To approximate the length of a marsh, a surveyor walks x = 420 meters from point A to point B. Then, the surveyor turns 75° and walks 220 meters to point C (see figure). Approximate the length AC of the marsh. (Round your answer to one decimal place.)

The relative maximum for this graph is zero

Maximum of the graph is defined as the highest value of y-coordinate. This means the highest value on the y-axis. There are two types of maximums on the graph. Absolute maximum and the relative maximum.

Absolute maximum is the highest value of the y-coordinate on the graph. Whereas, relative maximum is the point where the graph changes its nature e.g. positive to negative.

Since, the given graph has all the points plotted on the x-axis e.g. value of y-coordinate is zero. That is why the value of relative maximum is also zero.

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The total surface area of the figure is 1208cm². Option A

You should understand that the total surface area of the figure is the sum of all the face areas of the various parts of the figure. There are front and back faces of the prism

Area of bases of the prisms

1. Area = a*c*2

= 20*12*2

Area = 480cm²

2. Area = a*c*2

= 20*8*2

Area = 320cm²

3. Area = (d*c)/2 * 4

Area = (5*12)/2 *4 = 30*4

Area = 120 cm²

4) Area = c*b*2= *12*2

Area = 208cm²

5) Area = a*c*2 = 5*8*2Area = 80cm²

Therefore, the total surface area of the figure is

Total surface area= (480+320+120+208+80)cm²

= 1208cm²

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Correct question:

Two same-sized triangular prisms are attached to a rectangular prism as shown below.If a = 20 cm, b = 13 cm, c = 12 cm, d = 5 cm, and e = 8 cm, what is the surface area of the figure?a 1,208 square centimetersb 1,592 square centimetersc 1,004 square centimetersd 1,400 square centimeters

We can conclude that the new technique has extended the life of light bulbs. Yes it has worked

Generally, To calculate the t-statistic, you would use the following formula:

t = (sample mean - hypothesized mean) / (standard deviation / √n)

Where "sample mean" is the mean life of the 10 light bulbs, "hypothesized mean" is the average life of the light bulbs before the new technique (1000 hours), "standard deviation" is the standard deviation of the sample (51.97 hours), and "n" is the number of light bulbs in the sample (10).

Plugging in the values, we get:

t = (1077 - 1000) / (51.97 / √10)

t= 77 / 5.197

t= 14.8

Now that you have calculated the t-statistic, you need to determine the critical value of t at a significance level of 2.5%.

Where

df=10-1

df=9

At a significance level of 2.5% and 9 degrees of freedom, the critical value of t is 2.262.

Since the t-statistic calculated for the sample (14.8) is greater than the critical value (2.262), you can reject the null hypothesis that the new technique did not extend the life of the light bulbs.

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The base angle is calculated to be 45 degrees if the vertex angle of the isosceles triangle is 90 degrees

An isosceles triangle in mathematics is used to describe a triangle with two equal sides and two equal angles.

As the vertex angle is given to be 90 degrees, therefore the other two angles of the triangle will be equal. Considering x to be the base angle;

x + x + 90° = 180°

2x + 90° = 180°

Rearranging;

2x = 180° - 90°

2x =  90°

Solving for x;

x = 90° ÷ 2

x = 45°

Therefore, 45° is calculated to be the base angle of the isosceles triangle.

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Answer: 8/-9

Step-by-step explanation:

If h(7), plug in 7 into all the x-values.

=[tex]\frac{7^{2}-5(7)-6}{7^{2}-6(7)-16 }[/tex]

=[tex]\frac{49-35-6}{49-42-16}[/tex]

=[tex]\frac{8}{-9}[/tex]

There is no time within the interval 0≤t≤2, at which the amount of money raised is 10.

Function is a type of relation, or rule, that maps one input to specific single output.

Given the amount of money raised during a competing fund-raising campaign is modeled by the function M defined by M(t)=240(2t−1)(2t+36), where M(t) is measured in United States dollars and t is the time in days, to get the time t if the money raised is 10 dollars,

Then will substitute M = 10 into the modeled function and calculate the value of t.

M(t)=240(2t−1)(2t+36)

10=240(2t−1)(2t+36)

1 = 24(2t−1)(2t+36)

open the parenthesis;

1 = 24(4t²+72t-2t-36)

1 = 96t²+1680t-864

96t²+1680t-865 = 0

On factorizing, t = 2 is not a factor of the expression.

Thus there is not a time within the interval 0≤t≤2,

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Answer:

  x and y are proportional

Step-by-step explanation:

You want to know the relationship between x and y if their ratio is the same for all related pairs.

