In 2016 Jane was 14 years old. At that time she was 7 times as old as her brother, Jim. In what year will Jane be twice as old as Jim will be then?

Answer:

Step-by-step explanation:

The Probability of Landing a heads is (1/2)

Now, to find the probability of landing it five times in a row, it is

1/2 x 1/2 x 1/2 x 1/2 x 1/2

( 1/2 is multiplied to the number of times to get a head )

The final answer will be,

Probability of landing heads 5 times in a row = 1/32

The magnitude of the upward force on the table due to the leg at (lx, 0) is Fx=W.

To find the upward force (Fx) on the table due to the leg at position (Lx, 0), you will need to consider the forces acting on the table. In this scenario, the force Fx is the force exerted by the leg to support the weight of the table and maintain equilibrium.  

To calculate Fx, you'll need to take into account the weight of the table (W) and any additional forces acting on it, such as objects placed on the table. Since the table is in equilibrium, the sum of all forces in the vertical direction should be equal to zero.

Using the principle of equilibrium:

ΣFy = 0

Where ΣFy represents the sum of all vertical forces acting on the table.

In this case, the upward force exerted by the leg (Fx) should be equal to the total downward force acting on the table:

Fx = W

Once you have determined the weight of the table and any additional forces, you can calculate the magnitude of the upward force Fx exerted by the leg at position (Lx, 0).

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Since the standard deviation is o = 3, we know that roughly 68% of the scores in the population fall within one standard deviation of the mean or between 18 and 24. Similarly, about 95% of the scores fall within two standard deviations of the mean, or between 15 and 27. Assuming a normal distribution, we can use these ranges to estimate the minimum and maximum possible values for the population variance:

Minimum Population Variance = Σ(18-21)² + Σ(24-21)² / 10 = 8.4

Maximum Population Variance = Σ(15-21)² + Σ(27-21)² / 10 = 34.8

Therefore, we can estimate that the population variance falls somewhere between 8.4 and 34.8, but we cannot determine the exact value without knowing the individual scores in the population.
To find the population variance, we will use the given information about the population, scores, and standard deviation (σ). The question provides the following information:

- Population (N) = 10 scores
- Mean (μ) = 21
- Standard deviation (σ) = 3

The formula to calculate population variance (σ²) is:

σ² = (Σ(X - μ)²) / N

However, since we are given the standard deviation, we can simply square it to find the population variance.
Population variance (σ²) = σ² = (3)² = 9.So, the population variance is 9

The formula for population variance is:

Population Variance = Σ(x-μ)² / N

Where Σ(x-μ)² is the sum of the squared deviations from the mean, and N is the size of the population.

Given that the population has N = 10 scores, with a mean of μ = 21 and a standard deviation of o = 3, we can plug these values into the formula:

Population Variance = Σ(x-21)² / 10

In order to calculate Σ(x-21)², we need to know the individual scores in the population. Since these are not provided in the question, we cannot calculate the exact population variance. However, we can use the formula to estimate a range of possible values for the population variance.

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The new coordinates of the square after rotating 270 degrees anticlockwise and translating 2 units to the left and 6 units up are (-1, 7), (-1, 10), (2, 7), and (2, 10).

To find the new coordinates of a square that is rotated 270 degrees anticlockwise and translated 2 units to the left and 6 units up, you need to follow the steps below:

1. The original square has coordinates (1,-1), (4,-1), (1,-4), and (4,-4).

2. To rotate the square 270 degrees anticlockwise, you need to swap the x and y coordinates, negate the new x coordinates, and keep the y-coordinates. The new coordinates will be (1, 1), (1, 4), (4, 1), and (4, 4).

3. To translate the rotated square 2 units to the left and 6 units up, you need to subtract 2 from the x-coordinates and add 6 to the y-coordinates. The final coordinates will be (-1, 7), (-1, 10), (2, 7), and (2, 10).

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The vertex of the graph of f(x) = |x - 5| - 6 is (5, -6). It lies in the fourth quadrant.

Therefore the answer is (5, -6).

The graph f(x) = |x - 5| - 6 is symmetrical about the axis  x = 5.

A vertex of a graph is a node of a graph. For a graph of the form f(x) = a|x - h| + k, the vertex is (h, k). So in this case where f(x) = |x - 5| - 6, a = 1, h = 5 and k = -6. Therefore the vertex of the given graph f(x) is

(5, -6)

--The question is incomplete, answering to the question --

"What is the vertex of the graph of f(x) = |x - 5| - 6?"

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True

In a symmetrically shaped distribution of scores, regardless of whether it has one mode or two modes, the mean value tends to be similar to the median value.

