2dx = \frac{A }{x } + \frac{B}{x + 2 } + \frac{C }{x - 1}[/tex]

We  find the values of A, B, and C by  multiplying  both sides by the common denominator (x)(x+2)(x-1) and  substituting

fx-2dx = A(x+2)(x-1) + B(x)(x-1) + C(x)(x+2)

We set  x = 0

0 = -2A

A = 0.

We set  x = -2

-2 = 20B/(-2)(-4)

-2 = -5B

B = 2/5.

we set  x = 1

1 = 3C

C = 1/3.

fx-2dx = 0/x +  2/5/(x+2) +  1/3/(x-1)

We integrate each term separately and have the solution as :

[tex]\int\limits^a_b {\frac{x^{3} }{x^{2} + x -2 } } \, dx[/tex] =[tex]ln|x| + \frac{2}{5} ln|x+2| + \frac{1}{3} ln|x-1| + C[/tex].

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The book has a lower cost per minute than the movie.

To find the cost per minute of the book, we divide the cost by the number of minutes:

cost per minute of book = $15 / 200 minutes = $0.075 per minute

To find the cost per minute of the movie, we need to convert the time to minutes.

2 hours and 39 minutes is equal to:

2 hours x 60 minutes/hour = 120 minutes

39 minutes = 39 minutes

Total minutes = 120 + 39 = 159 minutes

cost per minute of movie = $14 / 159 minutes = $0.088 per minute

Therefore, the book has a lower cost per minute than the movie.

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The surface area of the box which is a rectangular prism would be = 24 square inches. That is option D.

To calculate the area of the given box the formula that should be used is the formula of the area of a rectangular prism. That is;

Area of rectangular prism = length×width×height

Where:

length = 4 inches

width = 3 inches

height = 2 inches

Area = 4×3×2 = 24 square inches

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Through the work that was shown, you have

     999x = 393

If you divide both sides of the equation by 999, you'd have

     [tex]x=\dfrac{393}{999} = \dfrac{131}{333}[/tex]

So, [tex]0.\overline{393} =\dfrac{131}{333}[/tex]

The expression that represent the perimeter of the triangle is 3d² - 4d + 1.

The perimeter of any two-dimensional figure is simply the distance around the figure.

Hence, the perimeter of the triangle is the sum of all its 3 side lengths.

From the diagram:

Side length 1 = ( d² + 3 )

Side length 2 = ( 4d² + 3d - 2 )

Side length 3 = ( -2d² - 7d )

Hence, the perimeter of the triangle will be:

Perimeter = side length 1 + side length 2 + side length 3

Plug in the expressions

Perimeter = ( d² + 3 ) + ( 4d² + 3d - 2 ) + ( -2d² - 7d )

Collect and add like terms:

Perimeter = d² + 3 + 4d² + 3d - 2 + -2d² - 7d

Perimeter = d² + 4d² - 2d² + 3d - 7d + 3 - 2

Perimeter = 3d² - 4d + 1

Therefore, the perimeter is 3d² - 4d + 1.

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The nth term of 11,13,15,17 is,

⇒ T (n) = 9 + 2n

Given that;

The sequence is,

11, 13, 15, 17, ....

Here, Common difference is,

13 - 11 = 2

15 - 13 = 2

Hence, Sequence is in Arithmetic sequence.

So, the nth term of 11,13,15,17 is,

⇒ T (n) = a + (n - 1)d

⇒ T (n) = 11 + (n - 1) 2

⇒ T (n) = 11 + 2n - 2

⇒ T (n) = 9 + 2n

Thus, The nth term of 11,13,15,17 is,

⇒ T (n) = 9 + 2n

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The number of times two yellow cards occurred in 400 simulations of the repeated experiment. will be 64.

The probability of getting yellow is calculated as,

P(YY) = 2/5 x 2/5

P(YY) = 4/25

The expected value is given below.

E(x) = np

Where n is the number of samples and p is the probability.

