(x − 1)2 = −4 How many distinct real solutions does the given equation have? A) Exactly one B) Exactly two C) Infinitely many D) Zero

Answer:

She has 27 quarters

Step-by-step explanation:

Let:

x = Number of nickels

y = Number of quarters

US$0.05 = 5 cents = monetary value of a nickel

US$0.25 = 25 cents = monetary value of a quarter

                      x + y = 68

                     x = 68 - y  ---- --------  (equation i)

                0.05x + 0.25y = 8.80----- (equation ii)

These two are linear simultaneous equations, which can be solved either by substitution, elimination or graphical method.

Substitution method:

Substitute (equation i) into (equation ii) to solve for y:

0.05(68 - y) + 0.25y = 8.80

Expand the brackets by applying the Distributive Law and then bring all the like terms together. y needs to be isolated and made the subject of the equation:

= 3.4 - 0.05y + 0.25y = 8.80

= 0.25y - 0.05y = 8.80 - 3.40

= 0.20y = 5.40

= y = [tex]\frac{5.40}{0.20}[/tex]

∴ y = number of quarters = 27

The angle measures for this problem are given as follows:

Angle 3 has the same measure as angle 1, thus:

m < 3 = m < 1 = 68º.

Angles 1, 2 and 3 form a ray, adding to 180º, meaning that the measure of angle 2 is obtained as follows:

m < 2 + 2 x 68 = 180

m < 2 = 44º.

The sum of the internal angles of a triangle is of 180º, hence the measure of angle 5 is given as follows:

44 + m < 5  + 35 = 180

m < 5 = 180 - 79

m < 5 = 101º.

Each exterior angle is supplementary with it's interior angle, having their measures adding to 180º, hence the measures of angles 4 and 7 are obtained as follows:

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The correct match for the people given their position near the water and the graph, is :

Line 1 is Person C because Line 1 starts from under the level of the water and Person C climbs out of the water then goes up the zipline. Line 2 represents Person A because Line 2 is a stright line which is elevated above the water. Person A stood on the dock and did not move so they are most likely the person on Line 2.

Person B is on Line 3 because they stood on a pole at first which is higher than the dock that Person A was on. They then ziplined into the water which is why Line 3 went below water level.

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Answer:

None of them?

Step-by-step explanation:

2 yards = 6 feet

6 feet = 72 inches

3 yard = 9 feet

9 feet = 108 inches

4 yards = 12 feet

12 feet = 144 inches

5 yards = 15 feet

15 feet = 180 inches

To convert 1.05 x 10^-8 to standard form, we simply need to move the decimal point 8 places to the left, since the exponent is negative.

1.05 x 10^-8 = 0.0000000105

Therefore, 1.05 x 10^-8 in standard form is 0.0000000105.

Answer:

0.0000000105.

Step-by-step explanation:

The Original price of each sketchbook when sales on each book was $3 off is $6.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

Mr. Olin bought 6 sketchbooks for the students in his art class.

Each sketchbook was on sale for $3 off.

If the sketchbooks cost $18 total before tax.

So, the equation to represent the Scenario is

6(x-3)= 18

6x - 18 = 18

6x = 36

x = 36/ 6

x = 6

Thus, the original price is $6.

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The point (-6, -5) is defined by a linear function y = 1.5x + 4

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

The slope intercept form of a linear equation is:

y = mx + b

Where m is the rate of change and b is the y intercept.

The line goes through the points (0, 4) and (-2, 1). Hence:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\substituting:\\\\y-4=\frac{1-4}{-2-0} (x-0)\\\\y=1.5x+4[/tex]

The equation of the line is y = 1.5x + 4

For the point (-6, -5):

-5 = 1.5(-6) + 4

-5 = -5

The point (-6, -5) is defined by a linear function

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A straight line that continuously approaches a certain curve without ever meeting it is an asymptote. In other words, an asymptote is a line that a curve travels towards as it approaches infinity.

Set the denominator to zero and solve for x to discover the vertical asymptotes. Set each factor to zero and solve as this has already been factored. The asymptotes are expressed as equations of lines since they are lines. Asymptotes for the vertical line are x = 3 and x = 1.

An asymptote of a curve in analytic geometry is a line where the distance between the curve and the line gets closer to zero as one or both of the x or y coordinates tends to infinity.

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9.) The transformation performed in the function[tex]f(x) = \frac{1}{2}^{-x}[/tex] is a reflection across the x-axis.

