Please solve! Solve for Y.

The population density of Kansas in people per square mile is 35.7.

From the given data table, we can see that data of different states are given with their population in the year 2020 and area in mile square. To find the population density of Kansas, we require :

Population of Kanas = 2,937,880

Area of Kanas = 82,278.36

Population density = Population / Area

Substituting values we get,

Population density = 2937880/82278.36

Population density = 35.7065941 people per square mile

Rounding to the nearest tenth we get,

Population density = 35.7 people per square mile

Therefore, Population density of Kansas in people per square mile is 35.7.

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The value of b = -3/2 and c = -5/4

To write the quadratic x² - 3x + 1 in the form (x + b)² + c, we can expand (x + b)² and compare it to the given expression:

(x + b)² = x² + 2bx + b²

Comparing this to the given expression x² - 3x + 1, we see that we need:

2bx = -3x, so b = -3/2

b² + c = 1, so substituting b = -3/2 gives:

(9/4) + c = 1

so c = 1 - 9/4

= 4/4 - 9/4

= -5/4

The quadratic x² - 3x + 1 can be written in the form (x - 3/2)² + ( - 5/4).

Therefore, the value of b = -3/2 and c = -5/4

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Given question is incomplete, the complete question is below

the quadratic x²-3x + 1 can be written in the form (x +b)² + c, where b and c are constants. what is b, c?

The factored function is given as follows:

[tex]x^4 + 2x^3 - 20x^2 + 64x - 32 = (x^2 + 6x - 4)(x^2 - 4x + 8)[/tex]

The function for this problem is defined as follows:

[tex]y = x^4 + 2x^3 - 20x^2 + 64x - 32[/tex]

The zeros are given as follows:

Hence the function is factored as follows:

[tex]x^4 + 2x^3 - 20x^2 + 64x - 32 = (ax^2 + bx + c)(x - 2 + 2i)(x - 2 - 2i)[/tex]

[tex]x^4 + 2x^3 - 20x^2 + 64x - 32 = (ax^2 + bx + c)(x^2 - 4x + 8)[/tex]

[tex]x^4 + 2x^3 - 20x^2 + 64x - 32 = ax^4 + (-4 + b)x^3 + \cdots + 8c[/tex]

Hence the value of a is given as follows:

a = 1.

The value of b is given as follows:

-4 + b = 2

b = 6.

The value of c is given as follows:

8c = -32

c = -4.

Hence the factored expression is of:

[tex]x^4 + 2x^3 - 20x^2 + 64x - 32 = (x^2 + 6x - 4)(x^2 - 4x + 8)[/tex]

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Thus,  there are 60,949,324,800 different batting orders possible. The correct option is A.

The number of different batting orders for a 20-person baseball roster with 9 people in each batting order can be calculated using the concept of permutations. In this case, we have 20 players to choose from, and we need to arrange 9 of them in a specific order.

The formula for permutations is: P(n, r) = n! / (n - r)!, where n is the total number of items (20 players), r is the number of items to be arranged (9 players), and ! denotes the factorial of a number (the product of all positive integers up to that number).

Applying this formula for your problem:
P(20, 9) = 20! / (20 - 9)!

Calculating the factorials:
20! = 2,432,902,008,176,640,000
11! = 39,916,800

Now, divide the factorials:
P(20, 9) = 2,432,902,008,176,640,000 / 39,916,800

P(20, 9) = 60,949,324,800

So, there are 60,949,324,800 different batting orders possible. The correct option is A.

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The probability of an event occurring 4 standard deviations from the mean in a normal distribution is extremely low. Specifically, the probability of an event occurring 4 standard deviations from the mean in a normal distribution is approximately 0.006%.

In a normal distribution, 68% of the values are within one standard deviation of the mean, 95% are within two standard deviations of the mean, and 99.7% are within three standard deviations of the mean. So, an event that is 4 standard deviations from the mean is extremely unlikely to occur.