The expected value is calculated as,

E(YY) = 400 x 4/25

E(YY) = 64

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The length and width of another rectangular park is 110 meters by 65 meters

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

A rectangular park is 70 meters wide and 105 meters long

This means that

Width = 70

Length = 105

The area is calculated as

Area = 70 * 105

Area = 7350

For smaller area, we decrease the width and increse the length

So, we have

Width = 70 - 5

Length = 105 + 5

Evaluate

Width = 65

Length = 110

Hence, the length and width of another rectangular park is 110 by 65

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The z-score for the raw score of 39 is 1.The z-score for the raw score of 30 is -0.8.Z-scores measure the number of standard deviations a raw score is from the mean. A positive z-score indicates a raw score above the mean, while a negative z-score indicates a raw score below the mean.

To find the z-scores, we need to use the formula:

z = (x - μ) / σ

where:

z is the z-score,x is the raw score,μ is the mean, andσ is the standard deviation.

Let's calculate the z-scores for the given mean of 34 and standard deviation of 5.For a raw score of 39:

z = (39 - 34) / 5

z = 5 / 5

z = 1

So, the z-score for the raw score of 39 is 1.For a raw score of 30:

z = (30 - 34) / 5

z = -4 / 5

z = -0.8

The z-score for the raw score of 30 is -0.8.

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Answer:

1

Step-by-step explanation:

6c - 2c = 4

      4c = 4

        c = 4/4

        c = 1

Answer:

-------------------------

The range of the data is the difference of maximum and minimum values.

According to description of the box plot, the minimum value is 6 and maximum value is 18.

Hence the range is:

The estimated cost of printing Sarah's 300-page book is $6.50.

The estimated cost would be $20.00.
1. The y-intercept for the trend line is 5.00. The real-world meaning of this point is that the base cost for printing a book, regardless of the number of pages, is $5.00.
2. To find the slope of the trend line, use the formula (y2 - y1) / (x2 - x1). With the y-intercept (0, 5) and the given point (200, 6), the slope is (6 - 5) / (200 - 0) = 1 / 200 = 0.005.
3. The real-world meaning of the slope is that for each additional page in the book, the printing cost increases by $0.005 or half a cent per page.
4. Using the slope and y-intercept, the equation for the trend line in slope-intercept form is y = 0.005x + 5.
5. To estimate the cost of printing Sarah's 300-page book, substitute x = 300 into the equation: y = 0.005(300) + 5. So, y = 1.5 + 5 = 6.5. The estimated cost of printing Sarah's 300-page book is $6.50.

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The set of ordered pairs above: is a function.

The mapping diagram above: is a function.

y = x²: is a function.

The table above: is not a function.

In Mathematics and Geometry, a function is a mathematical equation which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.

Based on the set of ordered pairs, mapping diagram, and the equation above, we can reasonably infer and logically deduce that it represent a function because the input values (domain, x-value, or independent values) are uniquely mapped to the output values (range, y-value or dependent values).

In this context, we can reasonably infer and logically deduce that the table does not represent a function because the input value (-1) has more than output values (2 and 4 respectively).

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Answer:

[tex]y(t)=\frac{1}{2}t^2+y_1t }[/tex]

Step-by-step explanation:

Refer to the attached image(s).

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Table of basic Laplace Transforms:}}\\1\rightarrow \frac{1}{s} \\t^n\rightarrow \frac{n!}{s^{n+1}}\\e^{at} \rightarrow\frac{1}{s-a}\\ \sin(at)\rightarrow\frac{a}{s^2+a^2}\\\cos(at)\rightarrow\frac{s}{s^2+a^2}\\e^{at}\sin(bt)\rightarrow\frac{b}{(s-a)^2+b^2}\\e^{at}\cos(bt)\rightarrow\frac{s-a}{(s-a)^2+b^2}\\t^ne^{at}\rightarrow\frac{n!}{(s-a)^{n+1}} \end{array}\right}[/tex]

Answer:

48

Step-by-step explanation:

Volume of triangular prism =1/2 bhl

=1/2 (4cm)(6cm)(4cm)

