Evaluate the following expression:
688 + 848 = ?

The range is $14.

The interquartile range is $8.5.

The mean absolute deviation is $4.

The Data set of the admission prices are: [tex]20, 20, 16, 12, 15, 25, 11[/tex]

The range = Maximum value - Minimum value

The range = $25 - $11

The range = $14

To get interquartile range, we will calculate first and third quartiles.

Arranging data in order, we get: [tex]11, 12, 15, 16, 20, 20, 25[/tex]

The first quartile is the median of the lower half of the data which is:

= (11+12)/2

= $11.5

The third quartile (Q3) is the median of the upper half of the data which is:

(20+20)/2

= $20

IQR = Q3 - Q1

IQR = $20 - $11.5

IQR = $8.5

To find the mean absolute deviation, we will calculate the mean.

Mean = sum of values / number of values

Mean = ($11 + $12 + $15 + $16 + $20 + $20 + $25) / 7

Mean = $17

|$11 - $17| = $6

|$12 - $17| = $5

|$15 - $17| = $2

|$16 - $17| = $1

|$20 - $17| = $3

|$20 - $17| = $3

|$25 - $17| = $8

MAD = Sum of absolute deviations / Number of values

MAD = (6 + 5 + 2 + 1 + 3 + 3 + 8) / 7

MAD = 4

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The required arc made by the angle ∠UQT in the given circle is arc UT.

Given the diagram of circle, which is marked with different line segments.

Arc is the part of the circle. Diameter is the line passing through the centre of the circle, radius of the circle is the line segment between centre and other point on the circle, the chord is the line segment  points on the circle and diameter is the biggest chord, tangent is the line segment which intersect the circle at only one point and that point is known as point of tangency and secant is the line segment which cuts the circles.

That implies, the arc made by the angle  ∠UQT is arc UT.

Therefore, the required arc made by the angle ∠UQT in the given circle is arc UT.

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The expected value is 0.8, variance is 0.48, and standard deviation is 0.693 with the given probability.

a. The probability of getting one success in two trials with p=0.4 is given by the binomial probability formula:

f(1) = 2C1 * (0.4)^1 * (0.6)^1 = 0.48

b. The probability of getting zero successes is:

f(0) = 2C0 * (0.4)^0 * (0.6)^2 = 0.36

c. The probability of getting two successes is:

f(2) = 2C2 * (0.4)^2 * (0.6)^0 = 0.16

d. The probability of at least one success is:

P(at least one success) = 1 - P(no success)

= 1 - f(0)

= 1 - 0.36

= 0.64

e. The expected value of a binomial distribution with n trials and probability of success p is given by:

E(X) = np

In this case, n = 2 and p = 0.4, so:

E(X) = 2 * 0.4 = 0.8

The variance of a binomial distribution is given by:

Var(X) = np(1-p)

So:

Var(X) = 2 * 0.4 * 0.6 = 0.48

The standard deviation is the square root of the variance:

SD(X) = sqrt(Var(X)) = sqrt(0.48) = 0.693.

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So the frequency of individuals with red hair in population b after 10 generations of migration is approximately 0.02%.

We need to use the Hardy-Weinberg equation, which describes how the frequencies of alleles in a population will change over time.
The equation is:
p^2 + 2pq + q^2 = 1
Where:
p = frequency of one allele
q = frequency of the other allele
p^2 = frequency of homozygous dominant individuals
2pq = frequency of heterozygous individuals
q^2 = frequency of homozygous recessive individuals
In this case, the recessive trait is red hair, so we'll use q to represent the frequency of the recessive allele.
In population a, q = 0.49, so p (the frequency of the dominant allele) = 1 - q = 0.51.
In population b, q = 0.25, so p = 0.75.
After the emigrants from population a migrate to population b, the new frequency of the recessive allele in population b will be:
q' = (0.1 x 0.49) + (0.9 x 0.25) = 0.286
This is the new value of q after one generation of migration. To calculate the frequency of red-haired individuals after 10 generations, we need to use the equation:
q^10 = (0.286)^10 = 0.0002
So the frequency of individuals with red hair in population b after 10 generations of migration is approximately 0.02%.
The frequency of individuals with red hair in population b after 10 generations of migration is approximately 0.02%. This is based on the assumption that the emigrants from population a mate randomly with members of population b and that the population sizes remain constant over time.
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To write the given quadratic equation, y = (x + 1)^2 - 4, in factored form, we can start by expanding the equation using the square of a binomial:

