Select the correct answer from each drop-down menu.
Consider quadrilateral EFGH on the coordinate grid.
-6
E
-4
1
LL
F
>+
Y
6-
2-
O
-4-
-6-
H
-N
G
05.
6
In quadrilateral EFGH, sides FG and EH are
are
X
because they
The area of quadrilateral EFGH is closest to
✓square units.
Sides EF and GH

First box ( not congruent, congruent).

Second box ( each have a length of 5.83, each have a length of 7.07, have different lengths)

Third box ( not congruent, congruent with lengths of 4.24, congruent with length of 5.83)

Fourth box (41, 34, 25, 30)

The equation of the line that is parallel to the line y = 7x - 7 and passes through the point (-6,6) is y = 7x + 48. The equation of the line perpendicular to the resulting line is y = (-1/7)x + 36/7.

To find the equation of a line that is parallel to another line and passes through a given point, we can use the slope-intercept form of a line (y = mx + b), where m is the slope and b is the y-intercept.

Since parallel lines have the same slope, the slope of the new line will also be 7.

To find the y-intercept, we can plug in the given point (-6, 6) into the equation and solve for b:

6 = 7(-6) + b

b = 6 + 42

b = 48

So the equation of the parallel line is y = 7x + 48.

To find the equation of a line that is perpendicular to another line, we can use the fact that the slope of a perpendicular line is the negative reciprocal of the original slope. So the slope of the perpendicular line will be -1/7.

Again, we can plug in the given point (-6, 6) into the equation and solve for b:

6 = (-1/7)(-6) + b

b = 6 - 6/7

b = 36/7

So the equation of the perpendicular line is y = (-1/7)x + 36/7.

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The inequality is given as 12x ≥ 15,000

An inequality in mathematics is a statement that compares two quantities or expressions using inequality symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).

The least number of rides needed for 15000 people is given as 12x ≥ 15,000.

12x ≥ 15,000.

x ≥ 15,000 / 12

x  ≥ 1250

The least number of rides needed for 15000 people is 1250.

If the park is open for 12 hours. 15000 / 12 is the number of persons that can ride in 1 hour

Hence it is not possible for the ride to have 15000 persons in a day

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Answer:

To find the volume of the right rectangular prism, we need to know its dimensions, which we can determine from the number of cubes it's made up of. Since the prism is made up of 24 cubes and each cube has an edge length of 3/4 cubic inch, we can find the dimensions of the prism as follows:

The number of cubes along the length of the prism is equal to the number of cubes along one of its edges. Since the edge length of each cube is 3/4 cubic inch, we can find the number of cubes along the length of the prism by dividing the total length of the prism by the edge length of each cube:

Number of cubes along the length = Total length / Edge length of each cube

= 24 cubes x (3/4) inch/cube

= 18 inches

Similarly, we can find the number of cubes along the width and height of the prism:

Number of cubes along the width = 24 cubes x (3/4) inch/cube = 12 inches

Number of cubes along the height = 24 cubes x (3/4) inch/cube = 8 inches

Now that we know the dimensions of the prism, we can find its volume by multiplying its length, width, and height:

Volume of the prism = Length x Width x Height

= 18 inches x 12 inches x 8 inches

= 1728 cubic inches

Therefore, the volume of the right rectangular prism is 1728 cubic inches.

Step-by-step explanation:

explanation of how to find the volume of the right rectangular prism made up of 24 cubes:

Given: The prism is made up of 24 cubes, and each cube has an edge length of 3/4 cubic inch.

