There are 4 times as many chickens as ducks, there are 72 more chickens than ducks how many chickens and ducks are there

The approximate surface area of the glass prism is approximately 1986.66 square millimeters.

To find the surface area of the glass prism, we need to determine the area of each of its faces and then add them together. The prism consists of two congruent equilateral triangles and three rectangular faces.

The area of an equilateral triangle with side length s and height h is given by:

A = (√(3)/4) * s²

Using this formula, we can find the area of each of the two equilateral triangles in the prism:

A = (√(3)/4) * 7² ≈ 21.22 mm²

Next, we need to find the area of each of the three rectangular faces. The length of each rectangular face is equal to the side length of the equilateral triangle (7 mm), and the height is equal to the length of the prism (93 mm). Therefore, the area of each rectangular face is:

A = length x height = 7 mm x 93 mm = 651 mm²

To find the total surface area of the prism, we add the areas of the two equilateral triangles and the three rectangular faces:

Total surface area ≈ 2 x 21.22 mm² + 3 x 651 mm² ≈ 1986.66 mm²

Therefore, the approximate surface area of the glass prism is approximately 1986.66 square millimeters.

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The ratio to make the portrait proportional is width/42 = 5/8

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

Photograph that is 5 inches wide by 8 inches high.

This means that

Ratio = width/height

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

Ratio = 5/8

Given that he wants the portrait to be proportional to the photograph and 42 inches high.

Then, we have

width/42 = 5/8

Hence, the ratio to make the portrait proportional is width/42 = 5/8

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The statement that best describes how pollination begins is that it starts when pollen from the male reproductive organ of a flower is transferred to the female reproductive organ of the same or a different flower. Pollination is an essential step in the reproduction of plants, and it allows for the exchange of genetic material between different plants.

Pollination can occur through various methods, including wind, water, and animals such as bees, butterflies, and birds. Once the pollen is transferred, it begins to grow and develop, ultimately leading to the formation of a seed and the growth of a new plant.

Pollination is vital to the continuation of plant life, and without it, many plant species would not be able to survive. It is essential for plant breeders to understand the pollination process, as they can use it to cross different plant varieties and produce new and improved plants.

In conclusion, pollination begins when pollen from the male reproductive organ of a flower is transferred to the female reproductive organ of the same or a different flower, allowing for the exchange of genetic material and the growth and development of new plants.

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Answer:

Jack now makes $10.45

Step-by-step explanation:

First, we need to find 10% of 9.50. To do that we must divide 9.50 by 10 or simply move the decimal one place to the left to get 0.95. 0.95 is 10% of 9.50. Now we must ADD 0.95 to 9.50 because Jack is getting a 10% raise.  0.95 + 9.50 = 10.45. Therefore Jack makes $10.45 per hour at his job.

This is a statistical question because it involves collecting data. Most employees work around 40 hours each week.

a. This is a statistical question because it involves collecting data on the number of hours worked by employees each week and analyzing the distribution or pattern of the data.

b. Here's a dot plot of the data provided:

   37: •
   38: ••
   39: ••
   40: ••••••••
   41: •••
   42: ••
   43: •
   47: •

The distribution of the data in the dot plot shows that the majority of employees worked around 40 hours each week, as this is where the data is most heavily clustered. Most of the data are clustered around 40 hours, with a peak at 40 hours. There is a gap between 43 and 47 hours.

c. Based on the distribution of the data, most employees work about 40 hours each week.

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Answer: 72

Step-by-step explanation:

Q is same as M = 72

N=36

L=x

All 3 angles of a triangle add to 180

72+36+x=180

x=72

The algebraic expression is equivalent to the expression is 125/4x + 34. Option B

Algebraic expressions are simply defined as expressions that are composed of terms, variables, constants, coefficients and factors.

These algebraic expressions are also composed of mathematical operations, such as;

From the information given, we have;

25/4(5x-4/5)+29

expand the bracket, we get;

125x - 100/5 + 29

Find the LCM, we get;

125x - 100 + 145/5

Divide the values

125/4x + 34

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The gardener used 36.9 gallons of gasoline in the lawnmowers in that month.

In mathematics, a proportion is a statement that two ratios are equal. It expresses the relationship between two or more quantities that are directly proportional to each other. A proportion can be represented as an equation of the form:

a/b = c/d

We know that the gardener used a total of 61.5 gallons of gasoline in a month and that 3/5 of that total was used in the lawnmowers.

To find out how much gasoline the gardener used in the lawnmowers, we need to multiply the total amount of gasoline by 3/5:

61.5 gallons x 3/5 = 36.9 gallons

Therefore, the gardener used 36.9 gallons of gasoline in the lawnmowers in that month.

