‼️WILL MARK BRAINLIEST‼️

Answer:

2. 1

3. [tex]\dfrac{x(x + 2)(x - 4)}{(x - 2)^2}[/tex]

Step-by-step explanation:

2.

[tex] \dfrac{x^2 - 81}{x + 81} \times \dfrac{x^2 + 81x}{x^3 - 81x} = [/tex]

Multiply the fractions together by multiplying the numerators and multiplying the denominators.

[tex] = \dfrac{(x^2 - 81)(x^2 + 81x)}{(x + 81)(x^3 - 81x)} [/tex]

Factor every numerator and denominator.

[tex] = \dfrac{(x + 9)(x - 9)x(x + 81)}{(x + 81)x(x^2 - 81)} [/tex]

[tex] = \dfrac{(x + 9)(x - 9)x(x + 81)}{(x + 81)x(x + 9)(x - 9)} [/tex]

Now divide the numerator and denominator by terms common to both. This is what is commonly called canceling terms in the numerator and denominator. Every term in the numerator has an equal term in the denominator. All terms cancel out leaving 1.

[tex] = 1 [/tex]

3.

Since you have a division here, first, multiply the first fraction by the reciprocal of the second fraction. Then factor the numerator and denominator and cancel out common terms.

[tex] \dfrac{x^2 + 4x}{x - 2} \div \dfrac{x^2 + 2x - 8}{x^2 - 2x - 8} = [/tex]

To divide fractions, multiply the first fraction by the reciprocal of the second fraction.

[tex] = \dfrac{x^2 + 4x}{x - 2} \times \dfrac{x^2 - 2x - 8}{x^2 + 2x - 8} [/tex]

[tex] = \dfrac{(x^2 + 4x)(x^2 - 2x - 8)}{(x - 2)(x^2 + 2x - 8)} [/tex]

Now factor every factorable expression.

[tex]= \dfrac{x(x + 4)(x + 2)(x - 4)}{(x - 2)(x + 4)(x - 2)}[/tex]

Now cancel equal terms in the numerator and denominator.

[tex]= \dfrac{x(x + 2)(x - 4)}{(x - 2)(x - 2)}[/tex]

[tex]= \dfrac{x(x + 2)(x - 4)}{(x - 2)^2}[/tex]

Step-by-step explanation:

Question 6,

x+3=2x-23

x- 2x=-23-3

-1x=-26

x=26

Answer:

A college student is buying a used car for $10,000. The student can either pay in full with cash from savings, or finance the car for 60 months at a monthly compounding interest rate of 4.25%, which

results in a monthly payment of $206.05 How much more is paid over the life of the loan versus paying in cash?

O $1,000 25

O $11,000 25

O $12,363 00

Step-by-step explanation:

You're welcome.

The required surface area of the cylinder is [tex]$40\pi$[/tex] square feet.

Region is the proportion of a locale's size on a surface. The region of a plane district or plane region alludes to the region of a shape or planar lamina, while surface region alludes to the region of an open surface or the limit of a three-layered object.

The formula for the surface area of a cylinder is:

[tex]$A = 2\pi r^2 + 2\pi rh$[/tex]

Where:

A = Surface area

r = Radius

h = Height

Here, r = 4 ft and h = 1 ft.

Plugging in the values:

[tex]$A = 2\pi (4^2) + 2\pi (4)(1)$[/tex]

[tex]$A = 2\pi (16) + 2\pi (4)$[/tex]

[tex]$A = 32\pi + 8\pi$[/tex]

[tex]$A = 40\pi$[/tex]

Therefore, the surface area of the cylinder is [tex]$40\pi$[/tex] square feet.

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Answer: 60

Step-by-step explanation:

To form a 3-digit positive integer using the digits 1, 3, 5, 7, and 9 without repeating any digit, we can use the counting principle.

There are 5 choices for the first digit (hundreds place) since any of the 5 digits (1, 3, 5, 7, or 9) can be placed there.