=48

A linear model that shows the miles Martin has run as the input, and the total time, in minutes, he has been running as the output is: y = 11x - 5

The general formula for the equation of a line between two coordinates is:

(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)

Using the coordinates as:

(5, 60), (9, 104) and (20, 225), we can say that the equation is expressed as:

(y - 60)/(x - 5) = (104 - 60)/(9 - 5)

(y - 60)/(x - 5) = 44/4

y - 60 = 11(x - 5)

y - 60 = 11x - 55

y = 11x - 5

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With regard to Neotraditionism, Denis' influence to write the first state  what was not objective comes from the desire to "put an end to all kind of naturalism and illusion" "Purely Plastic Art"

In order to create truly original works of art that went beyond what they saw as stagnating traditions of representation and illusionism both Denis and Kandinsky had their own unique visions for what constituted true artistic expression

Denis wanted to create a "purely plastic art" that would transcend nature altogether (Denis, 1890).

While Kandinsky believed that color held within it an almost mystical power capable of evoking deep emotions: "Color is...the soul is...the artist is..." he wrote poetically (p. 44).

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The approximate direction of the angle of the vector is determined as 45 degrees.

The approximate direction of the angle of the vector is calculated by applying the following formula for direction of a vector as follows;

The formula for the direction of a vector is given as;

tan θ = Vy / Vx

where;

The vector is given as;

V = 4i + 4j - 2k

The y component = 4, and the x component = 4

The direction of the vector is calculated as;

tan θ = 4 / 4

tan θ = 1

θ = arc tan (1 )

θ = 45⁰

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Answer:

-9

Step-by-step explanation:

Note that the rule that describes the transformation shown is: (x,y) → (x+7,-y)(Number 2)

We have,

A transformation is a broad phrase covering four distinct methods of changing the shape and/or location of a point, line, or geometric figure. The Pre-Image is the original shape of the item, and the Image is the final shape and location of the object after the transformation.

Thus, with regard to the transformation above,

At Point A: The original coordinate of point A was (-6,-6).

The coordinate after the transformation is A'(1,6), which eliminates option 3.

At Point B:

The original coordinate of point B was (-2,4).

After the transformation, we have B'(5,-4), which eliminates option 1 and option 4. It is therefore right to state that (x,y) → (x+7,-y) is the correct representation of the transformation.

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Full Question:

The missing options are:

Which rule describes the transformation shown?

1. (x,y) → (-y, x+7)

2. (x,y) → (x+7,-y)

3. (x,y) → (-x, y+7)

4. (x,y) → (y+7, -x)

The probability of obtaining a success given that X is less than 5, P(X < 5) is 0.8906.

The probability of obtaining a success is calculated as follows:

Given data:

X has a binomial distribution with n = 6 trials and p = 0.5, the probability of obtaining a success.

Using the binomial distribution function:

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

P(X = k) = [tex](_nC_k) * p^{k} * (1 - p)^{(n - k)}[/tex]

Therefore;

P(X < 5) = (₆C₀) * 0.5⁰ * 0.5⁶ + ( 1) * 0.5¹ * 0.5⁵ + (₆C₂) * 0.5² * 0.5⁴ + (₆C₃) * 0.5³ * 0.5³ + (₆C₄) * 0.5⁴ * 0.5²

P(X < 5) = 0.015625 + 0.09375 + 0.234375 + 0.3125 + 0.234375

P(X < 5) = 0.8906

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Answer: If we resolve, 10 to the power of 5 means 100,000.