y = (x + 1)(x + 1) - 4

y = (x^2 + 2x + 1) - 4

y = x^2 + 2x + 1 - 4

y = x^2 + 2x - 3

Now, to find the zeros of the equation, we set y = 0 and solve for x:

x^2 + 2x - 3 = 0 To factor this quadratic equation, we need to find two numbers whose product is -3 and whose sum is 2. The numbers that satisfy this condition are 3 and -1:

(x + 3)(x - 1) = 0

Now, setting each factor equal to zero, we can find the values of x:

x + 3 = 0  =>  x = -3

x - 1 = 0  =>  x = 1

Therefore, the factored form of the equation y = (x + 1)^2 - 4 is (x + 3)(x - 1) = 0, and the zeros of the equation are x = -3 and x = 1.

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The required function be  y = 5000 - 250x.

Given that,

Amount of saving = $5000

Amount of withdraw and spend = $250

Number of months = x

If the total money in Ken's savings account after x number of months is represented by y,

Then, to calculate the entire amount in his savings account after x number of months, the program deducts 250x from the beginning amount of $5000.

Therefore, The function be,

y = 5000 - 250x

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Answer:

150(2)^t

Step-by-step explanation:

The function that represents the worth, w(t), of the basketball at any given time, t, can be written as:

w(t) = 150(2)^t

where t is the number of years since the basketball was collected.

This function uses the formula for exponential growth, where the value of the basketball doubles each year. The initial value of the basketball is $150, and the value is multiplied by 2 for each year that passes. Therefore, after one year, the basketball is worth $300 (2 times $150), after two years it is worth $600 (2 times $300), and so on.

By plugging in different values of t, we can calculate the worth of the basketball at any given time.

So the equation of the parabola in standard form is y = (5/4)x^2 - (7/4)x + 2.

One way to approach this problem is to use the standard form of the equation for a parabola, which is y = ax^2 + bx + c. We can set up a system of three equations using the three points given and solve for the coefficients a, b, and c.

Starting with the point (-2, 18):

18 = a(-2)^2 + b(-2) + c

18 = 4a - 2b + c

Using the point (0, 2):

2 = a(0)^2 + b(0) + c

2 = c

Using the point (4, 42):

42 = a(4)^2 + b(4) + c

42 = 16a + 4b + c

Substituting c = 2 into the second equation, we get:

2 = 2

This is always true, so it doesn't provide any additional information.

Substituting c = 2 into the first and third equations, we get:

18 = 4a - 2b + 2

42 = 16a + 4b + 2

Simplifying each equation:

9 = 2a - b

20 = 4a + b

Solving this system of equations, we get:

a = 5/4

b = -7/4

Substituting these values for a and b, and c = 2, into the standard form equation for a parabola, we get:

y = (5/4)x^2 - (7/4)x + 2

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The height of prism B based on the information given will b 22cm.

Prisms are transparent optical elements that have at least two flat surfaces and refract light. They are usually made of glass or plastic and are used in a variety of optical applications, including scientific experiments, photography, and surveying. Prisms come in a variety of shapes and sizes, including triangular, rectangular, and pentagonal.

From the information, it should be noted that the surface area of prism A will be

= 60 × 2 + 7+ 384

= 576cm²

The surface area of prism A will be:

48 + 10h + 8h + 6h = 576

48 + 24h = 576

h = 528 / 24

h = 22cm

The height is 22cm

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The right triangular prisms shown have the same surface area. Find the height of prism B.

Prism A:

Height: 24 cm

Base: a right triangle with legs 3 cm and 20 cm

Depth: 6 cm

Prism B:

Height: ?

