The person's expenditure is $1,755. (30 words)
To find the expenditure, we need to determine the person's income first. Since the income tax is 13% of the income and is given as $585, we can calculate the income. Dividing the income tax by the tax rate gives us the income. So, $585 divided by 0.13 equals $4,500, which is the person's income.
Now, we can calculate the expenditure. Given that the expenditure is 75% of the income, we can multiply the income by 0.75 to find the expenditure. So, $4,500 multiplied by 0.75 equals $3,375. Therefore, the person's expenditure is $3,375. (120 words)
In summary, the person's expenditure is $3,375. To find this, we first determined the person's income by dividing the given income tax of $585 by the tax rate of 13%, resulting in an income of $4,500.
Then, we calculated the expenditure by multiplying the income by 0.75 since the expenditure is stated to be 75% of the income. Thus, the person's expenditure is $3,375.
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A national dog show had two types of poodles. This table
shows height data, in inches, for the two types of poodles.
Heights of Poodles
Type of Poodle
Miniature
Standard
Number of Dogs
18
24
Mean Height Variation in Height
(inches)
(inches)
13
23
2
2
What number completes the sentence?
The difference in inches, between the mean height for the two
types of poodles is
times the variation for
either type.
Enter your answer in the space provided.
What is the degree in leading coefficient of f(x) equals 3X -5
Answer:
1
Step-by-step explanation:
The degree of a polynomial is the exponent of the varieble x. So the exponent of x in that function is 1.
Find the local and absolute maximum and minimum points in (x, y) format for the
function f(x) = 3/5x^5 - 9x^3 + 2 on the closed interval [-4,5]. Answer the following
questions.
a) Find all critical numbers (x- coordinates only)
b) Find the intervals on which the graph is increasing Mark critical numbers
find the volume of a cube whose diagonal is 4√2
The volume of the cube with a diagonal of 4√2 is 64 cubic units.
To find the volume of a cube, we need to know the length of its side. In this case, we are given the length of the diagonal, which we can use to find the side length.
Let's assume the side length of the cube is represented by "s". We know that the diagonal of a cube forms a right triangle with two sides of equal length, which are the sides of the cube.
Using the Pythagorean theorem, we can set up the equation:
s² + s² = (4√2)²
Simplifying the equation:
[tex]2s² = 32[/tex]
Dividing both sides by 2:
[tex]s² = 16[/tex]
Taking the square root of both sides:
[tex]s = 4[/tex]
Now that we have the side length of the cube, we can find the volume by cubing the side length:
Volume = s³ = 4³ = 64 cubic units.
Therefore, the volume of the cube with a diagonal of 4√2 is 64 cubic units.
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The volume of the cube whose diagonal is 4√2 is 128√2 cubic units.
To find the volume of a cube, we need to know the length of its side. Given that the diagonal of the cube is 4√2, we can use this information to determine the side length.
In a cube, the diagonal is related to the side length (s) by the equation:
diagonal = s√3
The given diagonal is 4√2. So we can set up the equation:
4√2 = s√3
To find s, we can divide both sides of the equation by √3:
s = (4√2) / √3
To simplify this expression, we can rationalize the denominator by multiplying both the numerator and denominator by √3:
s = (4√2 ׳ √3) / (√3 × √3)
s = (4√6) / √3
Now, let's calculate the value of s:
s = (4√6) / √3
s = (4/√3) × √6
s = (4/√3) × (√3 × √2)
s = 4√2
So the side length of the cube is 4√2.
Now, to calculate the volume of the cube, we use the formula:
Volume = side^3
Volume = (4√2)³
Volume = 4³ × (√2)³
Volume = 64 × 2√2
Volume = 128√2
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which of the following will form the composite function G(F(x)) shown below G(F(x)) = 4√x
Suppose that the relation H is defined as follows. H = {(9, 3), (8, p), (3, q), (8, 0)) Give the domain and range of H. Write your answers using set notation.