To find the dimensions of the prism, we need to determine the number of cubes along each edge of the prism. Since the prism is made up of 24 cubes, we can divide the total number of cubes by the number of cubes along one of its edges to find the length of each edge:

Length of each edge = Total number of cubes^(1/3)

= 24^(1/3)

= 2.88 (rounded to two decimal places)

Now that we know the length of each edge of the prism, we can find its dimensions by multiplying the length of each edge by the edge length of each cube:

Length of the prism = 2.88 x 3/4 = 2.16 inches

Width of the prism = 2.88 x 3/4 = 2.16 inches

Height of the prism = 2.88 x 3/4 = 2.16 inches

Finally, we can find the volume of the prism by multiplying its length, width, and height:

Volume of the prism = Length x Width x Height

= 2.16 inches x 2.16 inches x 2.16 inches

= 10.79 cubic inches (rounded to two decimal places)

Therefore, the volume of the right rectangular prism made up of 24 cubes is 10.79 cubic inches.

The volume of the right rectangular prism is 27/2 cubic inches, and explains how that value was obtained from the given information.

Since the rectangular prism is made up of 24 cubes, we can find its volume by multiplying the number of cubes by the volume of each cube.

The edge length of each cube is 3/4 cubic inch, so the volume of each cube is:

(3/4)³ = 27/64 cubic inches.

Therefore, the volume of the rectangular prism is:

24 x (27/64) = (24 x 27)/(4 x 4 x 4) = 27/2 cubic inches.

So the volume of the rectangular prism is 27/2 cubic inches.

We are given that the right rectangular prism is made up of 24 cubes, and that each cube has an edge length of 3/4 cubic inch. We want to find the volume of the prism.

Find the volume of each cube:

The volume of a cube is given by V = s³, where s is the length of an edge. In this case, we are given that the length of an edge is 3/4 cubic inch, so we can substitute that value into the formula:

V = (3/4)³

V = 27/64 cubic inches

So the volume of each cube is 27/64 cubic inches.

Find the volume of the rectangular prism:

To find the volume of the rectangular prism, we need to multiply the number of cubes by the volume of each cube. We know that there are 24 cubes, so we can substitute that value into the formula:

Volume of prism = number of cubes x volume of each cube

Volume of prism = 24 x (27/64)

Volume of prism = (24 x 27)/(4 x 4 x 4)

Volume of prism = 27/2 cubic inches

So the volume of the rectangular prism is 27/2 cubic inches.

Therefore, the volume of the right rectangular prism is 27/2 cubic inches, and explains how that value was obtained from the given information.

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Answer:

Step-by-step explanation:

(h)

[tex]KE= \frac{1}{2}mv^{2} \\KE=\frac{mv^{2} }{2} \\2KE=mv^{2}\\2KEm=v^{2} \\v=\sqrt{2KEm}[/tex]

(g)

[tex]s=\frac{(u+v)t}{2} \\2s=(u+v)t\\\frac{2s}{t}=u+v\\u= \frac{2s}{t}-v[/tex]

(i)

[tex]s=ut+\frac{1}{2} at^{2} \\s-ut=\frac{at^{2} }{2} \\2s-2ut=at^{2} \\\sqrt{2s-2ut}=at\\a=\sqrt{2s-2ut}-t[/tex]

(j)

[tex]\frac{pV}{T} =nR\\T=\frac{pV}{nR}[/tex]

(k)

[tex]a^{2} -b^{2} +c^{2} \\a^{2} +c^{2} =b^{2} \\b=\sqrt{a^{2} +c^{2} }[/tex]

(i)sinθ[tex]=\frac{a}{b}[/tex]

       θ=[tex]\frac{a}{sin(b)}[/tex]

Answer:

34

Step-by-step explanation:

3dds

75. To find the linear speed of a point on the equator, we need to use the formula for the circumference of a circle: C = 2πr. The radius of the earth is 4000 mi, so the circumference of the earth at the equator is C = 2π(4000) = 8000π mi. The earth rotates one revolution every 24 hours, so the linear speed of a point on the equator is 8000π/24 = 333.33π mi/hr ≈ 1047.2 mi/hr.

76. To find the linear speed of the earth in its orbit, we need to use the same formula for the circumference of a circle, but this time the radius is the distance from the earth to the sun, which is 93,000,000 mi. The circumference of the earth's orbit is C = 2π(93,000,000) = 186,000,000π mi. The earth traverses its orbit every 365.25 days, or 8766 hours. So the linear speed of the earth in its orbit is 186,000,000π/8766 = 21,174.6π mi/hr ≈ 66,555.8 mi/hr.

