Use the substitution u=x^2+8 to evaluate the indefinite integral below.
∫2x(x^2+8)8 dx
Show your complete solution.

Answer:

[tex]\frac{75}{4\pi }[/tex] inches or approximately 5.97 inches  

Step-by-step explanation:

Use the cone volume formula: V = [tex]\pi[/tex]r²[tex]\frac{h}{3}[/tex]

The diameter is 8 inches, so the radius will be 4 inches.

Plug in the radius and volume, and solve for h

V = [tex]\pi[/tex]r²[tex]\frac{h}{3}[/tex]

100 = [tex]\pi[/tex](4²)([tex]\frac{h}{3}[/tex])

100 = 16[tex]\pi[/tex][tex]\frac{h}{3}[/tex]

Divide each side by 16[tex]\pi[/tex]

[tex]\frac{25}{4\pi }[/tex] = [tex]\frac{h}{3}[/tex]

Cross multiply and solve for h:

4[tex]\pi[/tex]h = 75

h = [tex]\frac{75}{4\pi }[/tex]

So, the cone's height is [tex]\frac{75}{4\pi }[/tex] or approximately 5.97 inches  

The correct interpretation of `f(6) = 44,500` is that in the year 2011, a company that opened in 2005 will produce 44,500 units of products is the answer.

Given, `f(t)` be the number of units produced by a company `t` years after opening in 2005.

According to the question, `f(6) = 44,500`. It means six years after the company opened, which is in the year 2011, the company will produce 44,500 units of products.

The statement "six years from now, 44,500 units will be produced" (option a) is not correct because the year is not specified. The company will produce 44,500 units of products in the year 2011, not six years from the present.

The statement "in 2009, 44,500 units are produced" (option b) is not correct because in the year 2009, the company will only have been open for four years, and not enough information is provided to calculate the number of units produced.

The statement "in 2006, 44,500 units are produced" (option c) is not correct because in the year 2006, the company will have only been open for one year, and not enough information is provided to calculate the number of units produced.

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Without changing the value, Marcus can add 3 positive counters and 3 negative counters. Option d is correct.

To determine the difference -8 - 3 (+3), Marcus wants to use a model with counters. He starts with 8 negative counters, and in order to add 3 positive counters without changing the value, he can add 3 positive counters and 3 negative counters.

By adding 3 positive counters, he is increasing the value by 3. However, since he wants to maintain the same value, he also needs to add 3 negative counters. This ensures that the net change in value remains zero.

So, by adding 3 positive counters and 3 negative counters to the model, Marcus can represent the difference -8 - 3 (+3) without changing the overall value. Therefore, d is correct.

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Answer:

...

Step-by-step explanation:

remeber that for every angle they give you, you need to subtract 90 from it to get the answer.

Answer:

12 crew members I think hope this helps :)

Step-by-step explanation:

☁️ Answer ☁️

12.

(66 2/3)

---------- (x) = 8

100

Solve for x

(66 2/3)x = 800

x = 800/(66 2/3)

x = 800/(200/3)

x = 800(3/200)

x = 4(3)

x = 12

Here's the link: https://www.wyzant.com/resources/answers/286307/a_crew_is_made_up_of_8_men_the_rest_are_women_66_2_3_are_men_how_many_people_are_in_the_crew

Hope it helps.

Have a nice day noona/hyung.

The joint density f(x, y) = 1 for -y < x < y and 0 < y < 1, or 0 elsewhere, the variables X and Y are uncorrelated but not independent.

The problem requires the determination of whether the random variables X and Y are independent and uncorrelated. For that, the expectation of the product of X and Y is needed. Evaluating E(XY). For the two variables X and Y, their joint density is given as:

f(x, y) = 1 for -y < x < y and 0 < y < 1, or 0 elsewhere

To evaluate the expectation of XY, multiply the variables X and Y as follows: E(XY) = ∫∫xy f(x,y) dy dx.

We evaluate the above equation over the range of the variables.

Since the domain of the density function is given by -y < x < y and 0 < y < 1, E(XY) = ∫∫xy f(x,y) dy dx = ∫0¹ ∫-[tex]y^{y}[/tex] xy dy dx

The above equation can be simplified as:

E(XY) = ∫0¹ (1/3)*y³ dy = 1/12

Hence the covariance between X and Y is given by: Cov (X, Y) = E(XY) - E(X)E(Y) = E(XY) = 1/12.

The variance of X is calculated as follows: E(X) = ∫∫xf(x, y) dy dx

For the two variables X and Y, their joint density is given as: f(x, y) = 1 for -y < x < y and 0 < y < 1, or 0 elsewhere.