Base: a right triangle with legs 8 cm and 20 cm

Depth: 3 cm

Both prisms have the same surface area.

Answer:

Yes

Step-by-step explanation:

If you look at the graph of y = 16x^4 - 81, you see that it intersects the x-axis at two distinct places so there are two real solutions.  Whenever a polynomial function intersects the x-axis, there are at least one or more real roots.

I attached a picture of the graph using Desmos, where you'll see that there are two real roots.

Answer:

The greatest negative integer is the number one less than 0 and the smallest positive integer is the number one greater than 0.

Step-by-step explanation:

The proportion of male babies less than two months old in the United States that weigh more than 10.1 pounds is 0.7554 or approximately 75.54%.

We are given the following information:

Mean = 11.9 pounds

Standard deviation = 2.6 pounds

To find the proportion of babies that weigh more than 10.1 pounds, we need to find the z-score and then find the corresponding area under the standard normal distribution curve.

1: Calculate the z-scoreWe can calculate the z-score using the formula:

z = (x - μ) / σ

where x is the weight of the baby in pounds, μ is the mean weight of male babies less than two months old in the United States, and σ is the standard deviation of the weights of male babies less than two months old in the United States.

Let's plug in the given values:x = 10.1 pounds

μ = 11.9 pounds

σ = 2.6 pounds

z = (10.1 - 11.9) / 2.6z = -0.6923 (rounded to four decimal places)

2: Find the area under the standard normal distribution curve

We can use a standard normal distribution table or a calculator to find the area under the curve for a z-score of -0.6923. Using a calculator, we get:

P(z > -0.6923) = 0.7554 (rounded to four decimal places)

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Answer: here are my answers.

Step-by-step explanation: Here are some brief answers to your questions:

1. The appearance of God is a matter of personal belief and varies across different religions and cultures.

2. This question is still debated by scientists and philosophers, and there is no clear answer. It is thought that the egg came first, as the evolution of birds and egg-laying animals predates the existence of chickens.

3. Views on what happens after death also vary across different religions and cultures. Some believe in an afterlife, while others do not.

4. Black holes are extremely dense regions in space where gravity is so strong that nothing, not even light, can escape.

5. Water is wet because it has a high surface tension, which allows it to adhere to other surfaces and create a thin film of water.

6. People die due to a variety of factors, including disease, injury, and aging.

7. The origin of the world is a complex question that has been studied by scientists, philosophers, and theologians for centuries. The most widely accepted scientific theory is the Big Bang theory, which suggests that the universe began with a massive explosion approximately 13.8 billion years ago.

8. Babies are formed through the fertilization of an egg by sperm, which occurs during sexual intercourse.

9. The sea is salty due to the presence of dissolved salts and minerals, which come from the weathering of rocks and volcanic activity.

10. The moon is sometimes visible during the day because its orbit around the Earth causes it to appear in different parts of the sky at different times.

11. The internet is a global network of interconnected computers and servers that communicate with each other using standardized protocols.

12. The sky appears blue because of the scattering of sunlight by the gases and particles in the Earth's atmosphere.

13. Wind is caused by differences in air pressure, which are created by variations in temperature, humidity, and other factors.

14. A leap year is a year that contains an extra day (February 29) to keep the calendar year synchronized with the astronomical year, which is approximately 365.25 days long.

15. The Earth spins on its axis due to the conservation of angular momentum from the formation of the solar system.

16. Blood is red because it contains hemoglobin, a protein that binds to oxygen and gives blood its characteristic color.

17. Infinity is a mathematical concept that represents a quantity that is larger than any finite number.

18. The Earth has a diameter of approximately 12,742 kilometers (7,918 miles) and a circumference of approximately 40,075 kilometers (24,901 miles).

19. The sky appears to be above us because the Earth's gravitational field holds the atmosphere in place around the planet.

20. Cutting onions releases a gas called syn-propanethial-S-oxide, which irritates the eyes and causes them to produce tears.

21. Planes fly by generating lift from their wings, which is created by the flow of air over the curved surface of the wing.

22. Telephones work by converting sound waves into electrical signals, which are transmitted over a network of wires or wireless connections.

23. Television works by transmitting images and sound over electromagnetic waves, which are received by a receiver and displayed on a screen.

24. Whether a person is right or left-handed is determined by the dominant hemisphere of their brain.

25. Electricity is a form of energy caused by the movement of electrons through a conductor.

26. Clouds float because they are made up of tiny water droplets or ice crystals that are lighter than the surrounding air.

27. Cars work by converting the energy stored in fuel into motion through a series of processes, including combustion, transmission, and propulsion.

28. The sun and moon appear to stay in the sky due to their position relative to the Earth's rotation and orbit.

29. The color of a person's eyes is determined by the amount and type of pigments in the iris.

30. Lightning is caused by the buildup and discharge of electrical energy in the atmosphere, typically between a cloud and the ground or between two clouds.

Answer:

x = -18.4

Step-by-step explanation:

3-8x=95-3x

add 3x to both sides

3-5x=95

subtract 3 from both sides

-5x=95-3

-5x=92

divide both sides by -5

x=-18.4

The correct answer is (c) Reject the null hypothesis. There is enough evidence to oppose the car manufacturer's claim.

The null hypothesis (H0) is that the true average speed is 145 mph, and the alternative hypothesis (H1) is that the average speed is not 145 mph.

Using a z-test, we can calculate the z-score as [tex](150-145)/(19 \sqrt(87)),[/tex]which is approximately 3.67.

For a two-tailed test at the 1% significance level, the critical z-scores are -2.576 and 2.576.

Since the calculated z-score is beyond this range, we can reject the null hypothesis.

Therefore, there is enough evidence to oppose the car manufacturer's claim.

The correct answer is (c) Reject the null hypothesis. There is enough evidence to oppose the car manufacturer's claim.

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Leo needs 100 star stickers to line the top and bottom edges of his 0.75-meter-long poster with 15-millimeter-wide stickers. Leo will need 50 star stickers for his poster.

First, we need to convert the length of Leo's poster from meters to millimeters since the width of the star stickers is given in millimeters.

0.75 meters x 1000 millimeters/meter = 750 millimeters

Now we can calculate how many stickers Leo needs by dividing the length of the poster by the width of each sticker:

750 millimeters ÷ 15 millimeters/sticker = 50 stickers

Therefore, Leo will need 50 star stickers for his poster.

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Answer:

x2+2x−132x2+16

Step-by-step explanation:

First, let's simplify the expression by combining like terms:

x - 7x^2 + 8 - x^2 - x + 6x^2 + 8

= -7x^2 + 5x^2 - x^2 + x + 16

= -x^2 + 2x + 16

Now we need to factor the quadratic expression -x^2 + 2x + 16. We can use the quadratic formula or complete the square to find the roots, but it turns out that the expression doesn't factor nicely. However, we can rewrite it as -(x^2 - 2x - 16) and then use the quadratic formula to find the roots of the expression inside the parentheses:

x = (-(-2) ± sqrt((-2)^2 - 4(-16)))/(2(1))

x = (2 ± sqrt(68))/2

x = 1 ± 2sqrt(17)/2

x = 1 ± sqrt(17)

So we have:

-x^2 + 2x + 16 = -(x - (1 + sqrt(17)))(x - (1 - sqrt(17)))

Therefore, the expression is equal to -x^2 + 2x + 16, which corresponds to the option:

x^2 + 2x - 13 / 2x^2 + 16

Answer:

Jack would have to buy 18 gum balls to be certain he gets 6 gum balls that are the same color.

Answer:

It's 16

Step-by-step explanation:

Imagine taking out 5 reds, after that 5 green ones and then 5 yellow gum balls. So the 16th must be number 6 of any color.

Answer:

Step-by-step explanation:

To show that points C(-4, 3), A(6, 1), and T(2, -3) form a right-angled triangle, we can calculate the slopes of the lines connecting these points.

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:

slope = (y2 - y1) / (x2 - x1)

Let's calculate the slopes of the lines formed by the points:

Slope of line CA:

m_CA = (1 - 3) / (6 - (-4))

= (-2) / 10

= -1/5

Slope of line CT:

m_CT = (-3 - 3) / (2 - (-4))

= (-6) / 6

= -1

Slope of line AT:

m_AT = (-3 - 1) / (2 - 6)

= (-4) / (-4)

= 1

Since two lines are perpendicular if and only if the product of their slopes is -1, we can check if the product of the slopes of CA and AT is -1. If it is, then the triangle formed by the points C, A, and T is a right-angled triangle.

Product of slopes m_CA and m_AT:

(-1/5) * (1) = -1/5

The product of the slopes is -1/5, which is not equal to -1. Therefore, the points C(-4, 3), A(6, 1), and T(2, -3) do not form a right-angled triangle.

Hence, we can conclude that the points C, A, and T do not form a right-angled triangle based on the slopes of the lines connecting them.

If A and B are mutually exclusive events, P(A ∩ B) = 0, and the general addition law can be simplified to the sum of the individual probabilities for A and B

Given data ,

If events A and B are mutually exclusive, it means that they cannot occur simultaneously. In this case, the intersection of events A and B, denoted as A ∩ B, would indeed have a probability of 0

And , P(A ∪ B) = P(A) + P(B)

Therefore , if A and B are mutually exclusive, the probability of either event A or event B occurring is equal to the sum of their individual probabilities.

Hence , the probability is solved

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Answer:

-------------------------

Simplify the expression.

First distribute, then collect like terms:

In both cases, the estimates depend on the specific characteristics of the box and the probabilities associated with each draw.

To estimate the chance that the sum of the draws will be more than 1,500, we need to know the distribution of values in the box and their probabilities. Without this information, we cannot provide a specific estimate.

(b) Similarly, to estimate the chance that the ticket [3] will be drawn fewer than 90 times, we need to know the distribution of values in the box and their probabilities. Without this information, we cannot provide a specific estimate.

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Two regular pentagons and a regular decagon, all with the same side length, can completely surround a point. A square, a regular pentagon, and a regular $n$-gon, all with the same side length, also completely surround a point. n is 20.

A polygon having 5 sides or 5 angles is called a pentagon. The terms "pentagon" and "gonia," which both denote five angles, are the components of the word "pentagon." End to end, the four sides of a hexagon come together to create a shape. The geometric form known as a pentagon has five sides or five angles. In this case, "Penta" stands for five, and "gon" for an angle. One of the several kinds of polygons is the pentagon.

A point has an angle sum of 360 degrees.

The square's internal angles are all 90 degrees.

The regular pentagon has 108 degree internal angles.

Our unidentified polygon's interior angle is 360 - 108 - 90, or 162 degrees.

We can quickly calculate that this polygon's outer angle is 18 degrees.

Any regular polygon's outward angles add up to 360 degrees.

You get 20 times when you divide 360 by 18.

So, the polygon we don't know has 20 sides.

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If the value of the coefficient of the x² term when the expression (3.5x²-5+2x) is multiplied by (-5x -0.75) . The coefficient of the x² term is -2.625.

When multiplying (3.5x² - 5 + 2x) by (-5x - 0.75), we need to discover the product of the parts that contain x² in order to determine the coefficient of the x² term.

Now let  write out the product of the two polynomials:

(3.5x² - 5 + 2x) × (-5x - 0.75)

= -17.5x³ - 2.625x² + 25x + 3.75

So,

The x² term's coefficient which is -2.625 is the coefficient of the term that contains x².

Therefore the coefficient is  -2.625.

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According to the information, the cuboid in the image is missing 3 faces of the following dimensions 1 face of 1 * 4, 1 face of 1 * 3 and 1 face of 3 * 3.

To complete the cuboid we must take into account that there are already three of its faces. Therefore, we must identify which faces are missing. As we know, cuboids are three-dimensional figures that have 6 faces. Another characteristic of non-regular cuboids is that they have pairs of equal faces.

Based on the information above, we can infer that the missing sides of this cuboid have the same dimensions as the existing sides on the graph. Therefore, the following sides would be missing:

Additionally, to know the surface of the area we must count the number of squares that the figure has in total, in this case it would be 38 squares, so the area is 38 units²

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Let's use x to represent the cost of one orange and y to represent the cost of one lemon. We can then set up a system of two equations:16x + 13y = 9.29 19x + 6y = 9.05 These equations represent the total cost of buying a certain number of oranges and lemons in two different scenarios.

To understand why we need two equations, let's consider the first equation: 16x + 13y = 9.29

This equation tells us that if we buy 16 oranges and 13 lemons, the total cost will be $9.29. But we don't know the individual prices of oranges and lemons yet. That's where the second equation comes in: 19x + 6y = 9.05

This equation tells us that if we buy 19 oranges and 6 lemons, the total cost will be $9.05. Again, we don't know the individual prices yet.

By setting up a system of equations, we can solve for x and y, which represent the prices of oranges and lemons, respectively.

One way to solve this system is by elimination. We can multiply the first equation by 19 and the second equation by -16, which will allow us to eliminate y:

304x + 247y = 176.51
-304x - 96y = -144.8

Adding these two equations together gives: 151y = 31.71
Dividing both sides by 151, we get: y = 0.21
Now we can substitute this value of y into one of the original equations to solve for x. Let's use the first equation:
16x + 13(0.21) = 9.29
16x + 2.73 = 9.29
16x = 6.56
x = 0.41

So the cost of one orange is $0.41 and the cost of one lemon is $0.21.

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Answer:

Maybe add a picture

Step-by-step explanation:

i can solve it with a picture

The twelve thrones of Olympus are occupied by the major gods and goddesses in Greek mythology, including Zeus, Hera, Poseidon, Demeter, Athena, Apollo, Artemis, Ares, Aphrodite, Hephaestus, Hermes, and Dionysus. However, there are two gods who are not given a place on the throne - Hades and Hestia.

Hades, the god of the underworld, is not included in the twelve thrones because he rules over the dead in the underworld. As a result, he does not need a place on Olympus. Hestia, the goddess of the hearth, voluntarily gave up her seat to Dionysus, as she preferred to live a peaceful and uneventful life on earth. She is regarded as one of the "lesser" gods but still holds great importance in Greek mythology, as she is responsible for the protection of the home and family.

Overall, while the 14 gods and goddesses play important roles in Greek mythology, only twelve are given seats on Olympus. Hades and Hestia have their own roles to play and, for different reasons, do not have a place on the thrones.

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First, we need to find the number of students who bring lunch:

1/3 x 36 = 12 students bring lunch.

Next, we need to find the number of students who order lunch:

1/2 x 12 = 6 students order lunch.

So, the total number of students who eat lunch each day is:

12 (who bring lunch) + 6 (who order lunch) = 18 students.

The answer is that there are 32 ways to place two indistinguishable kings on an empty chess board so that they do not attack each other.

To answer this question, we need to understand the basic rules of chess. A king can move one square in any direction, including diagonally. So, to ensure that two kings are not attacking each other, we need to place them on two squares that are not adjacent to each other, and not on the same diagonal line.
There are 64 squares on a chess board, and the first king can be placed on any of those squares. The second king, however, has fewer options because it cannot be placed on the same row, column or diagonal as the first king.
The number of ways to place the second king will depend on where the first king was placed. For example, if the first king was placed in one of the corners, then the second king will have only two possible squares to be placed in. On the other hand, if the first king was placed in the center of the board, then the second king will have fewer options.
Overall, there are 32 possible squares for the second king to be placed in, which means that there are 32 possible ways to place two indistinguishable kings on an empty chess board so that they do not attack each other.
In summary, the answer is that there are 32 ways to place two indistinguishable kings on an empty chess board so that they do not attack each other.

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