Answer:
The probability that all five lines will be in use when a customer calls customer service is 1/7776.
What is probability?
The proportion of favorable cases to all possible situations that can occur indicates how likely an event is to occur.
Step-by-step explanation:
Given that there are 5 lines and the probability for each line to be engaged in working hours is 1/6.
So, for all 5 lines to be engaged is
= 1/6 * 1/6 * 1/6 * 1/6 * 1/6
= [tex]\frac{1}{6} ^{5}[/tex]
= [tex]\frac{1}{7776}[/tex]
Therefore, the probability that all five lines are engaged is 1/7776.
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A certain forest covers an area of 2100 km2. Suppose that each year this area decreases by 4.25%. What will the area be after 10 years?
The area of the forest would decrease to 1360 km²
What is compounding in percentages?Divide the value of an investment at the end of the period by its value at the beginning of that period. Raise the result to an exponent of one divided by the number of years. Subtract one from the subsequent result. Multiply by 100 to convert the answer into a percentage.
Given here, an area of 2100 km² and each year it decreases by 4.25%
in the first year, the area of the forest becomes (2100 - 4.25/100 × 2100)
= 2010.75 km²
in the second year, the area becomes 2100 × (1-4.25/100)²
= 1925.29 km²
similarly, in the tenth year, the area becomes 2100 × ( 1- 4.25/100)¹⁰
= 1360 km²
Hence, the area of the forest reduces to 1360 km²
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Find the sum of 9x² + 6 and 2x² - x - 10.
Answer:
Submit Answer
By using addition, it can be calculated that, Sum of [tex]9x^2 + 6[/tex] and [tex]2x^2 - x - 10[/tex] is [tex]11x^2 - x -4[/tex]
What is addition?
Addition is a basic math operation that combines two or more numbers to create a new total. It is the process of combining two or more values to get a single sum. Addition is one of the four basic operations in math, alongside subtraction, multiplication, and division. It is a fundamental part of arithmetic and is widely used in everyday life for tasks such as counting, budgeting, and measuring. Addition can be performed with any type of number, including whole numbers, fractions, decimals, and even negative numbers. Addition is an incredibly useful tool for solving a variety of math problems.
Sum of [tex]9x^2 + 6[/tex] and [tex]2x^2 - x - 10[/tex]
[tex]9x^2 + 6 + 2x^2 - x - 10\\= 11x^2 -x - 4[/tex]
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F(x)=x+1 complete the table
The next day Tamika records the temperature of 0°F at 8:00 a.m. and 1°F
at 10:00 a.m. Assume the temperature has been rising linearly since sunrise
at 6:00 a.m.
Use point-slope form to write a linear function to model the
situation. (Hint: Solve for y, then replace y with f(x)).
The equation of line in the point slope form is y = 2x + 8
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation be represented as A
Let temperature be denoted as x
Let the time be denoted as y
Let the initial temperature be = 0°F
Let the final temperature be = 1°F
Let the initial time be = 8 : 00 AM
Let the final time be = 10 :00 AM
And , the first point be P = P ( 0 , 8 )
The second point be Q = Q ( 1 , 10 )
Now , the slope of the equation is given as
Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 10 - 8 ) / ( 1 - 0 )
Slope m = 2
Now , the equation of line is given as y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 8 = 2 ( x - 0 )
y - 8 = 2x
Adding 8 on both sides of the equation , we get
y = 2x + 8
Therefore , the value of A is y = 2x + 8
Hence , the equation is y = 2x + 8
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GottaGo rents portable toilets for small outdoor events. The El Paso softball league championship game is expected to draw several hundred participants, and the plan is to rent one portable toilet from GottaGo. During the event, one person will need to use the toilet every five minutes, with a standard deviation of five minutes. On average, a person uses the GottaGo toilet for two minutes, with a standard deviation of three minutes. What fraction of time (as a percent) is the GottaGo toilet occupied?
GottaGo rents portable toilets for small outdoor events. The El Paso softball league championship is expected to draw several hundred participants, and the plan is to rent one portable toilet from GottaGo. During the event, one person will need to use the toilet every five minutes, with a standard deviation of five minutes. On average, a person uses the GottaGo toilet for two minutes, with a standard deviation of three minutes. How long does a person have to wait, on average, before he or she can use the GottaGo toilet?
The average wait time before a person can use the GottaGo toilet is three minutes. This is calculated by subtracting the average usage time (two minutes) from the average time between uses (five minutes).
1. Calculate the total time the toilet is occupied by multiplying the average usage time (two minutes) by the average time between uses (five minutes). This gives a total time of 10 minutes.
