What are the solutions of the equation 2 log x = log (5x-6)? Select all that apply.
A x=1
B. x=2
C. x= 3
D. x = 5
E. x=6

The completed table with the values for composite functions in column 3, f(g(x)) and column 4, g(f(x))  included is presented as follows;

[tex]\begin{array}{|c|c|c|c|}f(x) & g(x) & f(g(x)) &g(f(x)) \\&&&\\x^2+1 &-2\cdot x + 5 &4\cdot x^2 -20\cdot x +26 & -2\cdot x^2+3 \\&&&\\2\cdot x^2 - 2\cdot x + 4 & x+3 & 2\cdot x^2 + 10\cdot x + 16& 2\cdot x^2 - 2\cdot x + 7 \\&&&\\ \sqrt{x-4} &2\cdot x^2+ 4 &x\cdot \sqrt{2} & 2\cdot x - 4 \\\end{matrix}[/tex]

f(g(x)) ≠ g(f(x)), because the operations and the order of operations in the functions are different

Composite functions are functions in which the input or argument are also functions.

The values of the composite functions based on the defined functions are found as follows;

f(x) = x² + 1, g(x) = -2·x + 5

Therefore; f(g(x)) is obtained by plugging in x = g(x) in f(x) as follows;

f(x) = x² + 1

f(g(x)) = (-2·x + 5)² + 1 = -2·x × (-2·x + 5) + 5 × (-2·x + 5) + 1

-2·x × (-2·x + 5) + 5 × (-2·x + 5) + 1 = 4·x² - 10·x - 10·x + 25 + 1

4·x² - 10·x - 10·x + 25 + 1  = 4·x² - 20·x + 26

When f(x) = x² + 1, and g(x) = -2·x + 5, f(g(x)) = 4·x² - 20·x + 26

g(f(x)) = is obtained by plugging in x = f(x) in g(x) as follows;

g(x) = -2·x + 5

f(x) = x² + 1

g(f(x)) = -2 × (x² + 1) + 5 = -2·x² - 2 + 5

g(f(x)) = -2·x² + 3

When f(x) = 2·x² - 2·x + 4, and g(x) = x + 3, we get;

f(g(x)) = 2×(x + 3)² - 2×(x + 3) + 4 = 2×(x² + 6·x + 9) - 2·x - 6 + 4

2×(x² + 6·x + 9) + 2·x + 6 + 4 = 2·x² + 10·x + 16

f(g(x)) = 2·x² + 10·x + 16

When f(x) = 2·x² - 2·x + 4, and g(x) = x + 3, f(g(x)) = 2·x² + 10·x + 16

g(f(x)) = is obtained by plugging in x = f(x) in g(x) as follows;

g(x) = x + 3

f(x) = 2·x² - 2·x + 4

g(f(x)) = 2·x² - 2·x + 4 + 3 = 2·x² - 2·x + 7

g(f(x)) = 2·x² - 2·x + 7

When f(x) = [tex]\sqrt{x - 4}[/tex], and g(x) = 2·x² + 4, we get;

f(g(x)) = [tex]\sqrt{2\cdot x^2 + 4 - 4} = x\cdot \sqrt{2}[/tex]

g(f(x)) = 2 × ([tex]\sqrt{x - 4}[/tex])² + 4 = 2 × (x - 4) + 4 = 2·x - 4

g(f(x)) = 2·x - 4

The values of the composite functions in column 3 and column 4 are included in the table in the first section of the response.

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Answer:

I think it’s D

Step-by-step explanation:

trust

Therefore , the solution to the given problem of angles comes out to be

∠RQS is 59.5 degrees as ∠RQS = ∠PQR.

Define angles.

An angled structure in geometry is composed of two rays that converge at the vertex, or core, of the angle. These rays are referred to as the angle's faces. Depending upon where they are situated, two beams may be able to form any angle within a plane. The intersection of two planes also produces an angle. Diahedral angles are the name for them. Light beams or lines that share the same endpoint in plane geometry can have a wide variety of shapes or angles. The English term "angle" derives from the Latin term "angulus," which meaning "horn." The intersection of the two rays is known as the vertex, or vertex of the angle.

Here,

QS cuts an angle. PQR, followed by ∠SQR = ∠ PQS and

∠PQS + ∠RQS = ∠PQR.

The equation then changes to

∠PQR = ∠PQS + ∠PQS

∠PQR = 2∠PQS

∠PQS equals ∠PQR/2

assuming∠ PQR = 119°

Replace in the resulting expression from the above;

∠PQS equals ∠PQR/2

∠PQS = 119/2

∠PQS = 59.5°

∠RQS is 59.5 degrees as ∠RQS = ∠PQR.

