HELP PLEASE
The stem-and-leaf plot displays data collected on the size of 15 classes at two different schools.


Sky View School Riverside School
0 5, 6, 9
9, 7, 2, 0 1 0, 2, 4, 5, 6, 7
8, 7, 6, 5, 5, 5, 4, 3, 1, 0 2 0, 0, 2, 3, 5
0 3
4 2
Key: 2 | 1 | 0 means 12 for Sky View and 10 for Riverside


Part A: Calculate the measures of center. Show all work. (5 points)

Part B: Calculate the measures of variability. Show all work. (5 points)

Part C: If you are interested in a larger class size, which school is a better choice for you? Explain your reasoning. (2 points)

Answer:

1/9 or about 11%

Step-by-step explanation:

Take 1/6 (probability of getting the number 5 once) times 4/6 (the number of times the die is tossed) and you get 1/9.

A nonparametric test for the equivalence of two populations would be used instead of a parametric test for the equivalence of the population parameters if:

a. No information about the populations is available.

Nonparametric tests do not rely on specific assumptions about the underlying population distribution or parameters. They are distribution-free and can be used when there is limited or no knowledge about the populations being compared. Nonparametric tests use ranks or categorical data to assess the equivalence or difference between populations.

Parametric tests, on the other hand, assume specific distributions or parameters and may require certain assumptions to be met, such as normality and equal variances.

Therefore, when no information about the populations is available, a nonparametric test is preferred as it provides a robust and reliable method for testing equivalence.

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The dramatic increase in the price of corn signals to both buyers and farmers that there is increased demand for corn due to the increased demand for ethanol biofuel.

The increase in price of corn impacts both buyers' and farmers' incentives. Buyers will be incentivized to find alternative sources of food and fuel, as the higher price of corn will make it less desirable. Farmers, on the other hand, will be incentivized to produce more corn in response to the higher price. This change in incentives may lead to changes in market behavior and production decisions, as well as potentially impacting other markets and industries. It is likely that both buyers and farmers responded to the dramatic price increase by adjusting their behavior in response to the new incentives created by the market conditions.

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Answer:

The percentage equivalent of 21/70 can be found by dividing 21 by 70 and then multiplying by 100 to convert to a percentage.

In order to find a percentage just divide two numbers  which the numerator divided by the denominator x 100 = to answer%

(21/70) x 100 = 30%

Therefore, the answer is 30%.

The possible Laurent series expansions centered at 0 for each of the following functions is  -1 / (2(z/√(2))² - 1)

To find the Laurent expansion of 1 / (z - √(2)) centered at 0, we can use the formula:

f(z) = 1 / (z - z0) = 1 / z0 * 1 / (1 - z/z0)

where z0 = √(2). Then, we can expand the denominator using the formula for a geometric series:

1 / (1 - z/z0) = 1 + z/z0 + (z/z0)² + ...

Substituting z = 0 into this series gives:

1 / (z - √(2)) = 1 / √(2) * (1 + z/√(2) + (z/√(2))² + ...)

This is the Laurent expansion of 1 / (z - √(2)) centered at 0. Note that this expansion is valid in the region |z/√(2)| < 1, which corresponds to the open disk centered at 0 with radius √(2).

Similarly, we can find the Laurent expansion of 1 / (z + √(2)) centered at 0 by using the same formula and substituting z0 = -√(2):

1 / (z + √(2)) = -1 / √(2) * (1 - z/√(2) + (z/√(2))² - ...)

Substituting this into the original expression for 1 / (z² - 2), we get:

=> 1 / (z² - 2) = 1 / (z - √(2)) - 1 / (z + √(2))

When we simplify this one then we get,

= 1 / √(2) * (1 + z/√(2) + (z/√(2))² + ...) - (-1 / √(2) * (1 - z/√(2) + (z/√(2))² - ...))

When we reduce the equation, then we get,

=> 2 / (2z² - 4) = -1 / (2(z/√(2))² - 1)

This is the Laurent expansion of 1 / (z² - 2) centered at 0.

