Probability 0.05 0.2 0.05 0.05 0.1 0.05 0.5 10 11 12 14 Find the expected value of the above random variable.

The value of the triple integral ∭_E x² dV over the given solid E is 64π/5.

To evaluate the triple integral ∭_E x^2 dV, where E is the solid that lies within the cylinder x² + y² = 4, above the plane z = 0, and below the cone z² = 4x² + 4y², we can express the integral in terms of cylindrical coordinates.

In cylindrical coordinates, we have:

x = r cos(theta)

y = r sin(theta)

z = z

The limits for the cylindrical coordinates are as follows:

0 ≤ r ≤ 2 (limits for the radius)

0 ≤ theta ≤ 2π (limits for the angle)

0 ≤ z ≤ sqrt(4r²) = 2r (limits for the height, as per the cone equation)

Now let's express the integral in cylindrical coordinates:

∭_E x² dV = ∭_E (r cos(theta))² r dz dr d(theta)

Let's evaluate the integral step by step:

∫[0 to 2π] ∫[0 to 2] ∫[0 to 2r] (r³ cos²(theta)) dz dr d(theta)

We can simplify the innermost integral with respect to z:

∫[0 to 2π] ∫[0 to 2] [r³ cos²(theta)z] |[0 to 2r] dr d(theta)

= ∫[0 to 2π] ∫[0 to 2] (r³ cos²(theta)(2r)) dr d(theta)

= 2 ∫[0 to 2π] ∫[0 to 2] (2r⁴ cos²(theta)) dr d(theta)

Now, let's integrate with respect to r:

2 ∫[0 to 2π] [(1/5) r⁵ cos²(theta)] |[0 to 2] d(theta)

= 2 ∫[0 to 2π] [(1/5)(32 cos²(theta))] d(theta)

= (64/5) ∫[0 to 2π] cos²(theta) d(theta)

To evaluate the remaining integral, we can use the identity cos²(theta) = (1 + cos(2theta))/2:

(64/5) ∫[0 to 2π] [(1 + cos(2theta))/2] d(theta)

= (64/10) ∫[0 to 2π] (1 + cos(2theta)) d(theta)

= (64/10) [(theta + (1/2)sin(2theta))] |[0 to 2π]

= (64/10) [(2π + (1/2)sin(4π)) - (0 + (1/2)sin(0))]

= (64/10) (2π + 0 - 0)

= (64/10) (2π)

= 128π/10

= 64π/5

Therefore, the value of the triple integral ∭_E x² dV over the given solid E is 64π/5.

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Answer:

if it is one gallon then it will take 75 more percent

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

it's probably C

Step-by-step explanation:

️‍♀️

Answer:

C

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

Formula

P = 2 * (L + W)

Solution

L = 6

W = 3

P = 2 (6 + 3)

P = 2 (9)

P = 18

The given statement "For a fixed confidence level, when the sample size decreases, the length of the confidence interval for a population mean decreases." is false, length of CI increases in this case.

When the sample size decreases, the length of the confidence interval for a population mean actually increases, not decreases.

The length of a confidence interval is influenced by several factors, including the sample size, the variability of the data, and the desired level of confidence. A confidence interval provides a range of values within which the population mean is estimated to lie.

When the sample size is smaller, there is less information available to estimate the population mean accurately. As a result, the confidence interval needs to be wider to accommodate the increased uncertainty. This wider interval allows for a larger range of potential values for the population mean.

On the other hand, as the sample size increases, there is more data available to estimate the population mean. This increased amount of information leads to a more precise estimate, allowing for a narrower confidence interval.

Therefore, for a fixed confidence level, as the sample size decreases, the length of the confidence interval for a population mean generally increases, not decreases.

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For the given equation x⁸ + y⁸ + z⁵ = 6xyz, the value of partial derivatives are ∂z/∂x = (6yz - 8x⁷) / (5z⁴ - 6xz) and ∂z/∂y = (6xz) / (8y⁷ - 6xy)

To find the partial derivatives ∂z/∂x and ∂z/∂y for the equation x⁸ + y⁸ + z⁵ = 6xyz, we need to differentiate the equation with respect to x and y while treating y and z as constants.

