Tree Diagrams
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1. A family has four children. How many outcomes are in the sample space that indicates the sex of the children?
Assume that the probability of male (M) and the probability of female (F) are each 1/2. Use a tree diagram to model this situation:
Child 1
Child 2
Child 3
Child 4
Possible Outcomes
2. What is the probability that all children are males?
3. What is the probability that they will have all one gender of children (all males or all females)?
4. What is the probability that there will be at least 2 female children?
5. You are bored and decide to flip a coin, then roll a 6 sided die, then flip a coin, then roll a 3-sided die. Create a tree diagram to model all possible outcomes
6. How many possible outcomes are there?
7. What is the probability of getting only heads on both coin tosses?

The rate of speed of the jet is given by S = 98 miles per hour

Speed is defined as the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude

Speed = Distance / Time

Given data ,

Let the rate of speed of the jet be represented as S

Now , the value of S is

The distance traveled by the jet D = 490 miles

The time taken by the jet to travel 490 miles T = 5 hours

So , the speed of the jet is given by

Speed = Distance / Time

On simplifying , we get

The speed of the jet S = 490 / 5

The speed of the jet S = 98 miles per hour

Now , the distance traveled by the jet in 11 hours be D₁

The time taken to travel D₁ distance is 11 hours

where D₁ = Speed x Time

On simplifying , we get

D₁ = 98 x 11

D₁ = 1,078 miles

Hence , the distance traveled at a speed of 98 mph for 11 hours is 1,078 miles

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Answer:

-1/5(x-6)^2+3

Step-by-step explanation:

+3 makes the graph go up by 3

-6 makes the graph go right 6

we put a negative outside of (x-6) since this goes down and is a -x^2 parabola

no clue about 1/5 just kept putting numbers outside of (x-6) to eventually get the width.

The interpretation the transformation that creates the graph is 1 unit to the left and 4 units to the right.

The link between lines and points is described by a network's mathematical representation, a graph.

Given, that Figure X was transformed to produce Figure Y.

We must ascertain the transformation that is applied in this case.

The process of changing an existing graph or graphed equation to create a different version of the following graph is known as graph transformation. A vertical reflection crosses the x-axis vertically and a horizontal reflection crosses the y-axis horizontally of a graph.

A graph can be horizontally translated by moving the base graph to the left or right in the y-axis direction.

Just a little bit of a tilt to the left and upward is made to the graph.

Figure X undergoes a translation of translation 1 unit left and 4 units up.

Hence translation 1 unit left, and 4 units up is the transformation which accomplish the graph.

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The complete question is:

Figure Y is the result of a transformation on Figure X. Which transformation would accomplish this?

The graph of straight line y = 2 - x with the given points are shown in graph.

Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.

Given that;

The equation of straight line is,

⇒ y = 2 - x

Now, We have to given that;

Points on the graph are,

x  =  -3, 0, 5

y  =  5, 2, -3

Hence, We can plot the points and join all the points.

We get;

The graph of straight line with the given points as shown in figure.

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Daffynition Decoder is a fun and challenging word puzzle that requires both creativity and logical thinking to solve. It is often found in puzzle books, newspapers, and online puzzle websites.

Daffynition Decoder is a word puzzle game that involves decoding phrases or sentences by using a letter-substitution method. The game provides a list of numbered words, where each word is a cryptic definition of a common word or phrase. The solver's goal is to figure out what each word represents and then use the letters from those words to decode a secret message. The game is typically played by filling in a chart or grid, where each row corresponds to a numbered word in the list, and each column represents a letter in the decoded message. The solver uses the numbered words to fill in the corresponding letters in the grid, eventually revealing the hidden message.

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Complete question:

What is project Daffynition Decoder?

Therefore , the solution of the given problem of unitary method comes out to be  fountain's diameter in the model is roughly 2.0556 inches.

