2.357 find the expanded notion.

Answer:

10.5

Step-by-step explanation:

250% = 2.5

What number is 250% of 4.2?
We Take

2.5 x 4.2 = 10.5

So, 10.5 is 250% of 4.2

Answer:

Step-by-step explanation:

Here is a step-by-step explanation of the solution and how it leads to the maximum revenue:

Let's start with the current revenue generated by the TV cable company, which is the product of the number of subscribers and the monthly fee:

Current revenue = Number of subscribers * Monthly fee

Current revenue = 6400 * $28

Current revenue = $179,200

To increase the revenue, the TV cable company can decrease the monthly fee by $0.50, which will result in an increase in the number of subscribers by 160 for each $0.50 decrease. Let's calculate the additional revenue generated by each $0.50 decrease in the monthly fee:

Additional revenue per decrease in monthly fee = Increase in subscribers * Decrease in monthly fee

Additional revenue per decrease in monthly fee = 160 * $0.50

Additional revenue per decrease in monthly fee = $80

The TV cable company can continue to decrease the monthly fee by $0.50 until the revenue stops increasing. Let's calculate the number of $0.50 decreases in monthly fee required to reach the maximum revenue:

Number of $0.50 decreases in monthly fee = (Total revenue - Current revenue) / Additional revenue per decrease in monthly fee

Number of $0.50 decreases in monthly fee = ($20,000,000 - $179,200) / $80

Number of $0.50 decreases in monthly fee = 248,525

The corresponding decrease in monthly fee is:

Decrease in monthly fee = Number of $0.50 decreases in monthly fee * Decrease in monthly fee

Decrease in monthly fee = 248,525 * $0.50

Decrease in monthly fee = $124,262.50

The corresponding increase in subscribers is:

Increase in subscribers = Number of $0.50 decreases in monthly fee * Increase in subscribers

Increase in subscribers = 248,525 * 160

Increase in subscribers = 39,764,000

The total number of subscribers at the maximum revenue point is:

Total subscribers = 6400 + Increase in subscribers

Total subscribers = 6400 + 39,764,000

Total subscribers = 39,770,400

The monthly fee at the maximum revenue point is:

Monthly fee = Current revenue / Total subscribers

Monthly fee = $179,200 / 39,770,400

Monthly fee = $0.0045

The maximum revenue is:

Maximum revenue = Total subscribers * Monthly fee

Maximum revenue = 39,770,400 * $0.0045

Maximum revenue = $178,966.80

Therefore, the TV cable company can generate maximum revenue of $178,966.80 per month by decreasing the monthly fee by $0.50 for each 160 additional subscribers.

1. The reason is that E bisects line AC and is perpendicular to line AC.

2. The reason is that the angles are alternate interior angles.

What are alternate interior angles?

Alternate interior angles are made when a transversal joins two co-planar lines. These can be found on the inner side of the parallel lines, but on their transverse sides. The transversal goes through the two co-planar lines at two separate points.

1. We are given a statement that E is the midpoint of AC.

The reason is that E bisects line AC and is perpendicular to line AC, therefore it is the mid point of AC.

2. We are given that ∠D ≅ ∠B.

The reason is that DC ║ AB. We know that when two lines are parallel, alternate interior angles are equal.

The angle ∠D and ∠B are alternate interior angles and therefore they are equal.

Hence, the required solutions have been obtained.

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The complete question has been attached below.

Answer:

The correct option is C. The best approximate for the given graph is [tex]\sqrt{28}[/tex].

Step-by-step explanation:

From the given graph it is noticed that the point lies between 5 and 6.

Let the square root of x is the best approximate for the given graph.

[tex]5 < \sqrt{x} < 6[/tex]

Taking square on each side.

[tex]5^2 < (\sqrt{x})^2 < 6^2[/tex]

[tex]25 < x < 36[/tex]

It means the value of x lies between 25 to 36 and the graph represents the approximate value between [tex]\sqrt{25}[/tex] to [tex]\sqrt{36}[/tex].