2. Calculate the total time the toilet is available by subtracting the total time the toilet is occupied (10 minutes) from the total time between uses (five minutes). This gives a total time of five minutes.
3. Calculate the fraction of time the toilet is occupied by dividing the total time the toilet is occupied (10 minutes) by the total time between uses (five minutes). This gives a fraction of two-fifths (2/5).
4. Convert the fraction to a percentage by multiplying the fraction by 100. This gives a percentage of 40%. Therefore, the GottaGo toilet is occupied 40% of the time.
Time occupied = 2 minutes * 5 minutes = 10 minutes
Time available = 5 minutes - 10 minutes = 5 minutes
Fraction of time occupied = 10 minutes / 5 minutes = 2/5
Percentage of time occupied = 2/5 * 100 = 40%
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The concept of best-, worst-, and average-case analyses extends beyond algorithms to other counting problems in mathematics. Recall that the height of a binary tree is the number of edges in the longest path from the root to a leaf. Find the best-case height of a binary tree with seven nodes.
the height of a binary tree is the number of edges in the longest path from the root to a leaf.The best-case height of a binary tree with seven nodes is 3.
A binary tree is a type of tree structure consisting of nodes that are connected by edges. The number of edges in the longest path from a binary tree's root to a leaf determines the tree's height.In the best-case scenario, the binary tree is perfectly balanced and each node has exactly two children. With seven nodes, the best-case height is three because each node has two children and three edges connect the root node to the leaves. This means that the longest path from the root to a leaf is three edges, resulting in a height of three.
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the function below satisfies the mean value theorem on the specified interval.find the value of c in the interval (1,2) where 1.2/x 1.6 (1,21)
By solving the mean value theorem, the value of c in the interval (1,2) is 0.75.
Explanation:
The mean value theorem states that if a function f(x) is continuous on a closed interval [a,b] and differentiable on the open interval (a,b), then there exists at least one point c in (a,b) where the equation f'(c) = (f(b) - f(a))/(b - a) is satisfied.
For the specified interval (1,2) and given equation 1.2/x - 1.6, we can rearrange the equation to solve for c:
1.2/c - 1.6 = 0
1.2/c = 1.6
c = 1.2/1.6
c = 0.75
Therefore, the value of c in the interval (1,2) is 0.75.
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Find a power series representation for the function; find the interval of convergence. (Give your power series representation centered at x = 0.)
f(x)= 1/(1-9x)
sum from n=0 to infinity [?] provided |x| < [?]
The power series representation for the given function is 1+ 9x + (9x) ^ 2 + (9x) ^ 3 + .... (9x) ^ n (where 0 ≤ n ≤ ∞).
Let u = 9x.
Return to the series above and replace each u with a 9x directly:
Where 0 n , 1 + 9x + (9x) 2 + (9x) 3 +.... (9x) n
Here, the interval of convergence is easily found. It follows that
|9x| 1 -1/9 x 1/9 because we know that geometric series must have | u | = 1
Finally, we may leverage the fact that geometric series have a sum to get the sum: S = a / (1 - u).
Here, u = 9x and a = 1
Therefore, the total is simply S = 1 /(1 - 9x).
Any sum can be calculated provided x is between -1/9 and x and less than 1/9.
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For the function f(x)=[tex]x^{2} +3x-18[/tex] solve the following. f(x)[tex]\geq 0[/tex]
mation. (See Example 5.)
30. ax² + 6x + c = 0; two real solutions
Answer:
Step-by-step explanation:
ax²+6x+c=0
disc=6²-4×a×c=36-4ac≥0,(∵ it has two real solutions.)
36-4ac≥0
36≥4ac
4ac≤36
ac≤9
3 divided by 7.14 (PLEASEE HURRRRYYY)
what function for 3x-5
Answer: 3
Step-by-step explanation:
TRUE/FALSE. the linear probability model always contains heteroskedasticity when the dependent variable is a binary variable unless all of the slope parameters are zero.
The Linear probability model always contains heteroskedasticity when the dependent variable is binary unless all of the slope parameters are zero. It's true.
Probability is the branch of mathematics concerning numerical descriptions of how probable an event is to do, or how likely it's that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.
In statistics, a direct probability model is a special case of a double retrogression model. Then the dependent variable for each observation takes values that are moreover 0 or 1.
The introductory sapience is that the direct probability model can be used whenever the relationship between probability and log odds is roughly direct over the range of modeled chances.
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For linear function f, f(2)=0 and f(4)=-6.
Write function f in slope-intercept form.
The function f(x) in slope-intercept form is Y= −3X−10.