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Complete Question:

Find all possible Laurent expansions centered at 0 of the following functions and state the region where each is defined:

a)  1 / z² - 2

in triangle ΔCDE:

CD ≈ √1466

∠C ≈ -17

∠D = 90

in triangle  ΔJKL:

JL ≈ √808

∠K = 102 - ∠L

∠L = ∠L

We have,

To solve for the missing values in the given triangles, we can use the angle sum property and the side length ratios in triangles.

so,

For ΔCDE:

Given:

∠E = 107 degrees

CE = 29

DE = 25

To find the CD, we can use the Pythagorean theorem because CDE is a right triangle:

CD² = CE² + DE²

CD² = 29² + 25²

CD²= 841 + 625

CD² = 1466

CD ≈ √1466

To find ∠C, we can use the fact that the sum of angles in a triangle is 180 degrees:

∠C = 180 - ∠E - ∠D

∠C = 180 - 107 - 90

∠C = 180 - 197

∠C ≈ -17 (The negative angle suggests that there might be an error or inconsistency in the given information)

To find ∠D, we can use the fact that the sum of angles in a triangle is 180 degrees:

∠D = 180 - ∠C - ∠E

∠D = 180 - (-17) - 107

∠D = 180 + 17 - 107

∠D = 90

And,

For ΔJKL:

Given:

∠J = 78 degrees

KJ = 18

KL = 22

To find JL, we can use the side length ratios in triangles:

JL² = KJ² + KL²

JL² = 18² + 22²

JL² = 324 + 484

JL² = 808

JL ≈ √808

To find ∠K, we can use the fact that the sum of angles in a triangle is 180 degrees:

∠K = 180 - ∠J - ∠L

∠K = 180 - 78 - ∠L

∠K = 180 - 78 - ∠L

∠K = 180 - 78 - ∠L

∠K = 180 - 78 - ∠L

∠K = 180 - 78 - ∠L

∠K = 102 - ∠L

To find ∠L, we can use the fact that the sum of angles in a triangle is 180 degrees:

∠L = 180 - ∠J - ∠K

∠L = 180 - 78 - (102 - ∠L)

∠L = 180 - 78 - 102 + ∠L

∠L = 180 - 180 + ∠L

∠L = ∠L

Therefore,

in ΔCDE:

CD ≈ √1466

∠C ≈ -17 (possible error or inconsistency in the given information)

∠D = 90

And,

in ΔJKL:

JL ≈ √808

∠K = 102 - ∠L

∠L = ∠L

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The probability of spinning "C" and flipping "heads" is 0.125 or 12.5%.

Assuming the spinner is fair and has 4 equal-sized sections, the probability of spinning "C" is 1/4 or 0.25. And the coin is fair, the probability of flipping "heads" is 1/2 or 0.5.

The probability of spinning "C" and flipping "heads" is calculated as,

P = (Probability of spinning "C") × (Probability of flipping "heads")

P = 0.25 × 0.5

P = 0.125

Therefore, the probability is 12.5%.

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The area under the normal curve between z = 0.0 and z = 1.79 is approximately 0.0359, which corresponds to answer choice b.

The area under the normal curve between z = 0.0 and z = 1.79 can be calculated using a standard normal distribution table or a calculator with a normal distribution function.

Using a standard normal distribution table, we can find the area under the curve between z = 0.0 and z = 1.79 in the body of the table, where the rows represent the tenths and hundredths digits of z, and the columns represent the hundredths digits of the area.

Looking up z = 0.0, we find the area to be 0.5000. Looking up z = 1.79, we find the area to be 0.4641. To find the area between these two values, we can subtract the smaller area from the larger area:
0.4641 - 0.5000 = -0.0359

However, since we are looking for the area under the curve (which cannot be negative), we need to take the absolute value of this result:
| -0.0359 | = 0.0359

Therefore, the area under the normal curve between z = 0.0 and z = 1.79 is approximately 0.0359, which corresponds to answer choice b.

