A man is trapped in a room at the center of a maze. The room has three exits. Exit 1 leads outside the maze after 3 minutes, on average. Exit 2 will bring him back to the same room after 5 minutes. Exit 3 will bring him back to the same room after 7 minutes. Assume that every time he makes a choice, he is equally likely to choose any exit. What is the expected time taken by him to leave the maze?Hint: Let X = time taken by the man to leave the maze from this room. Let Y = exit he chooses first. So Y belongs in { 1,2,3} Calculate the conditional expectation of time taken to leave the maze given that he chose each of the exits. Then use these conditional expectations to calculate the expectation of time taken to leave the maze.

De acuerdo con la información, podemos inferir que el volumen total de la figura sería 1,476.58 cm³

To find the volume of the figure we must divide it into different sections because it has cones, pyramids, hemispheres, cylinders, and rectangular cubes. Below is the procedure:

Volume of rectangular segments:

Volume of the pyramids:

First we must calculate the height of the pyramids.

Cone volume:

First we need to calculate the height of the cone.

Cylinder volume:

Volume of the hemisphere:

Finally we just have to add all the values and we will obtain the total volume of the figure:

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The measure of the larger acute angle of the right triangle is 73.7°. This can be calculated using trigonometry and the Pythagorean theorem.

The larger acute angle of the triangle can be found using trigonometry. First, we can find the length of the other leg using the Pythagorean theorem: a² + b² = c², where c is the hypotenuse and a and b are the legs. Plugging in the values we get: 4² + b² = 12², solving for b we get b = √(12² - 4²) = 8√3. Now we can use inverse tangent to find the larger acute angle: tan⁻¹(opposite/adjacent) = tan¹⁽⁸√³/⁴⁾ ≈ 73.7°. So, the measure of the larger acute angle is 73.7°.

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In the multiple regression model with k regressors, the variance of the stochastic errors in the population can be estimated by the residual mean square (MSE).

         Multiple regression is a statistical tool that allows the researcher to estimate the relationship between multiple independent variables and a dependent variable. It measures the impact of a given independent variable on the dependent variable after controlling for the other independent variables.

        In simple linear regression, there is only one independent variable, whereas, in multiple linear regression, there is more than one independent variable.

         Residual mean square (MSE) is the variance of the error term (the difference between the predicted and observed values). It represents the average variance of the errors or the average deviation of the dependent variable from its predicted value.

         The MSE can be used to estimate the variance of the stochastic errors in the population. It is calculated by dividing the sum of squared residuals by the degrees of freedom (n-k-1)

           Where n is the sample size and k is the number of regressors.

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The probability that a male passenger can fit through the doorway without bending is approximately 0.9599, or 95.99%.

What is probability?

Probability is a branch of mathematics that deals with the study of random events and their likelihood of occurrence. It is used to quantify uncertainty and to make informed decisions in the face of incomplete or uncertain information.

We can assume that the heights of male passengers follow a normal distribution with a mean of 69.0 in and a standard deviation of 2.8 in. Let X be the height of a male passenger in inches. Then, we need to find the probability that X is less than or equal to 74 in, which represents the height of the airliner's doors.

(a) Using the standard normal distribution, we can standardize X as follows:

z = (X - μ) / σ

where μ is the mean and σ is the standard deviation of the distribution, and z is the corresponding z-score.

Substituting the values, we get:

z = (74 - 69.0) / 2.8 = 1.75

Using a standard normal distribution table or calculator, we can find the probability that a standard normal random variable is less than or equal to 1.75:

P(Z ≤ 1.75) ≈ 0.9599

Therefore, the probability that a male passenger can fit through the doorway without bending is approximately 0.9599, or 95.99%.

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The value of x is 7, and NM and OL are both equal to 37.

Since LMNO is a parallelogram, its opposite sides must be parallel and equal in length. Therefore, we have,

NM = OL

We also have the following information:

NM = x + 30

OL = 4x + 9

Substituting the first equation into the second equation, we get:

x + 30 = 4x + 9

Simplifying this equation, we get:

3x = 21

Therefore, x = 7.