Answer:
See below
Step-by-step explanation:
Domain would be all the x-values, so this is {3, 8, 8, 9}
Range would be all the y-values, so this is {0, 3, p, q}
The cost to buy p pounds of potatoes at $0.32 per pound and n
pounds of onions at $0.48 per pound can be determined by using
the expression 0.32p + 0.48n. How much will it cost to buy 4.5
pounds of potatoes and 2.5 pounds of onions?
recursive formula for an=1/8(2)n-1
Answer:
The recursive formula for an=1/8(2)n-1 is:
a1=1/8 an+1=1/8(2)(n)
This formula defines a sequence where each term is equal to 1/8 of the previous term multiplied by 2.
Step-by-step explanation:
Please answer ASAP I will brainlist
Answer:
Step-by-step explanation:
(a) To find the linear cost function C(x), we need to consider the fixed cost and the marginal cost. The fixed cost is $100, and the marginal cost is $8 per pair of earrings.
The linear cost function can be represented as C(x) = mx + b, where m is the slope (marginal cost) and b is the y-intercept (fixed cost).
In this case, the slope (m) is $8, and the y-intercept (b) is $100. Therefore, the linear cost function is:
C(x) = 8x + 100.
(b) The average cost function (AC) can be found by dividing the total cost (C(x)) by the number of units produced (x):
AC(x) = C(x) / x.
Substituting the linear cost function C(x) = 8x + 100, we have:
AC(x) = (8x + 100) / x.
(c) To find C(5), we substitute x = 5 into the linear cost function:
C(5) = 8(5) + 100
= 40 + 100
= 140.
Interpretation: C(5) = 140 means that when the artist produces 5 pairs of earrings, the total cost (including fixed and variable costs) is $140.
(d) To find C(50), we substitute x = 50 into the linear cost function:
C(50) = 8(50) + 100
= 400 + 100
= 500.
Interpretation: C(50) = 500 means that when the artist produces 50 pairs of earrings, the total cost (including fixed and variable costs) is $500.
(e) The horizontal asymptote of C(x) represents the cost as the number of units produced becomes very large. In this case, the marginal cost is constant at $8 per pair of earrings, indicating that as the number of units produced increases, the cost per unit remains the same.
Therefore, the horizontal asymptote of C(x) is $8, indicating that the average cost per pair of earrings approaches $8 as the number of units produced increases indefinitely.
In practical terms, this means that for every additional pair of earrings produced beyond a certain point, the average cost will stabilize and remain around $8, regardless of the total number of earrings produced.
Jenny is watching her favorite soccer team playing a match. The odds against her favorite team winning are 7/10. What is the probability of her favorite team winning?
Answer:
70%
Step-by-step explanation:
(2x5)(10x−2) simplified
Answer:
200x - 40 (5x-1)
Step-by-step explanation:
2 x 10 = 20
20 x 10 = 200
20 x -2 = -40
200 - 40 = 100 - 20, 50 - 10, 20 - 4, 10 - 2, 5 -1
so the answer is either 5x - 1 or 200x - 40
The length of ribbons found at a seamstress are listed.
3, 11, 11, 13, 13, 21
What is the appropriate measure of variability for the data shown, and what is its value?
The mean is the best measure of variability and equals 11.
The median is the best measure of variability and equals 11.5.
The range is the best measure of variability and equals 18.
The IQR is the best measure of variability and equals 2.
There are 29 students in a homeroom. How many different ways can they be chosen to be elected President, Vice President, and Treasurer?