10.) The transformations performed in the function [tex]f(x) = -log_5(x-2)+17[/tex]are a reflection across the x-axis, a vertical shift upward by 17 units, and a horizontal shift to the right by 2 units.

12.) The horizontal asymptote of f(x) = 4^x + 6 is y = +∞.

What is the transformation of the function?

The term "transformation of a function" refers to the process of altering the appearance of a function, either by shifting, stretching, or reflecting it along the coordinate axes.

9.) The transformation performed in the function [tex]f(x) = \frac{1}{2}^{-x}[/tex] is a reflection across the x-axis.

10.) The transformations performed in the function[tex]f(x) = -log_5(x-2)+17[/tex]are a reflection across the x-axis, a vertical shift upward by 17 units, and a horizontal shift to the right by 2 units.

12.) The horizontal asymptote of f(x) = 4^x + 6 is y = +∞. As x approaches positive infinity, the value of 4^x approaches positive infinity, making the value of the function approach positive infinity.

Hence,

9.) The transformation performed in the function[tex]f(x) = \frac{1}{2}^{-x}[/tex] is a reflection across the x-axis.

10.) The transformations performed in the function [tex]f(x) = -log_5(x-2)+17[/tex]are a reflection across the x-axis, a vertical shift upward by 17 units, and a horizontal shift to the right by 2 units.

12.) The horizontal asymptote of f(x) = 4^x + 6 is y = +∞.

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Answer:

32 cubic [tex]cm^{3}[/tex]

Step-by-step explanation:

Since each cube is 1 by 1 we can just count blocks to get its width length and height.

Width = 2

Length = 4

Height = 4

Volume= LxWxH

Volume= 4x2x4

Volume = 32 cubic [tex]cm^{3}[/tex]

Answer: 3 jackets and 5 sweaters

Step-by-step explanation:

j = jeans      s = sweaters

175 = 25j + 20s  ---- this will calculate the cost

8 = j + s ----- how much she bought

j = 8 - s; plug this into the cost

175 = 25(8-s) + 20s

175 = 200 - 25 + 20s; subtract 200 on both sides

-25 = -5s divide -5 to isolate the s

s = 5 Shelly bought 5 sweaters

now plug s = 5 in how much she bought

8 = j + 5

j = 3 Shelly bought 3 jackets

Step-by-step explanation:

Solution: Let the current ages of the father be F and that of the son, S.

Three years ago their ages were (F-3) and (S-3) and the sum was 48, or

F+S = 48+3+3 = 54, or

F = 54-S …(1)

(F+3) : (S+3) = 3:1, or

F+3 = 3S+9, or

F = 3S+6 …(2)

Equate (1) and (2): 54-S = 3S+6, or

4S=48, or S = 12 and So F = 42.

The father is 42 years and the son 12 years,

Answer:

+3 year after now Dad = 45; Son = 15 ====>   30 years old

now                       Dad = 42; Son = 12 ====>   30 years old

-3 year after now Dad = 39; Son = 9 =====>   30 years old

Step-by-step explanation:

Before 3 year is 48 so after 3 year is + 6 right???

so ==> 48 + 6(father and son so it's 2) + 6(same same) ==> 60

the ratio is 3:1 so son gets 1 dad gets 3 right?

==> 4 is the sum

So son is 60/4x1 = 15

Dad is 60/4x3(dad have three remember?) = 45

so now dad and son will be:

Dad = 45 -3 (only dad ok?) = 42

Son = 15-3(only son) = 12

so you can find the before to by minus 3 again ok??

Thanks for seeing

Tell me if it's wrong or right :P | XD | (❁´◡`❁)

For the function,

y = log(x + 3), all the required values are given below.

Let the function f(x) and g(x) are two real functions.

The function provided by the basic function f(x) and the constant

g(x) = f(x - k),

may be drawn by horizontally moving the f(x) k unit coordinates.

The shift's direction depends on the value of k. Specifically,

The base graph moves k units to the right if k > 0, and

The base graph moves k units to the left if k < 0.

Given:

A graph of the function.

The function is y = log(x + 3)

The x-intercept is (-2, 0) and y-intercept is (0, 0.477).

The transformation is,

-3 units to the left.

The domain is,

(−3, ∞), {x|x>−3}

Range: (−∞, ∞), {y|y∈R}

Hence, all the required values are given above.