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The value that gives how much greater is the mass of Venus than the mass of Mercury is given as follows:

[tex]1.48 \times 10^1[/tex]

A number in scientific notation is given by the notation presented as follows:

[tex]a \times 10^b[/tex]

With the base being [tex]a \in [1, 10)[/tex], meaning that it can assume values from 1 to 10, with an open interval at 10 meaning that for 10 the number is written as 10 = 1 x 10¹, meaning that the base is 1, justifying the open interval at 10.

The masses are given as follows:

To obtain how many times greater the mass of Venus is, we divide the masses, hence:

[tex]\frac{4.87 \times 10^{24}}{3.3 \times 10^{23}} = 1.48 \times 10^1[/tex]

Because:

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The 74th apple will be placed in second basket of apples.

Apples are distributed, one at a time, into six baskets. the first apple goes into basket one, the second into basket two, the third into basket three, and so on, until each basket has one apple.  

This pattern is repeated, beginning each time with basket one

Since there are 6 baskets, the pattern of distribution repeats every 6 apples.

Hence, to determine which basket the 74th apple will be placed in, we need to find the remainder when 74 is divided by 6:

=> 74 ÷ 6 = 12 remainder 2

This means that the 74th apple will be placed in the second basket, since it follows the pattern of distributing apples starting with the first basket.

Therefore,

The 74th apple will be placed in second basket of apples.

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The value of the complementary angle of 54° is determined as  B = 36°.

Two angles are called complementary when their measures add to 90 degrees. Two angles are called supplementary when their measures add up to 180 degrees.

So if the measure of one angle is 54°, the value of its complementary angle is calculated as follows;

Mathematically, the formula for calculating the complementary angle of 54° is given as;

B + 54° = 90

B = 90 - 54°

B = 36°

Thus, the value of the complementary angle of 54° is determined as 36° since both angles will add up to 90 degrees.

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The complete question is below:

Use your knowledge of complementary and vertical angles to hit

this shot.

If angle A is 54° and angle B is its complementary angle. Angle B = ?

The general solution of the given differential equation [tex]$y = \left(-\frac{4\ln|x|}{x^3}\right)e^{-3x} + \frac{C}{x^3}$[/tex], where C is an arbitrary constant.

The given differential equation is a first-order linear ordinary differential equation of the form [tex]$xy' + 3y = f(x)$[/tex]  where [tex]$f(x) = \frac{4e^{-3x}}{x^2}$[/tex] .To solve this equation, we need to find an integrating factor, which is a function that when multiplied with the original equation, makes the left-hand side a derivative of a product of functions. To find the integrating factor, we multiply the equation by a function u(x), such that [tex]$u(x)xy' + 3u(x)y = u(x)f(x)$[/tex], and seek a function u(x) that makes the left-hand side a derivative of a product.

By comparing this equation with the product rule, we can see that the integrating factor is[tex]$u(x) = e^{3\ln{|x|}}$[/tex], which simplifies to [tex]$u(x) = x^3$[/tex].
Multiplying the original equation by the integrating factor, we get [tex]$x^3y' + 3x^2y = \frac{4e^{-3x}}{x}$[/tex]. The left-hand side is now a derivative of the product [tex]$(x^3y)$[/tex], so we can integrate both sides with respect to x to obtain the general solution: [tex]$x^3y = -4e^{-3x}\ln{|x|} + C$[/tex] where C is the constant of integration.

Dividing both sides by [tex]$x^3$[/tex], we get the final form of the general solution. Therefore, the general solution of the given differential equation is [tex]$y = \left(-\frac{4\ln{|x|}}{x^3}\right)e^{-3x} + \frac{C}{x^3}$[/tex], where C is an arbitrary constant. This solution satisfies the original differential equation for all x except x = 0, where the solution is not defined due to the singularity in the coefficient.

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The integral of e^x dx on x=y^3 from (-1,-1) to (1,1) is approximately 2.17.