Substituting this value back into the original equations, we get:

NM = x + 30 = 7 + 30 = 37

OL = 4x + 9 = 4(7) + 9 = 37

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The solution to the equation is x = -2 if x ≠ 0.

The equation  -1/x-1+2/x+5=1 can be rearranged to 2/x+1/x+5 = 0. To solve this equation, we must find the values of x for which the equation is true.
Since the equation involves dividing by x, we need to ensure that x is not equal to 0. Therefore, the restriction on the variable is x ≠ 0.
To solve the equation, we can first add -1/x to both sides to get 2/x + 5 = 1. Then, we can subtract 5 from both sides to get 2/x = -4. Finally, we can divide both sides by 2 to get x = -2.
Therefore, the solution to the equation is x = -2 if x ≠ 0.
To solve the given equation, we need to first find a common denominator. Here, the common denominator is (x - 1)(x + 5).-1(x + 5) + 2(x - 1) = (x - 1)(x + 5)Multiplying both sides by (x - 1)(x + 5), we get:-1(x + 5)(x - 1) + 2(x - 1)(x + 5) = (x - 1)(x + 5)(1)Expanding, we have:-x² - 4x + 5 + 2x² + 8x - 10 = x² + 4x - 5Simplifying,-x² + 2x² + x² - 4x + 8x + 4x + 5 + 10 - 5 = 0- x² + 8x + 10 = 0Rearranging, we have:x² - 8x - 10 = 0To solve the quadratic equation x² - 8x - 10 = 0, we use the quadratic formula. The formula is given byx = [-b ± sqrt(b² - 4ac)] / 2a Where a = 1, b = -8, and c = -10.Substituting these values, we get:[tex]x = [8 ± sqrt((-8)² - 4(1)(-10))] / 2(1)[/tex]

Simplifying = [8 ± sqrt(64 + 40)] / 2x = [8 ± sqrt(104)] / 2x = 4 ± sqrt(26)Therefore, the restrictions on the variable Are's ≠ 1 and x ≠ -5.

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The equation of  line of reflection that transforms shape P into shape Q is y=7.

a reflection is known as a flip. A reflection is a mirror image of its shape. An image will reflect through the line, known as the line of reflection. Every point in a figure is said to mirror the other figure when they are all equally spaced apart from one another.

In the given figure, Shape P and Shape Q touches the line y=7 and Shape Q forms exact reflection of Shape P

Hence, the equation of the line of reflection that

transforms shape P into shape Q. is y=7.

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The probability that a customer purchases a biography book given that they purchase cooking and BobVilla books is 0.08.

To calculate this probability, we need to consider the following components:

1. The total number of customers purchasing cooking and BobVilla books: This is the denominator of our equation, and it represents the total number of customers who purchased the two books.

2. The number of customers purchasing the biography book: This is the numerator of our equation, and it represents the number of customers who purchased the biography book.

3. The probability that a customer purchases a biography book given that they purchase cooking and BobVilla books: This is the fraction of customers who purchased the biography book over the total number of customers who purchased the two books.

To calculate the probability that a customer purchases a biography book given that they purchase cooking and BobVilla books, we need to divide the numerator (the number of customers purchasing the biography book) by the denominator (the total number of customers purchasing the two books).

This probability can be expressed as a decimal, which is 0.08. This value can also be rounded to two decimal places, which is 0.08.

In conclusion, the probability that a customer purchases a biography book given that they purchase cooking and BobVilla books is 0.08.

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The surface area of the triangular prism Milo paints red is equal to 186 square centimeters.

The triangular prism have two triangle and three rectangle faces, so we shall calculate for each area of the faces and add them to get the surface area of the triangular prism as follows:

area of triangle = 1/2(base × height)

area of one triangle face = 1/2(6 cm × 4 cm)

area of one triangle face = 12 cm²

area of two triangle faces = 2 × 12 cm² =24 cm²

area of one rectangle face = 10.8 cm × 5 cm

area of one rectangle face = 54 cm²

area of three rectangle faces = 162 cm²

area of the triangular prism = 24 cm² + 162 cm³

area of the triangular prism = 186 cm²

Therefore, the surface area of the triangular prism Milo paints red is equal to 186 square centimeters.