In the given question, linear function f, f(2)=0 and f(4)=-6.
We have to write function f(x) in slope-intercept form.
We have to find equation for f(x)
f(2)=0, and f(4)=−6,
Now we have to find slope
Slope(m)=−6−0/4−2
m = −6/2
m=−3
Now the general equation of line is
Y=MX+C
where M = slope of the line, C is the Y intercept value, X is independent variable and Y is dependent variable.
At point (2,4)
4 = (−3)×(2)+C
4 = −6+C
Add 6 on both side, we get
C = 10
Equation for f(x) is.
Y=(−3)X−(10)
Y= −3X−10
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Solve this question
(7w^7)k³
The value of the variable 'w' for the given equation 7 ( w + 7 )³ = 7(6³) is equal to w = -1.
As given in the question,
Given equation is equal to :
7 ( w + 7 )³ = 7(6³)
Divide both the side of the equation by 7 we get,
⇒ 7 ( w + 7 )³ / 7 = 7(6³) /7
⇒( w + 7 )³ = (6³)
Take cube root both the side of the equation we get,
⇒∛( w + 7 )³ = ∛(6³)
⇒ w + 7 = 6
Now subtract 7 from both the side of the equation we get,
⇒w + 7 - 7 = 6 - 7
⇒ w = -1
Therefore, the value of the variable 'w' for the given equation is equal to w = -1.
The complete question is:
Solve this equation:
7 ( w + 7 )³ = 7(6³)
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for which value of x does each expression make sense: square root of (x-2) / square root of (x-3)
Answer:
The expression makes sense when x > 3.------------------------------------
Given expression:[tex]\cfrac{\sqrt{x-2} }{\sqrt{x-3} }[/tex]The restrictions are:x - 2 ≥ 0, expression under square root can't be negative. x - 3 ≥ 0, same as above,x - 3 ≠ 0, denominator can't be zero.Solve each and combine:
x ≥ 2,x ≥ 3,x ≠ 3.The common interval is x > 3.
The following graphs show the sampling distributions for two different point estimators, R and W, of the same population parameter.
Which of the following statements is true?
Pilihan jawaban
Both R and W are unbiased.
R is biased, and W is unbiased
Both R and W are biased.
R is unbiased, and W is biased.
The assessment of bias is not possible, because the sampling distributions display too much variability.
The correct statement regarding bias in either distribution is given as follows:
R is biased, and W is unbiased.
How to identify bias in each distribution?We use the graphs showing the sampling distributions for the two different point estimates to identify bias.
Then the criteria to determine that there will be bias is given as follows:
Point estimate at the center: no bias.Point estimate not at the center: bias.From the graphs given at the end of the answer, we have that:
The point estimate of estimator R is not at the center.The point estimate of estimator W is at the center.As the point estimate of estimator R is not at the center, it contains bias, and thus the fourth statement is correct.
Missing InformationThe graphs are given by the image shown at the end of the answer.
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the following function should swap the values contained in two integer variables, nami and num2. what, if any void swap (int nomi, int num2) int temp
Yes, there is something wrong with the function.
Here, two integer variables, num1, and num2 are taken by this function as arguments. Then it assigns the value of num1 to a newly declared integer variable, temp. It then assigns the value of temp to num2, and the value of num2 to num1, thus swapping the values of the two variables effectively.
Here, the problem with the function is that the function operates on copies of the original variables rather than the variables themselves.
The variables num1 and num2 are passed by value, which means that to swap the values of the original variables, the function should use pointers or pass the variables by reference.
For example
void swap (int* num1, int* num2) {
int temp = *num1;
*num1 = *num2;
*num2 = temp;
}
Here, the function to modify the original variables directly as the variables num1 and num2 are passed as pointers.
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Complete Question
The following function should swap the values contained in two integer variables, num1, and num2. What, if anything, is wrong with this function?
void swap(int num1, int num2)
{
int temp = num2;
num2 = num1;
num1 = temp;
}
suppose that the mean outstanding credit card balance for all young couples in the us is $650 with a standard deviation of $420. the distribution is highly skewed to the right. suppose now that one random sample of size 200 is selected from the population of young couples. the mean of this sample is $623. based on this information, which of the following is true?
The probability is 0.2005.
What is a probability distribution?
A probability distribution is a function that describes the probabilities of different outcomes in a random event or experiment. It is used to represent the likelihood of different outcomes occurring in a given situation.
