The distribution of weights of female college cross country runners is approximately normal width mean 122 pounds and standard deviation 8 pounds. Which of the following is closest to the percent of the runners who’s way between 114 pounds in 138 pounds 

Answer:

3/2x

Step-by-step explanation:

when writing an equation for a graph its change in y over change in x

it goes up 3 over 2 and it's a positive slope

so the answer is f

a)There are 15,120 agent arrangements where order is important.b)The number of agent arrangements where order is not important is 1.

(a) When order is important, we are looking for the number of permutations. To calculate the number of agent arrangements for the 5 new customers, we use the formula:

nPr = n! / (n-r)!

where n is the number of agents (9), r is the number of customers (5), and ! represents the factorial.

9P5 = 9! / (9-5)!
= 9! / 4!
= 15,120

There are 15,120 agent arrangements where order is important.

(b) When order is not important, we are looking for the number of combinations. In this case, since each customer must be assigned an agent, there's only one way to distribute the agents, as all customers will receive service regardless of agent order. Therefore, the number of agent arrangements where order is not important is 1.

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Answer:

(1/4)^2

Step-by-step explanation:

Which expression is equivalent to (4^3)^2 ⋅ 4^−8?

(4^3)^2 * 4^-8 =

(4)^6 * (1/4)^-8 =

(1/4)^2 =   your answer

1/4 * 1/4 =

1/16     solved

The expression (4^3)^2 ⋅ 4^−8 simplifies to 4^−2 or 1/16 using the laws of exponents.

The expression (4^3)^2 ⋅ 4^−8 can be simplified by using the laws of exponents. According to these laws, when you raise a power to a power (as in (4^3)^2), you multiply the exponents. Therefore, the equivalent expression for (4^3)^2 is 4^6. For 4^−8, the negative exponent means that this is 'one over' the base raised to the positive of that exponent, which is 1/4^8.

So, the equivalent expression for the whole thing is 4^6 * 1/4^8 or 4^−2, which also equals to 1/4^2 or 1/16.

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The weighted average estimator Yˉω​ is considered to estimate the expectation μ. To be an unbiased estimator, the weights ω1​, ω2​, and ω3​ should satisfy the condition that their sum is equal to 1.

(a) To calculate E[Yˉω​], we can take the expectation inside the summation:

E[Yˉω​] = E[ω1​Y1​ + ω2​Y2​ + ω3​Y3​]

= ω1​E[Y1​] + ω2​E[Y2​] + ω3​E[Y3​]

= ω1​μ + ω2​μ + ω3​μ

= μ(ω1​ + ω2​ + ω3​)

For Yˉω​ to be an unbiased estimator, its expectation should be equal to the parameter being estimated, which is μ. Therefore, we have the condition ω1​ + ω2​ + ω3​ = 1.

(b) To calculate V[Yˉω​], we need to determine the variance inside the weighted average:

V[Yˉω​] = V[ω1​Y1​ + ω2​Y2​ + ω3​Y3​]

= ω1​^2V[Y1​] + ω2​^2V[Y2​] + ω3​^2V[Y3​]

= ω1​^2σ^2 + ω2​^2σ^2 + ω3​^2σ^2

= σ^2(ω1​^2 + ω2​^2 + ω3​^2)

To minimize the variance V[Yˉω​], we need to find the weights ω1​, ω2​, and ω3​ that minimize the expression ω1​^2 + ω2​^2 + ω3​^2, while still satisfying the condition ω1​ + ω2​ + ω3​ = 1. One approach to find the minimum variance is by using calculus techniques, such as Lagrange multipliers, to optimize the expression under the constraint. Solving this optimization problem will yield the specific weights that minimize the variance of Yˉω​, and the justification lies in the mathematical derivation of the optimal solution.

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a) The Beta distribution that would be used to model p, the true defect rate is Beta(2, 8).

(b) Using the distribution P(.15 ≤p ≤.25) is 0.086.

(c) The new Beta distribution that you would use to model p is Beta(3, 17).

(d) Using the new distribution P(.15 ≤p ≤.25) is 0.004.

(a) The Beta distribution that we would use to model p is Beta(α, β), where α is the number of defective parts found in the sample and β is the number of working parts found in the sample. In this case, α = 2 and β = 8, so the Beta distribution is Beta(2, 8).

(b) Using the Beta(2, 8) distribution, we want to find P(.15 ≤p ≤.25). This is equivalent to finding the probability that p falls between 0.15 and 0.25. We can use a Beta distribution calculator or software to find this probability, which is approximately 0.086.