Therefore , the solution to the given problem of angle comes out to be

∠RQS is 59.5 degrees as ∠RQS = ∠PQR.

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Answer:

9 and 4

Step-by-step explanation:

xy = 36

x+y = 13       or    13 - x = y    <====sub this into the first equation

x ( 13-x) = 36

-x^2 + 13x - 36 = 0  multiply the entire equation by -1  to make it easier solve

x^2 -13x+36 = 0     this factors to

(x -9)(x-4) = 0          showing x = 9 or 4     with y being 4 or 9

The differential equation is [tex]y=\frac{-7t^2+22t-7}{7t-22}[/tex]

We are given the Initial value problem:

y'=(t=y)²-1, y(3)=4

Substitute the value z=t+y

When t=3 and y=4 then z=3+4=7

y'=z²+1

Differentiate z w.r.t t

[tex]\frac{dz}{dt} =1+y'[/tex]

Then, we get [tex]z'=1+z'-1=z^2[/tex]

z⁻²dz=dt

Integrate on both sides:

-1/zdz=t+c

z=-1/t=c

Substitute t=3 and z=7

Then, we get

7=-1/3+c

21+7c=-1

7c=-1-21=-22

c=-22/7

Substitute the value of C then we get:

z=-1/t-22/7

z=-7/7t-22

y=z-t

y=-7/7t-22-t

y=-7-7t²+22t/7t-22

y=-7t²+22t-7/7t-22.

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Therefore , the circumference of the circle is 4 centimeters, while the length of the subtended arc is 16 centimeters.

Every point in the plane of a circle is equally separated from the center and is a closed, two-dimensional object. Each line tracing the circle contributes to the formation of the line of reflection symmetry. Additionally, each angle has rotational symmetry around the center.

Here,

calculation

The formula for arc length is (/2) 2r.

because of length of an arc equals r.

16 = 4θ

=> θ = 4

4r is the length of an arc.

Four times the radius, the subtended arc is longer.

Angle A is subtended by an arc if its length and radius are equal.

=> θ = 16 /4

=>4 rad

Therefore , the circumference of the circle is 4 centimeters, while the length of the subtended arc is 16 centimeters.

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Answer:

116 months

Step-by-step explanation:

A $659,000 property is depreciated for tax purposes by its owner with the straight-line depreciation method. The value of the building, y, after x months of use is given by:

y = 659,000 − 1800x

After how many months will the value of the building be $450,200?

y = 659,000 − 1800x

450,200 = 659,000 − 1800x

subtract 659,000 from both sides:

450,200 - 659,000 = 659,000 − 1800x - 659,000

-208,800 =  − 1800x

divide both sides by -1800:

-208,800/1800 =  − 1800x/1800

116= x

so:

x  = 116

Answer:

Step-by-step explanation: The formula for the line that intersects at (8,-5) and is parallel to line x+y = 8 is given by the algebraic expression y = -x +3.

What is Algebraic expression?

The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values.

Variables and constants can both be used in an algebraic expression.

A coefficient is any quantity that is added before a variable and then multiplied by it.

The Algebraic expression in this case is:

x + y = 8

which traverses points (8,-5)

Let's start by utilizing the point-intercept equation of line, which is provided by: to determine the slope of line m, that is parallel towards the line x + y = 8.

y = mx + c →(1)

x + y = 8

y = -x + 8

Comparing the aforementioned Algebraic expression to equation (1), we obtain

m = -1

The slope of the line parallel to the line x + y = 8 will now be the same, and it will be m = -1.

Let's use the point-slope equations of line to determine the linear equation now:

(y-y₁) = m(x-x₁)

Changing every value in the equation above to obtain the Algebraic expression for a line

(y-(-5)) = -1(x-8) (x-8)

(y+5) = -x+8

y + 5 = -x +8

y = -x +3

The formula for the line that intersects at (8,-5) and is parallel to line x+y = 8 is given by the algebraic expression y = -x +3

The <HDI of the circle is 70 degree. A circle is divides into 360 equal degrees.

A circle is divides into 360 equal degrees.

In relation to a circle, angles are measured in degrees or radians, with one full rotation being equal to 360 degrees or 2 Pi radians.

so, <EDI = 140 degree.

so

A circle is  360 equal degrees.