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Please help with #4
Step-by-step explanation:
Let the statement be:
"If p, then q"The converse of a statement is:
"If q, then p"Let's try it for each statement and see if the converse is true.
a) The converse is:
If the interior angles sum to 180°, then my shape is a triangle.It is true.
b) The converse is:
If alternate interior angles are equal, the two lines are parallel.It is true.
c) The converse is:
If I have a Rhombus, then I also have a Square.It is false, since not all rhombus have four right angles.
d) The converse is:
If I have a shape with four right angles, then I have a rectangle.It is false, since it could be a square.
a. Converse: If the interior angles sum to 180°, then my shape is a triangle. (Converse is not true)
b. Converse: If alternate interior angles are equal, then the lines are parallel. (Converse is true)
c. Converse: If I have a Rhombus, then I also have a Square. (Converse is not true)
d. Converse: If I have a shape with four right angles, then I have a rectangle. (Converse is true)
a. Converse: If the interior angles of a shape sum to 180°, then the shape is a triangle.
The converse of this statement is not true. There are many shapes other than triangles whose interior angles sum to 180°, such as quadrilaterals and polygons with more than four sides.
b. Converse: If alternate interior angles of two lines are equal, then the lines are parallel.
The converse of this statement is true. If the alternate interior angles of two lines are equal, then the lines are parallel. This is a property of parallel lines and can be proven using the corresponding angles postulate.
c. Converse: If I have a Rhombus, then I also have a Square.
The converse of this statement is not true. While all squares are rhombuses (a square is a special type of rhombus), not all rhombuses are squares. A rhombus is a quadrilateral with all sides of equal length, but its angles can be anything other than 90°.
d. Converse: If I have a shape with four right angles, then I have a rectangle.
The converse of this statement is true. If a shape has four right angles, then it is a rectangle. This is a defining characteristic of rectangles, as all rectangles have four right angles.
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The complete question is :
Write the converse of each statement and determine if the converse is true.
a. If my shape is a triangle, then the interior angles sum to 180°.
b. If two lines are parallel, then alternate interior angles are equal.
c. If I have a Square, then I also have a Rhombus.
d. If I have a rectangle, then I have a shape with four right angles.
B
E
7
4
3
1
-2 -1 0
D
Determine the line of reflection.
O Reflection across x = 4
Reflection across y = 4
Reflection across the x-axis
Reflection across the y-axis
3
4
C
D'
8
E'
9
10
B'
A'
11
Answer: 10
Step-by-step explanation: it is a 5+ 5 =
6. For each final matrix, state the solution.
Please answer this picture
The solutions associated with the final matrices representing a system of linear equations are listed below:
First case: x = 3, y = 1, z = 8
Second case: No solution
Third case: No solution
What are the solutions contained in each final matrix?
In this problem we find three of final matrices, each of them representing a system of linear equations. There are two rules to be considered:
A system has no solution if there is a row with only zeroes in the dependent coefficients matrix.A system has a solution if there is a singular matrix, there is, the dependent coefficients matrix has only ones in the main diagonal and the rest of elements are zeroes.Now we proceed to determine the solution associated with each matrix:
First matrix:
x = 3, y = 1, z = 8
Second matrix:
No solution
Third matrix:
No solution
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Step-by-step explanation:
For the left matrix, since the matrix is already in reduced row form,
The solutions to the matrix is (3,-1,8)
For the middle matrix, we need to convert the -6 to a zero,
notice how in the third row, every entry except the last one is 0, this implies that
0=-2, which is not the case thus the middle matrix has no solution.
For the last one, notice that we have 3 colums but only two non zero rows, this means that this matrix has infinite solutions.
Determine the domain of the following graph:
Answer:
-9 is less than x, which is less than or equal to 11
Step-by-step explanation:
Answer:
Step-by-step explanation:
Domain is where the function exists for x.
The functions domain goes in terms of x goes from -9 to 11 not including -9 and including 11.
Interval notation:
-9 < x ≤ 11
Set notation:
(-9, 11]
Tell whether the information in the diagram allows you to conclude that c is on the perpendicular bisect of ab
11. Yes, the information provided can be used to conclude that C is on the perpendicular bisector of AB because CE bisects AB.
12. Yes, the information provided can be used to conclude that C is on the perpendicular bisector of AB because C is equidistant from AB.
What is a perpendicular bisector?In Mathematics and Geometry, a perpendicular bisector divides or bisects a line segment exactly into two (2) equal halves, in order to form a right angle with a magnitude of 90° at the point of intersection.