5 (choices for the first digit) × 4 (choices for the second digit) × 3 (choices for the third digit) = 60

There are 60 ways to write a 3-digit positive integer using the digits 1, 3, 5, 7, and 9 without using any digit more than once.

The equation used to find the height of the stack is 2+xy and the number of bowls in a stack with a height of 14 inches is 16.

Finding the height of the stack :

To form the equation assume the number of bowls and height increased by stacking one into another with variables x and y and form the equation according to the given condition. Now use the resultant equation to find the number of bowls in the given stack.

Here we have

The diagram below shows 5 identical nesting bowls stacked one inside the other. The height of 1 bowl is 2 inches. The height of a stack of 5 bowls is 5 inches.

Part (A)

Let 'y' be the increase in the height of the stack and 'x' be the number of bowls stacked

Hence, Height of stack  = 2 + xy  

Therefore,

The equation that can be used to find the height of a stack is 2 + xy

From the given data,

Height of 5 bowls = 5 inches

=> 2 + xy = 5

=> xy = 3

Leaving the first bowl number bowls stacked = 4

=> x(4) = 3

=> x = 3/4

=> x = 0.75 inches

Part (B)

Given that height of the stack is 14 inches

Using the above equation

=> Height of stack, 2 + xy = 14

=> 2 + (0.75)y = 14

=> (0.75)y = 12

=>  y = 16

Therefore,

The equation used to find the height of the stack is 2+xy and the number of bowls in a stack with a height of 14 inches is 16.

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1. The value of c that completes the square is c = 36.

2. The value of c that completes the square is c = 16.

What is completing the square?

In algebra, completing the square is a technique used to manipulate quadratic expressions (expressions with variables raised to the second power) into a particular form that is useful for solving equations or analyzing the properties of a quadratic function. Specifically, completing the square involves adding and subtracting a constant term to a quadratic expression to create a perfect square trinomial, which can then be factored into a simpler form.

To complete the square for the expressions 1. x² + 12x + c and 2. x² + 8x + c, we need to add and subtract a constant term that will create a perfect square trinomial.

x² + 12x + c:

We can create a perfect square trinomial by adding and subtracting (12/2)^2 = 36 to the expression:

x² + 12x + 36 - 36 + c

(x + 6)² + (c - 36)

So the value of c that completes the square is c = 36.

x² + 8x + c:

We can create a perfect square trinomial by adding and subtracting (8/2)² = 16 to the expression:

x² + 8x + 16 - 16 + c

(x + 4)² + (c - 16)

So the value of c that completes the square is c = 16.

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The following are answers to the probability questions;

1. 2/3 or 0.67 or 0.7 chances

2. 2/3 or 0.67 or 0.7 chances

3. No probability is greater than the other. They are both 2/3.

4.  There are 36 possible outcomes

5. 3/36 or 1/12

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain.

To  calculate the probability of choosing a password with no Y's and With no O's we need to consider all the combinations that do not have Y and O. There are 20 combinations with no Y's and 20 combinations with no O.

Therefore, the probability of choosing a password with no Y's or O's are 20 each. When then calculate by sating

20/30, which simplifies to 2/3 or 0.67.

The number of possible outcomes for a single number cube is as follows;

1 2 3 4 5 6

1 1,1 1,2 1,3 1,4 1,5 1,6

2 2,1 2,2 2,3 2,4 2,5 2,6

3 3,1 3,2 3,3 3,4 3,5 3,6

4 4,1 4,2 4,3 4,4 4,5 4,6

5 5,1 5,2 5,3 5,4 5,5 5,6

6 6,1 6,2 6,3 6,4 6,5 6,6

In total, there are 36 combinations.

! There are three ways to obtain a sum of 10: rolling a 4 and a 6, rolling a 6 and a 4, or rolling two 5's. Since there are 36 possible outcomes in total (as we determined earlier), the probability of rolling two numbers that have a sum equal to 10 is:

P(sum of 10) = number of outcomes that add up to 10 / total number of possible outcomes

P(sum of 10) = 3 / 36

P(sum of 10) = 1/12

So the probability of rolling two numbers that add up to 10 is 1/12.