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Answer:

290

Step-by-step explanation:

Answer: 540 cm²

Step-by-step explanation:To find the area of the dilated rectangle, we need to first find the dimensions of the new rectangle after it has been dilated by a factor of 3.

The length of the new rectangle will be 3 times the original length, which is:

10 cm x 3 = 30 cm

The width of the new rectangle will also be 3 times the original width, which is:

6 cm x 3 = 18 cm

Therefore, the area of the dilated rectangle will be:

30 cm x 18 cm = 540 cm²

The  probability that at least 3 customers out of the first 6 will buy bread is 88.3% that is option B.

The binomial distribution is the discrete probability distribution used in probability theory and statistics that only allows for Success or Failure as the potential outcomes of an experiment. For instance, if we flip a coin, there are only two conceivable results: heads or tails, and if we take a test, there are only two possible outcomes: pass or fail. A binomial probability distribution is another name for this distribution.

The formula used is :

P(X=x) = [tex]C_n.x.p^x.(1-p)^n^-^x[/tex]

The parameters are:

x is the number of successes.

n is the number of trials.

p is the probability of a success on a single trial.

In this problem:

65% of customers who come into this store buy bread, hence p = 0.65.

A sample of 6 customers is taken, hence n = 6.

The probability that at least 3 customers out of the first 6 will buy bread is given by:

P(X≥3) = P(X=3) + P(X=4) + P(X=5) + P(X=6)

In which

P(X=x) = [tex]C_n.x.p^x.(1-p)^n^-^x[/tex]

P(X = 3) = C₆,₃(0.65)³ x (0.35)³ = 0.2355

P(X = 4) = C₆,₄(0.65)⁴ x (0.35)² = 0.328

P(X = 5) = C₆,₅(0.65)⁵ x (0.35)¹ = 0.2437

P(X = 6) = C₆,₆(0.65)⁶ x (0.35)⁰ = 0.0754

Then,

P(X≥3) = P(X=3) + P(X=4) + P(X=5) + P(X=6)

= 0.2355 + 0.328 + 0.2437 + 0.0754 = 0.8826

The probability that at least 3 customers out of the first 6 will buy bread is 0.8826 ≈ 88.3%.

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Complete  question;

A local bakery sells the freshest bread in town. In fact, 65% of customers who come into this store buy bread. What is the probability that at least 3 customers out of the first 6 will buy bread?

23.5%

88.3%

11.7%

76.5%

The width of the dumpster that minimizes its surface area is approximately 1.71 yards, and the length is approximately 3.42 yards.

The length of the rectangular dumpster is equal to two times its width, or 2x, if x is its width. The dumpster's height is not specified, however it is not necessary for this issue.

We need to determine the dumpster's size to reduce the amount of surface area it has. The following sources provide the rectangular dumpster's surface area:

A = lw + lh + lw

where w stands for width, l for length, and h for height.

Given that the container must hold [tex]20 yd3[/tex] of waste, we can use the formula for the volume of a rectangular solid to create the following sentence:

[tex]V = lwh = (2x) (x)\\h = 2x^2 h = 20\\h = 10/x^2[/tex]

Inputting this expression for h into the surface area A formula yields the following results:

[tex]A = 2lw + 2lh + 2wh = 2(x)(2x) + 2(x)(10/x) + 2(2x)(10/x) = 4(x)(2x) + 40(x)[/tex]

We can take the derivative of A with respect to x, set it equal to zero, and solve for x to determine the dimensions that minimise A:

[tex]dA/dx = 8x - 40/x^2 = 0\\8x = 40/x^2\\x^3 = 5\\x = (5)^(1/3)\\[/tex]

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Step-by-step explanation:

2(x+10y)+2(7x^2-x+9y)

= 2x+20y+14x^2-2x+18y

= (14x^2+38y) units^2

At alpha equal to 0.01 there is enough evidence to reject the claim that is the chance of a false positive.