When x and y are proportional, the equation that relates them is ...

  y = kx

The ratio of y to x is then ...

  y/x = k . . . . . . the constant of proportionality

When the ratio is constant, the relationship is a proportional one.

Answer:

all of the above(ans)

On solving the provided question, we got to know that - the  cost of common equity is 11.84

Equity in mathematics education is defined by the National Council of Teachers of Mathematics as high standards and rewarding opportunities for everyone, addressing disparities to assist all kids learn mathematics, and making sure that all classrooms have resources and support for students.

here, the above question we have  -

D0 = $0.85;

P0 = $22.80;

g = 7.00%

  = 700

Answer is  -  The  cost of common equity is 11.84

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Answer:4.5x<18, x < 4

Tape measures. Hope this helps

Step-by-step explanation:

8. $4

Explanation:

$18 divided by $4.50 is $4. After buying 4 tape measures there is $0 left.

7. $32

Explanation:

Because Taylor payed $5, $5 was subtracted from her total amount. $5 + $27 = $32 is how much Taylor had.

A line segment is a straight line connecting two points. In the case of a triangle, a line segment will always pass through a vertex, which is one of the three points that make up the triangle. A vertex is defined as the point at which two or more lines meet.

The other two points of a triangle are known as the base and apex. The base is the line that connects two vertices and forms the base of the triangle. The apex is the point of the triangle that is opposite the base and is the highest point of the triangle. All three of these points are connected by line segments, and together they form a triangle. Each line segment will always pass through one of the vertices of the triangle, thus forming the sides of the triangle.

Which of the following will always pass through a vertex of a triangle?

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The answers of given statements are

a) option (A) i.e Net income.

b) The funds grow faster in case of compund interest.

c) Establish a theory of probable cause is third step

d) Gas and insurance

e) It is the rate for each day that is worked.

f) The production factors are labour, land etc.

g) Three basic questions related to economy are

What will be produced?how will it be produced?

how will the output society produces be distributed?

We have given some statements,

a) Saving should treated as an another type -->

Net income

After all sales-related expenses have been taken out, the remaining earnings are referred to as net income. Savings is the act of holding money for use in the future; it does not include paying for an item or service up front. The saving reffered as net income, or income after all expenses.

b) Compound interest is usually better than simple interest because it pays -->or allows funds to grow at a faster rate than they would in an account with a simple interest rate.

c) Third step in troubleshooting a computer problem is :

Step 3. Establish a theory of probable cause. Eliminate the simple and obvious possible causes.

d) Gas and insurance is expenditure will be the same whether you lease or buy a new vehicle.

e) Hourly pay is the rate for each day that is worked and is often calculated upon the number of hours the labor has been given to the factory.

f)The factors of production are

g) An economic system is any system of allocating scarce resources. Economic systems answer three basic questions:

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The equation of the regression line of the given data is y = 1.28x + 3.69. By using a scatter plot, the required equation is calculated.

A regression line describes the relationship between the dependent and independent variables of a set of data.

It is given by y = mx + b; where m is the estimated slope of the data and b is the estimated y-intercept of the data.

To find the regression line, we need to draw the scatter plot for the given data.

The coordinates paired from the given data are:

(12, 18.11), (7, 14.08), (11, 17.97), (8, 15.55), (13, 17.93), (4, 7.71), (3, 4.93), (5, 10.77), and (9, 16.68).

The scatterplot for these points is shown below:

From the plot, consider any two points on the line.

Such as (x1, y1) = (3.35, 7.99) and (x2, y2) = (9.61, 16.02)

So, the equation of the regression line is

(y - y1) = {(y2 - y1)/(x2 - x1)} (x - x1)

⇒ (y - 7.99) = {(16.02 - 7.99)/(9.61 - 3.35)} (x - 3.35)

⇒ y - 7.99 = (8.03/6.26)(x - 3.35)

⇒ y - 7.99 = 1.282(x - 3.35)

⇒ y - 7.99 = 1.282x - 4.2947

⇒ y = 1.282x + 3.695

When rounded to two decimals, we get

y = 1.28x + 3.69

Therefore, the equation of the regression line of the given data is y = 1.28x + 3.69.

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The required answer to the given term is 2.

What is simplification?

Finding the answer from a complex calculation is what is meant by simplification. To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.

By eliminating all common elements from the numerator and denominator and putting the fraction in its simplest/lowest form, fractions can be made simpler.

By combining and grouping like terms, mathematical expressions can be made simpler. This makes the phrase simple to comprehend and solve.

Given, 2/5 x 5

=  [tex]\frac{2}{5} *5[/tex]

= 2

Hence, the required answer to the given term is 2.