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The solution of the equations will be x = 241 and y = -89.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the two equations are -16y=22+6x and -11y-4x=15. The equations by elimination method will be calculated as:-

-16y=22+6x

-11y-4x=15

Write the equations in the following way:-

6x + 16y = -22

-4x - 11y = 15

24x + 64y = 88

-24x - 66y = 90

____________

0     - 2y = 178

           y = 89

The value of x will be:-

-11y-4x=15

-11 x -89 - 4x = 15

979 - 4x = 15

-4x = -964

x = 241

Therefore, the value of x is 241 and the value of y is -89.

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Answer:

3.333

Step-by-step explanation:

[tex]3x - 6 = 4[/tex]

Add 6 to both sides of the equation

[tex]3x - 6 + 6 = 4 + 6[/tex]

[tex]3x = 10[/tex]

Divide both sides by 3

3x/3= 10/3

x = 3.333

Answer:

20.199

Step-by-step explanation:

ln (3x – 6) = 4

ln(3x-6)=2^2

x=2+e^4/3    

x=20.199

Both teams can complete the search in a time period of 4 hours.

Distance is a measurement of how far apart two points or objects are from one another. Time is a unit used to describe how long it takes for an object to travel between two points. Speed is a unit used to describe how quickly or slowly an item or a point moves.  

Here we have

Two search-and-rescue teams leave base camp at the same time,
looking for a lost child.

The first team, on horseback, heads north at 3 mph,  

The second team, on foot, heads south at 2.5 mph.

Let both teams complete searching in 'x' mins

The distance traveled by 1st team in 'x' mins = 3 × x  

= 3x  m

The distance traveled by 2nd team in 'x' mins = 2.5 × x  

= 2.5x m    

As we know total distance = 22 miles

=> 3x + 2.5x = 22 miles

=> 5.5x = 22 miles

=> x = 4 hrs  

Therefore,

Both teams can complete the search in a time period of 4 hours.

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The number of tone of sugar that will make the charge of the two company same is 18tons and the charge $5702

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 14 4x − 4y = 4.

Represent the amount of ton of sugar by x

T = 4500+ 150.25x equation 1

T = 3141 + 225.75 x equation 2

subtract equation 1 from 2

-1359 + 75.5x = 0

75.5x = 1359

x = 1359/75.5

x = 18

therefore the no of tones that will make the charge of the companies same is 18 tonnes of sugar.

And there cost will be ;

T = 4500+150.25(18)

T = $5702

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The value of the equation is f ( x ) = x³ + 3x² - 25x - 75 and ( x + 5 ) is a factor of the equation

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

f ( x ) = x³ + 3x² - 25x - 75   be equation (1)

Now , ( x + 5 ) is a factor of the equation ,

So , x + 5 = 0

Subtracting 5 on both sides of the equation , we get

x = -5

Substitute the value of x in equation (1) , we get

f ( -5 ) = ( -5 )³ + 3 ( -5 )² - ( 25 ) ( -5 ) - 75 = 0

-125 + 3 ( 25 ) + 125 - 75 = 0

-125 + 75 + 125 - 75 = 0

0 = 0

Hence , ( x + 5 ) is a factor of the equation

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Since slope of line passing through two points (x

1

,y

1

) and (x

2

,y

2

) is m=

x

2

−x

1

y

2

−y

1

We now find the slope of the line passing through the points (7,5) and (−9,5) as shown below:

m=

−9−7

5−5

=

−16

0

=0

Therefore, the slope of the line is 0.

Now use the slope and either of the two points to find the y-intercept.

y=mx+b

5=(0)(7)+b

b=5

Write the equation in slope intercept form as:

y=mx+b

y=(0)x+5

y=5

Hence, the equation of the line is y=5.

Answer:

a = 3

Step-by-step explanation:

Since the line passes through the origin, we can find its equation using the two given points.

The slope of the line is:

m = (3 - 9) / (40 - a - 2a - 50) = -6 / (10 - 3a)

Using the point (2a+50, 9), we can find the y-intercept (b) of the line:

9 = m(2a+50) + b

b = 9 - m(2a+50)

b = 9 + (6/(3a-10))(2a+50)

So the equation of the line is:

y = (-6 / (3a-10))x + (9 + (6/(3a-10))(2a+50))

Since the line passes through the origin, the y-intercept (b) must be zero. Therefore:

0 = 9 + (6/(3a-10))(2a+50)

6(2a+50) = -9(3a-10)

12a + 300 = -27a + 90

39a = 210

a = 210/39

a = 3

Answer:

The answer to your question is 22.0 rounded to the nearest tenth.