This is because the empirical rule states that in a normal distribution, approximately 68% of observations will fall within 1 standard deviation of the mean, 95% of observations will fall within 2 standard deviations of the mean, and 99.7% of observations will fall within 3 standard deviations of the mean. Thus, the probability of an observation falling more than 3 standard deviations from the mean is very small, and the probability of it falling 4 or more standard deviations from the mean is even smaller. This demonstrates the importance of considering outliers and extreme values when analyzing data in a normal distribution.

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The experimental probability is 29/100 and the number of workers that walk is 1102

The experimental probability of an event is based on the number of times the event has occurred during the experiment and the total number of times the experiment was conducted. Each possible outcome is uncertain and the set of all the possible outcomes is called the sample space.

The formula for this is given as;

P(E) = Number of occurrence of an event / Total number of times experiment is carried out.

a. Experimental probability = 29/100

b. To predict the total number of workers that walk, we can go as;

(29/100) * 3800 = 1102

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The solutions of the equation [tex]x^2 - 2x - 8 = 0[/tex] expressed in the form a + bi are 4 + 0i and -2 + 0i

To find the solutions of the equation [tex]x^2 - 2x - 8 = 0,[/tex]  we can use the quadratic formula:

[tex]x = (-b \pm \sqrt{(b^2 - 4ac)) / (2a), }[/tex]

where a, b, and c are the coefficients of the quadratic equation [tex]ax^2 + bx + c = 0.[/tex]

In this case, the coefficients are:

a = 1

b = -2

c = -8

Plugging these values into the quadratic formula, we get:

[tex]x = (-(-2) \pm \sqrt{ ((-2)^2 - 4(1)(-8))) / (2(1)) }[/tex]

= (2 ± √(4 + 32)) / 2

= (2 ± √36) / 2

= (2 ± 6) / 2

We have two possible solutions:

x = (2 + 6) / 2 = 8 / 2 = 4

x = (2 - 6) / 2 = -4 / 2 = -2

Therefore, the solutions to the equation[tex]x^2 - 2x - 8 = 0[/tex] are x = 4 and x = -2.

Expressing them in the form a + bi, where a and b are real numbers and i is the imaginary unit, we have:

x = 4 + 0i

x = -2 + 0i

Since both solutions are real numbers, there is no need to express them in the form a + bi. The solutions are 4 and -2.

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To identify the constant of proportionality based on a verbal description of the proportional relationship, we need to look for keywords that suggest proportionality.

These keywords include "directly proportional," "inversely proportional," "proportional to," or "varies directly/inversely." Once we have identified the keywords that suggest proportionality, we can then look for the quantities that are related and the specific values they take. From there, we can set up a proportion and solve for the constant of proportionality.

For example, if we are told that the time it takes to complete a task is directly proportional to the number of workers, and it takes 6 workers 4 hours to complete the task, we can set up the proportion: time/number of workers = constant of proportionality. Plugging in the values we have, we get 4/6 = k, which simplifies to 2/3 = k.

Therefore, the constant of proportionality in this case is 2/3, and we can use this to find the time it would take with a different number of workers.

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The amount of the principal investment is the sum of $10,000. The Option D is correct.

The equation "A = P(1+0.0430t)" represents the amount of money earned on a savings account with 4.3% annual simple interest, where a is the amount after t years, p is the principal investment, and 0.043 is the interest rate.

Given that the amount after 12 years is equal to $15,160, we can use the equation to solve for the principal investment:

[tex]\sf A = P(1+0.0430t)[/tex]

[tex]\sf \$15160 = P(1+0.043\times12)[/tex]

[tex]\sf\$15160 = P(1 + 0.516)[/tex]

[tex]\sf \$15160= P \times 1.516[/tex]

[tex]\sf P = \dfrac{\$15160}{1.516}[/tex]

[tex]\sf P = \$10000[/tex].

Therefore, the amount of the principal investment is the sum of $10,000.

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Answer:

-1 ± 2√10

Step-by-step explanation:

first of all, do -2 on top divided by 2 on bottom to get 1st part of answer -1.

now (2√40) / 2 = 1√40 which just equals √40.