The answers provided is based on the full questions below as seen in the picture;

12. Higher Order Thinking The table shows the sample space of picking a 2-character password using the letters Y, B, R, O, G, and P. If double letters are not allowed, what is the probability of choosing a password with no Y's? With no O's? Is one probability greater than the other? Explain.

Possible Combinations

Y, B          B, R            R, O          O, G       G, P            P. Y

Y, R          B, O           R, G           O, P       G, Y            P, B

Y, O         B, G            R, P           O, Y       G, B            P, R

Y, G         B, P            R, Y           O, B        G, R            P, O

Y, P         B, Y            R, B           O, R         G, O           P,G

13. A single number cube is rolled twice.

PART A

Determine the number of possible outcomes. Explain how you know you have found all the possible outcomes.

PART B

Find the probability of rolling two numbers that have a sum equal to 10.

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The zeros of the function attached in the graph are

(-6 , 0) and (2, 0)

The zero of a quadratic graph is the point at which the graph intersects the x-axis. It is the value(s) of x for which the function f(x) equals zero. In other words, it is the value(s) of x that make(s) the quadratic equation equal to zero.

The zeros of a quadratic graph are also known as the roots, x-intercepts, or solutions of the quadratic equation.

Tracing the point where the graph cuts the x-axis we can see that it is at the point -6 on the left hand side and 2 on the right hand side.

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Hence the trigonometry identity is proved [tex]\frac{1-2cos^{2}x}{sinxcosx}=tanx-cotx\\}[/tex]

Cos2x is a key identity in trigonometry that can be expressed in a variety of ways. Many trigonometric functions, such as sine, cosine, and tangent, can be used to characterize it. Cos2x is one of the double angle trigonometric identities because the angle in question is a multiple of 2, or the double of x.

In trigonometry, Cos2x is a crucial identity that can be stated in a variety of ways. It can be described using a variety of trigonometric functions, including sine, cosine, and tangent. Considering that the angle under discussion is a multiple of 2, or the double of x, cos2x is one of the double angle trigonometric identities.

we have to prove

[tex]\frac{1-2cos^{2}x}{sinxcosx}=tanx-cotx\\}[/tex]

We can write

1-2cos²x=sin²x+cos²x-2cos²x

1-2cos²x=sin²x-cos²x

LHS

[tex]\frac{1-2cos^2x}{sinxcosx}=\frac{sin^2x+cos^2x-2cos^2x}{sinxcosx}\\\\=\frac{sin^2x-cos^2x}{sinxcosx}[/tex]

[tex]\frac{sin^2x}{sinxcosx}-\frac{cos^2x}{sinxcosx}\\\\=\frac{sinx}{cosx}-\frac{cosx}{sinx}\\\\=tanx-cotx[/tex]RHS

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The (+2) and (-8) in y = (x + 2)² - 8 shift the graph up two units and down eight units, respectively.

It is called quadratic because the highest degree of the equation is two. This type of equation is used to calculate the roots of a polynomial, which are the values of x where the equation equals 0.

The (+2) in y = (x + 2)² - 8 shifts the graph up two units on the y-axis.

This is because the addition of two to x before squaring it creates a quadratic equation which will create a graph which is two units higher than the graph created by the original equation.

The (-8) in y = (x + 2)² - 8 shifts the graph down eight units on the y-axis. This is because subtracting 8 from the squared term creates a graph which is eight units lower than the graph created by the original equation.

Therefore, the (+2) and (-8) in y = (x + 2)² - 8 shift the graph up two units and down eight units, respectively.

This creates a graph which is six units lower than the graph created by the original equation.

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Therefore , the solution of the given problem of unitary method comes out to be [tex]a_n-1[/tex] and [tex]a_n[/tex] is the nth word in the sequence.