360 - 140 =  220

< IDH = <EDF = 2x

<FDG = <GDH = 2y

so

2x + 2y = 220

2 * 70  + 2 * 40 = 220 degree

so,

<HDI = 70 degree.

so

The <HDI of the circle is 70 degree.A circle is divided into 360 equal degrees.

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Answer:

[tex]\boxed{x = 8 \;m}[/tex]

Step-by-step explanation:

Nice drawing! :)

From the figure we see that the rectangle has a length of 30 m and a width of 20 m

The total area of the rectangle PQRS = 20 x 30 = 600 m²

The square footage of the planted area = area of figure MNSR = 388 m²

Therefore the rest of the area (the unshaded portion) is:
600 - 388 = 212 m²

This is the combined area of the two triangles ΔPNM and ΔMRG

Let's find the area of each of these triangles. Each of them is a right triangle which makes calculations easier

Area of a right triangle = (1/2) x base x height

ΔPNM has base = 30 - x and height = 20 -x

Area of ΔPNM

= (1/2) (30-x)(2-x)

We can use the FOIL method to evaluate (30-x)(2-x)

(30-x)(20-x)  

= 30·20 + (30)(-x) + x(20) + (-x)(-x)

= 600 - 30x + 20x + x²

= 600 -50x + x³

We usually rewrite with coefficients in decreasing magnitude of x degree

Area of ΔPNM

[tex]=\dfrac{x^2 - 50x + 600}{2}[/tex]

Let's now find the area of ΔMRQ with a base of x and a height of 20

Area of ΔMRQ
[tex]=\dfrac{1}{2}\cdot 20 = \dfrac{20x}{2}[/tex]

Adding both terms together we get
[tex]\dfrac{x^2 - 50x + 600}{2} + \dfrac{20x}{2} \\[/tex]

We have computed the area of the unshaded region as 212

So the above sum must be equal to 212

[tex]\dfrac{x^2 - 50x + 600}{2} + \dfrac{20x}{2} = 212[/tex]

Multiply throughout by 2 to get rid of the denominator:

[tex]\rightarrow \;\;x^2 - 50x + 600 + 20x = 212\times 2 = 424\\\\\rightarrow \;\;x^2 -30x + 600 =424\\[/tex]

Move 424 to the left:

[tex]x^2-30x+600-424=424-424\\\\x^2-30x+176=0[/tex][tex]\textrm{Factoring } x^2-30x+176=0\\\\\\\textrm{We get}\\\\x^2-30x+176=\left(x-8\right)\left(x-22\right)\\\\[/tex]

This is a quadratic equation which can be solved using the quadratic formula or by factoring

[tex]\textrm{Factoring } x^2-30x+176=0\\\\\\\textrm{We get}\\\\x^2-30x+176=\left(x-8\right)\left(x-22\right)\\\\[/tex]

So
[tex]x^2-30x+176=0 \rightarrow (x -8)(x-22) = 0\\\\[/tex]

So x = 8 or x = 22 are two possible solutions to this quadratic

If x = 22, it will be greater than the width of 20 and also 20-x = -2 so it is not a valid solution for this situation

Therefore we get the final answer as [tex]\boxed{x = 8 \;m}[/tex]

The equivalent expression of 2/5(s+20) is 2/5s+8 and expression (9+3)=12.

what are expressions?

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, nected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between which math, there are two types of expressions, numerical  expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.

e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.

Now,

Given expression 2/5(s + 20)

Using distributive property

2/5s+2/5*20

2/5s+2*4

2/5s+8

and (9+3)=12

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Right question:-

Use the distributive property to write an equivalent expression for 2/5(s + 20). Then evaluate the expression (9+3).

The complement of A∪B is A′∩B ′.

A set of components in the universal set that are not a part of the initial set is known as the complement of a set in mathematics. Discover what a subset and its complement are, how to calculate a subset's complement, and the proper notation to use when writing a subset and its complement.

Given, universal set, U={1,2,3,4,5,6,7}

A={1,2,5,7}

B={3,4,5,6}

(A∪B) ′=U−(A∪B)

={1,2,3,4,5,6,7}−{1,2,3,4,5,6,7}=ϕ

A′∩B′=(U−A)n(U−B)

={3,4,6}n{1,2,7}=ϕ

Hence ( A∪B)′=A′∩B ′.