The measurements taken from this nanosecond variable section must be multiplied by two in order to complete the task using the unitary technique. In essence, the characterised by a group and the colour sections are both removed from the unit expression method when a desired object is present. For example, 40 pens with a variable price would pay Inr ($1.01).

Here,

We can use proportionality to determine the breadth of the fountain in the model if the scale is 1 inch = 9 feet. The following percentage can be configured:

Model fountain width divided by one inch equals actual fountain width multiplied by nine feet.

The diameter of the fountain is stated to be 18 1/2 feet in real life, which is the same as 18.5 feet. Adding this number to the proportion results in:

1 inch of the model fountain's diameter divided by 18.5 feet by 9 feet

If we simplify, we get:

diameter of the model's fountain / 1 = 2.0556

By dividing the two edges by one inch, we obtain:

Modeled fountain width is 2.0556 inches.

As a result, the fountain's diameter in the model is roughly 2.0556 inches.

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The mean absolute variation for the group of integers 42, 45, 47, 50, 53, 56, 58, and 65 is therefore roughly 6.5.

What one standard deviation (SD) means. on a normal or bell-shaped distribution of the data. The region of a bell curve starting at position 13 on the y axis is approximately filled by 1 SD = one standard deviation = 68% of a ratings or data values.

Here's how to find the mean absolute deviation of the set of numbers 42, 45, 47, 50, 53, 56, 58, and 65:

Find the mean:

mean = (42 + 45 + 47 + 50 + 53 + 56 + 58 + 65) / 8

mean = 50.375

Find the absolute difference between each number and the mean:

|42 - 50.375| = 8.375

|45 - 50.375| = 5.375

|47 - 50.375| = 3.375

|50 - 50.375| = 0.375

|53 - 50.375| = 2.625

|56 - 50.375| = 5.625

|58 - 50.375| = 7.625

|65 - 50.375| = 14.625

Find the average of these absolute differences:

mean absolute deviation = (8.375 + 5.375 + 3.375 + 0.375 + 2.625 + 5.625 + 7.625 + 14.625) / 8

mean absolute deviation ≈ 6.5

Therefore, the mean absolute deviation of the set of numbers 42, 45, 47, 50, 53, 56, 58, and 65 is approximately 6.5.

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Therefore, we can estimate that having a 14 ft by 24 ft brick patio installed would cost around $3,033.33.

Cost is a key concept in economics. The price that was paid in return for any products or services is referred to. Cost is a monetary evaluation of the materials, labour, risks, expenses, and time required to purchase goods and services.

We can use proportions to estimate the cost of having a 14 ft by 24 ft brick patio installed based on the given information.

Let's use x to represent the estimated cost of having a 14 ft by 24 ft brick patio installed.

We can set up a proportion:

15/20 = 2275/x

To solve for x, we can cross-multiply and simplify:

15x = 20 x 2275

15x = 45500

x = 3033.33

So the estimated cost of having a 14 ft by 24 ft brick patio installed is approximately $3,033.33.

Therefore, we can estimate that having a 14 ft by 24 ft brick patio installed would cost around $3,033.33.

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Based on proportional multiplication, the quantity of medication in grams that the patient, who weighs 63 kg needs in 12 hours is 1,224.3 mg.

Proportional multiplication involves the cross-multiplication of two fractional ratios, which are equated to each other.

Proportions involve the equation of two ratios.

The dosage required by a patient in 4 hours with a weight of 9 kg = 58.3 mg

Proportionately, the dosage required by a patient in 12 hours with a weight of 63 kg = 1,224.3 mg (58.3 x 63/9 x 12/4).

Thus, if a patient weighing 9 kg receives 58.3 mg of medicine in 4 hours, proportionately, in 12 hours, a patient weighing 63 kg will receive 1,224.3 mg.

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Deck A the safe walk zone must be painted at the points 13.74 units left and right of the edge of the circle, whereas for Deck B it must be painted at 12.68 units.