√40 = √(4 X 10) = √4 X √10 = 2 X √10 = 2√10.

so our final answer becomes -1 ± 2√10

The recursive sequence to represent how many papers Josiah has remaining to grade after working for n hours is aₙ = aₙ₋₁ - 8

Let aₙ be the number of papers Josiah has remaining to grade after working for n hours.

In the first hour, Josiah grades 8 papers, so the number of papers remaining is:

a₁ = 44 - 8 = 36

In the second hour, Josiah grades another 8 papers, but this time he is grading papers from the remaining pile:

a₂ = a₁ - 8

= 36 - 8 = 28

In general, after n hours, Josiah will have graded 8n papers, and the number of papers remaining to be graded will be:

aₙ = aₙ₋₁ - 8

This is because he starts with a₀ = 44 papers, and each hour he grades 8 papers, reducing the number of papers remaining by 8.

Therefore, the recursive sequence to represent how many papers Josiah has remaining to grade after working for n hours is aₙ = aₙ₋₁ - 8

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Answer: 45 in.

Step-by-step explanation:

Step 1:

Length × Width = Area           How to find Area

Step 2:

5 in. × 9 in.       Equation

Answer:

45 in.       Multiply

The value of the expression is 1/8. Option C

Index forms are simply defined as mathematical forms used in the representation of numbers that are too large or too small in more convenient ways.

Index forms are also referred to as scientific notation or standard forms.

The rules of index forms are;

From the information given , we have;

2²/2⁵

Subtract the exponents

2²⁻⁵

2⁻³

Represent the value

1/8

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Answer:

1257cm²

Step-by-step explanation:

L'aire d'un cercle = [tex]\pi[/tex]r²

=  [tex]\pi[/tex][tex]\frac{d}{2}[/tex]²

=  [tex]\pi[/tex][tex]\frac{40cm}{2}[/tex]²

=  [tex]\pi[/tex](20cm)²

=  [tex]\pi[/tex]400cm²

= 1256.63706144cm²

Answer:A triangle can be defined as a two-dimensional shape that comprises three (3) sides, three (3) vertices and three (3) angles.

This ultimately implies that, any polygon with three (3) lengths of sides is a triangle.

In Geometry, there are three (3) main types of triangle based on the length of their sides and these are;

Equilateral triangle.

Scalene triangle.

Isosceles triangle.

An isosceles triangle has two (2) congruent sides that are equal in length and two (2) equal angles while the third side has a different length.

Step-by-step explanation:

For a given data set, the confidence interval will be wider for a 95% confidence level than for a 90% confidence level.

A confidence interval is a range within which we expect the true population parameter (e.g., mean or proportion) to fall, based on our sample data. The confidence level represents the probability that the confidence interval contains the true population parameter. A higher confidence level means we are more certain that the interval captures the true value. To achieve a higher confidence level (e.g., 95% instead of 90%), we need to include a larger range of values in the confidence interval.

This is because we are trying to be more certain that the interval contains the true population parameter. The width of the confidence interval is determined by the margin of error, which depends on the standard deviation, sample size, and the chosen confidence level (represented by the critical value, often denoted as "z" or "t"). As we increase the confidence level, the critical value increases, resulting in a larger margin of error and a wider confidence interval.

In summary, the confidence interval will be wider for a 95% confidence level than for a 90% confidence level because we need to include more values in the interval to be more certain that it contains the true population parameter.

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His record should not be changed. The correct option is A

An individual who works for an employer pursuant to an employment contract, whether it be written or verbal, is referred to as an employee.

David is an hourly worker, and since his compensation is remaining the same, his employee earnings record shouldn't be altered. Even if he transfers to a different department, his hourly rate and rate of pay need to stay the same. The employee's record's department or job code may be the only thing to change in this scenario, but the earnings record itself is unaffected.