Thus, E(X) = ∫∫x f(x, y) dy dx= ∫0¹ ∫-[tex]y^{y}[/tex] x dy dx= 0.

Hence, Var(X) = E(X²) - [E(X)]² = E(X²) - 0² = E(X²).

The variance of X² is calculated as follows:

E(X²) = ∫∫x² f(x, y) dy dx. For the two variables X and Y, their joint density is given as: f(x, y) = 1 for -y < x < y and 0 < y < 1, or 0 elsewhere.

Thus, E(X²) = ∫∫x² f(x, y) dy dx= ∫0¹ ∫-[tex]y^{y}[/tex] x² dy dx= 1/3

Hence, Var(X) = E(X²) - [E(X)] ² = 1/3 - 0 = 1/3

The variance of Y² is calculated as follows: E(Y²) = ∫∫y² f(x, y) dy dx

For the two variables X and Y, their joint density is given as: f(x, y) = 1 for -y < x < y and 0 < y < 1, or 0 elsewhere. Thus, E(Y²) = ∫∫y² f(x, y) dy dx= ∫0¹ ∫-[tex]y^{y}[/tex]y² dy dx= 1/3

Hence Var(Y) = E(Y²) - [E(Y)]² = 1/3 - [E(Y)]²

The covariance between X and Y is given by: Cov (X, Y) = E(XY) - E(X)E(Y) = 1/12 - 0 = 1/12.

We can evaluate the correlation between X and Y as: Corr (X, Y) = Cov (X, Y) / √Var (X) Var(Y)= (1/12) / [(1/3) * (1/3)] = 1/4

Thus, the variables X and Y are uncorrelated but not independent.

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Answer:

c

Step-by-step explanation:

circumference = perimeter around circle

The measure of the angle should be 170° as this angle looks like an obtuse angle.

Hope that helps!

they amount of money are not the same

reason why;

the reason why its not the same is because 2x8x9=144 and 3x9x12=324 and the amount of money spent is different

The difference in price per cubic inch between the two sizes of cereal boxes is $0.0128.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

The volume of the family-sized box of cereal is:

= 3 x 9 x 12

= 324 cubic inches

The volume of the regular-sized box of cereal is:

= 2 x 8 x 9

= 144 cubic inches

The price per cubic inch of the family-sized box is:

= 6 / 324

= 0.0185 dollars per cubic inch

The price per cubic inch of the regular-sized box is:

= 4.50 / 144

= 0.0313 dollars per cubic inch

The difference in price per cubic inch is:

= 0.0313 - 0.0185

= 0.0128 dollars per cubic inch

Therefore,

The difference in price per cubic inch between the two sizes of cereal boxes is $0.0128.

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Answer:(2,36)and (3,54)

Step-by-step explanation:

Answer:

(2, 36) and (3, 54)

Step-by-step explanation:

I just answer the question from iready and I got it correct.

Step-by-step explanation:

x - 3 > -4

= x > -4+3

= x > -1 _ Answer

The sum of the given function is  2x^3 +  log(x+4) + 100

Given the following functions

f(x)=2x^3 and;

g(x) = log(x+4) + 100

Take the sum of the functions

f(x) + g(x) = 2x^3 +  log(x+4) + 100

Hence the sum of the given function is  2x^3 +  log(x+4) + 100

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Answer:

Just do 8.4 times 7

Step-by-step explanation:

8.4 times 7 = 58.8

Answer:

(4, -2)

Step-by-step explanation:

The midpoint of two points is found by averaging the X coordinates and averaging the Y coordinates to create a new pair.

X: (5+3)/2     = 4

Y: (-10+6)/2   = -2

Answer:

(4,-2)

Step-by-step explanation:

add the x and divide by two. do the same with the y. this is the same as finding the average

Answer: 47.5 or just 47

Step-by-step explanation: Well, to start, set up a ratio.

x / 50 = 95 / 100

95 * 50 is 4750

4750 / 100 is 47.5.

Now, it's asking how many questions he got correct. You can't get 47.5 questions correct, it should be a whole number. Now, I don't know how the rules work with that question, but it is like 47.