Step-by-step explanation:

Area=LW, L=W in square so 479=L^2, square root both sides, L=W=21.88=22 rounded

I hope this helps and have a wonderful day!

Answer:

22.0

Step-by-step explanation:

Took the test but best of luck

Answer:

Step-by-step explanation:

To find the speed of the truck, we need to divide the distance by the time taken:

Speed = Distance ÷ Time

Here, the distance traveled is 350 miles, and the time taken is 8 3/4 hours. We can convert 8 3/4 hours to an improper fraction as follows:

8 3/4 = (8 × 4 + 3) / 4 = 35/4

Now we can substitute these values in the formula to get the speed:

Speed = Distance ÷ Time

Speed = 350 miles ÷ 35/4 hours

Speed = 350 miles × 4/35 hours

Speed = 40 miles/hour

Therefore, the speed of the truck is 40 miles per hour.

Step 1: Calculate the normal usage for the coming month. Since normal usage is one case of 12 cans per week and the coming month is expected to be very busy, requiring 50 percent more tomato juice than normal, the normal usage for the coming month can be calculated by multiplying 12 cans per week by 4 weeks, then multiplying that number by 1.5, which gives us a total of 72 cans.

Step 2: Calculate the desired ending inventory for the coming month. The desired ending inventory for the coming month is 18 cans.

Step 3: Calculate the quantity to order. To calculate the quantity to order, we need to subtract the quantity on hand (6 cans) and the desired ending inventory (18 cans) from the normal usage (72 cans). This gives us a total of 48 cans to order.

Step 4: Calculate the number of cases to order. To calculate the number of cases to order, divide the quantity to order (48 cans) by 12 cans per case, which gives us 4 cases.

Therefore, Harvey's Restaurant should order 4 cases of tomato juice today in order to meet the expected demand for the coming month.

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Chen here tried to classify shapes from least specific to most specific. But the order is incorrect. The correct order is Quadrilateral, parallelogram, rhombus, square.

A quadrilateral is a shape having four sides. Any shapes with a four side is a quadrilateral. It can be an undetermined shape or a parallelogram, rectangle, rhombus or square. Parallelogram have four sides. Opposite sides are parallel and congruent. A rhombus, rectangle, square can all be considered a parallelogram.

A rhombus have four congruent sides and opposite sides are parallel. All squares are rhombi, but not all rhombi are squares. Square is the most specific shape. All sides of the square must be equal and all angles must be 90°.

We can say all squares are rhombus, all rhombi are parallelograms, all parallelograms are quadrilaterals.

So the correct order from least to most specific according to shape is Quadrilateral, parallelogram, rhombus, square.

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The equation of slope-intercept form for the line is,

⇒ y = 1/2x - 8

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Slope = 1/2

y - intercept = - 8

We know that;

The equation of slope-intercept form for the line is,

y = mx + b

Where, m is slope and y - intercept of the line.

Substitute all the values we get;

y = mx + b

y = 1/2x - 8

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Step-by-step explanation:

The indefinite integral of the polynomial function (x^4 + 2x^3 + 3x^2 + 4x + 5) is:

∫(x^4 + 2x^3 + 3x^2 + 4x + 5)dx = (x^5)/5 + x^4 + (3/2)x^2 + (2/3)x^3 + 5x + C

where C is an arbitrary constant of integration.

Answer:

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

Question 3:

4/5 ×10.

To do fraction multiplication all you need to do is put the number that's not in a fraction and put 1 as the denominator:

For example Q3:

Put 10 over 1 so its 10/1.

now just multiply fractions as normal .

4/5 ×10/1= 40/5.

As this is an improper fraction you will have to see how many times 5 fits into 40 which is 8.

So for Q3 your answer is 8.

You can carry out these step for each question but only do the last step if the fraction is improper(top heavy).

Answer:10x+35

Step-by-step explanation:

The vertex of the function is (x, y) = (-4, -14), so the vertex is at (x = -4, y = -14).

The equation can be written in vertex form by completing the square:

M(x) = x^2 + 8x - 10 = (x^2 + 8x) - 10 + (8/2)^2

= (x + 4)^2 - 14

The vertex of the function is (x, y) = (-4, -14), so the vertex is at (x = -4, y = -14).

To find the vertex of a quadratic function, you can use the formula:

Vertex = (x, y) = ( -b / 2a, f( -b / 2a) )

Where "a", "b", and "c" are the coefficients of the quadratic function in the standard form:

f(x) = ax^2 + bx + c

Note that the vertex of a quadratic function is either a minimum or maximum point, depending on the sign of the coefficient "a". If "a" is positive, the vertex represents the minimum point of the parabola. If "a" is negative, the vertex represents the maximum point of the parabola.

