The length of a rectangle is 6 ft longer than its width. if the perimeter of the rectangle is 64 ft, find its length and width

Answer:

Step-by-step explanation:

The English language is an art that I am using to convey this message to you. Without this form of communication, we would be unable to talk or write without using another language. We think everyday with this awesome language, and don't think much about the language we think in. English is an amazing language, and I am proud to be able to verbalize it to you today.

The y intercept based on the information will be (0,29)

We want to find the value of the y-intercept for the given function.

The y-intercept is (0,29)

First, we define the y-intercept as the value of the function when evaluated in x = 0.

Here the given function is:

h(x) = 29*(5.2)ˣ

It should be noted that too get the y-intercept we just need to evaluate this at x = 0, then we get:

h(0) = 29*(5.2)⁰ = 29

The y-intercept is (0 29)

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2 1/7 x 4.3 (repeating the three) as a mixed number in simplest form is 9 2/7.

First, we can simplify the mixed number 4.3 (repeating the three) as follows:

Let x = 4.3 (repeating the three)

Then 10x = 43.33333...

Subtracting x from 10x, we get:

10x - x = 43.33333... - 4.33333...

9x = 39

x = 4.33333... / 9

x = 4 1/3

Now, we can multiply 2 1/7 by 4 1/3:

2 1/7 x 4 1/3 = (15/7) x (13/3)

= (15 x 13) / (7 x 3)

= 195 / 21

To write this as a mixed number in simplest form, we can divide 195 by 21 and write the quotient as a mixed number:

195 ÷ 21 = 9 with a remainder of 6

So, 195 / 21 = 9 6/21, which can be simplified to 9 2/7.

Therefore, 2 1/7 x 4.3 (repeating the three) as a mixed number in simplest form is 9 2/7.

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This is a linear equation in slope-intercept form, where the slope (m) is 50 and the y-intercept (b) is 62.

Since the milepost increases by a fixed amount of 50 for every hour that they drive, the most appropriate type of equation to describe this relationship is a linear equation.

A linear equation has the form y = mx + b, where m is the slope of the line and b is the y-intercept. In this case, the slope is 50, since the milepost increases by 50 for every hour of driving, and the y-intercept is 62, since they start at milepost 62.

Therefore, the equation that represents Abby's relationship between the milepost they pass, y, and the number of hours they drive, x, is:

y = 50x + 62

This is a linear equation in slope-intercept form, where the slope (m) is 50 and the y-intercept (b) is 62.

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Expressing this function as a piecewise function, we get;

y = -x + 1         for x< -5

y = -1/2x + 4    for x> 4

According to the question, we can see that the graph is a line for x < -5. We will find two points on this line to find out the slope.

( - 5,6) and ( -8,9)

The slope is m= ( y2-y1)/(x2-x1)

m = ( 9-6)/(-8 - -5) = 3/ ( -8+5) = 3/-3

The slope is -1

Using point-slope form, we will find the general equation of this line

y-y1 = m(x-x1)  and the point ( -8,9)

y -9 = -1(x - -8)

y -9 = -1(x +8)

y-9 =  -x - 8

y = -x + 1   for x< -5

The graph is a line for  x > 4

(4,2) and ( 6,1)

The slope is m= ( y2-y1)/(x2-x1)

m = ( 1 - 2)/(6 - 4) = -1/ (2) = -1/2

The slope is -1/2

Using point-slope form

y-y1 = m(x-x1)  and the point (6,1)

y -1 = -1/2(x - 6)

y-1 = -1/2 x  + 3

y = -1/2x + 4   for x> 4

Therefore, expressing this function as a piecewise function, we get;

y = -x + 1         for x< -5

y = -1/2x + 4    for x> 4

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Answer:

Ryan spent $72 on his shopping trip.

Step-by-step explanation:

To find out how much money Ryan spent, we need to add up the cost of the shirts and the sneakers.

First, we know that Ryan purchased two shirts for $16 each. So we can find the total cost of the shirts by multiplying the cost per shirt by the number of shirts:

So the total cost of the shirts is $32.