Taking the partial derivative with respect to x (∂z/∂x), we differentiate each term separately:

8x⁷ + 0 + 5z⁴ (∂z/∂x) = 6yz + 6xz(∂z/∂x)

Simplifying the equation, we get:

8x⁷ + 5z⁴ (∂z/∂x) = 6yz + 6xz(∂z/∂x)

Now, let's take the partial derivative with respect to y (∂z/∂y):

0 + 8y⁷ + 0 (∂z/∂y) = 6xz + 6xy(∂z/∂y)

Simplifying further:

8y⁷ (∂z/∂y) = 6xz + 6xy(∂z/∂y)

To find the values of ∂z/∂x and ∂z/∂y, we need to isolate the partial derivatives:

∂z/∂x = (6yz - 8x⁷) / (5z⁴ - 6xz)

∂z/∂y = (6xz) / (8y⁷ - 6xy)

These equations give the partial derivatives of z with respect to x and y for the given equation x⁸ + y⁸ + z⁵ = 6xyz.

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Answer:

B

Step-by-step explanation:

Please Give brainliest

Answer:

D

Step-by-step explanation:

The criterion that is least likely to be used in choosing bins (classes) in a frequency distribution is personal preference or subjective judgment.

When constructing a frequency distribution, it is important to consider objective criteria based on the nature of the data and statistical principles. Common criteria used for choosing bins include the range of the data, the desired number of bins, the shape of the data distribution, and the purpose of the analysis. These criteria help ensure that the bins effectively capture the variation in the data and provide meaningful insights. Personal preference or subjective judgment, on the other hand, may introduce bias and lack objectivity in determining the bin boundaries. It is essential to rely on objective criteria and statistical guidelines to make informed decisions when choosing bins for a frequency distribution.

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Answer:

[tex]2\frac{5}{8} cups = 1\frac{1}{2}\ batches[/tex]

Step-by-step explanation:

Given

[tex]1\frac{3}{4} cups = 1\ batch[/tex]

Required

Number of cups for [tex]1\frac{1}{2}[/tex] batches

[tex]1\frac{3}{4} cups = 1\ batch[/tex]

Multiply both sides by [tex]1\frac{1}{2}[/tex]

[tex]1\frac{1}{2} * 1\frac{3}{4} cups = 1\ batch * 1\frac{1}{2}[/tex]

[tex]1\frac{1}{2} * 1\frac{3}{4} cups = 1\frac{1}{2}\ batches[/tex]

Express fractions as improper fractions

[tex]\frac{3}{2} * \frac{7}{4} cups = 1\frac{1}{2}\ batches[/tex]

[tex]\frac{21}{8} cups = 1\frac{1}{2}\ batches[/tex]

Express fraction as improper fraction

[tex]2\frac{5}{8} cups = 1\frac{1}{2}\ batches[/tex]

Answer:

The point estimate is 0.88

Step-by-step explanation:

Given

[tex]n = 2000[/tex] -- sample size

[tex]x = 1760[/tex] -- adults who think future health of social security is a major economic concerm

Required

Determine the point estimate

This is calculated as:

[tex]\hat p= \frac{x}{n}[/tex]

[tex]\hat p= \frac{1760}{2000}[/tex]

[tex]\hat p = 0.88[/tex]

The point estimate is 0.88

That's a question about graphs.

In the Cartesian coordinate system, we have two axes: The x-axis (horizontal) and the y-axis (vertical).

When we want to represent a equation in the cartesian coodinate system, we associate a point in the x-axis and other in the y-axis. The Cartesian coordinate is represented by (x, y).

To represent some equation in a graph, we need at least two points to draw a line that cross these 2 points.

For example: To represent the equation [tex]y = x +1[/tex], let's replace the value of x:

Finally, if we draw a line tha cross these 2 points, we will have the graph that represents [tex]y = x +1[/tex].

Now you know about it, let's solve our problem?

In that question, we should to find the graph that represents the equation [tex]y = kx[/tex], but we don't know the value of k, so what should we do? It's easy:

k is a constant. That means that the value of k never changes. Now, let's analyze a specific case:

If x = 0, so y = 0 as well. But why? We know that any number multiplied by 0 is equal 0. Therefore:

With the informations that the problem give to us, these are the unique things that we can find, but that's enough.

When we look at the options, just the second graph have a line that cross the coordenate (0, 0). Therefore, the correct answer is the graph below:

I hope I've helped. :D

Enjoy your studies! \o/

Given equation is y''' + 343y = 0 which is a third-order linear differential equation. To find the general solution of the equation, we can use the characteristic equation of the differential equation as follows;

Let y = erx be the trial solution of the differential equation, where e is the exponential function and r is an unknown constant to be determined. Substituting the trial solution into the differential equation, we have; y''' + 343y = 0 y' = rerx, y'' = rerx, y''' = rerx. Substituting into the differential equation, we have;r³erx + 343erx = 0. Factorizing out erx, we have erx(r³ + 343) = 0For erx ≠ 0;r³ + 343 = 0r³ = -343r = (-343)¹/³ = -7 (r = -7, since we are working with real forms of the equation). Therefore, the general solution of the third order linear differential equation is;

y = c₁e^-7x + c₂e^-7x cos(12.124x) + c₃e^-7x sin(12.124x) where c₁, c₂, and c₃ are arbitrary constants.