Maximum Height refers to the vertical distance between the Reference Level and the highest point of a building's roof surface, including parapet walls, mechanical equipment installed on the roof, authorised Signage, and other permissible projections of any type.

The equation of the given circular space station is:

[tex]x^2 + y^2 = 15^2\\\\x^2 + y^2 = 225[/tex]

Given that, a 6-foot person can walk through the circular station.

Substitute the value of y = 6.

[tex]x^2 + 6^2 = 225\\\\x^2 = 225 - 36\\\\x = \sqrt{189}\\ \\x = \pm 13.74[/tex]

Also, Deck B is 2 feet below deck A thus,

[tex]x^2 + 8^2 = 225\\\\x^2 = 225 - 64\\\\x = \sqrt{161}\\ \\x = \pm 12.68[/tex]

Hence, for Deck A the safe walk zone must be painted at the points 13.74 units left and right of the edge of the circle, whereas for Deck B it must be painted at 12.68 units.

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Step-by-step explanation:

closest to all points on the graph

The derivative of given ƒ(x) is:

[tex]$f'(x) = \frac{3x^2 - 6 - 6\log(x)}{x(x^2+5)^2}$[/tex]

Differentiation is a mathematical process used to find the rate at which a function changes with respect to one of its variables. It is the process of finding the derivative of a function, which is a measure of how much the function changes as its input changes. The derivative is used to analyze the behavior of functions, find maximum and minimum values, and solve optimization problems. It is an important concept in calculus and is used in many areas of mathematics, science, and engineering.

We can use the quotient rule to differentiate ƒ(x):

[tex]f(x) &= \frac{2+3\log(x)}{x^2+5} \ \\ \\ \\f'(x) &= \frac{(x^2+5)\frac{d}{dx}(2+3\log(x)) - (2+3\log(x))\frac{d}{dx}(x^2+5)}{(x^2+5)^2} \\ \\\ &\\= \frac{(x^2+5)\left(0+\frac{3}{x}\right) - (2+3\log(x))(2x)}{(x^2+5)^2} \\\ \\ \\ &= \frac{3x^2-6-6\log(x)}{x(x^2+5)^2}[/tex]

Therefore, the derivative of given ƒ(x) is:

[tex]$f'(x) = \frac{3x^2 - 6 - 6\log(x)}{x(x^2+5)^2}$[/tex]

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The graph of both the exponential functions y = 3(11)ˣ  and y = (1/12)ˣ  can be plotted by assuming some arbitrary values of 'x' that correspond to

different values of 'y'.

A function is said to be n exponential function when the independent variable is the exponent.

For example -: aˣ.

The two exponential functions can be graphed by assuming some arbitrary values of 'x'.

In y = 3(11)ˣ.

At x = 1, y = 33.

At x = - 1, y = 3/11.

At x = 2, y = 363.

So, The points are (1, 33), (- 1, 3/11) and (2, 363).

Now we can plot these points and join them by free hand.

Similarly, y = (1/12)ˣ can also be graphed in a similar manner.

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Steps  he could  use to solve the quadratic equation by completing the square is 5(x² + 4x) = –7

A quadratic equation is a second-degree polynomial equation of the form ax² + bx + c = 0, where x is the variable and a, b, and c are constants. It typically has two solutions, which can be found using the quadratic formula or factoring the equation.

Solution:

The three steps that Sergey could use to solve the quadratic equation by completing the square are:

1.Write the equation in the form ax² + bx + c = 0

2.Add and subtract (b/2)² to complete the square, resulting in an expression of the form a(x + p)^2 + q = 0

3.Solve for x by isolating (x + p)² and taking the square root, resulting in x = (-b ± sqrt(b² - 4ac)) / 2a

Therefore, the three options that correspond to these steps are:

5(x² + 4x + 4) = –7 + 20

x + 2 = Plus or minus StartRoot StartFraction 27 Over 5 EndFraction EndRoot

5(x² + 4x) = –7

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SEE ATTACHED SOLUTION

The value of  (p o g)(-1) is -2 and the value of (q o p)(-1) is 15 which represents the composite of the function.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function p and q:

p(x) = 2x - 2

q(x) = x² - 1

= (p o q)(-1)