(c) To find the new Beta distribution, we need to combine the two samples. We now have a total of 3 defective parts and 17 working parts. Therefore, the new Beta distribution is Beta(3, 17).

(d) Using the Beta(3, 17) distribution, we want to find P(.15 ≤p ≤.25). Again, we can use a Beta distribution calculator or software to find this probability, which is approximately 0.004. This probability is smaller than the one we found in part (b) because the second sample had a lower proportion of defective parts, which reduced our uncertainty about the true defect rate.

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The classification technique that is nonparametric and does not rely on any underlying statistical model is regression trees via recursive partitioning. This method is based on splitting the data into smaller subsets and constructing decision trees to predict the target variable.

Unlike parametric methods like multinomial logistic regression and linear/quadratic discriminant analysis, regression trees do not make assumptions about the distribution of the data. Backward elimination is a technique used to select the most important variables for a statistical model by removing variables one at a time based on their p-value.

While it can be used with both parametric and nonparametric methods, it is not a classification technique in itself. In summary, if you want a nonparametric classification technique that does not rely on underlying statistical assumptions, regression trees via recursive partitioning are a good choice.

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The speed over the given path is √(9+(7/())^2+(5/(())^2) at t=1, where the notation "()" represents the parameterization of the path.

To find the speed over the given path, we need to first take the derivative of the parameterization with respect to t. We get: ()'=<0, 7/(), 5/(())^2>. Then, we can evaluate this derivative at t=1 to get ()'(1)=<0,7,5>. The speed at t=1 is given by the magnitude of this vector, which is √(0^2+7^2+5^2)=√74. Therefore, the speed over the given path at t=1 is √74.

In summary, to find the speed over the given path at t=1, we first take the derivative of the parameterization with respect to t and evaluate it at t=1 to get the velocity vector. Then, we find the magnitude of this vector to get the speed, which is √74.

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You should invest approximately 4,225.95 initially to have 12,000 after nine years at an annual interest rate of 11% compounded continuously.

The formula for the future value of an investment with continuous compounding is:

[tex]FV = PV \times e^{(r\times t)[/tex]

where PV is the present value (initial investment), r is the annual interest rate in decimal form, t is the time period in years, and e is the mathematical constant approximately equal to 2.71828.

In this problem, we want to find PV, so we can rearrange the formula to solve for it:

[tex]PV = FV / e^{(r\times t)[/tex]

Substituting the given values:

[tex]PV = 12000 / e^{(0.11 \times 9)[/tex]

Using a calculator:

PV ≈ 4225.95

Therefore, you should invest approximately 4,225.95 initially to have 12,000 after nine years at an annual interest rate of 11% compounded continuously.

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If a survey is taken at a movie theater in Winterville. The first 150 people who entered the theater were asked about their favorite type of movie. The  true about this situation is: C. The population is the total number of people who go to the movie theater, and the sample is the first 150 people at the theater.

In this situation, the survey was taken of the first 150 people who entered the movie theater. Therefore, the sample is the group of 150 people who were surveyed. The population of interest is the total number of people who go to the movie theater, as these are the individuals who could potentially have a favorite type of movie.

However, it is not practical to survey every person who goes to the movie theater, so a sample of 150 people was taken from the population.

Therefore, option C is the correct answer.

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The correct answer is: Seahawks; they have a larger median value of 23 inches.

To determine which team has the largest overall size hat for their players, we need to compare the central tendency measures of the two sets of data.

The best measure of center to use in this case is the median, which represents the middle value of the data when arranged in ascending or descending order.
Looking at the two tables, we can see that the median value for the Pelicans is 22 inches, while the median value for the Seahawks is 23 inches.

Therefore, the Seahawks have a larger median hat size and can be considered to have the largest overall size hat for their players.
The median is the best measure of center to compare in this case, as it represents the middle value and is less affected by outliers or extreme values.

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The latest start time of Activity A3 is 15 weeks.

We have the information from the question is:

We know that activity A3 could only be started after the completion of activity A1 and A2. The activity A2 can only be started after activity A1 is finished. Hence, to find the latest completion time, we need to find the time spend on both activity A1 and A2.

However, if the activities need to be performed sequentially (i.e., A1, followed by A2, and then A3):

=> Complete Activity A1, which takes 5 weeks.

=> Complete Activity A2, which takes 8 weeks. (Total time: 5 + 8 = 13 weeks)

=> Start and complete Activity A3, which takes 2 weeks. (Total time: 13 + 2 = 15 weeks)

In this case, the earliest completion time of Activity A3 is 15 weeks.