To solve this problem, we need to use substitution. Let y^3 = x, so that dx = 3y^2 dy. Substituting these expressions into the integral, we get:

∫e^x dx = ∫e^(y^3) * 3y^2 dy

We can now integrate this expression using the u-substitution method. Let u = y^3, so that du/dy = 3y^2. Substituting these expressions, we get:

∫e^(y^3) * 3y^2 dy = ∫e^u du

Integrating e^u with respect to u, we get e^u + C, where C is a constant of integration. Substituting back for u and simplifying, we get:

e^(y^3) + C

To find the value of the constant, we can use the limits of integration. Substituting (1,1) and (-1,-1) for (x,y), we get:

e^(1^3) - e^(-1^3) = e - 1/e

So the answer is approximately 2.17.

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To find the percentage of data that falls between 5 and 35 in a normally distributed data set with a mean of 20 and a standard deviation of 5, we can use the properties of the standard normal distribution.

First, we need to standardize the values 5 and 35 by converting them to z-scores. The z-score formula is:

z = (x - μ) / σ

Where:

x is the value,

μ is the mean, and

σ is the standard deviation.

For the value 5:

z1 = (5 - 20) / 5 = -3

For the value 35:

z2 = (35 - 20) / 5 = 3

Next, we can use a standard normal distribution table or calculator to find the area under the curve between the z-scores -3 and 3. This area represents the percentage of data between 5 and 35.

Using a standard normal distribution table or calculator, we find that the area under the curve between -3 and 3 is approximately 0.9973.

Therefore, approximately 99.73% of the data will fall between 5 and 35 in a normally distributed data set with a mean of 20 and a standard deviation of 5.

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Answer:

A,C,E

Step-by-step explanation:

Answer:

[tex]a. \: (2. \frac{ - 7}{5} )[/tex]

Step-by-step explanation:

Greetings!!!!

To get the answer substitute these values that are given in the choices to the equation and crosscheck the expression.

[tex]6(2) + 5( \frac{ - 7}{5} ) = 5[/tex]

cancel out 5 by 5

[tex]12 - 7 = 5[/tex]

subtract 7 from 12

[tex]5 = 5[/tex]

If you have any questions tag it on comments

Hope it helps!!!!

It would take the doctor 540 minutes (or 9 hours) to complete 12 appointments.

If the doctor takes 3/4 hour (45 minutes) to complete each appointment, we can calculate the total time required for 12 appointments by multiplying the time per appointment by the number of appointments:

Time for 12 appointments = (3/4 hour/appointment) * 12 appointments

To simplify the calculation, we can convert 3/4 hour to minutes:

Time for 12 appointments = (45 minutes/appointment) * 12 appointments

Now, let's calculate the total time:

Time for 12 appointments = 540 minutes

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Based on the information provided, with leading and countercyclical variables reaching a trough, we can expect that:
D. Aggregate economic activity will start increasing.

Leading variables are indicators that change before the overall economy changes, and countercyclical variables move in the opposite direction of the general economic trend.

When these variables reach a trough, it suggests that the lowest point of economic activity has been reached.

As a result, we can expect that aggregate economic activity will start increasing, signaling the end of a recession and the beginning of an expansion phase.

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Yes, it appears that the data are normally distributed. This is because the standard deviation (2.45 grammes) and the mean (20 grammes) both fall within acceptable bounds.

Since the data points are evenly spaced from the mean, the distribution is symmetric and corresponds to a normal distribution. The standard deviation is also not excessive in comparison to the mean, supporting the notion that the data is regularly distributed.

A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

In contrast, a high or low standard deviation indicates that the data points are, respectively, above or below the mean. A standard deviation that is close to zero implies that the data points are close to the mean.

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The standard form of the equation of the parabola is y = (9/25)x^2. To find the standard form of the equation of the parabola with a vertex at the origin and a vertical axis that passes through the point (5,9), we need to use the standard form of the equation of a parabola, which is y = a(x-h)^2 + k, where (h,k) is the vertex.