Find the value of q(-1):

q(-1) = 0

Plug the above value in the function p(x):

(p o q)(-1) = p(q(-1)) = -2

= (q o p)(-1)

Find the value of p(-1):

p(-1) = -4

(q o p)(-1) = q(p(-1)) = 15

Thus, the value of  (p o g)(-1) is -2 and the value of (q o p)(-1) is 15 which represents the composite of the function.

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The value of sin (x/2) is -√(26/27).

The value of cos (x/2) is -√(2/27)

The value of tan (x/2) is 1/12.

We know that sin(x) = -2/27 in Quadrant 3, which means that x lies between 180 degrees and 270 degrees.

a. To find sin(x/2), we can use the half-angle formula:

sin(x/2) = ±√[(1-cos(x))/2]

Since x lies in Quadrant 3, we know that cos(x) is negative. To find cos(x), we can use the Pythagorean identity:

sin²(x) + cos²(x) = 1

(-2/27)² + cos²(x) = 1

cos²(x) = 1 - (-2/27)²

cos(x) = -√(1 - (-2/27)²)

cos(x) = -25/27

Now we can substitute cos(x) into the half-angle formula:

sin(x/2) = ±√[(1-(-25/27))/2]

sin(x/2) = ±√[(27/27 + 25/27)/2]

sin(x/2) = ±√[52/54]

sin(x/2) = ±√(26/27)

Since x is in Quadrant 3, sin(x/2) is negative.

Therefore;

sin(x/2) = -√(26/27)

b. To find cos(x/2), we can use the half-angle formula:

cos(x/2) = ±√[(1+cos(x))/2]

Again, we know that cos(x) is negative, so we can use the value we found earlier:

cos(x/2) = ±√[(1-25/27)/2]

cos(x/2) = ±√[2/27]

Since x is in Quadrant 3, cos(x/2) is also negative.

Therefore;

cos(x/2) = -√(2/27)

c. Finally, to find tan(x/2), we can use the identity:

tan(x/2) = sin(x)/(1+cos(x))

We already know sin(x) and cos(x), so we can substitute them in:

tan(x/2) = (-2/27)/(1-25/27)

tan(x/2) = (-2/27)/(-24/27)

tan(x/2) = 1/12

Therefore,

tan(x/2) = 1/12

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Answer:

Step-by-step explanation:

pls finish question first

Answer:

Step-by-step explanation:

7 + 28 + 7 = 42 units^2     see image below

In order to resolve the ambiguity and find the correct solution, we need to use additional information such as the Law of Sines or the Law of Cosines.

what is a Triangle ?

Triangle can be defined in which it consists three sides, three angles and sum of three angles is always 180 degrees.

An ambiguous case in geometry refers to a situation where, given certain information about a triangle, there are two possible solutions for one of the unknown angles or sides. This situation arises in trigonometry when we have to solve a triangle using the Law of Sines or the Law of Cosines.

The conditions that create an ambiguous case with two possible solutions are as follows:

Given two sides and an angle opposite one of the sides:

If we are given two sides and an angle opposite one of the sides, there can be two possible solutions for the triangle. For example, if we are given side lengths of 4 and 5, and an angle of 40 degrees opposite the side of length 4, there are two possible triangles that can be formed.

Given two angles and a side opposite one of the angles:

If we are given two angles and a side opposite one of the angles, there can be two possible solutions for the triangle. For example, if we are given angles of 30 degrees and 60 degrees, and a side length of 4 opposite the 30-degree angle, there are two possible triangles that can be formed.

In both of these cases, the ambiguous case arises when the given information is not sufficient to uniquely determine the triangle.

Therefore,  In order to resolve the ambiguity and find the correct solution, we need to use additional information such as the Law of Sines or the Law of Cosines.