When reducing the alpha from 0.05 to 0.01 reduces the chance of a false positive also called a Type I error, it makes it harder to detect differences with a t-test and with any significant results one might obtain would be more trustworthy but there would probably be less of them.

We know that:

probability > 0.1: no evidence,

then, probability between 0.05 and 0.1: weak evidence

then, probability between 0.01 and 0.05: evidence

then, probability between 0.001 and 0.01: strong evidence

and probability < 0.001: very strong evidence

The alpha level set relates to the formal decision made rather than this informal interpretation, but both can be reported together.

Lower alpha levels are sometimes used while carrying out multiple tests at the same time and a common approach is to divide the alpha level by the number of tests being carried out.

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I think it equals 18 tens

Answer:

3 x 60 x 30 = 5400

Step-by-step explanation:

The amount accumulated after 8 years is $5,781.84. Rounded to the nearest cent, this is $5,781.84.

What is an amount?

Using the formula A = [tex]P(1 + r/k)^{kt}[/tex], where A is the amount accumulated, P is the principal, r is the annual interest rate, t is the number of years, and k is the number of times the interest is compounded per year, we can calculate the amount accumulated as follows:

P = $3,350 (given)

r = 6.2% = 0.062 (convert to decimal)

t = 8 (given)

k = 365 (given)

A = [tex]P(1 + r/k)^{kt}[/tex]

A = [tex]$3,350(1 + 0.062/365)^{365*8}[/tex]

A = [tex]$3,350(1.000170685)^{2920}[/tex]

A = $5,781.84

Therefore, the amount accumulated after 8 years is $5,781.84. Rounded to the nearest cent, this is $5,781.84.

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The Answer of the given question based on the triangle is angle ∠α ≈ 56.4° degrees , angle ∠β ≈ 33.6° degrees , side C ≈ 14.4° units.

In a right triangle, the hypotenuse is the longest side and it is opposite the right angle. It is the side that is directly opposite the right angle and is always opposite the largest angle of the triangle. The hypotenuse is also the side that connects the two legs of the right triangle. The length of hypotenuse can be found using Pythagorean theorem.

From the problem statement, we know that angle ∠gamma = 90° degrees, which means that BC is the hypotenuse of the right triangle. We also know that side A = 12 and side B = 8.

Using Pythagorean Theorem, we can find length of  hypotenuse by:

c² = a² + b²

c² = 12² + 8²

c² = 144 + 64

c² = 208

c = √(208)

c ≈ 14.4

So the length of BC is approximately 14.4 units.

To find the altitude CA, we can use the formula for the area of a right triangle:

area = (1/2) * base * height

Since angle gamma = 90° degrees, the altitude CA is equal to the length of side A:

CA = A = 12 units.

Now we can use the trigonometric ratios to find the acute angles∠α and :

sin(α) = opposite/hypotenuse = CA/c

sin(α) = 12/14.4

α ≈ 56.4° degrees

Since α and gamma are complementary angles (they add up to 90° degrees), we can find β using the following formula:

β = 90 - α

β ≈ 33.6° degrees

Therefore, the unknown values for the given right triangle are:

angle ∠α ≈ 56.4° degrees

angle ∠β ≈ 33.6° degrees

side C ≈ 14.4° units.

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The statement "dispersion models are selected based on the phase of the material being modeled in a release scenario" is true as Different dispersion models are needed for different phases (gas, liquid, solid) due to differences in behavior and transport mechanisms.

Dispersion models are used to predict the spread of pollutants, and they depend on the physical and chemical properties of the material being released.

Generally, different models are used for each phase of the material, such as the Gaussian plume model for gases, the plume rise model for heated gases, and the particle dispersion model for particles.

Each of these models is based on different characteristics and equations which allow for the most accurate prediction of the dispersion of pollutants.

For example, the Gaussian plume model considers the wind velocity, turbulence, and buoyancy of the released material, whereas the plume rise model considers the momentum, thermal expansion, and buoyancy of the released material.

Therefore, dispersion models are selected based on the phase of the material being modeled in a release scenario.