The standard deviation for the given test scores is 20, and the variance is 400

We have,

To find the standard deviation and variance for the given test scores, we can follow these steps:

Calculate the mean (average) of the test scores:

Mean (μ) = (92 + 92 + 92 + 52 + 52) / 5 = 80

Calculate the deviation of each test score from the mean:

Deviation = Test score - Mean

For the given test scores:

Deviations = (92 - 80), (92 - 80), (92 - 80), (52 - 80), (52 - 80)

= 12, 12, 12, -28, -28

Square each deviation:

Squared Deviations = Deviation²

Squared Deviations = 12², 12², 12², (-28)², (-28)²

= 144, 144, 144, 784, 784

Calculate the variance:

Variance = (Sum of Squared Deviations) / (Number of Scores)

Variance = (144 + 144 + 144 + 784 + 784) / 5

= 2000 / 5

= 400

Calculate the standard deviation:

Standard Deviation = √Variance

Standard Deviation = √400

= 20

Therefore,

The standard deviation for the given test scores is 20, and the variance is 400.

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Answer:

y = 3x - 4

Step-by-step explanation

If the line is perpendicular, then it means that the slope will be opposite. So if it's -1/3 then it will become 3.

y = 3x + b

-1 = 3(1) + b

-1 = 3 + b

-4 = b

The equation is y = 3x - 4

According to the Capital Asset Pricing Model (CAPM), A) the expected rate of return on a security increases in direct proportion to a decrease in the risk-free rate is the false statement.

According to the Capital Asset Pricing Model (CAPM), the expected rate of return on a security increases in direct proportion to an increase in the risk-free rate. Therefore, the statement that "The expected rate of return on a security increases in direct proportion to a decrease in the risk-free rate" is false.

The Capital Asset Pricing Model (CAPM) is a model that shows the relationship between risk and expected return and is used to calculate the expected return on an investment.CAPM is based on several assumptions, one of which is that investors are rational and risk-averse.

Another assumption is that the market is in equilibrium, meaning that supply equals demand for all securities. The model also assumes that investors have homogeneous expectations of future returns and that there are no taxes or transaction costs.CAPM states that the expected rate of return on an asset is a function of the risk-free rate, the expected market return, and the asset's beta.

Beta is a measure of the asset's volatility compared to the market. If an asset has a beta of 1, it is as volatile as the market. If it has a beta of less than 1, it is less volatile than the market, and if it has a beta of more than 1, it is more volatile than the market.

Therefore, according to CAPM, the expected rate of return on a security increases as its beta increases.In equilibrium, all securities lie on the security market line, and a fairly priced security has an alpha of zero.

Therefore, options B, C, and D are true, and the answer is option A, "The expected rate of return on a security increases in direct proportion to a decrease in the risk-free rate."

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The required basis of the orthogonal complement is {(2, 1, 0), (3, 0, 1)}.

Given that the line spanned by (-1, 2, 3) in R3.

To find the basis of the orthogonal complement, we need to find the vector which is orthogonal to (-1, 2, 3).

Let x = (x1, x2, x3) be a vector in the orthogonal complement of the given line.

Then we have: (-1, 2, 3)·x = 0-1x1 + 2x2 + 3x3 = 0x1 = 2x2 + 3x3

Thus, every vector x in the orthogonal complement has the form x = (2x2 + 3x3, x2, x3) = x2(2, 1, 0) + x3(3, 0, 1)

Therefore, the set { (2, 1, 0), (3, 0, 1) } is a basis of the orthogonal complement of the line spanned by (-1, 2, 3) in R3.

This is because both these vectors are linearly independent, and every vector in the orthogonal complement of the given line can be written as a linear combination of these two vectors.

Hence, the required basis of the orthogonal complement is {(2, 1, 0), (3, 0, 1)}.

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1. Volume of the Container: 1000 = l * b * h

2. Surface Area = 2(lw + lh + bh)

3. For the rectangular base container, the dimensions for the surface area to be a minimum will be the ones that satisfy the condition: l = 2b

1. Rectangular Base Container:

To sketch a rectangular base container that holds exactly one liter of liquid, we can assume the length of the rectangular base as 'l' and the breadth as 'b'. According to the given specifications, the length of the rectangular base must be twice the breadth.

Sketch:

       --------------------

      |                    |

      |                    |

      |                    |

      |        l           |

      |                    |

      |                    |

      ----------------------

                 bVolume of the Container:

The volume of a rectangular prism is calculated by multiplying the length, breadth, and height. In this case, the height will represent the depth of the container.

Volume = l * b * h

Since we want the container to hold exactly one liter of liquid, which is equivalent to 1000 cubic centimeters, we have:

1000 = l * b * h

2. Surface Area of the Container:

The surface area of a rectangular prism can be calculated using the formula:

Surface Area = 2(lw + lh + bh)

In our case, the lid of the container is also included in the surface area calculation.

Dimensions for Minimum Surface Area:

3. To determine the dimensions for the container's surface area to be a minimum, we can use calculus and find the critical points. In this case, we need to minimize the surface area formula by differentiating it with respect to one variable, setting it equal to zero, and solving for that variable.