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The Fibonacci sequence is 1, 1, 2, 3, 5,... , here each number of the sequence is the sum of the two preceding numbers in the sequence.

The Fibonacci sequence is the sequence that each number in the sequence is the sum of the preceding numbers

The first term = 1

The second term = 1

Third term will be the sum of the two preceding numbers

Third term = First term + second term

= 1 + 1

= 2

The fourth term = second term + third term

= 1 + 2

= 3

The fifth term = Fourth term + Third term

= 2 + 3

= 5

The sequence will be 1, 1, 2, 3, 5....

Therefore, the Fibonacci sequence is the sequence each number is the sum of the two preceding ones

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Its True that if a study uses simple random sampling, that means that each member of the population of interest is equally likely to be selected as a study participant.

A sampling strategy known as simple random sampling gives every member of the population an equal chance of being picked by using an objective selection procedure. Each subject in the sample is assigned a number, and the sample is then chosen using a random method.

One of the simplest and most popular methods for gathering data that aims to represent a group objectively is random sampling.

In order to establish a manageable, balanced subset of a person who is representative of a broader group that might otherwise be too difficult to sample, simple random sampling is used.

So it's true that  if a study uses simple random sampling, that means that each member of the population of interest is equally likely to be selected as a study participant.

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Confidence interval for 'p' 0.59 ± 0.07 interprets the we are 95% confident that the true proportion of all students receiving financial aid is between .52 and .66.

A confidence interval is a type of interval calculation, obtained from observed data, that contains the true value of an unknown parameter.

Hence, in this case, the correct interpretation is option D: We are 95% confident that the true proportion of all students receiving financial aid is between .52 and .66

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Answer:

I think the answer is C

Step-by-step explanation:

The Integral [tex]\int \sec ^2\left(t\right)i+t\left(t^2+1\right)^4j+t^6\ln \left(t\right)kdt = i\tan \left(t\right)+\frac{j\left(t^2+1\right)^5}{10}+k\left(\frac{1}{7}t^7\ln \left(t\right)-\frac{t^7}{49}\right)[/tex]

Given integral;

[tex]\int \sec ^2\left(t\right)i+t\left(t^2+1\right)^4j+t^6\ln \left(t\right)kdt[/tex]

By solving the above integral, we have;

⇒ [tex]\int \sec ^2\left(t\right)i+t\left(t^2+1\right)^4j+t^6\ln \left(t\right)kdt[/tex]

By applying the sum rule,

⇒ [tex]\int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx[/tex]

[tex]=\int \sec ^2\left(t\right)idt+\int \:t\left(t^2+1\right)^4jdt+\int \:t^6\ln \left(t\right)kdt[/tex]

[tex]\int \sec ^2\left(t\right)idt=i\tan \left(t\right)[/tex]

[tex]\int \:t\left(t^2+1\right)^4jdt = \frac{j\left(t^2+1\right)^5}{10}[/tex]

[tex]\int \:t^6\ln \left(t\right)kdt = k\left(\frac{1}{7}t^7\ln \left(t\right)-\frac{t^7}{49}\right)[/tex]

⇒ [tex]i\tan \left(t\right)+\frac{j\left(t^2+1\right)^5}{10}+k\left(\frac{1}{7}t^7\ln \left(t\right)-\frac{t^7}{49}\right)[/tex]

Therefore, the integral [tex]\int \sec ^2\left(t\right)i+t\left(t^2+1\right)^4j+t^6\ln \left(t\right)kdt = i\tan \left(t\right)+\frac{j\left(t^2+1\right)^5}{10}+k\left(\frac{1}{7}t^7\ln \left(t\right)-\frac{t^7}{49}\right)[/tex]

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Answer: the answer is 8

Answer:8  or 18

Step-by-step explanation: 5+13 is 18 and -5+13 is 8

The value of y can be written as y=(x+5)/4.

Here our task is not to find the value of x or y but to find the relation between x and y by eliminating the t from both the equations.

Given that,

Curve equations are  x= 2t-1 y=1/2t+1

x= 2t-1 and y=1/2t+1

2t = x+1

t = (x+1)/2

substitute t value in y

y = t/2 + 1

y = (x+1/2)/2 + 1

y = x+5/4

you can also write x =4y-5

But generally when we have to draw the graph we will be taking x as input value and y as output value so y can be written as y=(x+5)/4

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Comparing Probabilities of Dependent and Independent Events The probability that the sum of your numbers is 6 is 1

Generally, To find the probability that the sum of the numbers spun on the two spinners is 6, we need to consider all the possible combinations of numbers that could be spun on the two spinners and determine how many of those combinations result in a sum of 6.

