Resolver problema urgente!!!!

The joint density of the polar coordinates R and Θ is f(R,Θ) = 1/(πR), where 0 ≤ R ≤ 1 and 0 ≤ Θ ≤ 2π.

To find the joint density of the polar coordinates R and Θ, we need to use the transformation of variables formula for joint densities. Let us define the transformation from Cartesian coordinates (X, Y) to polar coordinates (R, Θ) as follows:

R = (X^2 + Y^2)^(1/2)

Θ = tan^-1(Y/X)

We can solve for X and Y in terms of R and Θ as follows:

X = R cos(Θ)

Y = R sin(Θ)

We can then compute the Jacobian of this transformation:

|dX/dR dX/dΘ| |cos(Θ) -R sin(Θ)|

| | = | |

|dY/dR dY/dΘ| |sin(Θ) R cos(Θ)|

The determinant of this matrix is R, so the joint density of R and Θ can be obtained as follows:

f(R,Θ) = f(X,Y) * |Jacobian|

= (1/π) * (1/(X^2 + Y^2)) * R

= (1/π) * (1/R^2) * R

= 1/(πR), 0 ≤ R ≤ 1, 0 ≤ Θ ≤ 2π

Therefore, the joint density of the polar coordinates R and Θ is f(R,Θ) = 1/(πR), where 0 ≤ R ≤ 1 and 0 ≤ Θ ≤ 2π.

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Answer:

[tex]49\pi \: cm {}^{2} [/tex]

Step-by-step explanation:

The radius of the circle is 7 so

Area of circle = pi radius² = pi 7² = 49 pi

The values of b0 and b1 are indeed estimates for the slope and intercept, respectively, of the line that relates the two variables.

True.

In simple linear regression, we are trying to model the relationship between two variables, typically denoted by x (the independent variable) and y (the dependent variable). The goal is to find a line of best fit that describes the relationship between x and y.

The line of best fit is typically represented by the equation y = b0 + b1*x, where b0 is the estimated intercept (the value of y when x = 0) and b1 is the estimated slope (the change in y for a one-unit increase in x).

So, in simple linear regression, the values of b0 and b1 are indeed estimates for the slope and intercept, respectively, of the line that relates the two variables.

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The point estimate for the population proportion of all customers who experienced an interruption is 0.131.

To find the point estimate for the population proportion of all customers who experienced an interruption, we need to divide the number of customers who experienced an interruption (72) by the total number of customers sampled (550).

Point estimate = (72 / 550)

After calculating this, we get:

Point estimate ≈ 0.131 (rounded to three decimal places)

So, the point estimate for the population proportion of all customers who experienced an interruption is approximately 0.131.

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Therefore, the least-squares error in the least-squares solution of ax = b is e = ||b - A(A^T A)^(-1) A^T b||^2.

The least-squares solution of ax = b is given by x = (A^T A)^(-1) A^T b, where A is the matrix whose columns are the coefficients of the variables in the system of equations. The least-squares error is the sum of the squares of the residuals, which are the differences between the values of b and the values of ax predicted by the least-squares solution.

The least-squares error can be calculated as follows:

e = ||b - Ax||^2

= ||b - A(A^T A)^(-1) A^T b||^2

where ||.|| denotes the Euclidean norm.

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The traditional (parametric) test for a sample mean assumes that the data is normally distributed. If the data is not normally distributed, then this test may not be appropriate. Additionally, the parametric test assumes that the sample size is sufficiently large (usually greater than 30) in order for the Central Limit Theorem to apply.

If the sample size is too small, then this test may not be reliable. Furthermore, if there are outliers or extreme values in the data, then the parametric test may not accurately reflect the true underlying population. In such cases, non-parametric tests may be more appropriate, as they do not rely on assumptions about the distribution of the data. It is important to carefully consider the nature of the data before choosing a statistical test to ensure accurate and reliable results.