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The possible solutions from the triangle does not exist

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

B = 50 degrees

a = 102 units

b = 41 units

The angle A is calculated as

sin(A)/a = sin(B)/b

So, we have

sin(A)/102 = sin(50)/41

This gives

sin(A) = 102 * sin(50)/41

Evaluate

sin(A) = 1.9057

Take the arc sin of both sides

A = DNE

This is so because the solution does not exist for the angle A

By extension, the values of angle C and side c cannot be calculated

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The break-even point is 45 tickets.

Algebraic expressions can include one or more variables, which are typically represented by letters, such as x, y, or z. These variables can be used to represent unknown quantities or to express relationships between different quantities in a problem.

Algebraic expressions can also include constants, which are fixed numbers, and coefficients, which are the numbers that multiply the variables in the expression. For example, in the algebraic expression 3x + 2y, the constants are 3 and 2, and the coefficients are 3 and 2, respectively.

To find the break-even point, we need to determine the number of tickets that need to be sold in order to cover the costs of the party.

Let's start by setting up an equation to represent the total cost of the party as a function of the number of tickets sold:

Total Cost = Room Rental + Entertainment + Decorations + Food Cost - Ticket Sales Revenue

Total Cost = 450 + 20n - 25n

where n is the number of tickets sold.

Simplifying this equation, we get:

Total Cost = 450 - 5n + 20n

Total Cost = 15n + 450

Now, we need to set the total cost equal to the revenue from ticket sales:

15n + 450 = 25n

Subtracting 15n from both sides, we get:

450 = 10n

Dividing both sides by 10, we get:

n = 45

Therefore, the break-even point is 45 tickets. If the organizers sell 45 tickets, the revenue from ticket sales will cover the total cost of the party, including the room rental, entertainment, decorations, and food cost.

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variables y = 1.5, x = 5, hence, the value of y is 9 when x is 30

Two variables, such as x and y, are proportional to one another and their ratio is constant when they vary directly. In other words, if y and x vary directly, their relationship can be written as y = kx, where k is the proportionality constant. With the knowledge that y = 1.5 when x = 5 as provided, we can utilise this information to find the value of y when x equals 30:

1.5 = k(5) \sk = 1.5/5 \sk = 0.3

We can use the equation y = kx to get the value of y for x = 30 now that we know the value of k:

y = 0.3(30) \sy = 9

Hence, the value of y is 9 when x is 30.

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v1, v2, and v3 are linearly independent

Yes, the vectors v1, v2, and v3 are linearly independent.

To verify this, we can set up the equation:
a1v1 + a2v2 + a3v3 = 0

If the vectors are linearly independent, then the only way to solve this equation is if a1 = a2 = a3 = 0.

Substituting the values for v1, v2, and v3 into the equation yields:

-123 - 3a1 + 16 - 4a2 - 4a3 - 1640a3 = 0

Solving for a1, a2, and a3, we get:

a1 = 0, a2 = 0, a3 = 0

Therefore, the vectors v1, v2, and v3 are linearly independent.

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The length of the body of the guitar is represented by the radical expression 24√3.

We can start by simplifying 8√147.

8√147 = 8√(49 × 3) (since 49 is a perfect square)

= 8 × 7√3

= 56√3

Next, we need to find the length of the body of the guitar, given that the neck measures 8√48. We know that the total length of the guitar is 56√3, so we can set up an equation:

total length = length of neck + length of body

56√3 = 8√48 + length of body

To solve for the length of the body, we can start by simplifying 8√48:

8√48 = 8√(16 × 3) (since 16 is a perfect square)

= 8 × 4√3

= 32√3

Substituting this back into the equation:

56√3 = 32√3 + length of body

Simplifying:

length of the body = 24√3

Therefore, the answer is A) 24√3.