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The numerical value of x in the supplementary angle is 15.

Supplementary angles simply refer to the pair of angles that always sum up to 180°.

Given that; angle ZJ and ZK are supplementary angles:

Since the two angles are supplementary angles, their sum will equal 180 degrees.

Hence:

Angle ZJ + Angle ZK = 180

Plug in the values and solve for x

9x + 45 = 180

Subtract 45 from both sides

9x + 45 - 45 = 180 - 45

9x = 180 - 45

9x = 135

Divide both sides by 9

x = 135/9

x = 15

Therefore, x has a value of 15.

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We need to compute the work done by the force field F~ along the given path. The work done by the force field F~ along the curve C is 2e^3 - e.

Recall that the work done by a force field F~ along a curve C is given by the line integral:

∫CF~ · dr~

where dr~ is a vector tangent to C.

First, we parameterize the curve C using a single variable t:

r~(t) = (t^2-1)i + tj

with 1 ≤ t ≤ 2.

Next, we compute the dot product F~ · dr~:

F~ · dr~ = (x^2yexi + xye^xj) · (2t~i + ~j) = (2t^2e^t^2-1 + te^t^2) dt

Hence, the line integral becomes:

∫CF~ · dr~ = ∫1^2 (2t^2e^t^2-1 + te^t^2) dt

We can evaluate this integral using integration by parts twice, with u = t and v' = e^(t^2-1), and then u = t^2 and v' = e^(t^2-1).

The final result is:

∫CF~ · dr~ = [te^(t^2-1)]_1^2 = 2e^3 - e

Therefore, the work done by the force field F~ along the curve C is 2e^3 - e.

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I think the area is 398.48m²

For the two triangles, the appropriate option is D) The triangles aren't similar.

When on comparing the properties of two triangles and a common relations hold, then the triangles are said to be similar. The sides of the similar triangles will have a representative fraction.

Representative fraction is the ration that shows how the corresponding sides of two triangles relate.

In the given triangle on comparing their sides, we have;

KP/ KN = KL/ KM

12/ 15 = 8/ 10

But,

12/ 15 ≠ 8/ 10

Therefore the triangles are not similar. Thus option D) The triangles aren't similar.

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Answer:

Step-by-step explanation:

(-2 , 1)

Its clear from the figure itself .

To find the function for the radius, we know that the rate of change of the radius is given as 3.3 feet per second. We can integrate this to get the function for the radius:

∫ dr/dt dt = ∫ 3.3 dt

r = 3.3t + C

We know that when t = 0, r = 0. So, we can solve for C as follows:

0 = 3.3(0) + C

C = 0

Therefore, the function for the radius is:

r(t) = 3.3t

To find the function for the area of the ripple in terms of r, we use the formula for the area of a circle:

A = πr^2

Substituting r = 3.3t, we get:

A(r) = π(3.3t)^2

A(r) = 34.56πt^2

Finally, to find (A o r)(t), we substitute r(t) into A(r) and get:

(A o r)(t) = A(r(t))

(A o r)(t) = A(3.3t)

(A o r)(t) = 34.56πt^2

Since h is not the zero transformation, its range must be all of R1. Therefore, the rank of h is 1.

To find the null space of the linear transformation h, we need to find all vectors x = (x1, x2, x3) in R3 such that h(x) = 0. We have:

h(x) = 3x1 - x2 - x3

Setting h(x) = 0, we get:

3x1 - x2 - x3 = 0

This is a system of equations in three variables. We can solve for x3 in terms of x1 and x2 to obtain:

x3 = 3x1 - x2

So any vector x in the null space of h must have the form:

x = (x1, x2, 3x1 - x2)

We can rewrite this vector as:

x = x1(1, 0, 3) + x2(0, -1, -1)

Therefore, a basis for the null space of h is the set { (1, 0, 3), (0, -1, -1) }.

To find the rank of h, we need to determine the dimension of the range of h. Since h is a linear transformation from R3 to R1, its range is a subspace of R1. The only subspaces of R1 are {0} and R1 itself. Since h is not the zero transformation, its range must be all of R1. Therefore, the rank of h is 1.

Geometrically, the null space of h is a plane in R3. This plane contains the origin and is parallel to the vector (1, 0, 3). The vector (0, -1, -1) is perpendicular to this plane.

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Therefore, The value of E°cell for the reaction that occurs when current is drawn from this cell at standard conditions is 1.20 V.

