A pair of dice is rolled and \( X \) is the random variable defined as the absolute value of the difference of the numbers of dots facing up on two dice. What is the expected value of \( X \).

Answer:

It is given that the North Pole is at a distance of 3,949 miles from the center of the earth. We also know that the sea floor is below 2.4 miles from the sea level. 3949 - 2.4 = 3946.6 miles

Answer:

16

Step-by-step explanation:

Answer:

yes

yes

yes

no

Step-by-step explanation:

The general integral is provided by y = C1e-t + C2te-t + (1/2)(t2)e-t.

(m + 1)2 =0 is the characteristic polynomial for the differential equation y" +2y' + y = e-t.

Roots -1, -1. yh = C1e-t + C2te-t is the answer to the homogeneous equation at that point.

Use the method of variation of parameters, taking into account the independent integrals y1 = e-t, y2 = te-t, and Wronskian

W(t) = e-2t, to derive the specific integral related to f(t) = e-t.

Then, use the conventional formula yp = - y1(t)(Integral of Y2(t)f(t)dt/W(t)) +y

Obtain yp = (1/2)(t2)e-t for the given situation.

As a result, the general integral is provided by

y = C1e-t + C2te-t + (1/2)(t2)e-t.

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Answer:

23

Step-by-step explanation:

10.6 > 11

7.067 > 7

4.78 > 5

11+7+5=23

Answer:

3.0pages

Step-by-step explanation:

If Tiffany type a page in an hour, then;;

1 page = 1 hour

To calculate the number of pages typed in 3 hours, we can express as;

x pages = 3 hours

Divide both expressions

1/x = 1/3

x* 1 = 1* 3

x = 3pages

She will type 3.0pages in 3 hours

a) The simplified left-hand side of the equation as B + CD + BD. Therefore, the equation is true. b) The simplified left-hand side of the equation as 2WY + WXZ + WYZ. Therefore, the equation is true. c) The left-hand side of the equation is also AD + AB + CD + BC, the equation is true.

(a) Using algebraic manipulation, we can simplify the left-hand side of the equation as follows:

ABC + BCD + BC + CD = BC(A + D) + CD(A + B)

= BC + CD (A + B + D)

Since B + CD = B(1 + D) + CD = B + CD + BD, we can rewrite the simplified left-hand side of the equation as B + CD + BD. Therefore, the equation is true.

(b) Similarly, we can simplify the left-hand side of the equation as follows:

WY + WYZ + WXZ + WXY = WY(1 + Z) + WX(Z + Y)

= WY + WXZ + WYZ + XYZ

Since WY + WXZ + XYZ = WY + WXZ + WY(1 + Z) = WY + WXZ + WY + WYZ = 2WY + WXZ + WYZ, we can rewrite the simplified left-hand side of the equation as 2WY + WXZ + WYZ. Therefore, the equation is true.

(c) Using algebraic manipulation, we can expand the right-hand side of the equation as follows:

(A + B + C + D)(A + B + C + D) = A2 + B2 + C2 + D2 + AB + AC + AD + BC + BD + CD

= AD + AB + CD + BC + A2 + B2 + C2 + D2 + AB + AC + BD

= AD + AB + CD + BC (A + B + C + D + A + B + C + D)

Since the left-hand side of the equation is also AD + AB + CD + BC, the equation is true.

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The rectangle-shaped tank is 10 feet by 8 feet by 8 feet is  4800 gallons of water.

Cubic foot holds 7.5 gallons of water

We need to find the amount of gallons of water can a rectangle-shaped tank is 10 feet by 8 feet by 8 feet.

Vol = L*W*H

10 x 8 x 8

640 cubic feet

1 cubic feet hold 7.5 gallons of water

640 cubic feet hold 7.5 x 640 = 4800

Therefore, the amount of gallons of water can a rectangle-shaped tank is 10 feet by 8 feet by 8 feet is  4800 gallons of water.

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Answer:

12-c

Step-by-step explanation:

Let c be Cindy's cookies

Solution:

Each child should have gotten 12 cookies because 96/8 is 12 but Cindy got c less so the answer would be 12-c.

The equations in  slope-intercept form are:

A. y = x - 5

B. y = -x + 1

The equation where m is the slope and b is the y-intercept, in slope-intercept form is given as y = mx + b.

If two lines are parallel, their slope will be the same, if they are perpendicular, their slope will be negative reciprocals of each other.