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The partial derivative using implicit differentiation is:

[tex]dz/dy = (-7x * e^(7xy) * (dx/dy) - 4) / (5x * cos(5xz))[/tex]

To calculate the partial derivative of the given equation with respect to y (dz/dy), we'll use implicit differentiation. The given equation is:

[tex]e^(7xy) + sin(5xz) + 4y = 0[/tex]

First, differentiate both sides of the equation with respect to y:

[tex]d(e^(7xy))/dy + d(sin(5xz))/dy + d(4y)/dy = 0[/tex]

Apply the chain rule for the first and second terms:

[tex](7x * e^(7xy)) * (dx/dy) + (5x * cos(5xz)) * (dz/dy) + 4 = 0[/tex]
Now, we are interested in finding dz/dy. To solve for it, rearrange the equation:

[tex](5x * cos(5xz)) * (dz/dy) = -7x * e^(7xy) * (dx/dy) - 4Finally, divide by (5x * cos(5xz)) to isolate dz/dy:dz/dy = (-7x * e^(7xy) * (dx/dy) - 4) / (5x * cos(5xz))[/tex]

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The quantity of heat which must be removed from the system in order to reduce the pressure from 2 bar to 1.6 bar is 4.23 kJ. The change in enthalpy per unit mass of the system is -123 kJ/kg, and the change in entropy per unit mass of the system is 0.134 kJ/kg-K.

To solve this problem, we need to use the steam tables to determine the properties of the steam at the initial and final conditions. We will assume that the system is undergoing a reversible, adiabatic process, so there is no heat transfer into or out of the system.

First, we determine the specific volume and enthalpy of the steam at the initial conditions of 2 bar and 0.9 dryness fraction. From the steam tables, we find that the specific volume is 0.4019 m^3/kg and the specific enthalpy is 2895.5 kJ/kg.

Next, we use the steam tables to find the specific volume and enthalpy of the steam at the final conditions of 1.6 bar. We find that the specific volume is 0.5059 m^3/kg and the specific enthalpy is 2772.5 kJ/kg.

The change in specific enthalpy per unit mass of the system is then given by:

Δh = h2 - h1 = 2772.5 - 2895.5 = -123 kJ/kg

The change in specific entropy per unit mass of the system is given by:

Δs = s2 - s1 = s2 - s1 = s2 - sf - x2*(sg - sf)

where sf and sg are the specific entropy of saturated liquid and saturated vapor at the final pressure of 1.6 bar, and x2 is the final dryness fraction. From the steam tables, we find that sf = 7.4332 kJ/kg-K, sg = 8.1248 kJ/kg-K, and x2 = 0.714.

Thus, we have:

Δs = s2 - s1 = s2 - sf - x2*(sg - sf) = (7.9757 - 7.4332) - 0.714*(8.1248 - 7.4332) = 0.134 kJ/kg-K

Finally, we can calculate the quantity of heat that must be removed from the system using the first law of thermodynamics:

Q = m*(h1 - h2) = m*Δh

where m is the mass of the steam in the system. To determine the mass of the steam, we use the specific volume at the initial conditions:

V = m/v1

where V is the volume of the system and v1 is the specific volume at the initial conditions. Substituting the given values, we have:

V = 85 L = 0.085 [tex]m^3[/tex]

m = Vv1 = 0.0850.4019 = 0.0344 kg

Substituting this value into the equation for Q, we obtain:

Q = mΔh = 0.0344(-123) = -4.23 kJ

Therefore, the quantity of heat which must be removed from the system in order to reduce the pressure from 2 bar to 1.6 bar is 4.23 kJ.

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Answer:

y = 9

Step-by-step explanation:

• Parallel lines have equal slopes

calculate the slope m of  TU using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = T(- 7, 4 ) and (x₂, y₂ ) = U(- 2, - 6 )

[tex]m_{TU}[/tex] = [tex]\frac{-6-4}{-2-(-7)}[/tex] = [tex]\frac{-10}{-2+7}[/tex] = [tex]\frac{-10}{5}[/tex] = - 2

now calculate the slope of VW and equate to - 2

with (x₁, y₁ ) = V(8, 7 ) and (x₂, y₂ ) = W(7, y )

[tex]m_{VW}[/tex] = [tex]\frac{y-7}{7-8}[/tex] = [tex]\frac{y-7}{-1}[/tex]

now equating gives

[tex]\frac{y-7}{-1}[/tex] = - 2 ( multiply both sides by - 1 to clear the fraction )

y - 7 = 2 ( add 7 to both sides )

y = 9

Answer:

2/5 < 0.42 < 43% < 3/7

Step-by-step explanation:

Let's convert them all to decimals:

43% = 0.43

2/5 = 0.4

3/7 = 0.428571...