Since the vertex is at the origin, we have h=0 and k=0, which simplifies the equation to y = ax^2. Now, we just need to find the value of "a" by plugging in the point (5,9).  9 = a(5)^2. Solving for a, we get a = 9/25.

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The coordinates of the four corners of the rectangle are A(3, 2), B(0, 3), C(-3, -2), and D(0, -3).

The rectangle has two pairs of parallel sides and right angles at each corner, and the diagonals intersect at the origin. We can use this information to find the coordinates of the four corners of the rectangle.

Let's start by drawing a diagram and labeling the coordinates of the intersection point of the diagonals, (0, 0).

B ________ C

  |                |

  |                |

  |                |

  |________|D

       (0,0)

Since the rectangle is 6 units long and 4 units wide, we know that the distance from the origin to each corner is a multiple of 2 or 3 units (using the Pythagorean theorem). We can also use the fact that the diagonals bisect each other to find the coordinates of the corners.

Starting with corner A, we can use the fact that it is 3 units to the right and 2 units up from the origin to find its coordinates: A(3, 2). Similarly, we can find the coordinates of corner C, which is 3 units to the left and 2 units down from the origin: C(-3, -2).

Next, we can use the fact that corner B is equidistant from A and C to find its coordinates. Since the rectangle is symmetric, we know that corner B is 3 units up from the origin: B(0, 3). Finally, we can find the coordinates of corner D, which is 3 units down from the origin: D(0, -3).

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if the equation Ax=b has at least two different solutions and is consistent, then it has infinitely many solutions.

If the equation Ax=b has at least two different solutions, then there exists more than one vector x that satisfies the equation. This means that the system of equations Ax=b has more than one solution. Since the system is consistent, there exists at least one solution.

If we have at least two solutions to the system Ax=b, say x1 and x2, then any linear combination of x1 and x2 is also a solution. That is, if we take any scalar values c1 and c2, then the vector y=c1x1+c2x2 is also a solution to the equation Ax=b.

Therefore, if the equation Ax=b has at least two different solutions and is consistent, then it has infinitely many solutions.

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The area of the given triangle is 24 square inches.

As per the shown triangle, the height is 4 inches and the base is 12 inches.

The area of a triangle can be found by multiplying the base by the height and dividing by 2.

So, the area of the triangle is:

The area of a triangle = (base x height) / 2

The area of a triangle = (12 inches x 4 inches) / 2

The area of a triangle = (48 inches) / 2

The area of a triangle = 24 square inches

Therefore, the area of the triangle is 24 square inches.

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The function "distance" should take in an array "data" containing a row of time values and a row of measurements, and return the calculated distance in miles.

To calculate the distance, we can use the formula: distance = (measurement / 5280) * time, where measurement is in feet, time is in seconds, and the factor 5280 is the number of feet in a mile.

So, in the function, we can loop through the two rows of data, calculate the distance for each pair of values using the above formula, and sum up the distances to get the total distance covered. Finally, we can return the total distance in miles.

With this function, we can pass in an array of time and measurement values, and get back the total distance covered in miles.

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Compute covariance matrix, perform eigen decomposition, determine its numbers, and then find standard deviation.

To answer your question, we need some additional information about the dataset and the desired percentage of variance explained. However, I can provide you with a general explanation of the process involved in reducing dimensionality while retaining a specified level of variance explained.

1. Compute the covariance matrix of the dataset to identify the relationships between different dimensions.

2. Perform eigendecomposition on the covariance matrix to obtain eigenvalues and eigenvectors.

3. Sort the eigenvalues in descending order and select the corresponding eigenvectors. The sorted eigenvalues represent the variances of the principal components (new dimensions), while the eigenvectors indicate the directions of these components.

4. Determine the number of dimensions to reduce to by considering the desired level of variance explained. Calculate the cumulative percentage of the total variance explained by adding the variances of the principal components (eigenvalues) in descending order. Stop when the desired percentage is reached or exceeded.