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Answer: 14,358 cubic feet

Step-by-step explanation:

Volume of hemisphere = 0.5 x volume of sphere

Volume of hemisphere = 0.5 x 4/3 pi r^3

Volume of hemisphere = 0.5 x 4/3 pi 19^3

Volume of hemisphere = 0.5 x 4/3 pi 6859

Volume of hemisphere ≅ 14,358 cubic feet

Answer:

81

Step-by-step explanation:

We can solve for x by first using the definition of logarithms, which states that log base a of b is equal to c if and only if a raised to the power of c equals b.

Using this definition, we can rewrite the given equation as:

3^4 = x

Simplifying this expression, we get:

81 = x

Therefore, the value of x is 81.

Answer:

the answer will be -3

Step-by-step explanation:

The hexadecimal expression of decimal integer -100 in the 8-bit signed binary integer system is "9C". The decimal integer expression of the signed binary number 11010111 is -41. The 8-bit fixed point binary number expression of decimal real number -3.47 is 10111011.

To obtain the hexadecimal expression of decimal integer -100 in the 8-bit signed binary integer system, we first need to represent -100 in binary form. Since the 8-bit signed binary integer system uses two's complement representation, we can find the binary representation of -100 by taking the two's complement of the binary representation of 100. The binary representation of 100 is 01100100, so the two's complement of this number is 10011100. Therefore, the binary representation of -100 is 10011100, and its hexadecimal expression is 9C.

To find the decimal integer expression of the signed binary number 11010111, we first need to determine its sign bit. Since the leftmost bit is a 1, the number is negative. To obtain its binary value, we can take the two's complement of the binary representation of 00101001, which is the binary representation of the absolute value of 11010111. The two's complement of 00101001 is 11010111, so the binary representation of -41 is 11010111 in the 8-bit signed binary integer system.

To obtain the 8-bit fixed point binary number expression of decimal real number -3.47, we first need to represent -3.47 in binary form. To do this, we can convert the integer part and the fractional part separately. The integer part of -3.47 is -3, which has a binary representation of 11111101 in the 8-bit signed binary integer system. The fractional part of -3.47 can be converted using the binary fraction representation method. Multiplying 0.47 by 2 yields 0.94, which has an integer part of 0. Multiplying 0.94 by 2 yields 1.88, which has an integer part of 1. Continuing in this way, we can obtain the binary fraction 01101101. Therefore, the binary representation of -3.47 is 11111101.01101101. To obtain the 8-bit fixed point binary number expression, we need to shift the binary point to the left by 4 bits, yielding 11010111.

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he inverse Laplace transform of f(s) is [tex]6(t-1)e^{(-6t)[/tex].

The inverse Laplace transform of f(s) = 6 / (s² + 12s + 36) first need to factor the denominator of f(s):

s² + 12s + 36 = (s + 6)²

We can rewrite f(s) as:

f(s) = 6 / [(s + 6)²]

The Laplace transform of the function [tex]6te^{(-6t)[/tex] has the Laplace transform:

[tex]L{6te^{(-6t)}[/tex] = 6 / (s + 6)²

The inverse Laplace transform of f(s), we get:

[tex]L^{-1}{f(s)}[/tex] =[tex]L^{-1}{6 / [(s + 6)^2]}[/tex]

= [tex]L^{-1}{6te^{(-6t)}[/tex]

= [tex]6(t-1)e^{(-6t)[/tex]

The inverse Laplace transform of f(s) is [tex]6(t-1)e^{(-6t)[/tex].

The denominator of f(s) before we can compute the inverse Laplace transform of f(s) = 6 / (s2 + 12s + 36):

s² + 12s + 36 = (s + 6)²

F(s) may be rewritten as f(s) = 6 / [(s + 6)2].

The function 6te(-6t)'s Laplace transform has the following properties:

[tex]L{6te^{(-6t)}[/tex]= 6 / (s + 6)²

The inverse Laplace transform to the function f(s) we obtain:

L-1f(s) = L-16 / [(s + 6)²]

= L-16te(-6t)

= 6(t-1)e(-6t).

6(t-1)e(-6t) is the inverse Laplace transform of the function f(s).