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The total number of listings possible for the 14 teams in the local little league is 11,664. This is because there are 14 teams, so the number of possible listings is equal to 14! (14 factorial). 14! is equal to 1x2x3x4x5x6x7x8x9x10x11x12x13x14, which equals 11,664.

To further explain, 14! is the number of ways to arrange 14 items. This is because the first item can be arranged in 14 ways, the second item in 13 ways, the third in 12, and so on. This means that the total number of possible arrangements is 14x13x12x11x10x9x8x7x6x5x4x3x2x1, which equals 11,664.

Therefore, the total number of listings possible for the 14 teams in the local little league is 11,664.

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The system of equation with the same solution with 2x + 2y = 16 3x  - y = 4 is 2x + 2y = 16, 6x - 2y = 8. Therefore, the answer is 2.

System of equation can be solved using different method such as elimination method, substitution method and graphical method.  Therefore, let's solve the system of equation as follows;

2x + 2y = 16

3x  - y = 4

multiply equation(ii) by 2

2x + 2y = 16

6x - 2y = 8

add the equations

8x = 24

x = 24  / 8

x = 3

y = 3x - 4

y = 3(3) - 4

y = 9 - 4

y = 5

Therefore,

2x + 2y = 16

6x - 2y = 8

add the equation

8x = 24

x = 24  / 8

x = 3

Therefore,

2(3) + 2y = 16

6 + 2y = 16

2y = 16 - 6

2y = 10

y = 5

Therefore, the equation with the same solution is 2x + 2y = 16

6x - 2y = 8.

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No, we cannot conclude that 90% of households have between .7 and 2.1 children based on the confidence interval alone.

Based on the confidence interval alone, we cannot come to the conclusion that 90% of households have a number of children between .7 and 2.1. A confidence interval only provides a range of values that likely contains the true population parameter (in this case, the average number of children per household) with a certain level of confidence (in this case, 90%). It does not provide information about the distribution of the variable within the population. Therefore, we cannot make any conclusions about what percentage of households have a certain number of children based on the confidence interval alone.

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Answer:

B. y = (x+1)(x-3)

Step-by-step explanation:

Bbecause when y intersect the x axis, y = 0

so (x+1)(x-3) = 0, which we get x = -1 and x = 3

As shown in the graph this is true, because the function does indeed also intersect with the x axis at x = -1 and x = 3 as well.

A searchlight is shaped like a paraboloid of revolution. if the light source is located 2 feet from the base along the axis of symmetry and the opening is 5 feet across, 2.5 feet deep should the searchlight be.

As per the given information,

A searchlight is shaped like a paraboloid of revolution. If the light source is located 2 feet from the base along the axis of symmetry and the opening is 5 feet across.

Here we have to Find: How deep should the searchlight be.

First of all, we need to find the equation of the paraboloid of revolution.

Let's assume that the axis of the paraboloid is along the y-axis and the vertex is at the origin (0, 0, 0).

So, the equation of the paraboloid is given by:

y² = 4ax

Where, a = 2 feet (distance of light source from vertex)

So, the equation of the paraboloid is:

y² = 8x ..... (1)

The opening of the paraboloid is given to be 5 feet across.

We know that the diameter of a circle is equal to twice the radius. Hence, the radius of the opening is 2.5 feet.

The vertex is the point (0, 0, 0). We need to find the depth of the searchlight. The depth is nothing but the perpendicular distance from the vertex to the plane of the opening. The plane of the opening is given by the equation x = -2.5 (since the opening is along the yz-plane)

The equation of the plane is given by x = -2.5

Now, we need to find the coordinates of the point where the paraboloid intersects the plane of the opening.

We can substitute x = -2.5 in equation (1) to get:

y² = -20

Squaring both sides, we get:

y = ±√(-20)

Since y can only be positive (since we are considering the upper half of the paraboloid),

y = √(-20) = i√20 = 2√5 i

So, the point where the paraboloid intersects the plane of the opening is (-2.5, 2√5 i, 0)

The depth is nothing but the perpendicular distance from the vertex (0, 0, 0) to the point (-2.5, 2√5 i, 0). Hence, the depth is given by:√((-2.5 - 0)² + (2√5 i - 0)² + (0 - 0)²)= √(6.25 + 20 - 0) = √26.25 = 2.5 feet

Hence, the depth of the searchlight should be 2.5 feet.

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The score located at -3sx (standard deviation) from the mean in a normal distribution is 75. This is because in a normal distribution, the mean is the center and -3sx is three standard deviations away from the mean. Therefore, the score located at -3sx would be the mean minus three standard deviations, which is 120-45=75.

To further explain, a normal distribution is a probability distribution characterized by a symmetrical bell-shaped graph, and it's determined by the mean and standard deviation of the dataset. In this case, the mean is 120 and the standard deviation is 15. Therefore, the data would have an average score of 120 and an average range of 30 (15 plus and minus from the mean). If the score is located at -3sx, it would be three standard deviations away from the mean and the score would be 75.

Therefore, the score located at -3sx would be the mean minus three standard deviations, which is 120-45=75.

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The CPA Practice Advisor reports that the mean preparation fee for federal income tax returns was 261. Use this price as the population mean and assume the population standard deviation of preparation fees is 120.

We need to find the probability of selecting a random sample of 20 tax returns and a standard deviation of the sample preparation fees of 50 or less.

We use the central limit theorem that states that, regardless of the shape of the population, the sampling distribution of the sample means approaches a normal distribution with mean μ and standard deviation

σ/√n

where μ is the population mean, σ is the population standard deviation, and n is the sample size.

Therefore, we have:

[tex]\mu = 261\]\\sigma = $120\]\\n = 20\][/tex]

[tex]S.E.= \frac{\sigma}{\sqrt{n}}\\S.E =\frac{\ 120}{\sqrt{20}}\\S.E =26.83[/tex]

The probability of selecting a random sample of 20 tax returns and a standard deviation of the sample preparation fees of 50 or less is given by:

[tex]P(Z < \frac{X - \mu}{S.E})\][/tex]

where X is the sample mean, μ is the population mean, and S.E is the standard error of the mean.

To calculate the probability, we standardize the distribution of the sample means using the z-score formula, i.e.,

[tex]\[z = \frac{X - \mu}{S.E} = \frac{\50 - \261}{\26.83} = -7.91\][/tex]

Therefore, the probability of selecting a random sample of 20 tax returns and a standard deviation of the sample preparation fees of 50 or less is zero because the z-score is less than the minimum z-score (i.e., -3.89) that corresponds to the probability of selecting a random sample of 20 tax returns and a standard deviation of the sample preparation fees of 50 or less.

Thus, it is impossible to obtain such a sample.

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Answer:

between 15 and 16

Step-by-step explanation:

31÷2=15.5 meaning 15.5 is between 15 and 16

The value of the interquartile range for the given subsample is 8.

The interquartile range (IQR) is a measure of the dispersion of a set of observations. It is defined as the difference between the third quartile and the first quartile (Q3-Q1). The subsample data is as follows: 24, 27, 35, 31, 21, 22, 28, 18, 25, 24, 36, 20. The interquartile range for the subsample data can be computed as follows:

Step 1: Arrange the data in ascending order: 18, 20, 21, 22, 24, 24, 25, 27, 28, 31, 35, 36.

Step 2: Find the median of the lower half of the data, which is called the first quartile, Q1. Here, the lower half of the data is 18, 20, 21, 22, 24, and 24. Hence, the median of the lower half of the data is the average of the two middle values, which is Q1 = (22 + 21)/2 = 21.5.

Step 3: Find the median of the upper half of the data, which is called the third quartile, Q3. Here, the upper half of the data is 24, 25, 27, 28, 31, 35, and 36. Hence, the median of the upper half of the data is the average of the two middle values, which is Q3 = (28 + 31)/2 = 29.5.

Step 4: Calculate the interquartile range as the difference between the third quartile and the first quartile: IQR = Q3 - Q1 = 29.5 - 21.5 = 8.

Therefore, the value of the interquartile range for the given subsample is 8.

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