Therefore best approximate for the given graph is [tex]\sqrt{28}[/tex]. Option C is correct.

C(N(x)) = 45 + 15(150 - x) = 45 + 2250 - 15x = 2295 - 15x. C(N(x)) = 2295 - 15x, which equals $2295 minus $15 for each guest fewer than 150. Therefore, $795 would be needed to prepare for 50 guests.

A group of terms joined with the operations +, -, x, or  form an expression, such as 4 x 3 or 5 x 2  3 x y + 17. A statement that starts with an equals sign, such as 4 b 2 = 6, says that two statements are equal in value and is known as an equation.

The functions are: C(x) = 45 plus 15x (Cost per guest)

N(x) = 150 - x (Number of guests)

We must simplify and replace the formula for N(x) with C(x) in order to evaluate C(N(x)):

C(N(x)) = 45 + 15(150 - x) = 45 + 2250 - 15x = 2295 - 15x

The expense of catering for x guests who are less than 150 is denoted by the expression 2295 - 15x.

The expense of catering a celebration for x guests fewer than 150 is denoted by the formula: C(N(x)) = 2295 - 15x, which equals $2295 minus $15 for each guest fewer than 150. This expression provides the total expense of catering for the number of guests defined by the function N.(x). For instance, if the event has 50 guests, then x = 100 and the expense of catering for 50 guests.

C(N(100)) = 2295 - 15(100)

= 2295 - 1500

= 795

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The desalination plant can produce [tex]9.84*10^6[/tex] gallons of water in four day in scientific notation.

We must divide the daily production rate by the number of days in order to get the total volume of water that a desalination plant can generate in four days:

4. days at a rate of [tex]2.46*10^6[/tex] gallons equals [tex]9.84*10^6[/tex] gallons.

Hence, in four days, the desalination plant can produce [tex]9.84 * 10^6[/tex] gallons of water.

Large or small numbers can be conveniently represented using scientific notation, especially when working with measurements in science and engineering. A number is written in scientific notation as a coefficient multiplied by 10 and raised to a power of some exponent. For example, [tex]2.46*10^6[/tex] denotes 2,460,000, which is 2.46 multiplied by 10 to the power of 6.

The solution in this case is [tex]9.84*10^6[/tex], or 9,840,000, which is 9.84 multiplied by 10 to the power of 6. Large numbers can be written and compared more easily using this format, and scientific notation rules can be used to conduct computations with them.

In conclusion, the desalination plant has a four-day capacity of [tex]9.84 * 10^6[/tex] gallons of water production.

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Answer: Given a 2x2 matrix A:

A = [a11 a12]

   [a21 a22]

The minor of any element a_ij is the determinant of the 1x1 matrix obtained by deleting the i-th row and j-th column from A. In other words, the minor of a_ij is given by:

M_ij = det(A_ij)

where A_ij is the matrix obtained by deleting the i-th row and j-th column from A.

For example, the minor of a11 is given by:

M_11 = det([a22])

    = a22

Similarly, we can find the minors of the other elements:

M_12 = det([a21])

    = a21

M_21 = det([a12])

    = a12

M_22 = det([a11])

    = a11

Therefore, the minors of the matrix A are:

M = [a22  a21]

   [a12  a11]

Step-by-step explanation:

Answer:

The quotient will have a larger value than the dividend.

Step-by-step explanation:

Example:

15 ÷ [tex]\frac{1}{2}[/tex]

[tex]\frac{5}{\frac{1}{2} }[/tex]

[tex]\frac{\frac{15}{1} }{\frac{1}{2} }[/tex]  x [tex]\frac{\frac{2}{1} }{\frac{2}{1} }[/tex] = [tex]\frac{\frac{30}{1} }{1}[/tex] = 30

Our quotient of 30 has a larger value than the dividend of 15.

Helping in the name of Jesus.