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The minimum and maximum values of f(x,y) subject to the constraint 8 - 2x - 5y^2 = 0 are both equal to 1.


We can use the method of Lagrange multipliers to solve this problem. Let's define the Lagrangian as L(x,y,λ) = x^2 y^2 + λ(8 - 2x - 5y^2). We need to find the values of x, y, and λ that minimize or maximize L subject to the constraint 8 - 2x - 5y^2 = 0.

Taking partial derivatives of L with respect to x, y, and λ, we get:

∂L/∂x = 2xy^2 - 2λ

∂L/∂y = 2x^2y - 10λy

∂L/∂λ = 8 - 2x - 5y^2

Setting these equal to zero and solving for x, y, and λ, we get:

x = ±√(2λ/y^2)

y = ±√(2λ/5)

λ = xy^2/2

Substituting these back into the constraint equation, we get:

8 - 2x - 5y^2 = 0

8 - 2(±√(2λ/y^2)) - 5(±√(2λ/5))^2 = 0

Simplifying this equation, we get:

√(5λ) = √2

λ = 2/5

Substituting this back into the equations for x and y, we get:

x = ±1

y = ±1

Now we can evaluate the function f(x,y) = x^2 y^2 at the four possible points (1,1), (-1,1), (1,-1), and (-1,-1):

f(1,1) = 1

f(-1,1) = 1

f(1,-1) = 1

f(-1,-1) = 1

Therefore, the minimum and maximum values of f(x,y) subject to the constraint 8 - 2x - 5y^2 = 0 are both equal to 1.

the minimum and maximum values of f(x,y) subject to the constraint 8 - 2x - 5y^2 = 0 are both equal to 1.

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The minimum and maximum values of f(x,y) subject to the constraint 8 - 2x - 5y^2 = 0 are both equal to 1.

We can use the method of Lagrange multipliers to solve this problem. Let's define the Lagrangian as L(x,y,λ) = x^2 y^2 + λ(8 - 2x - 5y^2). We need to find the values of x, y, and λ that minimize or maximize L subject to the constraint 8 - 2x - 5y^2 = 0.

Taking partial derivatives of L with respect to x, y, and λ, we get:

∂L/∂x = 2xy^2 - 2λ

∂L/∂y = 2x^2y - 10λy

∂L/∂λ = 8 - 2x - 5y^2

Setting these equal to zero and solving for x, y, and λ, we get:

x = ±√(2λ/y^2)

y = ±√(2λ/5)

λ = xy^2/2

Substituting these back into the constraint equation, we get:

8 - 2x - 5y^2 = 0

8 - 2(±√(2λ/y^2)) - 5(±√(2λ/5))^2 = 0

Simplifying this equation, we get:

√(5λ) = √2

λ = 2/5

Substituting this back into the equations for x and y, we get:

x = ±1

y = ±1

Now we can evaluate the function f(x,y) = x^2 y^2 at the four possible points (1,1), (-1,1), (1,-1), and (-1,-1):

f(1,1) = 1

f(-1,1) = 1

f(1,-1) = 1

f(-1,-1) = 1

Therefore, the minimum and maximum values of f(x,y) subject to the constraint 8 - 2x - 5y^2 = 0 are both equal to 1.

the minimum and maximum values of f(x,y) subject to the constraint 8 - 2x - 5y^2 = 0 are both equal to 1.

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The relative rate of change f′(t)/f(t) at t=1 can be found by first calculating the derivative of the function f(t) and evaluating it at t=1.

f(t) = ln(t^2 - 1)

f'(t) = 2t / (t^2 - 1)

f'(1) = 2 / (1^2 - 1) = 1

Next, we can evaluate f(1) and use the formula for relative rate of change:

f(1) = ln(1^2 - 1) = ln(0) = undefined

Therefore, the relative rate of change f′(1)/f(1) cannot be calculated.

The function f(t) is undefined at t=1 because ln(0) is undefined. This means that we cannot calculate the value of f(1) and hence, cannot determine the relative rate of change f′(1)/f(1).