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The question is -

Suppose the total length of the guitar is given by the expression 8√147. Which radical expression represents the length of the body if the neck measures 8√48? A) 24√3 B) 12√3 C) 8√3 D) 9√9

Answer:

The quotient of 5984 divided by 32 is 187.5

Step-by-step explanation:

Answer:

The quotient of 5984 divided by 32 is 187.

Answer: 1.64. To find the difference in orders of magnitude between the two distances, we first need to convert both distances to the same unit of measurement. We'll convert both distances to kilometers.

The distance from Boone to Charlotte is already in kilometers, so we don't need to do any conversion for that distance.
The distance from Boone to Anchorage is in miles, so we'll need to convert that distance to kilometers. To do this, we'll multiply the number of miles by the conversion factor 1.61 km/mi:
4,212.7 mi × 1.61 km/mi = 6,782.45 km

Now that both distances are in kilometers, we can compare them to find the difference in orders of magnitude. An order of magnitude is a factor of 10, so we'll divide the larger distance by the smaller distance and then take the base 10 logarithm of the result:
log10(6,782.45 km / 156.6 km) = log10(43.3) ≈ 1.64
So the distance from Boone to Anchorage is about 1.64 orders of magnitude larger than the distance from Boone to Charlotte.

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Lowering interest rate by a government's central bank can have a significant impact on the economy, as it affects the cost of borrowing money for businesses and individuals, as well as the return on savings and investments.

Lowering interest rate reduces the cost of borrowing money, making it easier for businesses and individuals to access credit. It can also encourage consumers to spend more money, as they may have more disposable income due to lower borrowing costs or higher investment returns.

It can also lead to increased inflation, as businesses and individuals have more money to spend and demand for goods and services increases and reduced returns on savings and investments, which can discourage people from saving and lead to more spending

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Answer:

parallelogram

Step-by-step explanation:

Answer:

Step-by-step explanation:

So when x is translated the + means going right. With y the - means going down. So P is gonna be (-9,-1), Q(-4,0) , and R (-2,-1). See if that helps but I think it is that, but I have another idea what it could be but see if this is right.

The mixed integer would be 2 3/4.

A mixed integer is a number that includes both a whole number and a fraction. For example, 2 1/2 is a mixed integer because it includes the whole number 2 and the fraction 1/2.

To rewrite a fraction as a mixed integer, you need to divide the numerator (the top number) by the denominator (the bottom number) and find the quotient and remainder. The quotient will be the whole number part of the mixed integer and the remainder will be the numerator of the fraction part. The denominator will stay the same.

For example, if you have the fraction 11/4, you can divide 11 by 4 to get a quotient of 2 and a remainder of 3. So the mixed integer would be 2 3/4.

Here are the steps to rewrite a fraction as a mixed integer:
1. Divide the numerator by the denominator.
2. Write the quotient as the whole number part of the mixed integer.
3. Write the remainder as the numerator of the fraction part of the mixed integer.
4. Keep the denominator the same.
5. Simplify the fraction if necessary.

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The factored form of the given polynomial is 5(x-9)(x-2).

To factor the given polynomial, 5x^(2)-55x+90, we first need to factor out the greatest common factor (GCF) which is 5. Factoring out the GCF will make the polynomial easier to factor completely.

5x^(2)-55x+90 = 5(x^(2)-11x+18)

Now, we need to factor the polynomial inside the parentheses completely. We can do this by finding two numbers that multiply to give us the constant term (18) and add to give us the coefficient of the x term (-11).

The two numbers that fit these criteria are -9 and -2. So, we can factor the polynomial inside the parentheses as follows:

x^(2)-11x+18 = (x-9)(x-2)

Putting it all together, we get the completely factored form of the given polynomial:

5x^(2)-55x+90 = 5(x-9)(x-2)

Therefore, the factored form of the given polynomial is 5(x-9)(x-2).