Part A: The slope (m) of the equation y = x + 4 is 1. The line parallel to the equation will have the same slope as m = 1.

Substitute m = 1 and (x, y) = (3, -2) into y = mx + b to find b:

-2 = 1(3) + b

-2 - 3 = b

b = -5

Write the equation in slope-intercept from by substituting b = -5 and m = 1 into y = mx + b:

y = x - 5

Part B: The slope (m) of the equation y = x + 4 is 1. The negative reciprocal of 1 is -1. Therefore, the line that is perpendicular to the equation will the slope as , m = -1.

Substitute m = -1 and (x, y) = (3, -2) into y = mx + b to find b:

-2 = -1(3) + b

-2 + 3 = b

b = 1

Write the equation in slope-intercept form by substituting b = -5 and m = -1 into y = mx + b:

y = -x + 1

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The gradient of the function f(x, y) = √(x² + y² is (∂f/∂x, ∂f/∂y) = (x / √(x² + y²), y / √(x² + y²)).

To find the gradient of the function f(x, y) = √(x² + y²), we need to calculate the partial derivatives with respect to x and y. Taking the partial derivative with respect to x, we use the chain rule to obtain (∂f/∂x) = x / √(x² + y²). Similarly, taking the partial derivative with respect to y, we have (∂f/∂y) = y / √(x² + y²).

The gradient represents the rate of change of the function in each direction. In this case, it gives us the direction and magnitude of the steepest ascent of the function at each point. The magnitude of the gradient vector (∂f/∂x, ∂f/∂y) is the rate of change of the function in that direction.

Therefore, the gradient of f(x, y) = √(x² + y²) is (∂f/∂x, ∂f/∂y) = (x / √(x² + y²), y / √(x² + y²)), representing the direction and magnitude of the steepest ascent of the function.

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Answer:

Option A would be the best option, as the payment would not change. Option B has a lower payment, but that payment is expected to rise and eventually be a bigger payment. Option C would require them to pay it off in 8 years, which would be too much based on their income and they would end up having to get another mortgage. Option C would be better if they wanted to live their temporarily, but Demarco and Tanya would like to live in their house permanently. This makes option A the best option because it is an affordable payment that will not change.

Step-by-step explanation:

The best option will be option A which will be chosen by Demarco and Tanya.

Finance deals with the study of money, management, creation, and investments. Also, finance is divided into the following board of categories such as personal finance, corporate finance, and public finance.

The best option will be option A which will be chosen by Demarco and Tanya as the payment plan would not change in this situation.

Option B has a lower payment, but the payment is expected to increase with time and eventually be a bigger payment.

Also, option C would require them to pay it off in 8 years but both of them want to live permanently not separately. Therefore, the best option to choose will be option A.

So, The best option will be option A which will be chosen by Demarco and Tanya.

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Answer:

Step-by-step explanation:

Scale factor is 2. 6/3=2, 8/4=2. So it’s 1/2

Answer:

i think 5

Step-by-step explanation:

Answer:

Hope this helps!!!!!!

Mark Brainlest!!!!!!!!!!

Step-by-step explanation:

Mark and Henry win some money and share it in the ratio 1:3. Mark gets £9. How much did Henry get?

Ratio = 1 : 3

Let Mark's share be 1x = x

and Henry's share be 3x

We know that Mark gets £9

So,

1x = x = £9

Then 3x = £(3 * 9) = £27

HENCE,

Mark's share = £9

Henry's share = £27

Total money = Mark's share + Henry's share = £9 + £27 = £36

Answer:

£27

Step-by-step explanation:

so it shows mark is 1 while Henry is 3

we know that Mark is 1/4 while Henry is 3/4

/4 because the total is 4 so whatever their ratio is over their total

so we do: 1 = 9

3 = ?

and then u cross multiply

3*9 = 27 ÷ 1 = 27

so Henry receives £27

Answer:

We can use trigonometry to solve this problem. The angle of elevation is the angle between the horizontal line and the line of sight from the observer to the top of the building.

We are given the angle of elevation (41°) and the distance from the observer to the building (60 feet).

We can use the tangent function to find the height of the building:

tan(41°) = height / 60

To find the height of the building we can multiply both sides of the equation by 60:

height = tan(41°) * 60

The height of the building is approximately 41.56 feet

Answer: Each paper clip is \(1\frac{1}{3}\)

Step-by-step explanation:

Simply divide how long the notebook is, by how many paper clips there are, \(10\frac{2}3}\) divided by 8.