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Answer:

y = -21

Step-by-step explanation:

Hope this helps! :))

Answer:

[tex]310 ^\circ F[/tex]

Step-by-step explanation:

The formula relating surface temperature in °F and time in t minutes after removal from the oven is given as

[tex]S(t)= 72 + 238 (0.97^t)\\\\\text{The initial temperature is when t = 0}\\\\\text{At t = 0}\\\\S(0) = 72 + 238(0.97^0)\\\\0,97^0 = 1 \text{ since any number raised to 0 = 1}\\\\\text{Therefore}\\S(0) = 72 + 238 \cdot 1\\= 72 + 238\\\\= 310 ^\circ F[/tex]

Answer:

Without coupon: 44 baseballs

With coupon: 56 baseballs

Step-by-step explanation:

Answer:18

Step-by-step explanation:

It would take approximately 11.6 years for the account balance to reach $20,000 if compounded annually.

The costs a borrower pays a lender for a loan are known as interest. For instance, banks charge interest on the loans that consumers take out.

Simple interest is the term used to describe interest that is based on the principle amount that a person borrows or invests. Contrarily, compound interest is computed on the principle borrowed or invested by the individual as well as the accrued interest from the prior period.

The formula for compound interest is:

A = P(1 + r/n)ⁿˣ

where, A is the amount

P is the principal amount = $10,000

r is the rate = 6% = 0.06

x is time.

n = 1

Substituting the values,

$20,000 = $10,000(1 + 0.06/1)¹ˣ

2 = (1.06)ˣ

Taking the natural logarithm of both sides:

ln(2) = t * ln(1.06)

t = ln(2) / ln(1.06) ≈ 11.6

Therefore, it would take approximately 11.6 years for the account balance to reach $20,000.

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Answer:

Step-by-step explanation:

Let's start by finding out what Denniel's weighted average grade is, given the grading system:

Tests: 40% of 70 = 0.4 x 70 = 28

Classwork: ? (we don't know this yet)

Homework: 0 (since he never does homework)

Weighted average grade: 0.4 x 28 + 0.4 x ? + 0.2 x 0 = 0.4 x ?

We know that his overall weighted average grade is 70, so we can set up an equation to solve for his classwork average:

0.4 x ? = 70 - 0.4 x 28 - 0.2 x 0

0.4 x ? = 42

? = 42 / 0.4

? = 105

So Denniel's classwork average is 105.

The solution to the variable x is 60/7

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

The similar polygons

The scale factor from the big to the small polygon is represented as

Scale factor = 5/7

Using the above as a guide, we have the following:

x = 12 * 5/7

Evaluate

x = 60/7

Hence, the solution is 60/7

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Answer:

2:3 , 8:12

Step-by-step explanation:

Equivalent ratio means, multiply/divide the numerator and the denominator of the fraction with the same number. So, we need to multiply the numerator and the denominator with the same number. Hence, another ratio that is equivalent to 4 : 6 is 8 : 12

Hope this helped :D

Since t = -2.41 < -2.145, reject [tex]H_o[/tex] and conclude Ha, i.e. that there is a significant difference in the mean numbers of uncontaminated eggplants for the two disinfectants tested.

(a) Are you willing to assume that the underlying variances are equal?

Absolutely not! The variances can NOT be assumed equal.

H_o: sigma1^2 = sigma2^2

H_a: sigma1^2 =/ sigma2^2

F = s1^2 / s2^2 = 2.78095 / 0.17143 = 16.222

alpha = .05, dfnum = 15-1 = 14 and dfdenom = 15-1 = 14

F-critical values

= .33573 = F.INV(.025,14,14) using Excel

= 2.978588 = F.INV(.025,14,14) using Excel

Since F = 16.222 > 2.978588, reject H_o and conclude H_a, i.e. that the population variances significantly differ.