Answer:

L= 18j^5k^10

Step-by-step explanation:

A = L x W

144j⁹k¹⁵=8j⁴k⁵(L)

L= 144j⁹k¹⁵

8j⁴k⁵

L= 18j^5k^10

Answer:

[tex]18 {j}^{5} {k}^{10} [/tex]

Step-by-step explanation:

Given:

[tex]a (area) = 144 {j}^{9} {k}^{15} [/tex]

[tex]w(width) = 8 {j}^{4} {k}^{5} [/tex]

Find: l (length) - ?

.

In order to find the length, we have to divide the area from the width (since a = w × l):

.

[tex]l = \frac{144 {j}^{9} {k}^{15} }{8 {j}^{4} {k}^{5} } = \frac{18 {j}^{9} {k}^{15} }{ {j}^{4} {k}^{5} } = 18 {j}^{5} {k}^{10} [/tex]

Use power properties (when dividing equal bases raised to different powers, power indicators are subtracted)

Let's assume that the number of diners at the Italian restaurant is "x" and the number of diners at the Mexican restaurant is "y". Then, we can write the following equations based on the given information:

Italian restaurant:

Donation = $462 + $1 per diner

Donation = $462 + $1x

Mexican restaurant:

Donation = $235 + $2 per diner

Donation = $235 + $2y

Since both restaurants will donate the same total amount, we can set their donations equal to each other:

$462 + $1x = $235 + $2y

Simplifying this equation, we get:

$2y - $1x = $227

We know that the number of diners has to be a whole number, so we can try different values of x and see which one gives us a whole number for y.

For example, if we try x = 200, then we can solve for y:

$2y - $1(200) = $227

$2y = $427

y = 213.5

Since y is not a whole number, we need to try a different value of x. If we try x = 250, then we get:

$2y - $1(250) = $227

$2y = $477

y = 238.5

Again, y is not a whole number, so we try another value of x. If we try x = 300, then we get:

$2y - $1(300) = $227

$2y = $527

y = 263.5

Still not a whole number, so we try x = 350:

$2y - $1(350) = $227

$2y = $577

y = 288.5

Finally, we get a whole number for y, so we have our solution:

Italian restaurant: x = 350 diners, donation = $812

Mexican restaurant: y = 289 diners, donation = $812

Therefore, 350 diners promised to participate and each restaurant would donate $812.

Answer:

Each bag of spinach weighs 0.833 kg or approximately 833 grams

Step-by-step explanation:

Fiona had 3 kg of spinach. She sold 1/2 kg of spinach to Mrs. Simon, which leaves her with:

3 kg - 1/2 kg = 2.5 kg

Fiona packed the remaining 2.5 kg of spinach equally into 3 bags. To find the mass of each bag of spinach, we can divide the total amount of spinach by the number of bags:

2.5 kg ÷ 3 = 0.833 kg

therefore, Each bag of spinach weighs 0.833 kg or approximately 833 grams

The value of x in the given equation of the quadrilateral is 20.

The value of x is determined by applying the property of a quadrilateral which states that adjacent angles of a quadrilateral are supplementary while the opposite angles are equal.

(2x + 14) + 126 = 180

We can simplify the left side of the equation by combining the terms inside the parentheses:

2x + 140 = 180

Next, we can isolate the variable x by subtracting 140 from both sides of the equation:

2x = 40

Finally, we can solve for x by dividing both sides of the equation by 2:

x = 20

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1. The probability that a single randomly selected salary is less than 144000 dollars is 0.5129. 2. The probability for n=75 is randomly selected with a mean that is less than 144000 dollars is 0.8781.

The central limit theorem, which states that the distribution of sample means will be about normal regardless of how skewed the original population distribution was if the sample size is large enough and the population is not very skewed, is a foundational concept in statistics. The central limit theorem precisely states that the sample means' mean is equal to the population's mean and that the sample means' standard deviation (also known as the standard error) is equal to the population's standard deviation divided by the square root of the sample size.

The z-score us given by the formula:

z = (x - μ) / σ

1. For salary less than 144000 dollars:

z = (144000 - 143000) / 31000 = 0.0323

Using the z-table:

z-score < 0.0323 = 0.5129

Hence, the probability that a single randomly selected salary is less than 144000 dollars is 0.5129.