5. The number of dimensions you have considered up to this point will be the reduced dimensions.

6. To find the standard deviation for the selected dimensions, simply take the square root of the corresponding eigenvalues.

Keep in mind that this explanation assumes you are using Principal Component Analysis (PCA) for dimensionality reduction. Without specific information about your dataset and desired variance explained, it's not possible to provide the exact number of reduced dimensions and their standard deviations.

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According to the information presented on the box plot:

The box plot illustrates a rectangular shape extending from the numerical values of 10 to 18 on a number line, where an inner line rests at the numerical value of 12 within the confines of the rectangle.

The median functions as the numeric value that effectively splits data in half, equally distributing percentages of 50% below and above it while defining its centrality.

In this case, the statement "A line in the box is at 11" defines the median.

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The probability that a randomly selected box of cereal is regular size or contains a prize is 50%

To find the probability that a randomly selected box of cereal is regular size or contains a prize, we can add the probabilities of these two events happening separately and subtract the probability of their intersection (i.e., the probability that a box is both regular size and contains a prize).

The table given shows that there are 4 boxes of regular size, of which only 1 contains a prize. There are also 6 boxes of mini size, of which 3 contain a prize. Thus, there are a total of 4 + 6 = 10 boxes that are either regular size or contain a prize. However, we have to subtract the intersection of these two events, which is the box that is both regular size and contains a prize, of which there is only 1.

Therefore, the probability that a randomly selected box of cereal is regular size or contains a prize is:

[tex](4 + 3 - 1) / 12 = 6/12 = 1/2[/tex]

So, the probability is 1/2 or 50%.

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The surface area of the prisms found from the sum of the areas  of the the individual surfaces of the prism are;

23) 60 cm²

24) 124 ft²

25) 48 mi²

26) 132 yd²

27)50.2 mi²

28) 72 km²

29) 112 yd²

30) 154 mi²

31) 150 mi²

32) 288 km²

33) 156 in²

34) 96.2 in²

The surface area of a prism is the sum of the surface areas of the faces on the prism surface.

23) Surface area = 3.5 × 2 × (2 + 6)/2 + 2 × 4 × 2 + 2 × 6 + 2 × 2 = 60

The surface area = 60 cm²

24) Surface area = 3.5 × 2 × (2 + 6)/2 + 2 × 4 × 6 + 6 × 6 + 2 × 6 = 124

The surface area of the prism = 124 ft²

25) Surface area = 2 × (1/2) × 4 × 3 + 3 × 5 + 3 × 3 + 4 × 3 = 48

The surface area = 48 mi²

26) Surface area = 2 × (8 × 3 + 3 × 6 + 3 × 8) = 132

The surface area = 132 yd²

27) Surface area = 1.7 × 2 × (2 + 4)/2 + 4 × 4  + 3 × 2 × 4 = 50.2

The surface area = 50.2 mi²

28) Surface area = 2 × (6 × 3 + 3 × 2 + 2 × 6) = 72

The surface area = 72 km²

29) Surface area = 4 × 4 × 4 + 2 × 6 × 4 = 112

The surface area = 112 yd²

30) Surface area = 4 × 2 × 7 + 2 × 7 × 7 = 154

The surface area = 154 mi²

31) Surface area = 6 × 5 × 5 = 150

The surface area = 150 mi²

32) Surface area = 4 × 5 × 8 + 2 × 8 × 8 = 288

The surface area = 288 km²

33) Surface area = 2.8 × 2 × (6 + 4)/2 + 2 × 8 × 3  + 4 × 8 + 8 × 6 = 156

The surface area = 156 in²

34) Surface area = 2.6 × 2 × (2 + 5)/2 + 2 × 6 × 3  + 2 × 6 + 5 × 6 = 96.2

The surface area = 96.2 mi²

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Answer:

x=72

y=92

Sum of Opposite angles of a cyclic quadrilateral is 180°