For the rectangular base container, the dimensions for the surface area to be a minimum will be the ones that satisfy the condition:

l = 2b

Substituting this value into the surface area formula, we can find the minimum surface area for a given volume of one liter.

By solving the equation for the surface area with respect to 'b' and substituting the result into the volume equation, we can find the exact dimensions of the container to satisfy the given conditions.

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The random variable x is uniformly distributed between 10 and 20. To compute the probability of 10 ≤ x ≤ 15, Hence, the probability of 10 ≤ x ≤ 15 is 0.5.

Since x is uniformly distributed between 10 and 20, the probability density function (PDF) of x is a constant within this range. The PDF is given by the reciprocal of the range, which in this case is 1/10.

To find the probability of 10 ≤ x ≤ 15, we need to calculate the area under the PDF curve between 10 and 15. Since the PDF is constant, the area under the curve corresponds to the proportion of the total range that falls within this interval.

The width of the interval 10 ≤ x ≤ 15 is 15 - 10 = 5. The total range of x is 20 - 10 = 10. Therefore, the proportion of the total range that falls within the interval is 5/10 = 0.5.

Hence, the probability of 10 ≤ x ≤ 15 is 0.5. This means that there is a 50% chance that a randomly chosen value of x will fall within the interval from 10 to 15.

It is important to note that in a uniform distribution, the probability of any subinterval within the range is proportional to the width of that subinterval. In this case, since the subinterval 10 ≤ x ≤ 15 has a width of 5 out of the total range of 10, the probability is 0.5 or 50%.

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Answer:

You add (9+3)

Step-by-step explanation:

because PEMDAS evaluates the parenthesis first,

Answer:

It' B

Step-by-step explanation:

I got a 100 on the test

Answer:

Step-by-step explanation:

B i took that same quiz

The general solution of the given equation, x^2(dw/dx) = sqrt(w)(3x+2), expressed explicitly as a function of the independent variable, is w(x) = (1/27)((9x^2 + 6x + C)^3), where C is an arbitrary constant.

To solve the given equation, we can separate the variables and integrate.

First, rewrite the equation as

(1/sqrt(w))dw = (3x+2)/x^2 dx.

Integrate both sides with respect to their respective variables:

∫(1/sqrt(w))dw = ∫(3x+2)/x^2 dx.

The integral of (1/sqrt(w)) with respect to w is 2√w, and the integral of (3x+2)/x^2 with respect to x can be found using partial fractions or another suitable method.

After integrating and simplifying, we obtain:

2√w = (1/27)(9x^2 + 6x + C),

where C is the arbitrary constant.

To find the explicit solution, isolate w by squaring both sides:

w(x) = (1/27)((9x^2 + 6x + C)^3),

where w(x) is the function expressing the solution explicitly in terms of the independent variable x, and C is the arbitrary constant.

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Answer:

first one is 432

Step-by-step explanation:took the test and got it right

The height and depth of locker is 40 inch and 5 inch.

In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.

here, we have,

As per the known fact, volume of rectangle is calculated by multiplying the entities width, height and depth. Let us assume the depth be d.

So, the height is 4d. Keep the values in formula to find the value of depth.

10800 = 12 × d × 4d

4d² = 10800 ÷ 12

Performing Division

4d² = 900

d² = 900 ÷ 4

Performing Division

d² = 225

d = ✓225

Taking square root

d = 15

The depth of locker is 15 inch.

So, the height = 4d

Height = 4 × 15

Performing multiplication

Height = 60 inch

Therefore, the depth and height of locker is 15 inch and 40 inch.

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complete question:

A locker in the shape of a rectangular prism has a width of 12 inches. Its height is four

times its depth. The volume of the locker is 10,800 cubic inches. Find the height and depth of the locker.

Height:

Answer:

the answer is B

I hope it helps have a great day

Answer:

2 + n < 14

Step-by-step explanation:

Hey!

==================================================================

Let's work this word by word.

"Two more than a number is less than 14"

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

"Two more than"

⇒ 2 +

"A number"

⇒ 2 + n

"Is less than"

⇒2 + n <

"14"

⇒2 + n < 14

==================================================================

Hope I Helped, Feel free to ask any questions to clarify :)

Have a great day!

More Love, More Peace, Less Hate.

       -Aadi x

Answer:

GASOLINE The table gives the cost of a

gallon of gasoline at two stations.

How much more does gasoline cost at

Gas For Less than at Cut-Rate?

Step-by-step explanation: