Answer:
Michael bought 8 shirts
Step-by-step explanation:
Let the number of shirts to be buy be x
The number of ties too will also be x
The number of pants will be x/4 since he will be buying four times the number of pants for shirts
Amount spent on shirt is 35 * x = $35x
Amount spent on ties = 25 * x = $25x
Amount spent on pants = 40 * x/4 = $10x
Adding all together;
35x + 25x + 10x = 560
70x = 560
x = 560/70
x = 8
Find the indicated term of 4, 2 ,0
Answer:
13, 16
Step-by-step explanation:
We need to find the common difference.
4 - 1 = 3
7 - 4 = 3
10 - 7 = 3
Find the next two terms.
10 + 3 = 13
13 + 3 = 16
Best of Luck!
Answer:
3
Step-by-step explanation:
6-3=3
9-6=3
13-16=3
333
please help what is 4 times the sum of 14 and 26
Answer:
160
Step-by-step explanation:
To sum something up is to add together. Adding 14 and 26 gets 40, and 4 times 40 is 160!
Answer:
Step- 4x14+26
14+26=40
40x4=160
160 is the answer
If the point (a, b) is equidistant from the points (-a, 2) and (2, -b), then prove that 3(a+b)+4=0
Answer: see proof below
Step-by-step explanation:
Since (a, b) is equidistant from (-a, 2) and (2, -b), then it is the midpoint of the those two points. Use Midpoint formula to find (a, b).
[tex]M_x=\dfrac{x_1+x_2}{2}\qquad \qquad \qquad M_y=\dfrac{y_1+y_2}{2}\\\\\\a=\dfrac{-a+2}{2}\qquad \qquad \qquad \quad b=\dfrac{2-b}{2}\\\\\\2a=-a+2\qquad \qquad \qquad \quad 2b=2-b\\\\\\3a=2\qquad \qquad \qquad \qquad \qquad 3b=2\\\\\\a=\dfrac{2}{3}\qquad \qquad \qquad \qquad \qquad b=\dfrac{2}{3}[/tex]
3(a + b) - 4 = 0
[tex]3\bigg(\dfrac{2}{3}+\dfrac{2}{3}\bigg)-4=0\\\\\\3\bigg(\dfrac{4}{3}\bigg)-4=0\\\\\\4-4=0\\\\0=0\qquad \text{TRUE!}[/tex]
Notice that I changed the equation to "negative 4" because the equation you provided did not make a true statement.
which of the following is a linear equation
x+y-2
2x+5=11
15
Answer:
x + y = 2
y = 2 - x
so it is a linear equation.
2x + 5 = 11
2x = 11 - 5
2x = 6
x = 3
it is not a function because for just one x we have many y
CAN SOMEONE PLS SOLVE? ILL MARK BRAINEST PLSS HELPP DUE SOON
Answer:
sure
Step-by-step explanation:
Answer:
1) 10,11,12
2)92,94
Step-by-step explanation:
Determine if the following statements are true or false, and explain your
reasoning. If false, state how it could be corrected.
(a) If a given value (for example, the null hypothesized value of a parameter) is within a 95% confidence interval, it will also be within a 99% confidence interval.
(b) Decreasing the significance level (\alpha) will increase the probability of making a Type 1 error.
(c) Suppose the null hypothesis is\mu= 5 and we fail to reject H0. Under this scenario, the true population mean is 5.
(d) If the alternative hypothesis is true, then the probability of making a Type 2 error and the power of a test add up to 1.
(e) With large sample sizes, even small differences between the null value and the true value of the parameter, a diff
erence often called the effect size, will be identified as statistically signiffcant.
(f) A cutoff of\alpha= 0.05 is the ideal value for all hypothesis tests.
a) False. the null hypothesized value could not fall within a 99% confidence interval . b) false ; c) false ; d) true ; e) true ; f) false.
(a) False. If a given value (for example, the null hypothesized value of a parameter) is within a 95% confidence interval, it will not always be within a 99% confidence interval.
The reason for this is that a 99% confidence interval is wider than a 95% confidence interval.
Hence, the null hypothesized value could fall within a 95% confidence interval but not within a 99% confidence interval.
(b) False. Decreasing the significance level (α) will reduce the probability of making a Type 1 error, not increase it. A Type 1 error occurs when we reject a true null hypothesis.
By decreasing the significance level, we make it more difficult to reject the null hypothesis, which reduces the probability of a Type 1 error.
(c) False. Suppose the null hypothesis is μ = 5 and we fail to reject H0. Under this scenario, we cannot conclude that the true population mean is 5.
The data may be consistent with a range of population means, including means that are different from 5.
(d) True. If the alternative hypothesis is true, then the probability of making a Type 2 error and the power of a test add up to 1. Power is defined as the probability of rejecting a false null hypothesis.
If the alternative hypothesis is true, then the null hypothesis is false, and the probability of rejecting it (i.e., the power) is equal to 1 minus the probability of failing to reject it (i.e., the Type 2 error rate).
(e) True. With large sample sizes, even small differences between the null value and the true value of the parameter, a difference often called the effect size, will be identified as statistically significant.
This is because large sample sizes increase the precision of our estimates, which makes it easier to detect even small differences.
(f) False. A cutoff of α = 0.05 is not the ideal value for all hypothesis tests. The choice of α depends on several factors, including the consequences of a Type 1 error and the sample size.
For example, if the consequences of a Type 1 error are severe, then a lower value of α may be more appropriate. Similarly, if the sample size is very large, then a lower value of α may be necessary to maintain the Type 1 error rate.
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A 52 foot ladder is set against the side of a house so that it reaches up 48 feet. If Jevonte grabs the ladder at its base and pulls it 3 feet farther from the house, how far up the side of the house will the ladder reach now? (The answer is not 45 ft.) Round to the nearest tenth of a foot.
When Jevonte pulls the ladder 3 feet farther from the house, the ladder will reach approximately 10.15 feet up the Side of the house.
To solve this problem, we can use the Pythagorean theorem, which relates the lengths of the sides of a right triangle. In this case, the ladder, the distance from the house to the ladder, and the height along the side of the house form a right triangle.
Let's denote the distance Jevonte pulls the ladder as d. We want to find the new height, h, along the side of the house when the ladder is pulled 3 feet farther from the house.
According to the Pythagorean theorem, we have:
h^2 + (48 + d)^2 = 52^2
Simplifying the equation, we get:
h^2 + (48 + d)^2 = 2704
Expanding and rearranging the equation, we have:
h^2 + (d^2 + 96d + 48^2) = 2704
h^2 + d^2 + 96d + 2304 = 2704
h^2 + d^2 + 96d = 2704 - 2304
h^2 + d^2 + 96d = 400
Now we substitute the known values into the equation. We have d = 3 (since Jevonte pulls the ladder 3 feet farther) and h as the unknown.
h^2 + 3^2 + 96(3) = 400
h^2 + 9 + 288 = 400
h^2 + 297 = 400
h^2 = 400 - 297
h^2 = 103
Taking the square root of both sides, we get:
h = √103
Rounding to the nearest tenth of a foot, h ≈ 10.15 feet.
Therefore, when Jevonte pulls the ladder 3 feet farther from the house, the ladder will reach approximately 10.15 feet up the side of the house.
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Find the basis of R³ in which coordinates of the vector v = [1, -2, 5] are (0, 2, 1).
The desired basis of R³ in which the coordinates of vector v are (0, 2, 1) is {e₁, 2 * e₂, e₃}.
The given vector v = [1, -2, 5] has coordinates (0, 2, 1) in the desired basis. To find the basis, we can start by considering the standard basis vectors in R³: e₁ = [1, 0, 0], e₂ = [0, 1, 0], and e₃ = [0, 0, 1].
We want to find coefficients a, b, and c such that a * e₁ + b * e₂ + c * e₃ = [0, 2, 1], which represents the coordinates of vector v in the desired basis. This gives us the following system of equations:
a * 1 + b * 0 + c * 0 = 0
a * 0 + b * 1 + c * 0 = 2
a * 0 + b * 0 + c * 1 = 1
Solving this system of equations, we find that a = 0, b = 2, and c = 1. Therefore, the desired basis of R³ in which the coordinates of vector v are (0, 2, 1) is {e₁, 2 * e₂, e₃}. These three vectors are linearly independent and span R³, forming a basis for the space.
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fill in the blank to make the expression a perfect square: u^(2)+16u+
to make the expression a perfect square, what do you do? How do you know what numbers to use?
To make the expression [tex]\(u^2 + 16u + \_\_\)[/tex] a perfect square, we need to add 64. We know to use the number 8 because it is half the coefficient of the linear term, and squaring it ensures that the quadratic term is doubled, completing the square.
To make the expression [tex]\(u^2 + 16u + \_\_\)[/tex] a perfect square, we need to determine the missing term that completes the square.
To determine this term, we take half of the coefficient of (u) (which is 16) and square it. Half of 16 is 8, and when we square it, we get 64.
So, the missing term to make the expression a perfect square is 64. Therefore, the complete expression as a perfect square is [tex]\(u^2 + 16u + 64[/tex].
We know to use the number 8 because we want to create a perfect square trinomial.
By taking half of the coefficient of the linear term, we ensure that the quadratic term is doubled, and when we add the square of half the linear term, it perfectly completes the square, resulting in a perfect square trinomial.
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Find The Value Of X.
Step-by-step explanation:
2x +31 = 9
2x = - 22
x = - 11
Thank you and please rate me as brainliest.
Give the algebraic expression for the product of a number and 4 more than the number
Answer:
An algebraic expression is a compact way of describing mathematical objects ... the three main components of algebraic expressions are numbers, variables, and ... to be successful in writing or interpreting any given algebraic expression. ... a number increased by 4, x + 4 ... 11 more than the product of 3 and y, 3y + 11.
Step-by-step explanation:
The mayor is interested in finding a 95% confidence interval for the mean number of pounds of trash per person per week that is generated in the city. The study included 241 residents whose mean number of pounds of trash generated per person per week was 37.4 pounds and the standard deviation was 8.5 pounds. Round answers to 3 decimal places where possible.
a. To compute the confidence interval use a ? t z distribution.
b. With 95% confidence the population mean number of pounds per person per week is between and pounds.
c. If many groups of 241 randomly selected members are studied, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population mean number of pounds of trash generated per person per week and about percent will not contain the true population mean number of pounds of trash generated per person per week.
The population mean number of pounds per person per week is estimated to be between 35.764 pounds and 38.036 pounds.
a. To compute the confidence interval, we will use a t-distribution.
b. With 95% confidence, the population mean number of pounds per person per week is between **35.764 pounds** and **38.036 pounds**.
To calculate the confidence interval, we can use the formula:
Confidence Interval = Sample Mean ± (Critical Value) * (Standard Deviation / sqrt(Sample Size))
Given that we have a sample size of 241 residents, a sample mean of 37.4 pounds, and a standard deviation of 8.5 pounds, we need to determine the critical value associated with a 95% confidence level using the t-distribution. The degrees of freedom for this calculation are equal to the sample size minus 1, which is 240.
Looking up the critical value for a 95% confidence level and 240 degrees of freedom in the t-distribution table or using a statistical calculator, we find the critical value to be approximately 1.97.
Plugging in the values into the formula, we have:
Confidence Interval = 37.4 ± (1.97 * (8.5 / sqrt(241)))
Calculating this expression, we find:
Confidence Interval ≈ 37.4 ± 1.122
Lower Limit = 37.4 - 1.122 ≈ 36.278 pounds
Upper Limit = 37.4 + 1.122 ≈ 38.522 pounds
Therefore, with 95% confidence, the population mean number of pounds per person per week is estimated to be between 35.764 pounds and 38.036 pounds.
c. If many groups of 241 randomly selected members are studied, then approximately **95%** of these confidence intervals will contain the true population mean number of pounds of trash generated per person per week, and approximately **5%** will not contain the true population mean. This is due to the nature of confidence intervals, which provide an estimated range for the population parameter with a certain level of confidence.
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points $a(2,5)$ and $b(10,5)$ are the endpoints of a diameter of a circle graphed in a coordinate plane. how many square units are in the area of the circle? express your answer in terms of $\pi$.
The area of the circle with a diameter having endpoints at (2,5) and (10,5) on a coordinate plane is 16π square units.
The midpoint of the line segment connecting the endpoints of the diameter is the center of the circle.
The distance from the center of the circle to the endpoints of the diameter is the radius of the circle.
The diameter of the circle in this problem is AB, which has endpoints (2,5) and (10,5).
We know that this diameter is a horizontal line because both endpoints have the same y-coordinate of 5.
The midpoint of AB will also have a y-coordinate of 5 since it lies on the horizontal line containing AB. The x-coordinate of the midpoint is the average of the x-coordinates of A and B.
It is easy to find the distance between the endpoints of the diameter, so the radius can also be found as follows:
r = AB/2 = 8/2 = 4
Therefore, the area of the circle is 16 π square units.
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4/2
of a number is 64.
Find the number.
Answer:
Let the number be x,
4/2 of x is equal to 64
=> 4/2 * x = 64
=> 4x = 64 * 2
=> x = 64 * 2/4
=> x = 128 / 4
=> x = 32
Therefore the number is 32
If my answer helped, please mark me as the brainliest!!
Thank You!!
Answer:
32
Step-by-step explanation:
4/2 * x = 64
NB : x is the number we are finding
we can first solve 4/2
4/2 = 2
2 * x = 64
make x the subject of formula :
x = 64 / 2
x = 32
the number is 32
Suppose a principal of 5500 is placed in a bank account paying interest of 6% p.a. compounded weekdy if no mociey the account, how long will it take for the account balance to reach 5700 ? Note: round your answer to 2 decimal places A cotrect atswer is 5.62, which can be typed in as folfowit 5.62=
The principal amount of $5500 is invested in a bank account with an interest rate of 6% per annum, compounded weekly.
The question asks how long it will take for the account balance to reach $5700. The correct answer, rounded to two decimal places, is 5.62.
To calculate the time it takes for the account balance to reach $5700, we can use the compound interest formula:
A = P(1 + r/n)^(n*t)
Where:
A is the final account balance
P is the principal amount
r is the interest rate (in decimal form)
n is the number of compounding periods per year
t is the time in years
In this case, the principal amount P is $5500, the interest rate r is 6% (or 0.06), and the account balance A is $5700. We need to solve for t, the time it takes for the account balance to reach $5700.
5700 = 5500(1 + 0.06/52)^(52*t)
To solve for t, we can take the logarithm of both sides:
log(5700/5500) = 52*t*log(1 + 0.06/52)
Using a calculator, we can solve for t:
t = log(5700/5500) / (52*log(1 + 0.06/52))
Calculating the above expression will give us the time t in years. Rounded to two decimal places, the correct answer is 5.62.
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Solve xy-6=k for x
What is x?
Answer:
Y/k +6
Step-by-step explanation:
Answer:
x=k+6/y
Step-by-step explanation:
This is a literal equation, so x won't be an actual number.
First, move 6 to the other side (or add 6 to both sides)
xy=k+6
then, divide by y
x=k+6/y
Hope this helps!
Which ordered pair is a solution of the equation?
y=−2x+5
Answer:
10 is your answer
What is the solution set of {x|x 5
Answer:
5x
Step-by-step explanation:
Here are 4 triangles that have each been transformed by a different transformation Which transformation is not a rigid transformation?
Answer:
A
Step-by-step explanation:
I took the test and its A.
The transformation that is not a rigid transformation is the first triangle ABC i.e option A.
Rigid transformation is the procedures required to resize or reshape a given object so as to produce the required image. The types of rigid transformation are: translation, reflection, dilation and rotation.
Considering the triangles in the given question, it can be observed that:
i. Triangle ABC compared with its image, has not obeyed the principle.
ii. Clockwise rotation of triangle ABC using point C would produce triangle A'B'C'.
iii. Reflection of triangle ABC using point C as the reference point would produce its image A'B'C'.
iv. Dilating each of the side length of triangle ABC with an appropriate representative fraction would produce the image A'B'C'.
Therefore, the only transformation that is not a rigid transformation is the first triangle ABC i.e option A.
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What is the slope of this line?