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The error made by the student is instead of taking +4 as common he has taken - 4 as common.

To factor an expression by grouping, we need to look for groups of terms that have common factors. Then, we factor out those common factors from each group and see if there is a common factor that can be further factored out.

Here we have

6x² ​ – x​ – 12  

The above expression can be factorized as follows

=> 6x² – x – 12

= 6x² – 9x + 8x – 12        [ Splitting the middle term ]

= 3x(2x – 3) + 4(2x – 3)     [ Grouping the terms ]  

= (3x + 4)(2x – 3)  

Hence, the factors of given expression are (3x + 4) and (2x – 3)  

The error made by the student is in step 3 instead of taking +4 as common he has taken - 4 as common which doesn't give the common factors in the next step taken.    

Therefore,

The error made by the student is instead of taking +4 as common he has taken - 4 as common.

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maxima_value = sp.sin(maxima)
minima_value = sp.sin(minima)

For part (a), to find the minima and maxima of the function y=sin(x) in the interval [2π, 4π], you can use the SymPy solves

et() function, which takes an equation, a variable and an interval (numn1​, num2​) as inputs. To do this, you can use the following code:

minima, maxima = sp.solveset(sp.Eq(sp.sin(x), 0), x, (sp.pi*2, sp.pi*4))

For part (b), to determine the x-values at which the maxima and minima occurs, you can use the minima and maxima values from the previous solveset() function and evaluate the sin(x) at those points. For example:

maxima_value = sp.sin(maxima)
minima_value = sp.sin(minima)

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The time is takes to manufacture the piece after two improvements is 28 minutes

From the question, we are to calculate how long it takes to manufacture a metal piece

First, we need to find the new time taken to manufacture the metal piece after the two improvements.

The first improvement reduces the time by 8%. This means that the new time is:

32 - (8% of 32)

= 32 - 2.56

= 29.44 minutes

The second improvement reduces the time by 5%. This means that the new time is:

29.44 - (5% of 29)

= 29.44 - 1.45

= 27.99 minutes

We can round this to the nearest minute, which gives us 28 minutes.

Hence, it takes 28 minutes to manufacture the metal piece.

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Answer: To calculate the incidence of cervical cancer among women in the United States in 2019, we need to divide the number of new cases (346) by the total population at risk (i.e., the number of women without cervical cancer) and then multiply by 100,000 to express the result per 100,000 women.

Number of women without cervical cancer = Total number of women - Number of women with cervical cancer

Number of women without cervical cancer = 166,238,619 - 295,382

Number of women without cervical cancer = 165,943,237

Incidence of Cervical Cancer = (New cases / Number of women without cervical cancer) x 100,000

Incidence of Cervical Cancer = (346 / 165,943,237) x 100,000

Incidence of Cervical Cancer = 0.21 per 100,000 women

Therefore, the incidence of cervical cancer among women in the United States in 2019 was 0.21 per 100,000 women.

Step-by-step explanation:

Answer: Your welcome!

Step-by-step explanation:

Part A: 2x^2 + 3x^2 - 4 + 3xy + 6 + 6 = 7x^2 - 4xy + 6

Part B: 0 = 7x^2 - 4xy + 6 - (2x^2 + 3x^2 - 4 + 3xy + 6 + 6)

= 0 = 5x^2 - 4xy

A) The expression that represents the amount of canned food collected by the three friends is [tex]5x^2 + 3xy + 2[/tex].

B) The expression that represents the number of cans the friends still need to collect to meet their goal is [tex]2x^2 - 7xy + 4[/tex].

Given: Number of cans collected

Jessa: 2x²

Tyree: 3x² - 4

Ben: 3xy + 6

Goal : [tex](7x^2 - 4xy + 6)[/tex]

A) The total amount collected:

Total = Jessa + Tyree + Ben

         = [tex]2x^2 + (3x^2 - 4) + (3xy + 6)[/tex]

         = [tex]2x^2 + 3x^2 - 4 + 3xy + 6[/tex]

         = [tex](2x^2 + 3x^2 + 3xy) + (-4 + 6)[/tex]

         = [tex]5x^2 + 3xy + 2[/tex]

Therefore, the expression is [tex]5x^2 + 3xy + 2[/tex].