Next, we know that Ryan purchased a pair of sneakers that cost 2 1/2 times as much as a shirt. We can use this information to find the cost of the sneakers.

If the cost of a shirt is $16, then we can find the cost of the sneakers by multiplying $16 by 2 1/2:

So the cost of the sneakers is $40.

Finally, we can find the total cost of Ryan's shopping trip by adding up the cost of the shirts and the sneakers:

Therefore, Ryan spent $72 on his shopping trip.

The quotient of the given division is 0.4082, under the condition that dividend is 4.082 and divisor is 10,000.

The count of zeros in 10,000 is 4, then we have to transfer the decimal point four places to the left to divide by 10,000. Here, we have to relie on the basic principles involved in division.

Then, in order to find the quotient of 4.082 and 10,000, we have to divide 4.082 by 10,000. To perform this, we expand the number by moving the decimal point forward of 4.082.

That is,

[tex] \frac{4.082 }{10000} [/tex]

= 0.4082

The quotient is 0.4082

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The variables of interest are both non-parametric and measured on an ordinal scale, a suitable analysis for determining the relationship between them would be the Spearman rank correlation coefficient.

The Spearman rank correlation coefficient is a non-parametric measure of the strength and direction of association between two variables.

It is based on the rank order of observations for each variable, rather than their actual numerical values.

The coefficient can range from -1 perfect negative correlation to +1 perfect positive correlation.

And with a value of 0 indicating no correlation.

Use the Spearman rank correlation coefficient to determine the strength and direction of the relationship between CI and student satisfaction.

The coefficient would tell us if there is a significant correlation between the two variables, and whether the correlation is positive or negative.

Perform the analysis, first rank the observations for both variables and calculate the difference in ranks between each pair of observations.

Calculate the Spearman rank correlation coefficient using the formula,

ρ = 1 - (6Σd² / n(n² - 1))

where ρ is the Spearman rank correlation coefficient,

d is the difference in ranks for each pair of observations,

n is the sample size,

and n² is the sum of the squares of the ranks.

A value of ρ close to +1 would indicate a strong positive correlation between the two variables.

A value close to -1 would indicate a strong negative correlation.

A value close to 0 would indicate no significant correlation between the two variables.

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Answer:

24°

Step-by-step explanation:

Supplementary angles: 2 angles that add up to 180°.

We are given that one angle is 156°, so we can write an equation:

180=156+x

subtract both sides by 156

24=x

So, the measure of the supplementary angle is 24°.

Hope this helps!

The task requires estimating the rate of change of atmospheric pressure with respect to altitude using the given data.

First, a table needs to be created to estimate the rate of change of pressure with respect to altitude. The rate of change will be the difference in pressure divided by the difference in altitude between two consecutive data points.

Second, two plots should be created: one illustrating the pressure depending on altitude, and another illustrating the estimated rate of change depending on altitude.

Third, a function should be constructed to model the pressure-altitude data. The function should be selected based on how well it fits the data points.

Fourth, the model function should be used to estimate the rate of change of atmospheric pressure with respect to altitude at different heights over the range from sea level to 10,000 ft.

Fifth, a comparison should be made between the rate of change information computed from the model function and the rate of change information estimated directly from the data. This comparison will be used to assess the accuracy of the model function.

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A telephone pole has a wire attached to its top that is anchored to the ground then conclude the height of the pole is approximately 51.53 feet.

Let h be the height of the pole. The equation h = (h - 69) + 6 represents the given information. Solving it gives h = 75.

Let's denote the height of the pole as "h". Then, according to the problem, the distance from the bottom of the pole to the anchor point is 69 feet less than the height of the pole, which means it is h - 69. Additionally, the wire is to be 6 feet longer than the height of the pole, so its length is h + 6.