0.42 = 0.42

Now we can arrange them in ascending order:

0.4

0.42

0.43

0.428571...

Answer:

A≈166.28

Step-by-step explanation:

Answer:

A≈166.28

Step-by-step explanation:

Answer:

1. 17.2

2. 1/4 or 0.25

3. 3/10 or 30%

4. 15/16

I hope this helped

Step-by-step explanation:

The probability of the two oldest Smith children being served first is 2/4 or 50%.

Assuming that all the children have an equal chance of being served first, there are a total of 4 possibilities for the order in which the two oldest Smith children can be served:

Out of these 4 possibilities, only the first 2 would satisfy the condition that the two oldest Smith children are served before the others. So the probability that the two oldest Smith children are served first is 2/4 or 50%.

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The value of the tangent segment b is 20.15.

The secant-tangent power theorem, also known as the tangent-secant theorem, states that if a tangent and a secant are drawn from a common external point to a circle, then the product of the length of the secant segment and its external part is equal to the square of the length of the tangent segment.

It is expressed as:

( tangent segment )² = External part of the secant segment + Secant segment.

From the diagram:

Tangent segment = WX = b

External part of the secant segment = YX = 14

Secant segment = ZX = 15 + 14 = 29

Plug these values into the above formula and solve for b.

( tangent segment )² = External part of the secant segment + Secant segment.

b² = 14 × 29

b² = 406

b = √406

b = 20.15

Therefore, the value of b is 20.15.

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The value of y is 116°.

Three given Adjacent angles are 28°, 36° and y°.

When two angles are adjacent, they have a common side between them and share a common vertex where the two sides meet. The angles are said to be adjacent because they are next to each other.

We know that if a ray stands on a straight line, then the sum of adjacent angles is 180°.

So, 28° + y° + 36° = 180°

y° + 64° = 180°

Subtracting 64° from both sides.

y°- 64° = 180° - 64°

y° = 116°

Hence, the value of y is 116°.

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1. The area of square C is 625 ft². 2. The perimeter of square C is 46 ft. 3. The area of square B is 1456 ft². 4. The length of square A is 4√15 ft.

A key idea in geometry that connects the lengths of a right triangle's sides is known as the Pythagorean Theorem. It says that the hypotenuse's square length, which is the side that faces the right angle, is equal to the sum of the squares of the lengths of the other two sides in a right triangle. It has the following mathematical expression:

a² + b² = c²

1. The area of square C can be found using the Pythagorean Theorem:

a² + b² = c²

Using the area the side is calculates as follows:

Side length of A = √225 = 15 ft

Side length of B = √400 = 20 ft

Now,

15² + 20² = c²

225 + 400 = c²

625 = c²

c = √625 = 25 ft

So the area of square C is:

Area of C = 25² = 625 ft²

2. The perimeter of square C can be found by adding up the side lengths of all three squares:

Perimeter of A = 36 ft, so each side length of A is 9 ft.

Perimeter of B = 48 ft, so each side length of B is 12 ft.

Perimeter of C = Side length of A + Side length of B + Side length of C

Perimeter of C = 9 + 12 + c

We found earlier that c = 25 ft, so we can substitute that in:

Perimeter of C = 9 + 12 + 25 = 46 ft

3. The area of square B can be found using the fact that the areas of squares A, B, and C are related by the equation:

Area of A + Area of B = Area of C

We know the area of A and the area of C, so we can solve for the area of B:

Area of A = 15² = 225 ft²

Area of C = 1681 ft²

Area of A + Area of B = Area of C

225 + Area of B = 1681

Area of B = 1456 ft²

4. Perimeter of B = 64 ft

Side length of B = 64 / 4 = 16 ft

Now we can use the Pythagorean Theorem to find the side length of C:

a² + b² = c²

a = 15 ft (side length of A)

b = 16 ft (side length of B)

c = √(a² + b²) = √(15² + 16²) = √481 = 22 ft

Finally, we can use the Pythagorean Theorem again to find the side length of A:

a² + b² = c²

b = 16 ft (side length of B)

c = 22 ft (side length of C)

a = √(c² - b²) = √(22² - 16²) = √240 = 4√15 ft

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The length of segment C'D' is given as follows:

C'D' = 2.

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

The length of segment CD is given as follows:

CD = 4. (4 vertical units of difference).

The scale factor is given as follows:

k = 1/2.

Hence the length of segment C'D' is given as follows:

C'D' = 1/2 x 4 = 2.