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The proof of "if group G has exactly one subgroup H of order k, then H is normal in G" is explained below.

If a "group-G" has exactly one subgroup H of order k, we want to show that H is normal in G. This means that for any element g in G, when we conjugate H by g, we get H again.

To prove this, we consider the left cosets of H in G. A left coset of H is formed by taking an element g in G and multiplying it with each element of H. Since H is the only subgroup of order k, each left coset has k elements.

Now, we take any element-g from G. Since the left cosets partition G, g must be in one of these left cosets, which we can write as gH.

When we conjugate H by g, we get gHg⁻¹. This means we multiply each element of H by g and then multiply the result by g⁻¹, the inverse of g.

Since G is a group, this multiplication follows the group's properties.  When we multiply any element of H by g and then by g⁻¹, the result is still an element of H.

Because of this, we can conclude that for any element g in G, the conjugate of H by g (gHg⁻¹) is still a subset of H.

Therefore, H is normal in G.

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The given question is incomplete, the complete question is

If a group G has exactly one subgroup H of order k, prove that H is normal in G.

Answer:

[tex]n=\sqrt[3]{-16}[/tex] or n ≈ -2.52

Step-by-step explanation:

If we allow n to represent the unknown number, we can use the equation n^3 / -2 = 8, where we must solve for n

Step 1:  Multiply both sides by -2

(n^3 / -2 = 8) * -2

n^3 = -16

Step 2:  Take the cube root of both sides to find n

∛(n^3) = ∛-16

n ≈ -2.52

You can either use the approximation (rounded to the nearest hundredth) or you can keep the answer as ∛-16, since it's more precise.

The angle that has been marked as x in the parallelogram that has been shown is 160°.

In a parallelogram, opposite angles are congruent, and adjacent angles are supplementary . Thus we must know that when we use the term supplementary what we are saying is that the angles would add up to one hundred and eighty degrees.

We know that the adjacent angle of a parallelogram are supplementary as such we have that;

x + 20 = 180

x = 180 - 20

x = 160°

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The equation, after the translation and reflection would take the form, y = 9 - √ ( x + 3 ).

First, the graph is translated to the left 3 units. You should replace x with ( x + 3 ) in the equation.

New equation: y = √ ( x + 3 )

Then translate the graph up 9 units: Add 9 to the y - value in the equation.

New equation: y = √ ( x + 3 ) + 9

Then finally, we reflect the graph over the x-axis: Change the sign of the y-value in the equation.

New equation: y = - √ ( x + 3 ) + 9

y = 9 - √ ( x + 3 )

In conclusion, option B is correct.

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The standard form of the equation of the parabola is y^2 = -56x.

The standard form of the equation of a parabola with a vertical axis of symmetry is given by:

(y - k)^2 = 4p(x - h)

where (h, k) is the vertex of the parabola, p is the distance from the vertex to the focus (or directrix), and the sign of p depends on the orientation of the parabola.

Since the directrix is y = 14, which is a horizontal line, the axis of symmetry of the parabola is the y-axis. This means that the vertex of the parabola is at the origin (0,0).

The focus of the parabola is (0, -14), which is below the vertex. This means that the parabola opens downwards. The distance from the vertex to the focus (or directrix) is |p| = 14.

Using the formula, we have:

(y - 0)^2 = 4(-14)x

Simplifying and rearranging, we get:

y^2 = -56x

Therefore, the standard form of the equation of the parabola is y^2 = -56x.

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Particle moves with its position given by x= cos(2t) and y= sin (t), where positions are given in feet from the origin and time t is in seconds. The speed of the particle at any time t is v = [tex]\sqrt[/tex](4sin²(2t) + cos²(t)).

For the speed of the particle, we can calculate the magnitude of its velocity vector.

The velocity vector can be obtained by differentiating the position vector with respect to time.