Now we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (in this case, the wire) is equal to the sum of the squares of the lengths of the other two sides (in this case, the height of the pole and the distance from the bottom of the pole to the anchor point). So we have:

(h - 69)^2 + h^2 = (h + 6)^2

h^2 - 138h + 4761 + h^2 = h^2 + 12h + 36

h^2 - 75h - 1602 = 0

h = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = -75, and c = -1602.

h = (75 ± sqrt(75^2 - 4(1)(-1602))) / 2(1)

h ≈ 51.53 or h ≈ -31.53

Since the height of the pole cannot be negative, we can ignore the negative solution and conclude that the height of the pole is approximately 51.53 feet.

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Answer:

h = 30 cm

Step-by-step explanation:

Given:

V (volume) = 69,120π cm^3

d (diameter) = 96 cm (r (radius) = 0,5 × 96 = 48 cm

Find: h (height) - ?

[tex]v = \frac{1}{3} \times \pi {r}^{2} \times h[/tex]

[tex] \frac{1}{3} \times \pi \times {48}^{2} \times h = 69120\pi[/tex]

Multiply the whole equation by 3 to eliminate the fraction:

[tex]2304\pi \times h = 69120\pi[/tex]

[tex]h = 30[/tex]

The scope of both functions is all real numbers.

To compute the values of (f+g)(x) and (f-g)(x), we apply the addition and subtraction of two distinct functions, respectively:

(f+g)(x) = f(x) + g(x) = [tex](-2x + 4) + (3x^2) = 3x^2 - 2x + 4[/tex]

(f-g)(x) = f(x) - g(x) = [tex](-2x + 4) - (3x^2) = -3x^2 - 2x + 4[/tex]

The scope of both functions is all real numbers.

Subsequently, we evaluate the expressions for x = -3:

(f+g)(-3) = [tex]3(-3)^2 - 2(-3) + 4[/tex] = 3(9) + 6 + 4 = 27 +6 +4 = 37

(f-g)(-3) = [tex]-3(-3)^2 - 2(-3) + 4[/tex]= -3(9) + 6 + 4 = -27 + 6 + 4 = -17

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Answer:

21

Step-by-step explanation:

70 · .30 = 21

Answer: 6,550.6666666666666666666666666667π

Step-by-step explanation:

Hope this helps! :)

Step-by-step explanation:

A, 7^(x+3) = 823, 543

7^(x+3) = 823, 543

7^(x+3) = 7^7 ....... write in the power form which it's base must be 7 in order to equalify the power

x+3 = 7

x = 4

B, 4^ -4x = 4^-8

4 ^ -4x = 1/65, 536

4^ -4x = 1/4^8 ........ write in the power form

4^ -4x = 4^-8

-4x = -8 ..... write equality among the power cause it's base is same

x=2

C, 1/(6^(x-5) ) = 1296

1/(6^(x-5) ) = 1296

6^-(x-5) = 1296

6^-(x-5) = 6^4........ write in the power form

-(x-5) = 4

-x + 5 = 4

-x = -11

x = 1

D, 1/3^x+7 = 1/243

1/3^x+7 = 1/243

3 ^ -(x+7) = 3^-5 .... write in the power form

-(x+7) = -5

-x-7 = -5

-x = 2

x= -2

Answer:

250

Step-by-step explanation:

5 x 2= 10

25 x 10= 250

Assuming that the trail is a total of "x" miles, we can set up the following equation to solve for "x":

816 = 0.48x

To solve for "x", we can divide both sides by 0.48:

x = 1700

Therefore, the total length of the trail is 1700 miles.

The unit vector that is oppositely directed to v = (3, -4) and half its length is approximately u = (-0.5547, 0.8321).

To find a unit vector that is oppositely directed to v = (3, -4) and half its length, we can follow these steps:

Find the length of vector v:

|v| = sqrt(3^2 + (-4)^2) = 5

Divide vector v by 2 to get a vector with half its length:

v/2 = (3/2, -2)

To get a vector that is oppositely directed to v, we can reverse the direction of v/2:

-(3/2, -2) = (-3/2, 2)

Finally, we can find the unit vector in the direction of (-3/2, 2) by dividing it by its length:

|(-3/2, 2)| = sqrt((-3/2)^2 + 2^2) = sqrt(13/4)

u = (-3/2, 2) / sqrt(13/4) = (-3/2) * (2/sqrt(13))/2 + (2/sqrt(13)) * (1/2)

Therefore, the unit vector that is oppositely directed to v = (3, -4) and half its length is approximately u = (-0.5547, 0.8321).