A unitary approach is a mathematical problem-solving methodology that includes determining the value or quantity of a single unit or a fraction of a single unit and then utilizing that value to determine the value or quantity of a greater or lesser number of units.

This generally recognized ease, preexisting variables, and any significant elements from the initial Diocesan customizable query may all be used to complete the task. If so, your may have another chance to interact alongside the item. Otherwise, all important influences on how algorithmic proof acts will be eliminated.  

Here,

The museum will have 75 items when it opens, and 3 more pieces will be added each month. The numerals in the pattern for the following eight months are as follows:

=> 75 + 3 = 78

=>  78 + 3 = 81

=>  81 + 3 = 84

=>  84 + 3 = 87

=>  87 + 3 = 90

=>  90 + 3 = 93

=>  93 + 3 = 96

=>  96 + 3 = 99

Each number is 3 more than the one before it, which is another pattern that can be seen in the numerals. With a common difference of three, the series is an arithmetic one. This pattern can be represented numerically as:

=> [tex]a_n = a_{n-1} + 3[/tex]

where the preceding term is called [tex]a_n-1[/tex] and [tex]a_n[/tex] is the nth word in the sequence.

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When it is said that the null hypothesis was rejected in a hypothesis test, it means that the sample data has given strong evidence against the null hypothesis and in favor of the alternative hypothesis.

What is a hypothesis?

A hypothesis is a statement that proposes a potential relationship between two variables. It's a conjecture about the nature of the relationship between the two variables that a researcher might test.In hypothesis testing, the null hypothesis is always the hypothesis being tested. A null hypothesis is a statement that assumes there is no relationship between the variables being studied. It is denoted by H0.The alternative hypothesis is a statement that negates the null hypothesis. It suggests that there is a relationship between the variables being studied. It is denoted by Ha.When it is said that the null hypothesis was rejected in a hypothesis test, it means that the sample data has given strong evidence against the null hypothesis and in favor of the alternative hypothesis. As a result, the researcher may conclude that the alternative hypothesis is true with a certain level of confidence.If the null hypothesis is not rejected in a hypothesis test, it means that there is insufficient evidence to support the alternative hypothesis. As a result, the researcher cannot conclude that the alternative hypothesis is true with a certain level of confidence.

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Answer:

Independent: the number of cups, c, that he sells

Dependent: the amount of money, m, that he makes each day

Step-by-step explanation:

* The independent variable determines the value of the dependent variable. The number of cups of frozen juice that Richard sells each day determines the amount of money that he makes each day.

* Side note: For your information, the linear equation that models this relationship would be m = 1.25 c. You would graph that as y = 1.25 x, and since x is independent while y is dependent, you know that c is independent and m is dependent.

* Good luck completing the table! I would help out with that if I could see it!

Answer:

90.6°

Step-by-step explanation:

It is given that x represents the number of minutes. You are solving for 8 minutes. Therefore, plug in 8 for x in the given equation, and simplify:

[tex]y = 8.2x + 25\\y = 8.2(8) + 25[/tex]

Simplify. Remember to follow PEMDAS. PEMDAS is the order of operations and stands for:

Parenthesis

Exponent (& Root)

Multiplication

Division

Addition

Subtraction

~

First, multiply 8.2 with 8:

[tex]y = (8.2 * 8) + 25\\y = (65.6) + 25\\[/tex]

Next, add:

[tex]y = 65.6 + 25\\y = 90.6[/tex]

90.6 is your answer.

~

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The maximum number of tickets the theater can sell is 39,572.

The maximum number means the greatest amount of something possible.

The theater sale each weekend is 761 tickets.

There are eight weekend days in a month and in case the month starts with a Saturday or a Sunday there can be an additional weekend.

To calculate the maximum number of tickets the theater can sell in 1 year, we can multiply the maximum number of tickets sold per weekend by the number of weekends in a year, which is 52.

So, 761 tickets x 52 weekends = 39,572 tickets

Therefore, the maximum number of tickets the theater can sell in 1 year is 39,572 tickets.