We have the position of the particle as x = cos(2t) and y = sin(t), we can differentiate these equations to find the corresponding velocity components:

vx = dx/dt = -2sin(2t)

vy = dy/dt = cos(t)

The magnitude of the velocity vector (v) is given by the square root of the sum of the squares of its components:

[tex]\sqrt[/tex](vx² + vy²) = [tex]\sqrt[/tex]((-2sin(2t))² + (cos(t))²)

Simplifying this expression:

v = [tex]\sqrt[/tex](4sin²(2t) + cos²(t))

This is the speed of the particle at any given time t.

Note that the speed is not constant but varies with time due to the periodic nature of the sine and cosine functions.

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The probability of selecting a card that is less than 7 or a spade is 4/13.

There are 52 cards in a deck, of which 13 are spades and 4 are less than 7 in each suit (2, 3, 4, 5, 6). There are 3 suits that have cards less than 7, so there are a total of 12 cards less than 7 in the deck.

To find the probability of selecting a card that is less than 7 or a spade, we need to add the probabilities of these two mutually exclusive events.

The probability of selecting a card less than 7 is 12/52, because there are 12 cards less than 7 in the deck.

The probability of selecting a spade is 13/52, because there are 13 spades in the deck.

Since we only want to count the spades that are not also less than 7, we need to subtract the probability of selecting a spade that is also less than 7. There are 9 cards that are both spades and less than 7 (2, 3, 4, 5, 6 of spades), so the probability of selecting a spade that is also less than 7 is 9/52.

Therefore, the probability of selecting a card that is less than 7 or a spade is:

P(less than 7 or spade) = P(less than 7) + P(spade) - P(less than 7 and spade)

= 12/52 + 13/52 - 9/52

= 16/52

= 4/13

So the probability of selecting a card that is less than 7 or a spade is 4/13.

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The point p such that vector v=pq is (-7,-5,2).

We have given the components of vector v as ⟨1.25, −12, 4⟩, and the components of vector q as (8.25, −7, 6). Let the components of the point p be (x, y, z). Then we can write the vector equation as follows:

v = pq → - ->

⟹ ⟨1.25, −12, 4⟩ = ⟨x, y, z⟩ - ⟨8.25, −7, 6⟩

Simplifying this equation, we get:

⟨1.25, −12, 4⟩ = ⟨x − 8.25, y + 7, z − 6⟩

⟹ x − 8.25 = 1.25, y + 7 = −12, and z − 6 = 4

⟹ x = 9.5, y = −19, and z = 10

Therefore, the point p is (9.5, −19, 10).

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Step-by-step explanation:

Circumference of a Circle = 2[tex]\pi[/tex]r

Diameter = 2r

1. Find the Radius (r)

35/2 cm = 2r

r = 8.75 cm

2. Plug into the Circumference Equation

C = 2 * (22/7) * (8.75)

C = 55 cm.

AnswerD.153

Step-by-step explanation:

multiply 17x9

To find the percent error between an estimated value and an actual value, we can use the formula: percent error = (|estimated value - actual value| / actual value) * 100.

To calculate the percent error, we first find the absolute difference between the estimated value and the actual value: |estimated value - actual value|. In this case, |56 - 43| = 13.

Next, we divide the absolute difference by the actual value: 13 / 43.

To express the result as a percentage, we multiply the quotient by 100: (13 / 43) * 100.

Calculating this expression gives us the percent error.

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To find the probability that a student gets at most 4 correct answers when guessing on all 12 multiple-choice questions, we can use the binomial probability formula.

The probability of guessing a correct answer on a single question is 1/4 since there are 4 choices for each question.

Now, let's calculate the probability of getting exactly 0, 1, 2, 3, or 4 correct answers and sum them up to find the probability of getting at most 4 correct answers.