Answer: you forgot to carry the 2

Step-by-step explanation: because i'm smart

Answer:

x-intercept: (2,0)

y-intercept: (0,-4/3)

vertical asymptote: x = -3

Step-by-step explanation:

To find the x-intercepts, we can set f(x) to 0, which is y=0:

2x-4/x+3 = 0

2x-4 = 0

2x = 4

x = 2

To find the y-intercepts, we can set x to 0:

2(0)-4/(0)+3 = y

y = -4/3

To find the vertical asymptote, we can set the denominator equal to 0:

x+3 = 0

x = -3

Answer:

\(x = \pm2 \sqrt 5\)

Step-by-step explanation:

\(~~~~~~x^2=20\\\\\implies x = \pm\sqrt{20}\\\\\implies x = \pm \sqrt{ 4 \times 5}\\\\\implies x = \pm2 \sqrt 5\)

The solution of the given equation is x = ± 2√5.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Given is an equation, x² = 20, we need to find the solution of the equation,

Therefore,

x² = 20

x = √20 or x = -√20

Now, √20 = √4×5 = 2√5

Therefore,

x = ± 2√5

Hence the solution of the given equation is x = ± 2√5.

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Answer:

see picture

Step-by-step explanation:

Answer: 7,176 inches

Step-by-step explanation:

Areas equation is Length times width so applying that we have 78 times 92 giving you the answer of 7,176

The given sequence {0,1,0,0,1,0,0,0,1} converges to 1.

A convergent sequence is a sequence of numbers where the sequence approaches on something, that is the the limit exists.

It is finite.

Divergent sequence are sequences which does not contain the limit. The limit will be ±∞.

Given sequence is {0,1,0,0,1,0,0,0,1}.

Here there are 9 numbers in the sequence.

This sequence isfinite and approaches to 1.

So the limit is 1 and the sequence converges.

If the sequence was {0,1,0,0,1,0,0,0,1, ......}, the sequence is continuing.

The terms are either 0 or 1.

But it does not end.

So the sequence diverges.

Hence the given sequence converges to 1.

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The graph of the equation 7x² + 3 = y² is symmetric with respect to B. X-axis and y-axis only.

To test for symmetry with respect to the x-axis, y-axis, and the origin, we need to check if replacing 'x' with '-x', 'y' with '-y', or both leaves the equation unchanged.

For the given equation, when we replace 'x' with '-x', the equation becomes 7(-x)² + 3 = y², which simplifies to 7x² + 3 = y². This indicates that the equation remains the same, so the graph is symmetric with respect to the y-axis.

When we replace 'y' with '-y', the equation becomes 7x² + 3 = (-y)², which simplifies to 7x² + 3 = y². Again, the equation remains the same, indicating symmetry with respect to the origin.

However, when we replace both 'x' with '-x' and 'y' with '-y', the equation becomes 7(-x)² + 3 = (-y)², which simplifies to 7x² + 3 = y². Here, the equation does not remain the same, indicating that the graph is not symmetric with respect to the x-axis.

To visually verify these symmetries, one can use a graphing calculator to plot the graph of the equation. The graph will exhibit symmetry with respect to the y-axis and the origin, but not with respect to the x-axis. Therefore, the correct answer is B. X-axis and y-axis only.

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The coordinates are simple. Hope you understand this and you can draw it out.

Answer: the right answer is D

Step-by-step explanation:

If you multiply 4 by 2 you get 8. If this goes on the answers are aways the same and it’s going to be proportional

Answer:

m=2

Step-by-step explanation:

-16=m-18

-16+18=m

2=m

Answer:

2 dollars and 35 cents

Step-by-step explanation:

Three quaters its 75 cents plus five dimes its 50 cents plus 22 nickels its 110 in total its $2.35

EXPLANATION:

Given;

We are given two triangles labeled MRS and NSR.

Required;

We are required touse the information provided rto rove tside SM is equal to side RN.

Solution;

If two sides and the included angle of one triangle are congruent to the corresponding parts of a second triangle, then we can conclude that both triangles are congruent.

Therefore;

The gradient of the marginal log-likelihood can be represented as the posterior-expected gradient of the complete-data log-likelihood, and when EM converges, it converges at a local optimum of the MLL.