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a) The percentage of men with a height less than or equal to 55.8 inches is approximately 0.00007 or 0.007%.

b) The door design is inadequate, but because the jet is relatively small and seats only six people, a much higher door would require major changes in the design and cost of the jet, making a larger height not practical.

Option (a) is correct.

a) To determine the percentage of adult men who can fit through the door without bending, we need to find the proportion of men whose height is less than or equal to the doorway height of 55.8 inches. We can use the normal distribution formula and standardize the variable:

Z = (X - μ) / σ

Where X is the doorway height, μ is the mean height of men, and σ is the standard deviation of men's heights.

Z = (55.8 - 67.8) / 3.1 = -3.87

Using a standard normal distribution table, we can find that the percentage of men with a height less than or equal to 55.8 inches is approximately 0.00007 or 0.007%.

Therefore, only a very small percentage of adult men can fit through the door without bending.

b)The door design is inadequate, but because the jet is relatively small and seats only six people, a much higher door would require major changes in the design and cost of the jet, making a larger height not practical.

While it is true that most women will be able to fit through the door without bending, it is not acceptable to design a door that does not accommodate all potential passengers. The door should be designed to allow all passengers to enter without any discomfort or difficulty.

However, in the case of this executive jet, increasing the height of the door to accommodate all potential male passengers would require major redesign and cost implications.

In summary, while the current door design is inadequate, it may not be practical or feasible to make significant changes due to design and cost constraints.

Therefore, the correct option is a.

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After formula for the volume of a cylinder, the increase in water level results in approximately 260 more cubic feet of water in the tank.

The current water level is 10 feet, which is 120 inches. When the water level increases by 2 inches, the new water level will be 122 inches.

The radius of the tank is half of the diameter, which is 30 feet or 360 inches.

The current volume of water in the tank can be calculated using the formula for the volume of a cylinder: V = πr²h, where r is the radius and h is the height of the water level.

V = π(360²)(120) ≈ 15,465,920 cubic inches

When the water level increases by 2 inches, the new height of the water level is 122 inches.

The new volume of water in the tank can be calculated using the same formula:

V = π(360²)(122) ≈ 15,914,693 cubic inches

The difference in volume between the two levels is:

15,914,693 - 15,465,920 = 448,773 cubic inches

To convert cubic inches to cubic feet, we divide by 1728:

448,773 ÷ 1728 ≈ 259.6 cubic feet

Rounding to the nearest cubic foot, we get:

260 cubic feet

Therefore, the increase in water level results in approximately 260 more cubic feet of water in the tank.

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The number does MOVED represent 1110.

Since GOD=605, we know that D=5. We can now substitute this value of D into the addition problem to get:

GOD+ DOG = MOVED

605+ 506 = 1111

Since M cannot be 0 (otherwise it wouldn't be a 4-digit number), we know that M=1.

We can now subtract 1 from both sides of the equation to get:

604+ 506 = 1110

Now we can see that E+4=10, so E=6. We can also see that O+0=0, so O=0. Finally, we can see that G+D=1, so G=6 and D=5.

Therefore, MOVED = 1110.