P(X ≤ 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

Using the binomial probability formula, where n is the number of trials (12 questions) and p is the probability of success (1/4):

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

Let's calculate each individual probability and sum them up:

P(X ≤ 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

= C(12, 0) * (1/4)^0 * (3/4)^12 + C(12, 1) * (1/4)^1 * (3/4)^11 + C(12, 2) * (1/4)^2 * (3/4)^10 + C(12, 3) * (1/4)^3 * (3/4)^9 + C(12, 4) * (1/4)^4 * (3/4)^8

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The probability of matching 4 balls from 5 draws from 50 balls in the lottery game is approximately 0.0978, or 9.78%.

To calculate the probability of matching 4 balls from 5 draws from 50 balls in a lottery game, we can use the combination formula.

The total number of ways to choose 4 balls from 50 is given by the combination formula:

C(50, 4) = 50! / (4! * (50 - 4)!) = 50! / (4! * 46!)

Similarly, the total number of ways to choose 5 balls from 50 is given by:

C(50, 5) = 50! / (5! * (50 - 5)!) = 50! / (5! * 45!)

The probability of matching 4 balls from 5 draws can be calculated by dividing the number of successful outcomes (matching 4 balls) by the total number of possible outcomes (choosing 5 balls from 50).

Probability = C(50, 4) / C(50, 5)

Substituting the values:

Probability = (50! / (4! * 46!)) / (50! / (5! * 45!))

Simplifying the expression:

Probability = (5! * 45!) / (4! * 46!)

Calculating the numerical value of the probability:

Probability = 5 * 45 / (4 * 46) ≈ 0.0978

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The distance traveled by the particle over the time interval [0, 5] is approximately 3.76 units.

We can find the distance traveled by the particle by calculating the length of the curve traced out by its path over the given time interval.

The length of the curve can be found using the arc length formula:

L = ∫[a, b] sqrt(dx/dt)² + (dy/dt)² dt

In this case, we have:

x = 4 sin²(t)

y = 4 cos²(t)

Taking the derivatives of x and y with respect to t, we get:

dx/dt = 8 sin(t) cos(t)

dy/dt = -8 sin(t) cos(t)

So, the length of the curve is:

L = ∫[0, 5] sqrt((8 sin(t) cos(t))² + (-8 sin(t) cos(t))²) dt

= ∫[0, 5] sqrt(64 sin²(t) cos²(t) + 64 sin²(t) cos²(t)) dt

= ∫[0, 5] sqrt(128 sin²(t) cos²(t)) dt

= ∫[0, 5] 8 sin(t) cos(t) dt

= 4 ∫[0, 5] sin(2t) dt

= 4 [-cos(2t)/2] from 0 to 5

= 2(cos(0) - cos(10))

≈ 3.76 units.

Therefore, the distance traveled by the particle over the time interval [0, 5] is approximately 3.76 units.

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The correct slope of the tangent line to y = f(t)g(2) at the point where r = 3 is 21, not 14 as Adam entered.

To find the slope of the tangent line to the function y = f(t)g(2) at the point where r = 3, we can use the product rule of differentiation. Let's analyze Adam's approach and identify the mistake(s).

Adam's mistake is in assuming that the slope of the tangent line to y = f(x)g(x) at the point where x = 3 is simply the product of the slopes of the individual tangent lines to f(x) and g(x) at x = 3. This assumption is incorrect because the product rule accounts for the interaction between the two functions.

To find the slope of the tangent line to y = f(t)g(2) at the point where r = 3, we need to apply the product rule:

(dy/dt) = (f'(t) * g(2)) + (f(t) * g'(2))

Given the information provided, we know:

f(3) = 5

f'(3) = 2

g(3) = -7

g'(3) = 7

Now, let's substitute these values into the product rule equation:

(dy/dt) = (f'(t) * g(2)) + (f(t) * g'(2))

(dy/dt) = (2 * g(2)) + (f(t) * 7)

(dy/dt) = (2 * g(2)) + (5 * 7)

(dy/dt) = (2 * g(2)) + 35

Since we are interested in the slope at the point where r = 3, we substitute r = 3 into the equation:

(dy/dt) = (2 * g(2)) + 35

(dy/dt) = (2 * (-7)) + 35

(dy/dt) = -14 + 35

(dy/dt) = 21

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The probability that the 5th card is the queen of spades is 4.9 x 10^-8 .