Question 11.
By critically observing the geometric shape, we can logically deduce that there is enough information to conclude that C is on the perpendicular bisector of AB because CE bisects AB:
AC ≅ BC
CD ≅ CD
AE ⊥ EC
Question 12.
By critically observing the geometric shape, we can logically deduce that there is enough information to conclude that C is on the perpendicular bisector because C is equidistant from line segment AB.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Evaluate the following expression when a = 5 and b = 1. Then, plot the resulting value on the provided number line. 12+2 (4 a²) ÷ 7 + 8
Answer:
To evaluate the expression when a = 5 and b = 1, we substitute the values into the expression:
12 + 2(4(5)²) ÷ 7 + 8
= 12 + 2(4 * 25) ÷ 7 + 8 (Note: 5² means 5 raised to the power of 2)
= 12 + 2(100) ÷ 7 + 8 (Note: 4 * 25 = 100)
= 12 + 200 ÷ 7 + 8
= 12 + 28.57 + 8 (Note: ÷ means divide)
= 48.57
To plot the resulting value on the provided number line , we would need to know the scale and range of the number line. Without this information, we cannot accurately plot the value.
Step-by-step explanation:
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Please help with 37
Answer:
Step-by-step explanation:
all circles have same round shape with no edges and corners so they all are similar in terms of their shape and appearance but not all the circles are congruent.
two circles are congruent if they have the same measurements of radius, circumference, diameter as well as the surface area. So, to determine whether the two circles are congruent or not we have to perform the calculations.
En la tabla se muestra la cantidad de zapatos vendidos en 1 almacén durante una semana, calcula las medidas de tendencia central y realiza el análisis correspondiente
Based on the information, we can infer that the mean is 14.28, the median is 15, and there is no unique mode (several repeated values).
How to calculate measures of central tendency?To calculate the measures of central tendency, we will use the data provided in the table. The pairs of shoes sold on each day are as follows: 10, 14, 15, 12, 16, 18, 16.
Mean:
The mean is calculated by adding all the values and dividing by the total number of items.
Mean = (10 + 14 + 15 + 12 + 16 + 18 + 16) / 7 = 101 / 7 = 14.28
Median:
The median is the value in the middle of an ordered data set. To calculate it, we first order the values from smallest to largest.
10, 12, 14, 15, 16, 16, 18
Since there are an odd number of values, the median is the value in the middle position, which in this case is 15. Therefore, the median is 15.
Mode:
The mode is the value that occurs most frequently in a data set. In this case, there is no value that is repeated more times than the others. The values 16 and 12 are repeated twice each, but there is no single mode. Therefore, there is no single mode in this data set.
Note: Here is the question in English:
The table shows the number of shoes sold in 1 store during a week, calculates the measures of central tendency, and perform the corresponding analysis.
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What is the square root of m^6?
m²
m³
m^4
m^5
The square root of m^6 is always positive.
The square root of m^6 can be calculated by dividing the exponent 6 by 2, since taking the square root is equivalent to raising a number to the power of 1/2.
In this case, m^6 divided by 2 gives us m^3.
Thus, the square root of m^6 is m^3.
This means that if we square m^3, the result will be m^6.
It is important to understand that the square root operation yields the positive root, so the square root of m^6 is always positive.
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what are the three arithmetic means between 10 and 130
The three arithmetic means between 10 and 130 are 40, 70, and 100.
To find the three arithmetic means between 10 and 130, we need to calculate the common difference between consecutive terms.
The common difference (d) can be found using the formula:
d = (last term - first term) / (number of terms - 1)
In this case, the first term is 10, the last term is 130, and we need to find three arithmetic means.
d = (130 - 10) / (3 + 1) = 120 / 4 = 30
Now, we can calculate the three arithmetic means by adding the common difference to the previous term:
First arithmetic mean = 10 + 30 = 40
Second arithmetic mean = 40 + 30 = 70
Third arithmetic mean = 70 + 30 = 100
So 40, 70, and 100 are the three arithmetic means between 10 and 130.