Mean = 650 * 200 = 130000
[tex]\sigma \bar x = \sqrt{n}\times\sigma\\\\=\sqrt{200}*420\\=5939.6970\\\\\\P(X < 125000)=P[Z < \frac{125000-130000}{5939.6970}]\\\\P(X < 125000)=P[Z < \frac{-5000}{5939.6970}]\\\\P(X < 125000)=P[Z < -0.84]\\\\P(X < 125000)=0.2005[/tex]
Hence, the probability is 0.2005.
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Mat hits a home run once every ten times at bat, and gets exactly two times at bat in every game. He wants to know the probability that he will hit at least one home run in a single game. Mat can use one of the following simulations to complete this probability. Model A - Use a random number generator to generate 500 two-digit numbers from 00 to 99. Assign "success" to the number value of 1, and count up all the random two-digit numbers that contain a 1. Model B - Use a spinner with ten different colors of equal area. Assign "success" to one of the colors. For one trial, spin the spinner twice. If the spinner lands on the color considered "success", start over. Count the trial if the spinner lands on the color considered "success" or not at all. Repeat this process for 20 trials. Model C - Use a standard six-sided die. Assign "success" to the number 1. For one trial, roll the die twice. If the die lands on 1, start over. Count the trial if the die either lands on 1 or not at all. Repeat this process for 50 trials. is the best simulation for this situation. Using this simulation, the probability that Mat will hit at least one home run in a single game is about .
Answer:Model A and 19%
Step-by-step explanation:
I saw the explanation on study island
The correct model for the probability is given as follows:
Model B.
The probability that Mat will hit at least one home run in a single game is about 0.19 = 19%.
A probability is calculated by the division of the number of desired outcomes by the number of total outcomes.
Mat hits a home run once every ten times at bat, and gets exactly two times at bat in every game, hence the total number of outcomes is of:
10² = 100.
This is why Model B is the correct model, as it has two trials of 10 outcomes, and each trial has a 0.1 probability of success.
The probability that he hits no home runs is of:
0.9² = 0.81.
Hence the probability of hitting at least one home run is of:
1 - 0.81 = 0.19 = 19%.
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If you saw 12-1 / 16''off a board that is 20-3/4 " long, the length of the remaining board will be
8 -1/4''
8 -11 /16''
11 -1/4''
17 -3/8''
The remaining length of the board is 8 11/16 feet.
Length of board = 20 3/4 feet
Length that was cut off = 12 1/16 feet
To obtain the length of the remaining part of the board ;
We subtract the length that was cut off from the total length of the board ;
(Total length - length that was cut off)
20 3/4 = 83/4
12 1/16 = 193/16
(83/4 - 193/16) =
L. C. M of 4 and 16 = 16
(332 - 193)/16 = 139/16
139/16 = 8 11/16 feet
The remaining length of the board is 8 11/16 feet.
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Solve for the Lengths of XZ and YZ
Answer:
we know that
XY+YZ=XZ
solve for YZ
YZ=XZ-XY
XZ=21
XY=8
so
YZ=21-8
YZ=13
therefore
the answer is
YZ=13
Step-by-step explanation:
assume that the heights of of adult males in a certain region are normally distributed. the heights (in inches) of 20 randomly selected adult males from this region are listed below: 70 72 71 70 69 73 69 68 70 71 67 71 70 74 69 68 71 71 71 72 use this sample data and a .05 significance level to test the claim that the variance of all heights in this region is less than 6.25.
Using the null hypothesis test we calculate that variance is less than 6.25 .
Data sample is 0.05.
20 people make up the sample.
And ,
The theories are:
H₀ : μ² = 6.25
H₁ : μ² < 6.25
The critical value = 10.117.
If the test statistic is less than this number, the null hypothesis will be rejected. When the p-value is less than or equal to your significance level, we reject the null hypothesis. The alternative theory, which contends that the effect is widespread, is supported by your sample data. The null must be removed when the p-value is low, as a mnemonic device.
This is the test statistic:
2.976 × 19 / 6.25 = 9.047.
Therefore, we disregard the null hypothesis. The difference is less than 6.25 since it is not 6.25.
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Raul has read 4/5 of a chapter. The chapter has 25 pages. How many pages has he read so far?
Answer:
20
Step-by-step explanation
25 / 5 = 5 (each part of the chapter)
5 * 4 = 20 (the number of pages he has read
A bicyclist travels 120 miles in 5 hours. A motorcyclist travels 3 times as fast as the motorcyclist. Find the speed of the motorcyclist. HELP ASAP
Answer: first you have to find the speec of the bicycle by using the formula speed = distance/time
120/5=24miles per h
speed of the motorcycle is 3 times as fast as the bicycle so 24x3 = 72miles per hour is the speed for the motorcycle.