When a distribution is symmetric, it means that the data is evenly distributed around the central point, resulting in a bell-shaped curve. In such cases, the mean, median, and mode are typically close to each other.

The mean is the arithmetic average of all the scores in a distribution, while the median represents the middle value when the scores are arranged in ascending or descending order. In a symmetric distribution, the mean and median are located at the exact center of the distribution.

If the distribution has only one mode, it means that there is one prominent peak or high point in the data. In this case, the mean and median will coincide with the mode and will be similar.

If the distribution has two modes, it means that there are two prominent peaks in the data, but they are symmetrical around the center. Even though there are multiple modes, the mean and median will still be similar and tend to be located between the two modes.

In summary, in symmetrically shaped distributions, regardless of the presence of one or two modes, the mean and median values are expected to be close to each other.

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To solve the equation sin2(t) − 3 sin(t) − 4 = 0 in the interval [0, 2), we can use the substitution u = sin(t). This gives us the quadratic equation u2 − 3u − 4 = 0.

Factoring this equation, we get (u − 4)(u + 1) = 0. Solving for u, we have u = 4 or u = -1. However, since the interval is [0, 2), we need to check which of these solutions fall within this range. For u = 4, there are no corresponding values of t within the interval [0, 2), so we discard this solution. For u = -1, we can solve for t using the inverse sine function, giving us t = (7π/6) or t = (11π/6). Therefore, the solutions in the interval [0, 2) are (7π/6, 11π/6).

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The units such as meters, square meters, and cubic meters may be used to describe length, area, and volume

A unit of measurement is a standard quantity of a physical quantity that has been agreed upon and approved by a convention or law.

Units of measurement are widely utilized in the natural sciences, such as physics and chemistry, as well as in engineering and other applied sciences in order to quantify physical quantities such as length, time, mass, energy, and so on.

They are defined as a specific quantity used to specify a physical quantity and accepted by convention or law.

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Total amount that Subway collect in franchise fees  = $2,189,250,000

Total number of subway franchisees = 42,000

Average annual store revenue           = $417,000

Total paying percentage of franchisees               = 12.5%

12.5% of average revenue = (417000×12.5)÷100

                                              = $52,125

Total subway collection in franchise fee= total number of franchisees×amount of fees per franchisees

                                         = 42,000×52,125

                                         = $2,189,250,000

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Since subways has about 42000 franchisees and about $417000 average revenue is earned. Therefore, the total amount that Subway collect in franchise fees is $2,189,250,000.

Subways Franchise operate 16 submarine sandwich shop and they expanded quickly with its long time slogan "East Fresh".

Franchisor gives a franchisee the authority to do business in the franchisor's trade name using its business system it is called franchising.

Subways franchises pay 12.5% every week (gross sales minus the sales tax), 8% goes toward the franchise royalties and 45% gores towards advertising.

The company has the lowest start-up costs compared to many other fast food franchises but does take more royalty and advertising money.

The franchise fee:

Now, according to the question:

Total number of subway franchisees = 42,000

Average annual store revenue = $417,000

Total paying percentage of franchisees = 12.5%

∴ At 12.5% of average revenue = (417000 × 12.5) ÷ 100

                                                    = $52,125

Total subway collection in franchise fee

= total number of franchisees × amount of fees per franchises

= 42,000×52,125

= $2,189,250,000

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A cross-sectional effect diagram, also known as an axial force-shear force-bending moment diagram or simply an internal force diagram, is a graphical representation that shows the distribution of internal forces (axial force, shear force, and bending moment) along the length of a structural member, such as a beam or column.

To draw the cross-sectional effect diagrams for the beam whose loading condition is given in the figure, we need to follow these steps:

Step 1: Identify the type of loadingFor this question, the loading conditions are {N}, {T}, {M}. So, the loading types are axial force, shear force, and bending moment.

Step 2: Draw the cross-sectional diagram of the beam. We need to draw the diagram of the cross-section of the beam in the direction of the forces acting on the beam. In this case, it will be a rectangular beam.

Step 3: Draw the effect diagrams After drawing the cross-sectional diagram, we need to draw the effect diagrams for each loading condition.

The effect diagrams are as follows: 1. Axial force diagram (N):In this case, the axial force is positive (+) which means it is a tensile force. 2. Shear force diagram (T):The shear force is negative (-) from x = 0 to x = 1, which means the shear force is acting downward. It is zero at x = 1 and then becomes positive (+) from x = 1 to x = 2, which means the shear force is acting upward. 3. Bending moment diagram (M):The bending moment is zero at x = 0, becomes negative (-) from x = 0 to x = 1, reaches a minimum at x = 1, and then becomes positive (+) from x = 1 to x = 2.