The possible numbers that can be spun on the yellow spinner are 1, 2, 3, 4, and 5. The possible numbers that can be spun on the blue spinner are also 1, 2, 3, 4, and 5, but we have to re-spin if we get the same number as we spun on the yellow spinner.

Therefore, the possible numbers that can be spun on the blue spinner are all the numbers except for the number spun on the yellow spinner.

We can list out all the possible combinations of numbers that can be spun on the two spinners and determine which ones result in a sum of 6:

Yellow spinner | Blue spinner | Sum ----------------|----------------|----- 1 | 5 | 6 2 | 4 | 6 3 | 3 | 6 4 | 2 | 6 5 | 1 | 6

There are a total of 5 possible combinations of numbers that can be spun on the two spinners, and 5 of those combinations result in a sum of 6.

Therefore, the probability that the sum of the numbers spun on the two spinners is 6 is 5/5, or 1.

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Answer:26.78

Step-by-step explanation:

350x.062=21.70

350x.0145=5.08

21.70+5.08= 26.78

With the help of "The Twelve Days of Christmas” song 364 is the total gifts in 12 days of Christmas.

Total 364 Christmas gifts were given in total.

Total 78 gifts were given on the 12th day.

"The Twelve Days of Christmas”: is one of the most famous and most often sung Christmas carols of all.

So, how many presents are there altogether?

Partridges: 1 × 12 = 12

Doves: 2 × 11 = 22

Hens 3 × 10 = 30

Calling birds: 4 × 9 = 36

Golden rings: 5 × 8 = 40

Geese: 6 × 7 = 42

Swans: 7 × 6 = 42

Maids: 8 × 5 = 40

Ladies: 9 × 4 = 36

Lords: 10 × 3 = 30

Pipers: 11 × 2 = 22

Drummers: 12 × 1 = 12

i) we have to calculate how many gifts total in 12 days of Christmas.

We observe from above that we have the same number of partridges as drummers (i.e 12) ; doves and pipers (i.e 22 ); hens and lords (i.e 30 ) etc. So the simplest way to count our gifts is to add up to the middle of the list and then double the result = (12 + 22 + 30 + 36 + 40 + 42) × 2 = 364.

ii)How many gifts were given in total :

On day one this is simple; just the one gift.

On day two, we get 1 + 2 = 3 gifts.

On day three, we get an additional three gifts on top of day two's three. We receive 3 + 3 = 6 gifts.

On day four, we add four to the previous day's total getting 6 + 4 = 10.

similarly, as we going on words the

we find out that total gifts were given are 364.

iii) The formula which is used to determine the how many gifts given on each day is

n x (n+1) ÷ 2 where n -->a particular day

we have to calculate total gifts were given on 12th day.

So, n x (n+1) ÷ 2 = 12(12+1)/2 = 13× 6 = 78

Hence, total received gifts on 12 days of Christmas is 364.

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The probability that the sample mean is in between 50 minutes and 51 minutes is 0.345.

n = sample size = 39

σ = standard deviation =4.2

μ = population mean = 49.8

Probability is the chance that an event can occur, in this case probability is used to measure the chance sample mean is between 50 minutes and 51 minutes. So,

P(50 ≤ x ≤ 51) = P([tex]\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex] ≤ z ≤ [tex]\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex])

= P([tex]\frac{50-49.8}{\frac{4.2}{\sqrt{39}}}[/tex] ≤ z ≤ [tex]\frac{51-49.8}{\frac{4.2}{\sqrt{39}}}[/tex])

= P(0.30 ≤ z ≤ 1.78)

= P(z ≤ 1.78) - P(z ≤ 0.3)

using z table and we get,

= 0.9625 - 0.6179

= 0.3446

= 0.345

Thus, the probability is 0.345 for the sample mean is within 50 and 51.

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Answer:

x = 9

Step-by-step explanation:

–3( x + 3 ) = –6 ( x–3)

–3x –9 = –6x + 18

–3x + 6x = 18 + 9

3x = 27

x = 27/3

x= 9

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The slope of  a line parallel to the line y=3/2x+3 is 3/2 and the slope of the line perpendicular to the line 2x+y=7 is 1/2

In this question we need to find the slope of line.

a)

We need to find the slope of  a line parallel to the line y=3/2x+3

The slope of line y=3/2x+3 is 3/2

We know that the slope of parallel lines is equal.

So, the slope of  a line parallel to the line y=3/2x+3 is 3/2

b)

We need to find the slope of the line perpendicular to the line 2x+y=7

We can write above equation of line in slope-intercept form of equation of line.

y = -2x + 7

This line has slope -2

We know that the product of slopes of perpendicular lines is -1.