This is an example of a situation where the relative rate of change cannot be determined due to the function being undefined or having a singularity at the point of interest.

It is important to be aware of such situations when dealing with calculus and to check for any potential issues with the function or point of interest before attempting to calculate the relative rate of change.

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The volume of the prism is 259 units³.

The volume of the prism can be calculated as follows:

volume of a prism = base area × height

The prism is a triangular base prism. The area of the base of the prism is 37 units² and the height of the prism is 7 units.

Therefore,

Base area of the prism = 37 units²

height  = 7 units

Hence,

volume of a prism = 37 × 7

volume of a prism = 259 units³

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Answer: I think its 9 i could be wrong

Step-by-step explanation:

Answer:

Answer C.   x=10

Step-by-step explanation:

Similar triangles

Given that the base lines are parallel, the base angles will be corresponding angles for the transversal and will be congruent.  If one allows the up-down lines to continue to an intersection, one could form several triangles, all of which would be "Similar" to each other, due to their Angle-Angle congruence.

Similar triangles have all corresponding angles congruent between their triangles, and a consequence, all corresponding side-lengths between two triangles form a common proportion.

In other words, the ratio of the left side-length to the right side length is the same for both triangles.

Proportions

Despite that we don't actually have any full triangles, this concept extends for portions of a side length, so long as the bases are parallel.

So, since the ratio of the left side-length to the right side length is the same for both triangles, we can set up the following equation because both ratios are equal:

[tex]\dfrac{short~left~side}{long~left~side}=\dfrac{short~right~side}{long~right~side}[/tex]

[tex]\dfrac{6}{15}=\dfrac{x}{25}[/tex]

Solving a one-variable equation

From here, we're solving a single variable equation, where the variable only shows up once.  To solve for x, we need to disconnect the "dividing by 25" from it.  To undo that, we apply the opposite operation: multiplication.

Multiply both sides of the equation by 25...

[tex]\dfrac{6}{15}*25=\dfrac{x}{25}*25[/tex]

Notice on the right side of the equation that x is divided by 25, and then immediately multiplied by 25.  This will bring us right back to the value of x.

[tex]\dfrac{6}{15}*25=x[/tex]

Computing without a calculator

On the left side of the equation, to calculate it without a calculator, we could factor each number, and cancel common factors between the numerator and denominator:

[tex]\dfrac{2*3}{3*5}*5*5=x[/tex]

Notice that there is a 3 in the numerator and denominator.  Since there is no multiplication, this is effectively starting with 2, multiplying by 3, and then immediately dividing by 3, which will just bring us back to 2, before dividing by 5.  So, the 3s cancel, as collectively, they won't change the value of 2.

[tex]\dfrac{2}{5}*5*5=x[/tex]

Now, we have the same process with the 5s.  2 is first divided by 5, and then immediately multiplied by 5 (before being multiplied by another 5).  The division by 5 and the first multiplication by 5 will cancel, as they collectively won't change the value of the 2.

[tex]2*5=x[/tex]

Lastly, 2*5 is 10

[tex]10=x[/tex]

If you were allowed to use a calculator to calculate it, then that simplifies the work to getting that answer.

Answer:

Top right

Step-by-step explanation:

It goes through most of the plotted data

Shape D can be rotated [tex]\underline{270^{o}}[/tex] clockwise about the point (1, 3) to give shape C.

To find the values of blanks, the rotational relationship between Shape C and Shape D should be considered. Shape C is rotated 90° clockwise about the point (1, 3) to give Shape D.

We can conclude that Shape D can be rotated 270° because a full rotation is [tex]360^{o}[/tex]. It means turning around until your point in same direction again.

So, C [tex]\xrightarrow{90^{o}\ clockwise }[/tex] D [tex]\xrightarrow{270^{o}\ clockwise }[/tex] C

The center if rotation should stay the same.

This means that if we rotate Shape D 270° clockwise about the point (1, 3), we will obtain Shape C.

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