2. For n = 75:

z = (x - μ) / (σ / √(n))

z = (144000 - 143000) / (31000 / √(75)) = 1.164

Using z-table:

z-score is less than 1.164 = 0.8781.

Hence, the probability that a sample of size n=75 is randomly selected with a mean that is less than 144000 dollars is 0.8781.

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Answer:

38.4 megabytes for 16 electronic books

Step-by-step explanation:

2.4 megabytes per electronic book

2.4 megabytes x 16 electronic books = 38.4 megabytes

According to the question the value of the test statistic [tex]0.55[/tex]

Data variation from the mean is referred to as "standard deviation." If the standard deviation appears low, the data tend to cluster around the mean; on the other hand, if it appears large, the data are widely spread.

The data deviate from the mean value is indicated by the standard . It is useful for contrasting huge datasets with distinct ranges but the same mean.

The other, though, is without a doubt more spread. The standard deviation reveals the degree of data dispersion. It describes how far away from the mean each number obtained is.

We must compute the t-score, which is represented by: in order to determine the value of the test statistic.

[tex]t = x -[/tex] μ[tex]/(s/\sqrt{n}[/tex]

s= sampling standard deviation, n= sample size,[tex]x=[/tex] sampling rate μ = population mean

[tex]x = 69.5 bpm,[/tex] μ[tex]= 69 bpm, s = 11.4 bpm, n = 154[/tex]

[tex]t = (69.5- 69)/ 11.4/\sqrt{154} \\t = 0.5/ (11.4/12.4)\\t = 0.5/ 0.917\\t = 0.546[/tex]

Therefore the value of the test statistics is [tex]0.55[/tex]

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In a rectangle, there are 2 pairs of congruent sides. Therefore, the area of a rectangle can be found using:

[tex]\text{A}=\text{l} \times \text{w}[/tex]

We know that the length is 18 and the width is 12, so we can multiply 18 in for l, and 12 in for w.

[tex]\text{A}=\text{18} \times \text{12}[/tex]

Multiply the numbers together

[tex]\text{A}=216[/tex]

So, the area is 216 inches.

To find the area of a rectangular placemat, you multiply the length by the width. In this case, the length is 18 inches and the width is 12 inches. Therefore, the area of the tablecloth is:

Area = Length × Width

Area = 18 inches × 12 inches

Area = 216 square inches

So, the correct answer is option a. 216.

Possible rational zeros of the polynomial is

±1, ±1/2, ±1/4, ±2, ±5, ±5/2, ±5/4, ±10.

Polynomials are particular type of algebraic expressions which consists of variables and coefficients. Various arithmetic operations such as addition, subtraction, multiplication, and also positive integer exponents for polynomial expressions can be performed on polynomial but not division by variable. An example of a polynomial is x-12 . Here it has two  terms:  x and -12.

Given polynomial p(x)= 4x⁵-2x³+10

The polynomial can be rewritten as p(x)= 4x⁵+ 0x⁴-2x³+0x²+0x+10

Comparing the polynomial with

p(x) = aₙ xⁿ + aₙ₋₁xⁿ⁻¹+ ---------- + a₁ x + a₀ we get the  leading coefficient

aₙ= 4 and the constant term a₀= 10

So the possible zeros are=  ±( factors of a₀)/ (factors of aₙ)

Factors of 10:

1, 2, 5, 10

Factors of 4:

1, 2, 4

Hence, Possible rational zeros:

±1, ±1/2, ±1/4, ±2, ±5, ±5/2, ±5/4, ±10

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The critical point of the function g is (0,0), the value of D(0,0) is -6272, and the critical point is a saddle point.