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Answer:

I don't understand this at all but I wanted to take a stab at it anyway.

It's not an even number, it's less than 50, it has to be divisible by six or three in order to be 5 more than a perfect square, and it has to be two or three digits that equal 40.

Sounds hard.

Okay first I want to get all the odd numbered equations that could equal 40

1+39      19+21

3+37      17+23

5+35      15+25

7+33      

9+31      

11+29    

13+27    

This is taking so much brain power, wow... So none of those so far would work, which makes me think that it would be a single digit equation to make it double digit, but nothing, not even 9+9 equals 40, so at least one of the numbers would have to be double digit but that makes no sense because then the number would have to have three digits, which makes it more than 100!

This is impossible. I think I have to rephrase my answer above in saying that the number has to be more than 100, but that means I have no idea what that first line means...

I'm so frustrated by this imao... Asker of the question, if you've figured out the answer please let me know because I am so confused.

Answer:

I DONT KNOW

Step-by-step explanation:

hehe

Answer:

1.33333 hours

Step-by-step explanation:

Given :

Time taken by Libby = 2 hours

Time taken by Ethan = 4 hours

rate = 1 / time taken

Libby's rate = 1 /2

Ethan's rate = 1/4

Combined rate = Libby's rate + Ethan's rate

Combined rate = 1/2 + 1/4 = 3/4

Time taken = 1 / combined rate

Time taken = 1 / (3/4)

Time taken = 4 /3

Time taken = 1.33333 hours

Answer:

Dot Plot

Step-by-step explanation:

The probability of z being less than or equal to,-1.09 is approximately 0.1379,-1.5 is approximately 0.0668, 1.3 is approximately 0.0968.2.54 is approximately 0.0057,-0.71 and 2.54 (exclusive) is approximately 0.6467.

To compute these probabilities, we can use the standard normal distribution table or a statistical software. In the standard normal distribution table, we look up the given z-values and find the corresponding probabilities.

For (a), the probability of z being less than or equal to -1.09 is approximately 0.1379.

For (b), the probability of z being less than or equal to -1.5 is approximately 0.0668.

For (c), the probability of z being greater than or equal to 1.3 is approximately 0.0968.

For (d), the probability of z being greater than or equal to 2.54 is approximately 0.0057.

For (e), we subtract the probability of z being less than or equal to -0.71 from the probability of z being less than or equal to 2.54. This gives us approximately 0.6467.

These probabilities provide information about the likelihood of certain values occurring in a standard normal distribution.

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Answer:

The radius is 9.28 inches.

Step-by-step explanation:

Since there are 7 Move Ahead zones, and 3 Go Backwards zones on the spinner, there must be 2 other zones (the Freeze! +Bonus pts)

2 out of 12 zones are Freeze! +Bonus pts. That is 1/6 of the spinner. They said the area of the the Freeze!+Bonus pts is 45.1 inches squared.

45.1 × 6

= 270.6

The entire spinner has the area 270.6

The area of a circle is:

A = pi•r^2

We are looking for r. Thats the radius they asked for in the question.

270.6 = pi•r^2

pi is a number, I'm using the pi button on the calculator bc it is most exact.

270.6 = pi•r^2

Divide both sides by pi.

86.134655 = r^2

square root both sides.

9.28 = r

The radius is 9.28 inches.

Answer:

A. 77

B. 3,773

Step-by-step explanation:

According to the problem, computation of given data are as follows,

Population in 2017 = 3,850

Decrease rate = 2% per year

(A) We can calculate number of population decrease from 2017 to 2018 by using following formula,

Number of population decrease = Population in 2017 × Decrease rate

= 3,850 × 2%

= 77

(B). Total population in 2018 = 3,850 - 77

= 3,773

Answer:

Plot attached

Step-by-step explanation:

We want to locate √36 and ∛36 on the given number line

Now, √36 = 6.

And ∛36 = 3.3

I have attached a plot number line both values as we are told in the question

The critical t-value that corresponds to a 95% confidence level with 15 degrees of freedom is approximately 2.131.

To find the critical t-value that corresponds to a 95% confidence level with 15 degrees of freedom, we can use a t-table or a statistical software.

Using a t-table or a statistical software, we look up the critical t-value for a two-tailed test with a confidence level of 95% and 15 degrees of freedom.

For a two-tailed test, we divide the desired confidence level by 2 to account for both tails of the t-distribution. In this case, we divide 95% by 2, which gives us 0.475.