6.1. To show that the gradient of the marginal log-likelihood can be represented as the posterior-expected gradient of the complete-data log-likelihood, we will apply the chain rule to the logarithm function.

Let's consider the marginal log-likelihood, denoted as L(θ), which is the log probability of the observed data:

L(θ) = log p(x)

Using the chain rule, we can express the gradient of the marginal log-likelihood:

∇_θ L(θ) = ∇_θ log p(x)

Next, let's consider the complete-data log-likelihood, denoted as Q(θ, z), which is the log probability of both the observed data and the unobserved latent variables:

Q(θ, z) = log p(x, z)

The gradient of the complete-data log-likelihood can be expressed as:

∇_θ Q(θ, z)

Now, we want to show that the gradient of the marginal log-likelihood can be represented as the posterior-expected gradient of the complete-data log-likelihood:

∇_θ L(θ) = E_p(z|x) [∇_θ Q(θ, z)]

To prove this, we need to compute the expectation of the gradient of the complete-data log-likelihood with respect to the posterior distribution of the latent variables given the observed data.

Taking the expectation with respect to the posterior distribution, denoted as p(z|x), we have:

E_p(z|x) [∇_θ Q(θ, z)] = ∫ [∇_θ Q(θ, z)] p(z|x) dz

Now, using the property of logarithms, we know that the logarithm of a product is equal to the sum of the logarithms:

log p(x, z) = log p(x|z) + log p(z)

Applying the chain rule to the logarithm function in the complete-data log-likelihood:

∇_θ Q(θ, z) = ∇_θ [log p(x|z) + log p(z)]

= ∇_θ log p(x|z) + ∇_θ log p(z)

Now, substituting this back into the expression for the expected gradient:

E_p(z|x) [∇_θ Q(θ, z)] = ∫ [∇_θ log p(x|z) + ∇_θ log p(z)] p(z|x) dz

= ∫ ∇_θ log p(x|z) p(z|x) dz + ∫ ∇_θ log p(z) p(z|x) dz

= ∇_θ ∫ log p(x|z) p(z|x) dz + ∫ ∇_θ log p(z) p(z|x) dz

= ∇_θ ∫ p(z|x) log p(x|z) dz + ∇_θ ∫ p(z|x) log p(z) dz

= ∇_θ ∫ p(z|x) [log p(x|z) + log p(z)] dz

= ∇_θ ∫ p(z|x) log p(x, z) dz

= ∇_θ ∫ p(z|x) [log p(x, z) - log p(x)] dz

Using the definition of conditional probability, p(z|x) = p(x, z) / p(x), we have:

∇_θ ∫ p(z|x) [log p(x, z) - log p(x)] dz = ∇_θ ∫ p(z|x) log [p(x, z) / p(x)] dz

Since the integral of p(z|x) over all possible values of z equals 1, we can simplify this expression further:

∇_θ ∫ p(z|x) log [p(x, z) / p(x)] dz = ∇_θ E_p(z|x) [log [p(x, z) / p(x)]]

= ∇_θ E_p(z|x) [log p(x, z)] - ∇_θ E_p(z|x) [log p(x)]

Now, we know that the term ∇_θ E_p(z|x) [log p(x)] is zero since it does not depend on θ. Therefore, we are left with:

∇_θ L(θ) = E_p(z|x) [∇_θ Q(θ, z)]

This proves that the gradient of the marginal log-likelihood can be represented as the posterior-expected gradient of the complete-data log-likelihood.

6.2. The fact that EM converges to a local optimum of the MLL can be shown using the result from 6.1.

In the EM algorithm, the E-step involves computing the posterior distribution of the latent variables given the observed data, and the M-step involves maximizing the expected complete-data log-likelihood with respect to the model parameters.

By maximizing the expected complete-data log-likelihood, we are effectively maximizing the posterior-expected complete-data log-likelihood. From 6.1, we know that the gradient of the marginal log-likelihood is equal to the posterior-expected gradient of the complete-data log-likelihood.

Since EM iteratively updates the parameters by maximizing the expected complete-data log-likelihood, it follows that the updates are driven by the gradients of the marginal log-likelihood. As a result, EM converges to a local optimum of the marginal log-likelihood.

Therefore, when EM converges, it converges at a local optimum of the MLL.

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