Step-by-step explanation:
You have a combination lock with 3 secret digits. Find the 3 correct digits using the following clues
Answer:
987
Step-by-step explanation:
Clue 4: There is no 2, 4, 5.
Clues 1 & 2: There is no 1.
7 must be on the right.
_ _ 7
Clue 5: 9 is in the first or second place
9 _ 7 or _ 9 7
937 or 987 or 397 or 897
Try all 4 possibilities above through all 5 clues.
Only 987 works.
Answer: 987
The length of a rectangle is 5 cm more than twice the width. The perimeter of the rectangle is five times the width. What are the dimensions of the rectangle?
Answer:
Wyzant
ALGEBRA WORD PROBLEM
Kieryn T. asked • 01/10/18
The length of a rectangle is 5 cm more than twice the width. The perimeter of the rectangle is 34 cm. Find the dimensions of the rectangle.
I am having trouble with this problem. I asked my parents and they didnt know what to do. I am stuck and i have looked through my notes and nothing has helped.
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Mikaila D. answered • 01/10/18
TUTOR 4.5 (8)
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The dimensions of the rectangle are two unknowns: The length "l" and the width "w"
The perimeter of a rectangle is found as P = 2*l + 2*w
We also know that the length is 5cm more than twice the width. l = 2*w + 5
These two equations gives us a system of linear equations.
P = 2*l + 2*w
l = 2*w + 5
We can use substitution to replace the "l" in the first equation with 2*w + 5
P = 2*(2*w + 5) + 2*w
P = 4*w + 10 + 2*w
P = 6*w + 10
We know that P = 34cm
34 = 6*w + 10
Subtract 10 from both sides
24 = 6 * w
Divide both sides by 6
4 = w
Now that we know the width, we can find the length by substituting 4 for "w" in the second equation.
l = 2*4 + 5
l = 8 + 5
l = 13
Consider function h h(x)= 2x-6/x+3 true or false?
Answer: false
Step-by-step explanation:
Im going to assume you are asking if 2x-6 is divisible by x+3
In this case, it is false.
x+3 * 2 = 2x+6
2x+6[tex]\neq[/tex]2x-6
Brian is buying salad and pizza for company lunch: Suppose that bowl of salad costs $5.00_ and slice of pizza costs 52.00 Let E be the amount in dollars that Brian spends on salad and pizza If Brian buvs money he spends ( E ) can be represented by the equation bowls of salad and slices of pizza_ then the total amount of Now rearrange the equation yoyu wrote above so that equation written terms of E and The quantity of pizza he buys can be represented by the equationSuppose Brian has 540.00 to spend on salad and pizza; that i5, E = 540.00 _ Complete the following table with the values of $ or P that make the equation true: Hint: To complete the first row, determine the number of pizza slices Brian can purchase with $40.00, when the number of salad bowls he purchases Budget (Dollars) Salad Pizza (Bowls) (Slices) 40.00 40.00 40.00
The equation to represent money spend and the quantity of salad and pizza is E = $5.00*x + $2.00*y
where x represent the quantity of bowl of salad and y represent the quantity of slice of pizza.
What is equation in mathematics?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
Equations come in two varieties: identities and conditional equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true.
According to the given question:
The equation to represent money spend and the quantity of salad and pizza is E = $5.00*x + $2.00*y
where x represent the quantity of bowl of salad and y represent the quantity of slice of pizza.
The table to represent the result of above equation is
Budget (in $) Salad (bowl) Pizza (slices)
40.00 0 20
40.00 2 15
40.00 4 10
40.00 6 5
40.00 8 0
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Select the correct answer.
What is the value of x in the triangle?
45°
Ο Α. 4
OB. 2
45°
C. 4√2
2√2
O D.
The value of the variable 'x' in the given isosceles right angle triangle is 2√2. By applying the Pythagoras theorem, we get the required value.
What is an isosceles right angle triangle?An isosceles right angle triangle has a right angle and equal lengths of two sides. (the other two angles are also the same in measure for an isosceles triangle).
Calculation:Given triangle has two angles of 45° and one angle of 90°, then the triangle is "an isosceles right angle triangle.
It is also given that, hypotenuse h = 4 and the opposite side is given by x.
Since it is an isosceles right triangle, the two sides are also equal in measure.
I.e., opposite side length = adjacent side length = x
Then, applying the Pythagoras theorem, we get
h² = (opp)² + (adj)²
⇒ (4)² = x² + x²
⇒ 16 = 2x²
⇒ x² = 8
∴ x = 2√2
Thus, the value of the length x = 2√2.
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