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We are this cut into 32, that is, 32 centimeters long is cut into 2 pieces. So let's do that. First, we're going to cut this ore into 2 pieces, didn't say down the middle, so we're going to say this has a piece length of x, which means this piece is going to have a length of 32 minus x. So what we're going to do is we're going to take each 1 of these pieces. Let me get them in different colors here and we're going to make a square out of each 1 of those pieces so for the blue piece, we're going to have this square and for the green piece we're going to have a square. That'S a little bit longer and we want to know the function for the area. Well, let's see how for the area, then we're going to need to take sides squared, so we need to figure out what the sides are for each 1 of these squares. Well, since we're wrapping it around we're going to separate this into 4 separate pieces, so that's going to be x over 4 would be a length of that side. We'Re going to do the same thing here and get 32 minus x over 4. Wrapping that green around to get that particular length. So that means the area of this blue square is going to be x over 4 squared. The area of this green square is gonna, be 32 minus x over 4 squared. So our total area is going to be x over 4 squared plus 32 minus x over 4 squared. They now want us to minimize this. We have to simplify this. That'S gonna, be x, squared over 16 plus and that's going to be over 16 was 32 times. 32 poiokay 1024 minus 64 x plus x, squared all that's over 16 point, so it's going to end up being 2 x, squared minus 64 x plus 1024. Over 16 point. I want to make this a pretty polly. So im gonna make this x squared over 8 minus 4 x and then that's going to be 64 point. Well, we want to minimize the area i see here. We have a quadratic with a leading coefficient that is positive, so means we're going to have a parabola that opens down, so our vertex is going to be our minimum. We'Re going to look at that and say that our vertex is going to be negative b over 2 a when i look at this particular equation. I see that we have a coefficient of 1 eighth on my square term. That'S going to be my value of a and we have a negative 4 on our ex term. That'S going to be our value of b! So i'm going to substitute that here and get negative negative 4 over 2 times 18 point. So that's going to be 4 over 1. Fourth, which is going to be 116 point, so x is going to have a value of 116 point. What is going to be that area for we now need to take that 1 sixteenth and put it in place of x. So i'm going to do that in a of x. I winna get a of 116 point, so thats gonna be 1 eighth times 1. Sixteenth squared minus 4 times 1, sixteenth minus 64 point. So let's see what that's going to be. This should have been 16, not 116 point. So i'm going to go back and redo this with 16 point where's, my racer! Sorry about that gem! Reciprocal is mixed up. So that's gonna be 16 point. So let's see what that's going to be: that's going to be 1 over 8 times, 16 times 16 point. So that's going to be 32 point and then we're goin to have minus 64 minus 64 point something all right. So that should ave been a plus so were maximum area is going to be mum area.

Answer:  a) 0.00000047 = 4.7*10 7square. b) 0.0000000738 = 73.8 * 10 9 square .

Step-by-step explanation:

Answer: [tex]4.7 x 10^{-7}[/tex]

If the length of of a square increases from 3 inches to 7inches,the perimeter will increase from 12 inches to 28 inches. The perimeter will increase by 16inches

Square is a regular quadrilateral, which has all the four sides of equal length and all four angles are also equal. The angles of the square are at right-angle or equal to 90-degrees. Also, the diagonals of the square are equal and bisect each other at 90 degrees.

The perimeter of a square is determined by adding all the sides together.

Therefore the perimeter of square = 4l

when the length is 3 inches, the perimeter = 4×3 = 12inches

when the length is 7inches , the = 4× 7 = 28inches

Therefore the perimeter increased from 12inches to 28inches. It increases by 16 inches

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When the side length of a square increased from 3 inches to 7 inches, the perimeter increased from 12 inches to 28 inches

The perimeter of a square can be represented as follows:

The perimeter of a square is the sum of the whole sides of the square.

perimeter of a square  = 4l

where

l  = side length

Recall the whole sides of a square is equal.

Therefore,

The side of the square is formally 3 inches.

Hence,

perimeter of a square = 4 × 3

perimeter of a square = 12 inches.

When the side length is increased to 7 inches.

Hence,

perimeter of a square = 4 × 7

perimeter of a square = 28 inches

Therefore, when the side length of a square increased from 3 inches to 7 inches, the perimeter increased from 12 inches to 28 inches

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