To calculate the probability, we can use the multiplication rule of probability, which states that the probability of two independent events occurring together is the product of their individual probabilities.

There are 52 cards in a standard deck, and only one of them is the queen of spades. When the first card is dealt, there are 52 possible cards that could be dealt.

Since the cards are well-shuffled, each of these 52 cards is equally likely to be chosen.

Therefore, the probability that the first card is the queen of spades is 1/52.

Assuming that the queen of spades was not the first card dealt, there are now only 51 cards left in the deck, and only one of them is the queen of spades.

So the probability that the second card is the queen of spades is 1/51.

The probability that the third card is the queen of spades is 1/50, the probability that the fourth card is the queen of spades is 1/49, and the probability that the fifth card is the queen of spades is 1/48.

Therefore, the probability that the fifth card is the queen of spades is the product of these individual probabilities:

P(queen of spades is fifth card) = (1/52) x (51/52) x (1/51) x (50/51) x (1/50) x (49/50) x (1/49) x (48/48)

Simplifying this expression, we get:

P(queen of spades is fifth card) = 1/52 x 1/51 x 1/50 x 1/49

P(queen of spades is fifth card) ≈ 0.000000049 or 4.9 x 10^-8

Therefore, the probability that the fifth card is the queen of spades is very low, at approximately 4.9 in 100 million.

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(a) The lower bound of the confidence interval is 7.917 minutes.

(b) The upper bound of the confidence interval is 8.483 minutes.

(c) The margin of error is 0.283 minutes.

(a) The point estimate of the population mean is 8.2 minutes.

To calculate the lower bound of the 90% confidence interval, we use the formula: lower bound = point estimate - z* (standard error), where z* is the z-score for the 90% confidence level, which is 1.645, and the standard error is equal to the population standard deviation divided by the square root of the sample size, i.e., 2.2 / sqrt(200) = 0.156.

Substituting these values in the formula, we get the lower bound as 8.2 - 1.645 * 0.156 = 7.917 minutes.

(b) To calculate the upper bound of the 90% confidence interval, we use the same formula: upper bound = point estimate + z* (standard error). Substituting the values, we get the upper bound as 8.2 + 1.645 * 0.156 = 8.483 minutes.

(c) The margin of error is the difference between the point estimate and the upper or lower bound of the confidence interval. In this case, it is equal to half the width of the confidence interval, which is (8.483 - 7.917) / 2 = 0.283 minutes.

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The measure of lengths of the right triangle is solved by trigonometric relations and

a) A = 32°

b) b = 22.4 units

c) c = 26.4 units

Given data ,

Let the triangle be represented as ΔABC

Now , the measure of sides of the triangle are

The measure of ∠A = 180° - ( 90° + 58° )

The measure of ∠A = 32°

From the trigonometric relation , we get

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

So , tan 58° = b / 14

Multiply by 14 on both sides , we get

b = 22.4 units

Now , sin 58° = 22.4 / c

Multiply by c on both sides , we get

c = 22.4 / sin 58°

c = 26.4 units

Hence , the triangle is solved

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Answer:

C.  19

Step-by-step explanation:

Given inequalities:

An integral value refers to a value that is a whole number, either positive, negative, or zero.

The greatest possible integral value of b - a is when b is its greatest value and a is its smallest value.

The greatest value of b is 12.

The smallest value of a is -7.

Therefore:

[tex]\begin{aligned}b-a&=12-(-7)\\&=12+7\\&=19\end{aligned}[/tex]

So the greatest possible integral value of b - a is 19.

The expected return on this portfolio is 5%.