(a) To find the critical point of g, we need to find the partial derivatives of g with respect to x and y, and set them equal to zero:

[tex]∂g/∂x = -8xe^(-4x^2+7y^2+14√8y) = 0[/tex]

[tex]∂g/∂y = 14ye^(-4x^2+7y^2+14√8y) + 14√8e^(-4x^2+7y^2+14√8y) = 0[/tex]

From the first equation, we get x = 0. Substituting this value into the second equation, we get:

[tex]14ye^(7y^2+14√8y) + 14√8e^(7y^2+14√8y) = 0[/tex]

Dividing both sides by [tex]14e^(7y^2+14√8y)[/tex], we get:

y + √8 = 0

Thus, the critical point of g is (0, -√8).

(b) To find the value of D(a,b) from the Second Partials test, we need to compute the second-order partial derivatives of g with respect to x and y:

[tex]∂^2g/∂x^2 = 32x^2e^(-4x^2+7y^2+14√8y) - 8e^(-4x^2+7y^2+14√8y)[/tex]

[tex]∂^2g/∂y^2 = 98y^2e^(-4x^2+7y^2+14√8y) + 196√8ye^(-4x^2+7y^2+14√8y) + 686e^(-4x^2+7y^2+14√8y)[/tex]

[tex]∂^2g/∂x∂y = -112xye^(-4x^2+7y^2+14√8y) - 196√8xe^(-4x^2+7y^2+14√8y)[/tex]

At the critical point (0, -√8), we have:

[tex]∂^2g/∂x^2 = -8[/tex]

[tex]∂^2g/∂y^2 = 686[/tex]

[tex]∂^2g/∂x∂y = 0[/tex]

Therefore, D(0, -√8) =[tex](∂^2g/∂x^2)(∂^2g/∂y^2) - (∂^2g/∂x∂y)^2[/tex] = (-8)(686) - [tex](0)^2[/tex] = -5488.

(c) Since D(0, -√8) is negative, and [tex]∂^2g/∂x^2[/tex] is negative at the critical point, the Second Partials test tells us that (0, -√8) is a saddle point.

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The Two figures are (Not similar) because 2/5 ( does not equal) 3/6.

What is similar rectangle?

If two rectangles are similar, their corresponding sides are proportionately equal.

Now comparing the length and width of the two rectangles then.

=> 2/5 = 3/6

Which is not equally proportional.

Hence the both rectangles are similar because 2/5 does not equal 3/6 .

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Answer: 5

Step-by-step explanation:

If the area of a square equals 25 square inches, then the side length of the square can be found by taking the square root of the area. The formula for the area of a square is A = s^2, where A is the area and s is the length of a side of the square.

So, in this case, we have:

A = 25 sq inches

s = sqrt(A) = sqrt(25 sq inches) = 5 inches

Therefore, the side of the square is 5 inches.

The rectangular pyramid's surface area therefore approximates 622.6 in2, which is closest to option 4.

A rectangular is a four-sided polygon in geometry with opposite sides that are parallel and of equal length. It contains four diagonals that cross one another at 90 degree angles. A rectangle is also a rhombus, a rectangle with all sides of equal length, and a parallelogram, a trapezoid with the opposite sides parallel. In the formula A = l w, where l stands for length and w for width, the area of such a rectangle is determined. P = 2l + 2w is a formula that yields the perimeter. In the fields of engineering, design, and architecture, rectangles are used frequently.

given

The Pythagorean theorem can be used to determine the base of the smaller triangle, which equals the pyramid's slant height.

Slant height is equal to (12.5 + 12.9) in (rounded to one decimal place)

Hence, the smaller triangle's area is:

A(small triangular) = 1/2 x 17.8 in, 17.8 in, and 12.9 in, or 115.1 in2.

By summing the areas of all the pyramid's faces, we can determine the overall surface area of the structure:

A (base) + 2 x A (big triangle) + A Equals total surface area (small triangle)

Surface area total = 238 in2 + 2 x 84 in2 + 115.1 in2

Surface area total = 622.1 in2 (rounded to one decimal place)

The rectangular pyramid's surface area therefore approximates 622.6 in2, which is closest to option 4.

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A circle graph would be best to display the data.

A circle graph, also known as a pie chart, is useful for displaying categorical data where the parts represent a percentage of a whole. In this case, the whole is the total number of purchases, which is 125. The different types of items purchased can be represented as sections of a circle, with the size of each section proportional to the percentage of purchases that fall into that category. A circle graph would allow the viewer to easily see the relative frequency of each category in the data set.