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Answer:does anyone have the image

Step-by-step explanation:

a) The equation of the regression line is Travel Time = β₀ + β₁(Distance Traveled) + ɛ. b) The slope of the regression line indicates the increase in travel time and the intercept represents the estimated travel time. c) R₂ is 0.404. d) Regression equation will be used. e) Residual cannot be calculated. f) No, the given linear model is not appropriate to use.

a) The equation of the regression line for predicting travel time is

Travel Time = β₀ + β₁(Distance Traveled) + ɛ

where β₀ is the intercept, β₁ is the slope, Distance Traveled is the independent variable, and Travel Time is the dependent variable.

b) The slope of the regression line indicates the increase in travel time (in minutes) for every one-mile increase in distance traveled. The intercept represents the estimated travel time (in minutes) when the distance traveled is zero. In this context, the intercept is not meaningful since there cannot be a distance of zero between two stops.

c) To calculate R₂, we need to first calculate the correlation coefficient (r) between Travel Time and Distance Traveled

r = (covariance of Travel Time and Distance Traveled) / (standard deviation of Travel Time × standard deviation of Distance Traveled)

Using the given values, we have

r = (0.636 × 113 × 99) / (113 × 99) = 0.636

Then, we can calculate R₂ as

R₂ = r₂ = 0.6362 = 0.404

R₂ represents the proportion of variance in Travel Time that is explained by Distance Traveled. In this context, R₂=0.404 indicates that 40.4% of the variation in travel time from one stop to the next on the Coast Starlight can be explained by the distance traveled between those stops.

d) To estimate the time it takes for the Starlight to travel between Santa Barbara and Los Angeles, we need to use the regression equation

Travel Time = β₀ + β₁(Distance Traveled)

We know that the distance between Santa Barbara and Los Angeles is 103 miles. So, we plug this value into the equation

Travel Time = β₀ + β₁(103)

To solve for the travel time, we need to know the values of β₀ and β₁. We can use the given mean and standard deviation values to estimate these parameters using linear regression. However, we are not given this information in the question.

e) To calculate the residual, we need to first calculate the predicted travel time based on the regression equation

Travel Time = β₀ + β₁(Distance Traveled)

We are told that the distance between Santa Barbara and Los Angeles is 103 miles, so we can plug this value into the equation to get the predicted travel time

Predicted Travel Time = β₀ + β₁(103)

However, we are not given the values of β₀ and β₁, so we cannot calculate the predicted travel time.

The residual is the difference between the actual travel time and the predicted travel time. In this case, we are told that the actual travel time is 168 minutes, and we do not have the predicted travel time. Therefore, we cannot calculate the residual.

f) It would not be appropriate to use this linear model to predict the travel time from Los Angeles to a point 500 miles away from Los Angeles, because the linear relationship between travel time and distance traveled may not hold beyond the range of distances that were used to estimate the regression equation. The linear model assumes that the relationship between travel time and distance traveled is constant across all distances, which may not be true. Additionally, adding a stop at a point 500 miles away from Los Angeles may affect the relationship between travel time and distance traveled, since there may be other factors that influence travel time at that distance. Therefore, a new regression model would need to be estimated using data that includes stops at or beyond the 500-mile mark.

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The critical value is approximately 2.681. Since the absolute value of the test statistic (4.114) is greater than the critical value (2.681), we can reject the null hypothesis at the 0.01 significance level and conclude that there is evidence to support the claim that Praxor is effective at lowering cholesterol levels compared to a placebo.

Hypothesis testing is a statistical method used to determine whether there is enough evidence to support a claim about a population.

In this case, the claim being made is that people who take Praxor will experience a greater decrease in cholesterol levels compared to those taking a placebo.

The first step in hypothesis testing is to state the null and alternative hypotheses. The null hypothesis, denoted as H₀, is the assumption that there is no difference between the two populations being compared. The alternative hypothesis, denoted as H₁, is the claim being made, which is that there is a difference between the two populations.

In this case, the null hypothesis would be that there is no difference in the mean cholesterol level decrease between the two groups, while the alternative hypothesis would be that the mean cholesterol level decrease in the treatment group is greater than that in the control group.

Next, a significance level, denoted as α, is chosen. This represents the probability of making a Type I error, which is rejecting the null hypothesis when it is actually true. In this case, a significance level of 0.01 is chosen.

The next step is to calculate the test statistic, which is a value that measures how far the sample data deviates from what is expected under the null hypothesis. The test statistic used in this case is the two-sample t-test. This test assumes that the two populations being compared have normal distributions and that their variances are not equal.