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The probability of not spinning 5 is 81/200.

What is the probability?

The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place.

Here, we have

Given: You spin the spinner, flip a coin, then spin the spinner again.

We have to find the probability of not spinning a 5. Flipping tails, then spinning a 5.

P(not spinning a 5) = 9/10

P(heads)= 1/2 because there is an equal chance to get heads or tails

P(not spinning a 5)= same as before, 9/10 (independent events).

= [tex]\frac{9}{10}[/tex] × [tex]\frac{1}{2}[/tex] × [tex]\frac{9}{10}[/tex]

= [tex]\frac{81}{200}[/tex]

Hence, the probability of not spinning 5 is 81/200.

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If a white dwarf in a binary star system gains mass beyond the Chandrasekhar limit (approximately 1.4 solar masses), it undergoes a runaway nuclear reaction, causing it to collapse and explode in a Type Ia supernova.

A white dwarf is a dense stellar remnant that is left behind after a star has exhausted all its nuclear fuel and has shed its outer layers. In a binary star system, the white dwarf may gain mass from its companion star, either through accretion or a merger. If the mass of the white dwarf exceeds the Chandrasekhar limit, the gravitational forces become so strong that the electrons in the atoms are forced to combine with the atomic nuclei, forming neutrons. This process is called electron capture, and it releases a tremendous amount of energy.

The energy released is enough to ignite a runaway nuclear reaction, causing the white dwarf to collapse and explode in a Type Ia supernova. Type Ia supernovae are important cosmic events because they are used as standard candles to measure the distance to distant galaxies. These explosions are also believed to play a significant role in the chemical evolution of the universe, as they produce heavy elements such as iron and nickel that are scattered into the interstellar medium.

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Answer:

x = 58°

Step-by-step explanation:

Label the point where the diagonals cross as T

Diagonals always meet at right angles

m∠SRT = 32

Sum of interior angles of ΔSRT = 180

x = 180 - 90 - 32 = 58

By observing the given protractor we know that option (C) is correct which says ∠NOP = ∠ROS.

An instrument for measuring angles is a protractor, which is often made of transparent plastic or glass.

Protractors might be straightforward half-discs or complete circles. Protractors with more complex features, like the bevel protractor, include one or two swinging arms that can be used to measure angles.

To draw arcs or circles, use a compass.

To measure angles, one uses a protractor.

So, we need to observe the given image of the protractor:
We will easily find that ∠NOP = ∠ROS

Therefore, by observing the given protractor we know that option (C) is correct which says ∠NOP = ∠ROS.

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Entonces, concluimos que las papas cuestan 4 pesos por kilogramo y el arroz cuesta 9 pesos por kilogramo.

Para resolver este problema, necesitamos plantear un sistema de ecuaciones lineales con dos incógnitas: el precio por kilogramo de papas y el precio por kilogramo de arroz. Podemos escribir:

12p + 6r = 102

9p + 13r = 153

Donde p es el precio por kilogramo de papas y r es el precio por kilogramo de arroz. Podemos resolver este sistema de ecuaciones usando el método de eliminación. Multiplicando la primera ecuación por 13 y la segunda ecuación por -6, obtenemos:

156p + 78r = 1326

-54p - 78r = -918

Sumando estas ecuaciones, obtenemos: 102p = 408

Dividiendo ambos lados por 102, encontramos que p = 4. Por lo tanto, el precio por kilogramo de papas es de 4 pesos.

Para encontrar el precio por kilogramo de arroz, podemos sustituir p = 4 en una de las ecuaciones originales y resolver para r. Por ejemplo, usando la primera ecuación:

12(4) + 6r = 102

48 + 6r = 102

6r = 54

r = 9

Por lo tanto, el precio por kilogramo de arroz es de 9 pesos.

Entonces, concluimos que las papas cuestan 4 pesos por kilogramo y el arroz cuesta 9 pesos por kilogramo.

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La fórmula para calcular el área de un triángulo es:

área = base * altura / 2

Podemos despejar la altura de esta fórmula y sustituir los valores que conocemos:

área * 2 / base = altura

1.5 * 2 / 1.5 = 2

Por lo tanto, la altura del triángulo es de 2 metros.

The system of equations to represent the scenario is 1.73x + 3.38y ≤ 28,

and the ordered pair is (8,4).

What is the Linear equation?

A linear equation is an algebraic equation that represents a straight line on a coordinate plane. A linear equation has the form y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept (the point where the line intersects the y-axis).

What is a system of equations?