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The type of sampling described, where the researchers intentionally select a sample with 50% straight and 50% LGBTQ+ respondents, is known as "disproportionate stratified sampling."

A. Disproportionate stratified sampling involves dividing the population into different groups (strata) based on certain characteristics and then intentionally selecting a different proportion of individuals from each group. In this case, the researchers are dividing the population based on sexual orientation (straight and LGBTQ+) and selecting an equal proportion from each group.

B. Availability sampling (also known as convenience sampling) refers to selecting individuals who are readily available or convenient for the researcher. This type of sampling does not guarantee representative or unbiased results and may introduce bias into the study.

C. Snowball sampling involves starting with a small number of participants who meet certain criteria and then asking them to refer other potential participants who also meet the criteria. This sampling method is often used when the target population is difficult to reach or identify, such as in hidden or marginalized communities.

D. Simple random sampling involves randomly selecting individuals from the population without any specific stratification or deliberate imbalance. Each individual in the population has an equal chance of being selected.

Given the description provided, the sampling method of intentionally selecting 50% straight and 50% LGBTQ+ respondents represents disproportionate stratified sampling.

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Step-by-step explanation:

Or the other way around

(0,3)

(1,3)

(2,1)

(3,3)

by the way this is a function because all the outputs have one input. Nothing is being shared.

The first figure has a 629.86 square metre area.

The sum of a rectangle's length and breadth gives the area of the rectangle.

Length times width equals the rectangle's area.

To determine the area of the first figure, we must first calculate the combined areas of the rectangle and the semicircles.

This gives us the figure's overall area.

The rectangle measures 28 metres in length. We can observe that the rectangle's length is divided in half by the semicircle's diameter.

Thus, D = 14 m and radius = 7 m.

Area of the 2 semicircles is equal to

 = 7x7x7 = 49 square metres

The rectangle's width is equal to 24 minus r.

= 24 - 7 = 17m

Length times width equals the rectangle's area.

28 times 17 is 476 square metres.

The total size is 629.86 square metres.

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A ' (4,0)

B ' (6,3)

C ' (3,4)

================================================

Explanation:

I'm assuming the center of dilation is the origin.

If so, then we multiply the scale factor 1/4 = 0.25 by each of the coordinates of the three points.

Point A(16,0) will move to A ' (4,0) since

Point B(24,12) will move to B ' (6,3) since

We have enough information to see that choice B is the final answer

If you wanted to keep going, then point C(12,16) will move to C ' (3,4) for similar reasoning/steps as the previous two points.

The resulting image triangle A'B'C' will have its side lengths 1/4 of that compared to the side lengths of the preimage triangle ABC.

The scale factor k is such that 0 < k < 1, which indicates the image will be smaller compared to the preimage. If k > 1, then the image would have been larger than the preimage.

Answer:

The volume of the largest cylinder is 3.14(10)^2(30) = 9424.78cm^3

The volume of the smallest cylinder is 3141.59cm^3

The volume of the medium cylinder is 6282.67 cm^3

Step-by-step explanation:

the equation for a cylinder's volume is pi(r)^2(height)

The volume of the largest cylinder is 3.14(10)^2(30) = 9424.78cm^3 (remember the units!)

The volume of t he smallest cylinder is 1/3 the largest or: 9424.78/3 = 3141.59cm^3 (remember the units!)

The volume of the medium cylinder is 2/3 the largest or 9424.78(2/3) = 6282.67 cm^3

Answer:

The new ratio of the history to the maths to the science books would be 22:43:55. With the addition of 20 history, 40 maths, and 10 science books, the total number of books in the library is now 570. The new ratio of the history to the maths to the science books is therefore 22:43:55.

Step-by-step explanation:

The Pearson correlation coefficient between the scores on the first and final exams is approximately -0.165. This indicates a weak negative correlation between the two variables.

What is correlation coefficient?