B) The number of cans the friends still need to collect to meet their goal is

Cans still needed = Goal - Total

                              [tex]= (7x^2 - 4xy + 6) - (5x^2 + 3xy + 2)[/tex]

                              [tex]= 7x^2 - 4xy + 6 - 5x^2 - 3xy - 2[/tex]

                              [tex]= (7x^2 - 5x^2) + (-4xy - 3xy) + (6 - 2)[/tex]

                              [tex]= 2x^2 - 7xy + 4[/tex]

Therefore, the expression is [tex]2x^2 - 7xy + 4[/tex].

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Answer: 7

Step-by-step explanation:

The slope is the number being multiplied by x

The system of equations for the two plans is:

y = 8x + 25

y = 12x + 5

To write a system of equations for each plan, let:

x = number of month

y = Total amount

Equation of plan A:

one-time membership fee = initial value or y-intercept (b) = 8

Monthly fee per month = slope/unit rate (m) = 25

The equation would be y = 8x + 25

Equation of plan B:

one-time membership fee = initial value or y-intercept (b) = 12

Monthly fee per month = slope/unit rate (m) = 5

The equation would be y = 12x + 5

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The exact form of the zeros of the polynomial function c(x)=3x^(4)-2x^(3)-39x^(2)-10x+24 are x=-4, x=-3/2, x=2, and x=1.

To find all the zeros of the polynomial function c(x)=3x^(4)-2x^(3)-39x^(2)-10x+24, we need to find the values of x that make c(x)=0. One way to do this is by using the Rational Root Theorem, which states that if a polynomial has rational zeros, then they must be in the form of p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

The factors of the constant term, 24, are ±1, ±2, ±3, ±4, ±6, ±8, ±12, and ±24. The factors of the leading coefficient, 3, are ±1 and ±3. Therefore, the possible rational zeros are ±1, ±2, ±3, ±4, ±6, ±8, ±12, and ±24.

Using synthetic division, we can test these possible zeros to see if they are actually zeros of the polynomial. After testing, we find that the zeros are -4, -3/2, 2, and 1.

So, the exact form of the zeros of the polynomial function c(x)=3x^(4)-2x^(3)-39x^(2)-10x+24 are x=-4, x=-3/2, x=2, and x=1.

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Yes, the graph represents a function.

A relation is a function if it has only One y-value for each x-value.

The given ordered pairs from the given graph are (-7, 3), (-3, -3), (0,1), (2, 4), (3, -1), (5, -6)

The given graph represents a relation.

Since each value of x has unique y value.

So the given graph represents a function.

Hence, yes the graph represents a function.

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Answer:  1.09 is closer to 1

The basis of the subspace of R4 defined by the equation3x1​−9x2​+2x3​−3x4​=0 is  {(3, 1, 0, 0), (-2/3, 0, 1, 0), (1, 0, 0, 1)}

A basis of the subspace of R4 defined by the equation 3x1​−9x2​+2x3​−3x4​=0 can be found by solving the equation for one of the variables in terms of the others and then writing the general solution as a linear combination of vectors.

First, solve the equation for x1 in terms of the other variables:

3x1 = 9x2 - 2x3 + 3x4

x1 = 3x2 - (2/3)x3 + x4

Next, write the general solution as a linear combination of vectors:

(x1, x2, x3, x4) = (3x2 - (2/3)x3 + x4, x2, x3, x4)

= x2(3, 1, 0, 0) + x3(-2/3, 0, 1, 0) + x4(1, 0, 0, 1)

Finally, the basis of the subspace is the set of vectors that make up the linear combination:

{(3, 1, 0, 0), (-2/3, 0, 1, 0), (1, 0, 0, 1)}

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