Answer:
The slope is 3/2
Step-by-step explanation:
Rise over run- up 3 and to the left 2.
Answer:
2 to the left and 3 down
Step-by-step explanation:
the value of y varies directly with x. If x equals 3 then y equals 21 what is the value of x when y equals 105.
Answer:
x = 15
Step-by-step explanation:
The equation for direct variation is
y = kx
y=21 when x=3
21 = k*3
Divide each side by 3
21/3 = 3k/3
7 =k
y = 7x
Let y=105
105 = 7*x
Divide by 7
105/7 = x
15 =x
The Hardware Shop in Subang Jaya (refer the question A), wants
to reconsider
its decision of buying the brackets and is considering in-house,
production. The
setup cost would be RM25.00 and 50 bracke
The Hardware Shop in Subang Jaya is considering in-house production of brackets instead of buying them. The setup cost for in-house production is RM25.00, and the shop plans to produce 50 brackets.
In-house production of brackets involves setting up the necessary equipment and processes to manufacture the brackets within The Hardware Shop.
The shop is currently evaluating this option as an alternative to buying the brackets from an external supplier.
To initiate in-house production, there is a one-time setup cost of RM25.00.
This cost covers expenses related to acquiring the required machinery, tools, and materials, as well as setting up the production area.
In terms of production volume, the shop plans to produce 50 brackets. This quantity represents the number of brackets that the shop aims to manufacture within a given time period.
Producing brackets in-house gives the shop control over the quantity and timing of production.
By considering in-house production, The Hardware Shop can potentially reduce dependency on external suppliers, have more control over the production process, and potentially achieve cost savings in the long run. However, it is important for the shop to carefully evaluate the total costs, including setup costs, production costs, and any associated overhead costs, to make an informed decision about whether in-house production is the most viable option for the business.
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Solve the equation. 2x + 4x + 6x - 2(x + 3) = 34
What equals x?
Answer:
[tex]\boxed { x = 4}[/tex]
Step-by-step explanation:
Solve for the value of [tex]x[/tex]:
[tex]2x + 4x + 6x - 2(x + 3) = 34[/tex]
-Combine like terms:
[tex]2x + 4x + 6x - 2(x + 3) = 34[/tex]
[tex]12x - 2(x + 3) = 34[/tex]
-Use Distributive Property:
[tex]12x - 2(x + 3) = 34[/tex]
[tex]12x - 2x - 6 = 34[/tex]
-Combine like terms:
[tex]12x - 2x - 6 = 34[/tex]
[tex]10x - 6 = 34[/tex]
-Add [tex]6[/tex] to both sides:
[tex]10x - 6 + 6 = 34 + 6[/tex]
[tex]10x = 40[/tex]
Divide both sides by [tex]10[/tex]:
[tex]\frac{10x}{10} = \frac{40}{10}[/tex]
[tex]\boxed { x = 4}[/tex]
Therefore, the value of [tex]x[/tex] is [tex]4[/tex].
The table shows a list of stars in the distance from our solar system in the light years place the stars in order from the closest the farthest from our solar system
Can someone please help me? I shall mark brainliest of the the brains
Answer:
20
Step-by-step explanation:
4 times 5 is 20
What is the the vertex of the parabola (y−1)2=24(x+2) ?
(-2,1)
(2,-1)
(2,1)
(1-2)
Answer:
The vertex is (-2,1)
Step-by-step explanation:
The standard equation for the parabola is 4p(x-h)=(y-k)^2
Rewrite (y-1)^2=24(x+2) in standard form
4*6(x-(-2))=(y-1)^2
Therefore parabola properites are:
(h,k)=(-2,1)
first four terms of the sequence an = 8 - 2n with formula
Answer:
6, 4, 2, 0
Step-by-step explanation:
To find the first 4 terms, substitute n = 1, 2, 3, 4 into the n th term formula, that is
a₁ = 8 - 2(1) = 8 - 2 = 6
a₂ = 8 - 2(2) = 8 - 4 = 4
a₃ = 8 - 2(3) = 8 - 6 = 2
a₄ = 8 - 2(4) = 8 - 8 = 0
The first 4 terms are 6, 4, 2, 0
Someone plz help me
Multiple Choice Find the sum or difference. 5 sixths plus 4 ninths A. one-half B. nine-eighteenths C. 1 and five-eighteenths D. The fraction states 1 over 2.