To find the Pearson correlation coefficient between the scores on the first and final exams, we need to use the formula:

r = ΣZxZy / √(ΣZx² * ΣZy²)

Using the given data, we can calculate the values of Zx and Zy (standardized scores for first and final exam scores, respectively) and then calculate r as follows:

ΣZxZy = (0.481)(-0.345) + (-0.102)(0.366) + (1.720)(-0.548) + (-0.904)(-0.548) + (0.189)(-0.041) + (-0.612)(-0.650) + (0.991)(0.670) + (1.280)(1.280) + (-1.767)(-0.410) = -0.023

ΣZx² = 0.723 + 0.011 + 2.958 + 0.818 + 0.036 + 0.374 + 0.982 + 1.638 + 3.127 = 10.667

ΣZy² = 0.119 + 0.135 + 0.302 + 0.302 + 0.002 + 0.423 + 0.449 + 1.638 + 3.125 = 6.695

r = -0.023 / √(10.667 * 6.695) = -0.165

Therefore, the Pearson correlation coefficient between the scores on the first and final exams is approximately -0.165. This indicates a weak negative correlation between the two variables.

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The area between z=1.1 and z=2.1 is approximately 0.982 - 0.864 = 0.118, rounded to three decimal places.

To find the area below z=1.04 for an Upper N(0,1) density, you will need to use the standard normal distribution table or a calculator with a z-table function. Here are the steps:

1. Locate the value of z=1.04 in the table or use the calculator's function.
2. Find the corresponding area value (which represents the probability or percentage of values below z=1.04).

The area below z=1.04 is approximately 0.851, rounded to three decimal places.

(b) To find the area above z=-1.4 for an Upper N(0,1) density, follow these steps:

1. Locate the value of z=-1.4 in the table or use the calculator's function.
2. Find the corresponding area value.
3. Since we need the area above z=-1.4, subtract the area value found in step 2 from 1.

The area above z=-1.4 is approximately 1 - 0.0808 = 0.919, rounded to three decimal places.

(c) To find the area between z=1.1 and z=2.1 for an Upper N(0,1) density, follow these steps:

1. Locate the values of z=1.1 and z=2.1 in the table or use the calculator's function.
2. Find the corresponding area values for both z=1.1 and z=2.1.
3. Subtract the area value of z=1.1 from the area value of z=2.1 to find the area between them.

The area between z=1.1 and z=2.1 is approximately 0.982 - 0.864 = 0.118, rounded to three decimal places.

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Answer: A., D., and E.

Step-by-step explanation: On Edge!!

The given information none of the statements about triangle LMN confirmed as true.

Based on the given options, "Check all that apply," I'll evaluate each statement about triangle LMN:

The triangle is scalene: A scalene triangle is a triangle with three unequal side lengths. Since no information is provided about the side lengths of triangle LMN,  determine if it is scalene. Thus, it cannot be confirmed as true.

The triangle is equilateral: An equilateral triangle is a triangle with three equal side lengths. Without any information about the side lengths of triangle LMN, determine if it is equilateral. Thus, it cannot be confirmed as true.

The triangle is isosceles: An isosceles triangle is a triangle with at least two equal side lengths. Without any information about the side lengths of triangle LMN,  determine if it is isosceles. Thus, it cannot be confirmed as true.

The triangle is a right triangle: A right triangle is a triangle with one right angle (90 degrees). No information is given about the angles of triangle LMN, so determine if it has a right angle. Thus, it cannot be confirmed as true.

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A function g(x) is defined as follows:G(x) = Start Layout enlarged left-brace 1st Row 1st column 2 3 x, 2nd column 0 less-than-or-equal-to x less-than 4 2nd Row 1st column 0. 5 x 10, 2nd column 4 less-than-or-equal-to x less-than 8 3rd Row 1st column 16, 2nd column x greater-than-or-equal-to 8 .

The correct option is option (d)

EndLayoutThe given function g(x) can be graphed as follows:Graph of g(x)We can clearly see that for x equals 4, we have the inequality:4 < 8Hence, g(4) = 16. Therefore, the value of g(4) is 16. Hence, the correct option is option (d) 16.Note: If there is a need to find the value of g(x) at any other value of x, just follow the same procedure as above. Just plug in the value of x in the inequality in which it lies, and the result will be the value of g(x).

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Answer:

108 pi inches cubed

Step-by-step explanation:

The volume of a cylinder is base area times volume. Since we have our base area of 12 pi, and our height of 9, we have the are as 12* 9 = 108 pi inches cubed. Thus, the answer is D.

Answer:

108

Step-by-step explanation:

Given :

The original price of the candy = $10

Using an exponential function, it is found that:

a) \(N(t) = 75(0.5)^{\frac{t}{3.8}}\)

b) 37.5 grams of the gas remains after 3.8 days.

c) The amount remaining will be of 10 grams after approximately 11 days.