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The cost of  each piece of trim is $1.63

To find the cost of one piece of trim, we can use the unitary method, which involves dividing the total cost by the number of pieces. In this case, we can use the following formula

Cost of one piece of trim = Total cost / Number of pieces

We know that Kevin bought 4 pieces of trim for a total of $6.52, so we can substitute these values into the formula

Cost of one piece of trim = $6.52 / 4

Simplifying this expression, we get

Cost of one piece of trim = $ 1.63

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A teacher compares the pretest and posttest scores of students is an example of a matched-pairs design. Therefore, option d is the correct answer.

A matched-pairs design is an experimental design where the researcher analyzes the differences between two sets of data that are related.

It is used to minimize the effects of variables that are not of interest, such as individual difference.

Based on the given options,

option d : a teacher compares the pretest and posttest scores of students is an example of a matched-pairs design.

In this design, the teacher compares the students' performance before and after a specific treatment.

The design is used to minimize the differences in the individual differences in the students' academic performance is an example of a matched-pairs design.

option d is the correct answer.

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Answer:

The probability that she has breast cancer if she gives a positive test result is P=0.16

Step-by-step explanation:

And according to the Bayes theorem I got 0.16

The probability that the woman who underwent routine screening and has a positive test has breast cancer is 0.017.

Let A denote the event that the woman has breast cancer, and let B denote the event that she has a positive test result. Then we need to find P(A|B), the probability that A occurs given that B has occurred. By Bayes' theorem, we have:

P(A|B) = P(B|A)P(A) / [P(B|A)P(A) + P(B|not A)P(not A)]

where P(not A) = 1 - P(A) is the probability that the woman does not have breast cancer.

From the problem statement, we have:

P(A) = 1/101, P(B|A) = 0.8, and P(B|not A) = 0.05.

Therefore,

P(not A) = 100/101,

and

P(A|B) = (0.8 x 1/101) / [(0.8 x 1/101) + (0.05 x 100/101)] = 0.017 (to three decimal places).

Therefore, the probability that the woman who underwent routine screening and has a positive test has breast cancer is 0.017.

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base area πr²=64πm²

so r=8m

h=2r=2(8)=16m

volume=πr²h

=(22×64×16)/7

=3218.2m³

it is approximately 3217.0m³

The probability that he will reach out into his pocket and pull out a $10 bill each time is 1/7. The correct option is the second option 1/7

From the question, we are to determine the probability of William pulling out a $10 bill twice without replacement

The probability of pulling out a $10 bill on the first draw is 3/7, since William has three $10 bills out of a total of seven bills in his wallet.

Since William does not replace the first bill when he pulls out the second one, there will be one less bill in the wallet for the second draw. Therefore,

The probability of pulling out another $10 bill on the second draw is 2/6 (since there will be two $10 bills left out of six bills in the wallet).

Thus,

The probability that he will reach out into his pocket and pull out a $10 bill each time is

P(two $10 bill) = 3/7 × 2/6

P(two $10 bill) = 3/7 × 1/3

P(two $10 bill) = 1/7

Hence, the probability is 1/7

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The musical theater group should charge $14.25 per ticket to maximize revenue. To find the ticket price that maximizes revenue, we need to determine the revenue function and then differentiate it with respect to the ticket price to find the critical points.

We can then evaluate the revenue at these points to determine the maximum. Let x be the number of dollars charged for admission above the base price of $7.75, and let y be the number of tickets sold at that price. Then, the revenue function is given by:

R(x) = (1200 - 50x)(7.75 + x)

Expanding this expression, we get:

R(x) = 9300 + 650x - 50x^2

To find the ticket price that maximizes revenue, we need to find the critical points of the revenue function. We can do this by differentiating the revenue function with respect to x and setting the derivative equal to zero:

R'(x) = 650 - 100x = 0

Solving for x, we get:

x = 6.5

This means that the additional charge above the base price that maximizes revenue is $6.50. Therefore, the ticket price that maximizes revenue is:

7.75 + 6.50 = $14.25

So, the musical theater group should charge $14.25 per ticket to maximize revenue.