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
The value of x in ΔSTU is in the range (2, 32).
Given that ΔSTU is a triangle,
ST = 15,
US = x,
UT = 17.
We need to find the length of x in the triangle STU.
To solve this question, we need to apply the triangle inequality theorem.
According to the theorem, the sum of the lengths of any two sides of a triangle is greater than the length of the third side.
Therefore, using this theorem, we get:
ST + US > UT => 15 + x > 17
=> x > 17 - 15
=> x > 2US + UT > ST
=> x + 17 > 15 => x > 15 - 17
=> x > -2UT + ST > US
=> 17 + 15 > x
=> 32 > x
In this case ST = 15, US = x, UT = 17. Let's apply the triangle inequality to the sides of the triangle STU:
ST + US > UT
15 + x > 17
Simplify the inequality:
x > 17 - 15
x > 2
Triangle STU is valid The length of US(x) must be greater than 2 to be a perfect triangle.
However, without further information, we cannot determine the exact value of x.
You can specify any value greater than 2.
Therefore, from the above conditions, we conclude that 2 < x < 32.
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3. Pi is defined as the ratio of the circumference of a circle to the diameter of that circle. Which of the following correctly explains why the formula for the circumference of a circle is 2 mr 7 (1 point)
Two times equals the distance from one side of the circle to the other. When you multiply that by r, you get the distance around the circle, or the circumference.
Pi times requals the diameter of the circle. The diameter is half the circle, so when you multiply it by 2, you get the distance around the entire circle, or the circumference.
Two times requals the diameter of the circle. Pi is needed for all circle formulas, so you multiply by since you are finding the circumference.
Two times requals the diameter of the circle. Pi equals the circumference divided by the diameter. When you multiply, the diameter is in both the numerator and the denominator, which cancels out, leaving the circumference.
Answer:
The correct answer is "Two times r equals the diameter of the circle. When you multiply that by pi, you get the distance around the circle, or the circumference." This is because the circumference of a circle is equal to the distance around it, which is the same as the length of its perimeter. The diameter of a circle is the straight line that passes through the center of the circle and touches both sides. Therefore, if you multiply the diameter by pi, which is the ratio of the circumference to the diameter of a circle, you get the circumference. Alternatively, you can also use the formula C = 2πr, where C is the circumference and r is the radius of the circle. Since the radius is half the diameter, the formula can also be stated as C = πd, where d is the diameter of the circle.
Step-by-step explanation:
A given city is at 35°S and 200°W. How far is it from this city to A. the North Pole and B. the Equator C. the south pole
The distance from the given city to the South Pole is 125 degrees of latitude.
To determine the distance from the given city to various locations, we need to consider the latitude and longitude coordinates.
Distance to the North Pole:
The North Pole is located at 90°N latitude. Since the given city is at 35°S latitude, we need to calculate the difference in latitude between the city and the North Pole.
Distance to the North Pole = 90° - 35° = 55°
The distance from the given city to the North Pole is 55 degrees of latitude.
Distance to the Equator:
The Equator is located at 0° latitude. To determine the distance from the city to the Equator, we need to calculate the absolute value of the latitude of the city.
Distance to the Equator = |35°| = 35°
The distance from the given city to the Equator is 35 degrees of latitude.
Distance to the South Pole:
The South Pole is located at 90°S latitude. Since the given city is at 35°S latitude, we need to calculate the difference in latitude between the city and the South Pole.
Distance to the South Pole = 35° - (-90°) = 35° + 90° = 125°
The distance from the given city to the South Pole is 125 degrees of latitude.
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Show 2x -6 in a line graph
The resulting line graph will be a straight line that starts below the y-axis, crosses it at the point (0, -6), and continues upwards as the x-values increase.
To plot the line graph of the equation 2x - 6, we need to assign values to the variable x and calculate the corresponding values of y.