Or, using the p-value from the TI-84... p-value = 5.59E-6 = .00000559 < alpha = .05, so we can reject H_o and conclude H_a, i.e. that the population variances significantly differ.

(b) Using the information from part a), are you willing to conclude that there is a significant difference in the mean numbers of uncontaminated eggplants for the two disinfectants tested ?

Note: Since the population variances ARE significantly different, we can NOT use the pooled t-test as rapunzel shows.

H_o: mu1 = mu2

H_a: mu1 =/ mu2

t = (xbar1-xbar2) / sqrt(s1^2/n1 + s2^2/n2)

t = (3.73 - 4.80) / sqrt(2.78095/15 + .17143/15)

Note: We do NOT square the variances. They are already squared.

t = -2.41

t-critcal values

df = smaller of n1-1 and n2-1, i.e. the smaller of 15-1 = 14 and 15-1 = 14

--> df = 14

left tail critical value = -2.145 <-- alpha/2 = .025, df = 14

right tail critical value = +2.145 <-- alpha/2 = .025, df = 14

Since t = -2.41 < -2.145, reject H_o and conclude H_a, i.e. that there is a significant difference in the mean numbers of uncontaminated eggplants for the two disinfectants tested.

Or, using the p-value from the TI-84... p-value = .028486... < alpha = .05, so we can reject H_o and conclude H_a, i.e. that there is a significant difference in the mean numbers of uncontaminated eggplants for the two disinfectants tested.

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An experiment published in The American Biology Teacher studied the efficacy of using 95% ethanol and 20% bleach as a disinfectant in removing bacterial and fungal contamination when culturing plant tissues. The experiment was repeated 15 times with each disinfectant, using eggplant as the plant tissue being cultured. Five cuttings per plant were placed on a petri dish for each disinfectant and stored at 25 centigrades for 4 weeks. The observation reported was the number of uncontaminated eggplant cuttings after the 4-week storage.

Disinfectant 95% Ethanols 20% Bleach

Mean 3.73 4.80

Variance 2.78095 0.17143

Pooled variance: 1.47619

Are you willing to assume that the underlying variances are equal?

Using the information from part a), are you willing to conclude that there is a significant difference in the mean numbers of uncontaminated eggplants for the two disinfectants tested ?

The table makes it abundantly evident that buying costs less than renting does. Buying a house is therefore better over the course of 15 years. By buying a home instead of renting one, you can save $5,222.4.

Every object's length can be determined using measuring tools like a ruler, measuring tape, etc. For example, a ruler may be utilized to measure the length in inches of a pencil. A foot scale can be used in a classroom to gauge the heights of the students.

Step 1

Buying a home is more advantageous if someone is looking for somewhere to live for an extended period of time. Second, if a person buys the home, it can be sold at a higher price in the future since rental prices after a specified term and after a few years, say 10 or 15, cumulative rental charges become greater than the initial purchase price.

However, according to the above table, renting a property is preferable if the need for the home is for a shorter duration, like fewer then 5 or 10 years, in order to save money.

Step 2

1 year

The cost for Purchasing a house = 30,000 + 1 × 12 × 809.32 = $39,711.84

The cost of renting a house = 1 × 12× 900 = $10,800

So, it is evident that there's a difference between buying and renting a home of $28,911.84. So, renting a home is preferable.

Step 3

5 year

The cost of purchasing the home for five years is listed as $78559.20, whereas the cost of renting the home for five years was $54,900.

Again, renting is more affordable than buying. By renting a home, one could save $23,659.2 (78559.20-54900).

10 years

The cost of purchasing the home over 10 years is shown as $127,118.40, while the cost of renting the home for 10 years was $115,200.

Renting is less expensive than buying. Yet, buying a house is advantageous if it can be bought or rented out; otherwise, leasing one is advantageous.

Step 4

15 years

The table clearly shows that purchasing is less expensive than renting. Over the period of fifteen years, purchasing a home is therefore preferable. You can save $5,222.4 by buying a house instead of renting one.

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