The formula for the two-sample t-test is:

t = (x₁ - x₂) / √√(s₁²/n1 + s₂²/n₂)

Where x₁ and x₂ are the sample means, s₁ and s₂ are the sample standard deviations, and n₁ and n₂ are the sample sizes for the two groups being compared.

Substituting the values in the formula we get,

= (19.9 - 19.3) / √((3.9²/32) + (1.3²/36))

t ≈ 4.114

Finally, we compare the test statistic to a critical value from a t-distribution table with degrees of freedom equal to n₁ + n₂ - 2 and a significance level of 0.01. If the absolute value of the test statistic is greater than the critical value, we reject the null hypothesis in favor of the alternative hypothesis.

In this case, the critical value is approximately 2.681. Since the absolute value of the test statistic (4.114) is greater than the critical value (2.681), we can reject the null hypothesis at the 0.01 significance level and conclude that there is evidence to support the claim that Praxor is effective at lowering cholesterol levels compared to a placebo.

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Answer:  B.
Given expression: (-9x) / (x^2 - 9)
Simplify the rational expression by factoring the denominator:
(x^2 - 9) = (x + 3)(x - 3)
= (-9x) / [(x + 3)(x - 3)]

Now, we can evaluate the limit as x approaches 3:
lim (x -> 3) [(-9x) / ((x + 3)(x - 3))]

Since the expression is defined and continuous at x = 3, we can directly substitute the value of x:
((-9 * 3) / ((3 + 3)(3 - 3))) = (-27) / (6 * 0)

The denominator becomes zero, which means the limit does not exist, and is neither ∞ nor -∞. So, the correct choice is B. The limit does not exist and is neither ∞ nor -∞.

Answer:

0.80x400

Step-by-step explanation:

The true statements are Numbers with same absolute value are opposites because they are same distance from each other and from 0 on the number line. The |7.1| = 7.1. So, correct options are B, C and E.

b) Numbers with the same absolute value are opposites because they are the same distance from each other. This is true because absolute value is the distance from a number to zero on the number line, and if two numbers have the same distance from zero, then they must be equidistant from zero and therefore, they are opposite in sign.

c) The |7.1| = 7.1 because the distance from 7.1 to 0 on the number line is 7.1 units. This is true because the absolute value of a number is always positive, and it represents the distance of that number from zero on the number line.

d) The |-8.4| = 8.4 because the distance from -8.4 to 8.4 on the number line is 0 units. This is false, as the distance between -8.4 and 8.4 on the number line is 16.8 units. The correct value of the absolute value of -8.4 is 8.4.

e) Numbers with the same absolute value are opposites because they are the same distance from 0 on the number line. This is true because 0 is the midpoint of the number line, and if two numbers have the same distance from 0, then they must be equidistant from zero and therefore, they are opposite in sign.

Therefore, the correct statements are b, c, and e.

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The sequence (n){(1-2)/(3^n+1) + 3} is bounded and decreasing. The GLB is 3 and the LUB is 1.

To determine the boundedness and monotonicity of the sequence, we can look at the limit as n approaches infinity.

Taking the limit of the sequence, we have:

lim(n→∞) [(1-2)/(3^n+1) + 3] = 3

This means that the sequence approaches a finite value as n gets larger, so the sequence is bounded.

Next, to check the monotonicity of the sequence, we can take the first derivative of the sequence with respect to n:

d/dn [(1-2)/(3^n+1) + 3] = [(2-1)(-ln3)(3^n+1)]/[(3^n+1)^2]

Simplifying, we get:

d/dn [(1-2)/(3^n+1) + 3] = (-ln3)/(3^n+1)^2

Since the derivative is negative for all n, the sequence is decreasing.

To find the GLB and LUB, we can use the fact that the sequence is decreasing and bounded. Since the sequence approaches 3 as n approaches infinity, 3 is the lower bound.

To find the upper bound, we can use the fact that the sequence is decreasing and start with the second term, which is 2. Therefore, the upper bound is 2. Since 1 < 2, we can conclude that the LUB is 1.

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