Let's choose a range of x-values and calculate the corresponding y-values:
For example, let's choose x = -3, -2, -1, 0, 1, 2, and 3.
Substituting these values into the equation 2x - 6, we get:
For x = -3: y = 2(-3) - 6 = -12
For x = -2: y = 2(-2) - 6 = -10
For x = -1: y = 2(-1) - 6 = -8
For x = 0: y = 2(0) - 6 = -6
For x = 1: y = 2(1) - 6 = -4
For x = 2: y = 2(2) - 6 = -2
For x = 3: y = 2(3) - 6 = 0
Now, we can plot these points on a graph with x as the horizontal axis and y as the vertical axis:
(-3, -12), (-2, -10), (-1, -8), (0, -6), (1, -4), (2, -2), (3, 0)
We can then connect these points with a straight line. Since the equation is in the form y = 2x - 6, the line will have a slope of 2 and a y-intercept of -6. The line will have a positive slope, meaning it will slant upwards from left to right.
The resulting line graph will be a straight line that starts below the y-axis, crosses it at the point (0, -6), and continues upwards as the x-values increase.
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What are the coordinates of the midpoint of the line segment whose end points are (2, 6) and (10, 4)?
The midpoint of the line segment with endpoints (2, 6) and (10, 4) is (6, 5).
To find the midpoint of a line segment, we can use the midpoint formula, which states that the coordinates of the midpoint are the average of the coordinates of the endpoints.
Let's denote the coordinates of the first endpoint as (x1, y1) and the coordinates of the second endpoint as (x2, y2).
In this case, the first endpoint is (2, 6) with coordinates (x1, y1) = (2, 6), and the second endpoint is (10, 4) with coordinates (x2, y2) = (10, 4).
To find the midpoint, we use the midpoint formula:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
Plugging in the values, we have:
Midpoint = ((2 + 10) / 2, (6 + 4) / 2)
= (12 / 2, 10 / 2)
= (6, 5)
As a result, (6, 5) is the point on the line segment where the endpoints are (2, 6) and (10, 4) respectively.
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The shaded part of the circle represents the part of gas used to fill up the gas tank of a lawn mower what part of the container is needed to fill up the gas tank of the lawn mower 4 times is the answer 8/48 8/12 6/16 or 6/12
The fraction of the container needed to fill up the gas tank of the lawn mower four times is 6/12. Option D.
The shaded part of the circle represents the fraction of gas needed to fill up the gas tank of the lawn mower once. To determine the fraction needed to fill it up four times, we can simply multiply the fraction by 4.
Let's assume that the shaded part of the circle represents x part of the whole container. Therefore, the fraction needed to fill up the gas tank of the lawn mower once is x.
To fill up the gas tank four times, we need to multiply x by 4. Therefore, the fraction needed to fill up the gas tank four times is 4x.
Now, we can compare this to the answer choices given:
8/48: This can be simplified to 1/6, which is not equal to 4x.
8/12: This can be simplified to 2/3, which is not equal to 4x.
6/16: This can be simplified to 3/8, which is not equal to 4x.
6/12: This can be simplified to 1/2, which is equal to 4x.
Therefore, the correct answer is 6/12, which represents the fraction of the container needed to fill up the gas tank of the lawn mower four times. so Option D is correct.
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Note the complete question is
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The result of the row operation on the matrix is given as follows:
[tex]\left[\begin{array}{cccc}1&0&0&8\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]
How to apply the row operation to the matrix?The matrix in this problem is defined as follows:
[tex]\left[\begin{array}{cccc}2&0&0&16\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]
The row operation is given as follows:
[tex]R_1 \rightarrow \frac{1}{2}R_1[/tex]
The first row of the matrix is given as follows:
[2 0 0 16]
The meaning of the operation is that every element of the first row of the matrix is divided by two.
Hence the resulting matrix is given as follows:
[tex]\left[\begin{array}{cccc}1&0&0&8\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]
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