A decaying exponential function is modeled by:

\(A(t) = A(0)(1 - r)^t\)

In which:

Item a:

We start with 75 grams, and then work with a half-life of 3.8 days, hence the amount after t daus is given by:

\(N(t) = 75(0.5)^{\frac{t}{3.8}}\)

Item b:

This is N when t = 3.8, hence:

\(N(t) = 75(0.5)^{\frac{3.8}{3.8}} = 37.5\)

37.5 grams of the gas remains after 3.8 days.

Item c:

This is t for which N(t) = 10, hence:

\(N(t) = 75(0.5)^{\frac{t}{3.8}}\)

\(10 = 75(0.5)^{\frac{t}{3.8}}\)

\((0.5)^{\frac{t}{3.8}} = \frac{10}{75}\)

\(\log{(0.5)^{\frac{t}{3.8}}} = \log{\frac{10}{75}}\)

\(\frac{t}{3.8}\log{0.5} = \log{\frac{10}{75}}\)

\(t = 3.8\frac{\log{\frac{10}{75}}}{\log{0.5}}\)

\(t \approx 11\)

The amount remaining will be of 10 grams after approximately 11 days.

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Answer:

x = 59/12

Step-by-step explanation:

4x + 1/3 = 20

4x = 20 - 1/3

12x/3 = 60/3 - 1/3

12x = 60 - 1

12x = 59

x = 59/12

Check:

4*59/12 + 1/3 = 20

236/12 + 4/12 = 20

240/12 = 20

Answer:

The total population = 9514.2857143 people.

Step-by-step explanation:

Let the total population be represented by X

In the question, we are told that,1332 people are under the age of 20 and this value = 14% of the total population.

Therefore, the total population is calculated as

14% of X = 1332

14/100 × X = 1332

14X/100 = 1332

Cross Multiply

14X = 1332 × 100

X = 1332 × 100/14

X = 9514.2857143

Therefore, the total population = 9514.2857143 people.

The male long jumper's jump, which ranked in the 75th percentile, was approximately 272.436 inches long.

To find the length of the male long jumper's jump at the 75th percentile, we can use the concept of z-scores and the standard normal distribution.

The 75th percentile corresponds to a z-score of 0.674. Using this z-score, we can calculate the distance of the jump by multiplying it by the standard deviation and adding it to the mean:

Distance = (z-score * standard deviation) + mean

Distance = (0.674 * 14) + 263

Distance ≈ 9.436 + 263

Distance ≈ 272.436

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Answer:

11.8 units

Step-by-step explanation:

The circle equation is given as:

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2Where

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2r

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we have

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we haver^2 = 35

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we haver^2 = 35Take the square root of both sides

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we haver^2 = 35Take the square root of both sidesr = 5.9

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we haver^2 = 35Take the square root of both sidesr = 5.9Multiply by 2

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we haver^2 = 35Take the square root of both sidesr = 5.9Multiply by 22r = 11.8

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we haver^2 = 35Take the square root of both sidesr = 5.9Multiply by 22r = 11.8Hence, the diameter of the circle is 11.8 units

Answer: 8,9.

Step-by-step explanation:

\((x-2)^2+(y+6)^2=20\\Circle \ equation\\\boxed {(x-a)^2+(y-b)^2=r^2}\\r^2=20\\r*r=\sqrt{20}*\sqrt{20}\\ r=\sqrt{20}\\ r=\sqrt{4*5}\\ r=2\sqrt{5} \\ D=2r\\D=2*2\sqrt{5}\\ D=4\sqrt{5}\\ D\approx8,9.\)

To maximize the expected value (E[W]) in the given game, the optimal strategy is to stop rolling the die and accept the value of X if X is greater than the expected value of Y.

Otherwise, roll the die again for the second time and accept the value of Y. The maximum E[W] achievable using this strategy is the maximum between the expected value of X and the expected value of Y.

To determine the optimal strategy, we need to compare the expected values of X and Y. Since the die is fair, each face has an equal probability of 1/6. Thus, the expected value of X is E[X] = (1+2+3+4+5+6)/6 = 3.5.

If we choose to roll the die for the second time, we have to consider all possible outcomes. The expected value of Y can be calculated by averaging the values from 1 to 6 with each having a probability of 1/6. Therefore, E[Y] = (1+2+3+4+5+6)/6 = 3.5.

Now, to maximize E[W], we compare E[X] and E[Y]. If E[X] > E[Y], then it is optimal to stop the game and accept the value of X. If E[X] ≤ E[Y], then it is optimal to roll the die for the second time and accept the value of Y.

Since E[X] = E[Y] = 3.5, the strategy is indifferent between stopping the game or rolling the die again. Thus, the maximum E[W] achievable is 3.5, which is obtained by either accepting X or rolling for Y.

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