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We can use the formula:

[tex]m = (y2 - y1) / (x2 - x1) = (5 - 3) / (-4 - 1) = 2/5[/tex]

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

20) The point-slope form of a line is[tex]y - y1 = m(x - x1)[/tex], where [tex](x1, y1)[/tex] is a point on the line and m is the slope. The slope of the line can be found by using the coordinates of two points on the line. To find the slope between the points [tex](1, 3)[/tex] and [tex](-4, 5)[/tex], we can use the formula:

[tex]m = (y2 - y1) / (x2 - x1) = (5 - 3) / (-4 - 1) = 2/5[/tex]

The point-slope form of the line is then:

[tex]y - 3 = (2/5)(x - 1)[/tex]

To convert this to slope-intercept form (y = mx + b), we can solve for y:

[tex]y = (2/5)x + (3 - (2/5)) = (2/5)x + (12/5)[/tex]

21) The line is parallel to [tex]y = -2x - 5[/tex], so we know that the slope of the line is -2. We can use the point [tex](4, -7)[/tex]and the slope -2 to write the equation in point-slope form:

[tex]y - (-7) = -2(x - 4)[/tex]

or

[tex]y + 7 = -2x + 8[/tex]

To convert this to slope-intercept form [tex](y = mx + b)[/tex], we can solve for y:

[tex]y = -2x + 1[/tex]

22) The line is perpendicular to [tex]y = -3/2x + 1[/tex], so we know that the slope of the line is the negative reciprocal of [tex]-3/2[/tex]. The slope of the line is [tex]2/3[/tex]. We can use the point [tex](3, 5)[/tex] and the slope [tex]2/3[/tex] to write the equation in point-slope form:

[tex]y - 5 = (2/3)(x - 3)[/tex]

or

[tex]y = (2/3)x + (5 - (2/3)3) = (2/3)x + (5 - 2) = (2/3)x + 3[/tex]

To convert this to slope-intercept form [tex](y = mx + b)[/tex], we can solve for y:

[tex]y = (2/3)x + 3[/tex]

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According to the solving the lengths of right angle triangle using Pythagorean theorem x = 6, y = 3

A fundamental relationship in Euclidean geometry between a right triangle's three sides is known as the Pythagorean theorem or Pythagoras' theorem. According to this rule, the area of the square with the hypotenuse side is equal to the sum of the areas of the squares with the other two sides.

The following is one way to perform the calculation. It may not be the best way.

c = b/cos(α)

= 6

a = √c2 - b2

= √62 - 5.192

= √9.0639

= 3.01063

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The Fencing Mrs. Jones will need in centimeters is 1220 cm

The fencing is a measure of the perimeter of the region to be covered

With the dimensions in meters deduced form the problem as 3.4 m by 2.7 m. the perimeter is calculated using the formula

= 2( length * width)

= 2(3.4 + 2.7)

= 2(6.1)

= 12.2 m

To convert 12.2 m to cm we use the factor, 1 m i= 100 cm, therefore

= 12.2 * 100

= 1220 cm

the perimeter is 1220 cm

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The manager of the clothing store always orders 2 small T-shirts and 3 small T-shirts for every 4 medium T-shirts.

What in mathematics is a linear equation?

According to Wolfram MathWorld A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

The manager plans to order 24 medium T-shirts and we want to find out how many small T-shirts the manager should order.

We can use the information given to set up an equation to represent the relationship between the number of small T-shirts and medium T-shirts. Let S be the number of small T-shirts and M be the number of medium T-shirts.

We know that:

S = 2 + (3/4)M

We are given that the manager plans to order 24 medium T-shirts, so we can substitute this value into the equation:

S = 2 + (3/4) * 24

We can simplify and solve for S:

S = 2 + (3/4) * 24

S = 2 + 18

S = 20

Therefore, the manager should order 20 small T-shirts.

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The value of y when x = 28 in the proportional relationship is 112.

Proportional relationships are relationships between two variables where their ratios are equivalent.

The value of y is directly proportional to the value of x. When x = 3.5, the value of y is 14.

Therefore, let's find the constant of proportionality.

y = kx

14  = 3.5k

divide both sides by 3.5

k = 14 / 3.5

k = 4

Let's find the value of y when x = 28.

Hence,

y = 4x

y = 4 × 28

Therefore,

y = 112

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On solving the provided question we can say that the expression of the emaily number will be as =[tex]\frac{1}{4}n - 3[/tex]

In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted. Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expression, all of which are separated by the arithmetic sign +.

here,

the expression of the emaily number will be as =[tex]\frac{1}{4}n - 3[/tex]

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Option A, The degrees of freedom for a small-sample test of hypothesis for [tex]H_1[/tex] and [tex]H_2[/tex], assuming [tex]o_{12}[/tex], [tex]o_{22}[/tex], and [tex]n_1[/tex], [tex]n_2[/tex] is 15.