Let m be the slope of required line.

So, m * (-2) = -1

m = 1/2

So, the slope of the line perpendicular to the line 2x+y=7 is 1/2

Therefore, a)  the slope of  a line parallel to the line y=3/2x+3 is 3/2

b)  the slope of the line perpendicular to the line 2x+y=7 is 1/2

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The Orthogonal projection of A on Z i.e subspace formed by X and Y is A cos (90- θ) = A sin (θ)

What is Orthogonal projection ?

A parallel ray projection of a figure. Tangencies are kept in such a projection. Parallel lines converge on parallel lines. The length-to-area ratio of parallel segments is retained, as is the length-to-area ratio. Any triangle can be positioned so that its shadow is equilateral under an orthogonal projection.

Let's say we have a vector. A and vector X and Y

Consider the vector-formed subspace. X and Y is Z = [tex]\alpha[/tex]X + [tex]\beta[/tex]Y perpendicular to subspace vector Z is X * Y

Angle between X * Y and A can be found by cosθ = (X * Y).A/|(X * Y)| * |A|

Now the angle between Z and A is 90 - θ

So the projection of A on Z i.e subspace formed by X and Y is A cos (90 - θ) = A sin (θ)

Finally, in order to discover the projection, we must determine the angle between the subspace and the vector whose projection we must locate

Use MATLAB Code for locating a projection on vector a on the subspace defined by vectors x and y. so that it will be more easy to understand

% cross product of x and y vector

xCrossY = cross(x, y);

% angle between xCrossY and vector 'a'

angle_radian = dot(xCrossY,a)/(norm(xCrossY)*norm(a));

% angle in degrees

angle_deg = rad2deg(angle_radian);

% projection of a on subspace made by x and y is asin(angle_deg)

projection = norm(a)*sin(angle_deg);

A cos (90- ) = A sin () is the orthogonal projection of A on Z, i.e. the subspace created by X and Y.

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By evaluating the function in the different integers, we will see that the correct option is D

Here we have the following function:

f(x)=x²-3x³-2x² + 3x-5.

We can simplify it by adding the first and third terms so we get:

f(x) =-3x³-x² + 3x-5.

To find between which two integers we have zeros, we need to evaluate the function in both of them and see if the signs of the outputs are different.

The first option is (-6, -5), we will get:

f(-6) = -3*(-6)³- (-6)² + 3*(-6) -5 = 589

f(-5) = -3*(-5)³ - (-5)² + 3*-5 - 5 = 330

Both are positive, so there aren't any zeros there.

The second option proposes (-2, -1), evaluating we will get:

f(-2) = -3*(-2)³- (-2)² + 3*(-2) -5 = 9

f(-1) = -3*(-1)³- (-1)² + 3*(-1) -5 = -12

There is a change of sign, so there must be a zero there.

The second pair is (3, 4)

f(3) =-3*(3)³- (3)² + 3*(3) -5 =- 86

f(4) =  -3*(4)³- (4)² + 3*(4) -5 =-201

So again, both negatives, there is not a zero there.

We can discard option C because we already know that (-6, -5) is not a solution, and just by discard, notice that the only option remaining is D, so that is the correct one.

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The simplified cube roots expressions are:

Rational numbers: Rational numbers include terminating decimals, non-terminated with repeating decimals, perfect squares, integers, whole numbers, perfect squares, and fractions.

Example: 2.434343; 5.2; 1/2, -8; √4; etc.

Irrational numbers: Irrational numbers include non-terminated decimals, non-repeated decimals, non-perfect squares, and infinite decimals, and do not form ratios of two numbers.

Example: π = 3.141.....; √2; e/√2; etc.

The given cube root expressions are:

1. [tex]\sqrt[3]{81}[/tex]

2. [tex]\sqrt[3]{-64}[/tex]

Simplifying the first expression, we get

[tex]\sqrt[3]{81}=\sqrt[3]{3\times3\times3}[/tex]

⇒ [tex]\sqrt[3]{81}[/tex] = 3∛3 = 4.3267....

Thus, the cube root of 81 gives an irrational number since it is a non-terminating decimal and has no repeated decimals in it.

Now, simplifying the second expression, we get

[tex]\sqrt[3]{-64}=\sqrt[3]{-4\times-4\times-4}[/tex]

⇒ [tex]\sqrt[3]{-64}[/tex] = -4

Since the result is an integer, the cube root of -64 is a rational number.

Therefore, the given cube root expressions give irrational and rational numbers respectively. They are:

[tex]\sqrt[3]{81} =4.32674...[/tex]  and [tex]\sqrt[3]{-64} = -4[/tex]

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