A system of equations is a set of two or more equations that involve the same variables. In a system of equations, the solution is a set of values for the variables that satisfy all the equations in the system simultaneously. For example, the system of equations:

2x + 3y = 7

x - 2y = 5

has two equations with two variables x and y. The solution to the system is the set of values for x and y that satisfy both equations simultaneously.

According to the given information:

Part 1:

We are given that Apple needs 12 ounces of the stir fry mix, which is made up of rice and dehydrated veggies. Let x be the amount of rice in ounces and y be the amount of dehydrated veggies in ounces.

The total amount of stir fry mix needed is 12 ounces, so we have:

x + y = 12

The cost of the rice is $1.73 per ounce and the cost of the dehydrated veggies is $3.38 per ounce. Apple has $28 to spend and plans to spend it all, so the cost of the stir fry mix must be less than or equal to $28:

1.73x + 3.38y ≤ 28

Part 2:

To solve the system of equations, we can use substitution or elimination. Here, we will use substitution to solve for one variable in terms of the other:

x + y = 12 --> y = 12 - x

Substituting y = 12 - x into the second equation, we get:

1.73x + 3.38(12 - x) ≤ 28

Simplifying and solving for x, we get:

1.73x + 40.56 - 3.38x ≤ 28

-1.65x ≤ -12.56

x ≥ 7.616

We round up to the nearest whole number since we cannot buy a fraction of an ounce of rice. Thus, x = 8 ounces.

Substituting x = 8 into the equation y = 12 - x, we get:

y = 12 - 8

y = 4 ounces

Therefore, Apple buys 8 ounces of rice and 4 ounces of dehydrated veggies. The ordered pair is (8,4).

Part 3:

Our solution (8, 4) means that Apple needs to buy 8 ounces of rice and 4 ounces of dehydrated veggies to make 12 ounces of stir fry mix. The cost of the stir fry mix can be calculated by substituting these values into the cost equation:

1.73(8) + 3.38(4) = $21.48

Since this is less than or equal to the $28 that Apple has to spend, they can afford to buy the necessary ingredients to make the stir fry mix.

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Answer:

-7x^2 + 15x +7

Step-by-step explanation:

-7x^2 + 5x + 10 - (-10x + 3)

-7x^2 + 5x + 10 + 10x -3.......when u distribute it multiple by -1

-7x^2 + 15x +7 ...... simplify by collecting like term.

Tardarán aproximadamente 3.6 horas.

Para resolver este problema, podemos establecer una relación proporcional entre el número de hojas impresas y el tiempo requerido. Si 4 impresoras tardan 3 horas en imprimir 5000 hojas, podemos establecer la proporción

4 impresoras / 3 horas = 5000 hojas / x horas

Donde x representa el tiempo que tardarán en imprimir 6000 hojas. Podemos resolver esta proporción utilizando regla de tres:

4 / 3 = 5000 / x

Multiplicando en cruz, obtenemos:

4x = 3 * 5000

4x = 15000

x = 15000 / 4

x = 3750

Por lo tanto, tardarán aproximadamente 3750 horas en imprimir 6000 hojas.

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The length of the diagonal of a wide screen TV with an area of 150 inches and an aspect ratio of 2.39:1 is approximately 11.25 inches.

Aspect ratio refers to the proportional relationship between the width and height of an image or screen. In the case of a wide screen TV, the aspect ratio is 2.39:1, which means that for every 2.39 units of width, there is 1 unit of height.

To find the length of the diagonal of a wide screen TV with an area of 150 inches, we need to use the Pythagorean theorem, which states that the square of the length of the diagonal is equal to the sum of the squares of the width and height.

First, we need to find the width and height of the TV screen. We can do this by setting up the equation:

2.39x^2 = 150

where x is the width of the screen. Solving for x, we get:

x = √(150/2.39) = 10.87 inches

Now we can find the height by dividing the width by the aspect ratio:

h = 10.87 / 2.39 = 4.55 inches

Using the Pythagorean theorem, we can find the length of the diagonal:

d^2 = 10.87^2 + 4.55^2 = 126.68

d = √126.68 = 11.25 inches

Therefore, the length of the diagonal of a wide screen TV with an area of 150 inches and an aspect ratio of 2.39:1 is approximately 11.25 inches.

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The height of the tree is approximately 20.1 feet.

To determine the height of the tree, we can use the tangent function, which relates the opposite side (the height of the tree) to the adjacent side (the length of the shadow) of a right triangle.

tan(35°) = height of tree / 35 feet shadow

Rearranging this formula, we get:

height of tree = 35 feet shadow x tan(35°)

Plugging in the given values and using a calculator, we get:

height of tree = 35 x tan(35°) ≈ 20.1 feet

Therefore, the height of the tree is approximately 20.1 feet.

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