To calculate the degrees of freedom for a small-sample test of hypothesis for [tex]H_1[/tex] and [tex]H_2[/tex], assuming [tex]o_{12}[/tex], [tex]o_{22}[/tex] and [tex]n_1[/tex], [tex]n_2[/tex], you would use the following formula:

df = ([tex]o_{12}^2[/tex]/n_1) + ([tex]o_{22}^2[/tex]/n_2)

In this case, the degrees of freedom would be:

df = ([tex]o_{12}^2[/tex]/16) + ([tex]o_{22}^2[/tex]/16) = 15 and represents the number of values that are free to vary in the sample.

So, the answer would be A. 15

It's important to note that this formula is only used for small sample sizes. For large sample sizes, the degrees of freedom are approximated using the Welch-Satterthwaite approximation.

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The difference in the monthly payments for a 20-year mortgage and a 30-year mortgage on a $135,000 loan at 3.32% APR is $430.

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CuI's molar solubility is determined to be 1.27 x 10⁻¹².

The quantity of ions dissolved per litre of solution is measured by molar solubility. The quantity of ions that are dissolved in this situation's amount of solvent is represented as solubility.

Think about the equation.

Cu+(aq) CuI.(s) + I- (aq)

Let's assume that CuI (s) has a molar solubility of "S" mol/L.

Thus,

Product of solubility = [Cu+(aq)] + [ I-(aq)] → [Cu+(aq)] Ksp

[ I-(aq)] ———(1)

We are aware of

For CuI, the solubility product Ksp is 1.27 x 10⁻¹².

Consequently, from equation (1)

1.27 × 10⁻¹² = S.S

S² =1.27 × 10⁻¹²

= (1.27 × 10⁻¹² )½ = 1.127 x 10⁻⁶ M

Therefore, CuI has a molar solubility of 1.127 x 10-6 M.

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Answer: To determine how many hours John needs to work to earn R750, you would need to know his hourly wage. If John earns R50 per hour, he would need to work 15 hours to earn R750 (R750 / R50/hour = 15 hours). If his hourly wage is different, the number of hours he needs to work will be different.

Step-by-step explanation:

Answer:

the answer is 338.13

Step-by-step explanation:

289,00×.17=49.23

49.13+289.00

hope this helps:)

Answer:

Step-by-step explanation:

it depends on where each point is on each chart because they can't be blank

The quotient of the division (x^2-3x+5) divided (x-1) is x - 2 with a remainder of 3

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

(x^2-3x+5) divided (x-1)

Using the long division method of quotient, we have

x - 1 | x^2 - 3x + 5

The division steps are as follows

           x - 2

x - 1 | x^2 - 3x + 5

        x^2 - x

------------------------------------------------

             -2x + 5

             -2x + 2

------------------------------------------------

                         3

Hence, the quotient is x - 2

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Answer:

(0,5) and (3,320)

Step-by-step explanation:

Plug in the ordered pair into the function and see if it makes sense.

Plug in 5 for y and 0 for x:

5= 5(4)^0
4^0 = 1 (anything to the power of 0 except 0 is one)
5x1 = 5
5=5
(0,5) works

320 = 5(4)^3

4^3 = 64

64x5 = 320

320=320

320=320 (3,320) works

(0,5) and (3,320) both work.

The terms in given expression like variables, coefficient, constant are respectively, y, 1, -9

An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.

For example, 2x+3

Given that,

An expression,

⇒ y-9

In given expression, y is term which is variable

And coefficient of y is 1

constant term is -9

Therefore, we can write our terms are,  y, 1, -9

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On solving the provided question, we can say that  vertex form of the equation is in the form of y = a(x-h)^2 + k.

A vertex, or particular point, is a place where two or more lines or edges meet in a mathematical object. Angles, polygons, polyhedral, and graphs are where vertices are most frequently seen. Nodes and vertices in a graph are the same thing.

Recall that a parabola's General Form is y = ax2 + bx + c. The x-coordinate of the vertices, which is x = - b/2a, must first be discovered in order to find the vertex from this form. You will use this number to replace x in the parabola equation once you have determined the x-coordinate of the vertex.

a = -1/4 * (4 - 12) = -1

h = -b/(2a) = 12/(2(-1)) = -6

k = f(h) = -(-6)^2 + 12(-6) - 4 = 36

Therefore, the vertex form of the equation is y = -(x+6)^2 + 36.

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