Step-by-step explanation:

[1st Picture] Answer: x = 3.98

Step-by-step explanation:

    We are given the opposite side and adjacent side from our reference angle. This will use the tangent function. tanθ = [tex]\frac{opposite}{adjacent}[/tex].

tan(53°) = [tex]\frac{x}{3}[/tex]

3tan(53°) = x

x = 3.98

[2nd Picture] Answer: x = 3.13

Step-by-step explanation:

    Here, we are given the opposite side from our reference angle and the hypotenuse. This will use the sine function. sinθ = [tex]\frac{opposite}{hypotenuse}[/tex].

sin(23°) = [tex]\frac{x}{8}[/tex]

8sin(23°) = x

x = 3.13

[3rd Picture - #6] Answer: θ = 63.4°

Step-by-step explanation:

    Again, we are given the opposite side from our reference angle and the hypotenuse. This will use the sine function. sinθ = [tex]\frac{opposite}{hypotenuse}[/tex]. To find the angle measurement of theta at the end, we will use the inverse of sine.

sin(θ) = [tex]\frac{6}{6.71}[/tex]

[tex]sin^{-1}[/tex](sin(θ)) = [tex]sin^{-1}[/tex]([tex]\frac{6}{6.71}[/tex])

θ = 63.4°

The value of the area of a triangle is equal to 133 in^2.

We are given that;

Dimensions= 19in 13in

Now,

To determine the area of a triangle, we can use the formula A = (1/2) bh, where b is the base and h is the height.

The base and the height are the sides that are perpendicular to each other. For example, the area of a right triangle with base 12 in and height 9 in is;

A = (1/2) * 12 * 9

A = 54 in^2.

To find the area of the given triangle, we need to identify the base and the height. The base could be any side of the triangle, but the height must be perpendicular to it. In this case, we can choose the side with length 19 in as the base, and the side with length 14 in as the height. Using the formula, we get:

A = (1/2) * b * h

A = (1/2) * 19 * 14

A = 133 in^2

Therefore, by the area, the answer will be 133 in^2.

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The vertices of the image after a dilation with the origin as its center and a scale factor of 2 are having coordinates A' = (12, 8), B' = (4, 8), C' = (12, -4) and D' = (4, -4)

To dilate a figure with the origin as the center, we only need to multiply each coordinate by the scale factor. In this case, the scale factor is 2.

So, for vertex A(6, 4), we have:

x-coordinate after dilation: 2 × 6 = 12

y-coordinate after dilation: 2 × 4 = 8

Similarly, for vertex B(2, 4), we have:

x-coordinate after dilation: 2 × 2 = 4

y-coordinate after dilation: 2 × 4 = 8

For vertex C(6, -2), we have:

x-coordinate after dilation: 2 × 6 = 12

y-coordinate after dilation: 2 × (-2) = -4

Finally, for vertex D(2, -2), we have:

x-coordinate after dilation: 2 × 2 = 4

y-coordinate after dilation: 2 × (-2) = -4

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The correct interpretations of the slope and y-intercept are:

For each increase in speed of 1 mph, an additional 46.4 calories are predicted to be burned.

About 71.9 calories are burned at rest.

These interpretations are based on the regression equation given as

ŷ = 71.9 + 46.4x,

where ŷ represents the predicted calories burned and x represents the speed in miles per hour.

The slope of 46.4 indicates that for each 1 mph increase in speed, there is an additional predicted burn of 46.4 calories.

The y-intercept of 71.9 suggests that at a speed of 0 mph (resting), approximately 71.9 calories are burned.

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Answer:

26 units

Step-by-step explanation:

AD = 9 -2 = 7 units long. BC is the same. so we have 2 X 7 = 14.

DC is 9 - 3 = 6 units long. AB is the same. so we have 2 X 6 = 12.

perimeter = 14 + 12 = 26 units

The volume of the figure is V = 5,730.265 cm³

Given data ,

Let the figure be represented as V

Now , the figure consists of a cone and hemisphere

So , V = Volume of cone + volume of hemisphere

where height = 14 cm

And , radius r = 12 cm

On simplifying , we get

V = ( 1/3 ) πr²h + ( 2/3 )πr³

V = ( 1/3 ) ( 3.14 ) ( 12 )² ( 14 ) + ( 2/3 ) ( 3.14 ) ( 12 )³

V = 2,111.15026 + 3,619.1147369

On further simplification , we get

V = 5,730.265 cm³

Hence , the volume is V = 5,730.265 cm³

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The complete question is attached below :

Find the volume of the figure. Use 3.14 for . 12 cm 14 cm