Looking up the critical t-value for a confidence level of 0.475 and 15 degrees of freedom, we find that the critical t-value is approximately 2.131.

Therefore, the critical t-value that corresponds to a 95% confidence level with 15 degrees of freedom is approximately 2.131.

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Answer:

a diagonal one??? like its linear uhm okay here i have a picture one sec

Step-by-step explanation:

Answer:

See explanations below

Step-by-step explanation:

Mean is the average of the data

Mean = sum of data/sample size

Sum of data = 89+99+80+5+90+0+100+95

Sum of data = 558

Sample size = 8

Mean = 558/8

Mean = 69.75

Median is the data value in the middle after rearrangement

Rearrange

0 , 5, 80) 89, 90, (95, 99 100

Median = 89+90/2

Median = 89.5

The parameter that gives a better picture of the scores is the Mean since all the given datas are taken into consideration

The mean test score is

✔ 69.75

.

The median test score is

✔ 89.5

.

Which measure of center best represents the test data?

✔ median

I hope this helps!

Answer:

(2 - a) (x² - y)

Step-by-step explanation:

2x² + ay - ax² - 2y

=> 2x² - 2y + ay - ax²

=> 2 (x² - y) + -a (-y + x²)

=> 2 (x² - y) + -a (x² - y)

=> (2 - a) (x² - y)

Answer:

La jerarquía de operaciones es un método para resolver operaciones con múltiples operadores; saber realizarla te servirá para resolver los diversos problemas que te presenten en tu examen CENEVAL EXANI-II.  En primer lugar, se deben resolver las operaciones de potencias y raíces.

Step-by-step explanation:

the approximate values of y at x = X₀ + 0.1 and x = X₀ + 0.2 are:

y ≈ 0.9282 at x = 0.1

y ≈ 0.8281 at x = 0.2

To solve the given differential equation, we will use an appropriate method, such as the Euler's method, to approximate the values of y at specific points.

The Euler's method uses the equation:

y₍ₙ₊₁₎ = yₙ + h * f(xₙ, yₙ),

where:

yₙ is the value of y at xₙ

h is the step size,

f(x, y) is the derivative of y with respect to x (i.e., dy/dx), and

y₍ₙ₊₁₎ is the approximation of y at the next point x₍ₙ₊₁₎ = xₙ + h.

Let's apply Euler's method to find the values of y at x = X₀ + 0.1 and x = X₀ + 0.2, where X₀ is the initial condition x = 0 and y(X₀) = 1.

Given the differential equation:

dy/dx + xy = 3x² - [tex]e^y[/tex] + 2

Rewriting the equation in the form:

dy/dx = -xy + 3x² - [tex]e^y[/tex] + 2

We have the initial condition:

y(0) = 1

Using Euler's method with a step size of h = 0.1:

1. At x = X₀ + 0.1:

  y₁ = y₀ + h * [ -x₀ * y₀ + 3 * x₀² - [tex]e^y_0[/tex] + 2 ]

      = 1 + 0.1 * [ -(0) * (1) + 3 * (0)² - e¹ + 2 ]

      = 1 + 0.1 * (0 - e + 2)

      = 1 + 0.1 * (-e + 2)

      = 1 + 0.1 * (-2.7183 + 2)

      = 1 + 0.1 * (-0.7183)

      = 1 - 0.07183

      ≈ 0.9282

2. At x = X₀ + 0.2:

  y₂ = y₁ + h * [ -x₁ * y₁ + 3 * x₁² - [tex]e^y_1[/tex] + 2 ]

      = 0.9282 + 0.1 * [ -(0.1) * (0.9282) + 3 * (0.1)₂ - [tex]e^{0.9282}[/tex] + 2 ]

      = 0.9282 + 0.1 * (-0.009282 + 0.003 - [tex]e^{0.9282}[/tex] + 2)

      ≈ 0.8281

Therefore, the approximate values of y at x = X₀ + 0.1 and x = X₀ + 0.2 are:

y ≈ 0.9282 (correct to four decimal places) at x = 0.1

y ≈ 0.8281 (correct to four decimal places) at x = 0.2

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Answer:

Step-by-step explanation:

For observers right at the north pole and the south pole, there are only two seasons – an almost six-month long winter night followed by an almost six-month long summer day!

Answer:

y = 2/3 x - 3

Step-by-step explanation:

substitute the given slope and the coordinate into the slope-intercpet form:

y = mx + b  to solve for b,

-1 = 2/3(3) + b

=> b = -3

y = 2/3 x - 3

Answer:

A

Step-by-step explanation:

got it correct in edu