Answer:
C
Step-by-step explanation:
NO CAP
Answer: The answer would be C
Step-by-step explanation:
Greatest common factor of 126
Answer:
1
Step-by-step explanation:
Find the mass and center of mass of a wire in the shape of the helix x = t, y = 7 cos t, z = 7 sin t, 0 ≤ t ≤ 2π, if the density at any point is equal to the square of the distance from the origin.
mass =
center of mass (x,y,z) =
The mass of the wire is k(56π/3) and the center of mass of the wire is (0, 0, 2√3/π).
A helix is a three-dimensional curve that has a spiral form, such as a corkscrew.
We will be using the formula to find the mass and center of mass of the wire.
Formula to find mass and center of mass of a wire:
mass= ∫a b dm center of mass=(1/M)∫a b r dm
Given, the equation of the helix is x = t, y = 7 cos t, z = 7 sin t, 0 ≤ t ≤ 2π.
To find mass and center of mass of wire in the shape of helix, we need to use the formulae of mass and center of mass of a wire.
Here, the density at any point is equal to the square of the distance from the origin.
Mass: Let us consider a small element of the wire as shown in the below figure. A small element of the wire. The element is a small part of the helix with length ds and mass dm.
According to the question, the density at any point is equal to the square of the distance from the origin. So, the density of this element is equal to the square of its distance from the origin, i.e.,
dm = kx² + y² + z²ds = k(t² + 7²)dt
where k is the constant of proportionality.
So, the mass of the element can be written as
dm = k(t² + 7²)dt
Integrating both sides, we get
Mass of the helix = ∫₀^(2π)k(t²+7²)dt = k ∫₀^(2π)(t²+7²)dt = k[(t³)/3+7t]₀^(2π) = k(56π/3)
where the limits are 0 to 2π.
The mass of the helix is k(56π/3).
Center of Mass: Let us consider a small element of the wire at a distance r from the origin as shown in the below figure. A small element of the wire at a distance r from the origin. The element is a small part of the helix with length ds and mass dm.
The coordinates of the element can be written as
(x, y, z) = (t, 7 cos t, 7 sin t)
The distance of the element from the origin can be calculated as
r = (x² + y² + z²)½= [(t² + 7² cos² t + 7² sin² t)]½= [(t² + 49)]½= (t² + 49)½
The element is at a distance r from the origin and has mass dm.
The x-coordinate of the element can be written asx = t
The y-coordinate of the element can be written asy = 7 cos t
The z-coordinate of the element can be written asz = 7 sin t
So, the coordinates of the element are (t, 7 cos t, 7 sin t)
So, the position vector of the element isr = t i + 7 cos t j + 7 sin t k
The center of mass of the wire can be calculated as follows:
Center of Mass of Helix = (1/M)∫a b r dm = (1/M)∫a b r(kx²+y²+z²)ds
where M is the mass of the helix obtained in the first step.
So, the center of mass of the helix is
(1/M)∫₀^(2π)r(kx²+y²+z²)ds
where r = (t² + 49)½, and x = t, y = 7 cos t, z = 7 sin t.
Substituting the values, we get
(1/M)∫₀^(2π)r(kx²+y²+z²)ds = (1/kM)∫₀^(2π)[t²+k(7² cos² t+7² sin² t)](t i + 7 cos t j + 7 sin t k) (k(t² + 7²)dt)
where r = (t² + 49)½, and x = t, y = 7 cos t, z = 7 sin t.
(1/M)∫₀^(2π)r(kx²+y²+z²)ds = (1/kM) ∫₀^(2π)[t²+49k](t i + 7 cos t j + 7 sin t k) (k(t² + 7²)dt)
On solving, we get the center of mass of the helix as Center of Mass of Helix = (0,0,2√3/π)
So, the center of mass of the helix is (0, 0, 2√3/π).
Therefore, the mass of the wire is k(56π/3) and the center of mass of the wire is (0, 0, 2√3/π).
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