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The correct volume of the prism is 4637 cm² and the mistake that the student made is not getting the base of the prism first.

The correct volume of the prism can be gotten by first determining the base and multiplying this by height. When we apply this formula, the base of the prism will be:

6 * 9.2 * 8 * 1/2

= 220.8 cm²

Having gotten the base, we will now multiply this by the volume.

Volume = 220.8 cm²  * 21 cm

= 4637 cm²

So, the volume of the prism is equal to 4637 cm².

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We are given that the quadratic function has the equation:

y = a(x + 6)(x - 2)

To find the value of a, we can use the fact that the function passes through the point (3, 36). This means that when x = 3, y = 36. Substituting these values into the equation, we get:

36 = a(3 + 6)(3 - 2)

36 = 9a

a = 4

Therefore, the value of a is 4.

To find the area of the shaded region subtract the unshaded region from the total area, so we got 87.

Square Area equals Side x Side. The square's size is therefore equal to side square units. and a square's circumference equals four side units.

To find the area of the shaded region first we need to find the sum of the area of all quadrilaterals and then subtract the area of the unshaded region.

Area of first quadrilateral A1  = [tex]16^{2}[/tex] = 256

Area of first quadrilateral A2  = [tex]3^{2}[/tex] = 9

Area of first quadrilateral A3  = [tex]3^{2}[/tex] = 9

Area of first quadrilateral A4  = [tex]19^{2}[/tex] = 361

To find the area of the shaded region subtract the unshaded region from the total area = Area of first quadrilateral A4 - (Area of first quadrilateral A1  + Area of first quadrilateral A2 + Area of first quadrilateral A3)

= 361 - (9 + 9 + 256)

=87

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The name of a function identifies it and must be used when the function is called - True

A function serves as its unique identifier and must be used when calling the function. A function in a computer language is given a name when it is created so that the user can invoke it later on in their particular code. The function is identified by its name which also serves to set it apart from similar functions with potentially different titles.

Depending on its definition, the parentheses that come after the function name may or may not contain arguments or parameters when calling a function. A function is called, executed, and its outcomes are returned to the caller code. Due to the reason that it is a crucial part of the function's definition, its name must always be employed when a function is called.

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Answer:

x ≈ 19,47°

Step-by-step explanation:

Use trigonometry:

[tex] \sin(∠cab) = \frac{cb}{ab} [/tex]

[tex] \sin(x°) = \frac{2}{6} [/tex]

[tex]x ≈19.47°[/tex]

Answer:

Step-by-step explanation:

x = 9

Rounding to the nearest whole number, we get that Carson's commute would be longer than 44 minutes about 168 times per year.

What is the normal distribution?

The normal distribution is a probability distribution that is commonly used in statistical analysis. It is a continuous probability distribution that describes a set of data that tends to cluster around a mean value, with fewer observations further from the mean.

We can use the normal distribution formula to solve this problem. Let X be the amount of time it takes Carson to commute to work in minutes.

Then we have:

X ~ N(47, 4²)

We want to find P(X > 44), the probability that Carson's commute takes longer than 44 minutes. We can standardize X using the formula:

Z = (X - μ) / σ

where μ is the mean and σ is the standard deviation. Substituting the given values, we get:

Z = (44 - 47) / 4 = -0.75

We can use a standard normal distribution table or a calculator to find the probability that Z is greater than -0.75. Using a standard normal distribution table, we find:

P(Z > -0.75) = 1 - P(Z ≤ -0.75) = 1 - 0.2266 = 0.7734

Therefore, the probability that Carson's commute takes longer than 44 minutes is 0.7734.

To find the number of times this would happen out of 217 days, we can multiply the probability by the number of days:

0.7734 * 217 = 167.9

Hence, Rounding to the nearest whole number, we get that Carson's commute would be longer than 44 minutes about 168 times per year.

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