Box plots, scatter plots, and histograms are all graphical representations that are better suited for displaying continuous data, rather than categorical data.

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Answer:

5x + 12

Step-by-step explanation:

3(x + 2) + 2(x + 3)

= 3x + 6 + 2x + 6 (distributing the coefficients)

= 5x + 12 (combining like terms)

Answer:5x+12

Step-by-step explanation:

3(x+2)= 3x+6

2)x+3) = 2x+6

3x+2x+6+6=5x+12

HOPE I HELPED :)

Answer:

Area = π+4

Perimeter = 4π+4

Step-by-step explanation:

1) The two semi-circles make one whole circle

2) one square.

Area

1) formula for the area of a circle = [tex]r^{2}\pi[/tex]

The diameter is 2 which means the radius is 1

so the area of the circle is equal to π

2) to find the area of a square you multiply the sides

2x2=4

So to find the total area you add [tex]\pi +4[/tex]

which leaves us with [tex]\pi +4[/tex]

Perimeter

1) the formula for the perimeter of a circle = [tex]2\pi r[/tex]

Since the radius is 1

the perimeter of both circles is 4π

2) to find the perimeter of only part of the square (two sides), you have to add them together

2+2=4

So the total perimeter is 4π+4

Each student will read 2 1/2 pages aloud. The answer is option B, 2 1/2.

What is arithmetic sequence?

An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term.

For example, the sequence 2, 5, 8, 11, 14, ... is an arithmetic sequence with a common difference of 3, since each term after the first is found by adding 3 to the preceding term.

Ms. Avila's reading class has 18 students and they are going to read aloud from a book that has 45 pages. To determine the total number of pages that each student will read, we need to divide the total number of pages by the number of students.

So, 45 divided by 18 equals 2 1/2 pages per student.

This means that each student will read 2 1/2 pages aloud.

Therefore, the answer to the question is option B, 2 1/2.

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Adama can expect the die to land on a number less than 10 about 36 times in 40 rolls.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is essentially what probability means.

The die has 10 faces, with numbers 1 through 10, but we are interested in the number of times it will land on a number less than 10. That means, there are 9 possible outcomes for each roll to be less than 10.

The expected number of times the die will land on a number less than 10 can be calculated by multiplying the probability of getting a number less than 10 on each roll by the total number of rolls.

The probability of getting a number less than 10 on each roll is 9/10, since there are 9 faces with numbers less than 10 out of the total of 10 faces.

Therefore, the expected number of times the die will land on a number less than 10 is:

E = (9/10) x 40 = 36

Therefore, Adama can expect the die to land on a number less than 10 about 36 times in 40 rolls.

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☆ 36 times.

— your in college ? im in seventh grade and got this question !

a. Your friend's mistake is that the reflection of EFG to its image E'F'G' is not a reflection across the x-axis.

b. The correct description of the reflection is a reflection across the line y = x.

The correct description of the reflection are:

a. Your friend's mistake is that the reflection of EFG to its image E'F'G' is not a reflection across the x-axis.

b. The correct description of the reflection is a reflection across the line y = x.

This is because the line of reflection is the perpendicular bisector of the segment connecting each point to its image. In this case, the segment connecting E to E' has a slope of 1 (since it is a diagonal line), so the perpendicular bisector of this segment must have a slope of -1.

The line with slope -1 passing through the midpoint of this segment (which is the point on the line y = x) is the line of reflection. Therefore, the reflection of EFG to its image E'F' is a reflection across the line y = x, not the x-axis.

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The function f(2) from the piecewise function has a value of 0

From the question, we have the following parameters that can be used in our computation:

The piecewise function

The x value of 2 belongs to the domain x > 2

So, we have

f(x) = -x + 2

Substitute the known values in the above equation, so, we have the following representation

f(2) = -2 + 2

Evaluate

f(2) = 0

Hence, the value iss 0

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