1. Assign probabilities to each scenario:

In this case, since each scenario is equally likely, we assign a probability of 1/3 to each scenario. This means that there is a 1/3 chance of a financial boom, a 1/3 chance of normal times, and a 1/3 chance of a recession.

2. Calculate the expected return:

To calculate the expected return, we multiply the return for each scenario by its respective probability and sum up the results.

a. Financial Boom Return:

The return during a financial boom is 18%. Multiplying it by the probability of 1/3 gives us:

Financial Boom Return = 18% * (1/3) = 6%

b. Normal Times Return:

The return during normal times is 9%. Multiplying it by the probability of 1/3 gives us:

Normal Times Return = 9% * (1/3) = 3%

c. Recession Return:

The return during a recession is -12%. Multiplying it by the probability of 1/3 gives us:

Recession Return = -12% * (1/3) = -4%

Now we can sum up the results to obtain the expected return:

Expected Return = Financial Boom Return + Normal Times Return + Recession Return

Expected Return = 6% + 3% - 4%

Expected Return = 5%

Therefore, the expected return on this portfolio, assuming each scenario is equally likely, is 5%.

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Using these traces, we can sketch the surface as an ellipsoid in three dimensions centered at the origin, with semi-major axis of length 6 along the z-axis, semi-major axis of length 3 along the y-axis, and semi-major axis of length 2 along the x-axis.

To sketch the surface 9x^2 + 4y^2 + z^2 = 36 using traces, we can fix values of x, y, and z and plot the resulting curves. When we fix x = 0, we get 4y^2 + z^2 = 36, which is an ellipse in the yz-plane centered at the origin with semi-major axis of length 6 along the z-axis and semi-minor axis of length 3 along the y-axis.

When we fix y = 0, we get 9x^2 + z^2 = 36, which is also an ellipse in the xz-plane centered at the origin with semi-major axis of length 6 along the z-axis and semi-minor axis of length 2 along the x-axis. When we fix z = 0, we get 9x^2 + 4y^2 = 36, which is a horizontal ellipse in the xy-plane centered at the origin with semi-major axis of length 2 along the x-axis and semi-minor axis of length 3 along the y-axis.

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The probability are: P(Lyme Disease) = 0.35, P(Arthritis) = 0.8, P(Lyme Disease or Arthritis) = 0.97, P(Lyme Disease and Arthritis) = 0.15

To calculate the probabilities, we need to understand the concepts of probability and set theory.

Let's define:

L = Event of having Lyme Disease

A = Event of having Arthritis

Given information:

Total dogs tested = 120

Dogs with Lyme Disease (L) = 42

Dogs with Arthritis (A) = 96

Dogs with both Lyme Disease and Arthritis (L ∩ A) = 18

We can calculate the probabilities using the following formulas:

1. P(Lyme Disease): Probability of having Lyme Disease

P(L) = (Number of dogs with Lyme Disease) / (Total number of dogs tested)

P(L) = 42 / 120

P(L) = 0.35

2. P(Arthritis): Probability of having Arthritis

P(A) = (Number of dogs with Arthritis) / (Total number of dogs tested)

P(A) = 96 / 120

P(A) = 0.8

3. P(Lyme Disease or Arthritis): Probability of having Lyme Disease or Arthritis

P(L or A) = P(L) + P(A) - P(L ∩ A)

P(L or A) = 0.35 + 0.8 - 0.18

P(L or A) = 0.97

4. P(Lyme Disease and Arthritis): Probability of having both Lyme Disease and Arthritis

P(L and A) = P(L ∩ A) / (Total number of dogs tested)

P(L and A) = 18 / 120

P(L and A) = 0.15

Therefore:

- P(Lyme Disease) = 0.35

- P(Arthritis) = 0.8

- P(Lyme Disease or Arthritis) = 0.97

- P(Lyme Disease and Arthritis) = 0.15

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