Explanation: The given cell is a galvanic cell. The standard cell potential for this cell can be calculated using the Nernst equation.
Ecell = E°cell - (0.0592/n) log Q
Here, n = number of electrons transferred = 2
At standard conditions, Q = 1, as all species are at their standard states.
Thus,
Ecell = E°cell - (0.0592/2) log 1
Ecell = E°cell
The standard cell potential can be calculated using standard reduction potentials for the given half-reactions.
Zn2+(aq) + 2e- → Zn(s)   E° = -0.76 V
Fe2+(aq) + 2e- → Fe(s)    E° = -0.44 V
E°cell = E°reduction (cathode) - E°reduction (anode)
E°cell = 0.44 - (-0.76) = 1.20 V

Therefore, The value of E°cell for the reaction that occurs when current is drawn from this cell at standard conditions is 1.20 V.

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Answer:

72 percent

Step-by-step explanation:

There is a typo in the problem statement, as two restaurants are mentioned but only one is named. I will assume it was intended to say that 18 employees want to go to Restaurant A and 7 employees want to go to Restaurant B.

To find the fraction of employees who want to go to Restaurant A, we can divide the number of employees who want to go to Restaurant A by the total number of employees:

Fraction = Number of employees who want to go to Restaurant A / Total number of employees

Fraction = 18 / 25

So the fraction of employees who want to go to Restaurant A is 18/25.

To find the percentage of employees who want to go to Restaurant A, we can multiply the fraction by 100:

Percentage = Fraction * 100

Percentage = 18/25 * 100

Percentage = 72

So 72% of the employees want to go to Restaurant A.

The graphical representation that would be best to display the data is given as follows:

Histogram.

An histogram is a graph that shows the number of times each element of x was observed.

The four types of products are given as follows:

Each of these item would represent a bin, and the values of each bin are given as follows:

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The surface area of the pyramid is approximately 197.15 square inches.

To find the surface area of a pyramid, we need to add the area of the base to the area of the lateral faces. For a triangular pyramid, we can break down the lateral faces into three triangles and then find the area of each triangle.

First, we need to find the area of the equilateral triangle base. Since the legs of the equilateral triangle are all 10 inches long, the altitude of the triangle can be found using the Pythagorean theorem:

a² + (8.7)² = 10²

a² = 100 - (8.7)²

a ≈ 6.43

Therefore, the area of the base is:

A₁ = (1/2)bh = (1/2)(10)(6.43) = 32.15 square inches

Next, we need to find the area of each of the three lateral faces. Each of these faces is a triangle with base equal to 10 inches (one of the legs of the equilateral triangle) and height equal to the slant height of the pyramid, which is 11 inches. Therefore, the area of each of these triangles is:

A₂ = (1/2)bh = (1/2)(10)(11) = 55 square inches

Finally, we can add up the areas of the base and the three lateral faces to get the total surface area:

A = A₁ + 3A₂ = 32.15 + 3(55) = 197.15 square inches

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The equation for the tangent plane at point P_0(2,1,2) on the surface 2x^2 + 4y^2 + 3z^2 = 24 is 5x + 4y + 3z = 20. The equation for the normal line at the point P_0(2,1,2) is parametrically represented by x = 2 + 5t, y = 1 + 4t, z = 2 + 3t.

To find the equation for the tangent plane, we first take the partial derivatives of the given surface equation with respect to x, y, and z, and evaluate them at point P_0(2,1,2). Then, we use these values and the point to write the equation for the tangent plane in the form Ax + By + Cz = D.  To find the equation for the normal line, we use the gradient vector of the surface equation at point P_0(2,1,2), which is orthogonal to the tangent plane at that point. This gradient vector provides the direction of the normal line, and we can use the point-slope form to write the equation for the line in terms of the given point and the direction vector.

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The side length of BD is 17.14 and the length of side of DC is 12.86.

The side length of BD is calculated by subtracting the side length DC from BC as shown below;

Apply congruence theorem on the two triangles ABC and ADC as follows;

Two triangles are similar if their corresponding angles are congruent, and their corresponding sides are in proportion.

From the given diagram, triangle ABC is similar to triangle ADC, and are represented as follows;

ABC ≅ ADC

BC/BA = DC/AC

30/28 = DC/12

DC = 12(30/28)

DC = 12.86

Length BD = 30 - 12.86 = 17.14

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To solve without a calculator, we can use the identity cos(180° - θ) = -cosθ, which means that:

cos 20° = cos(180° - 20°) = -cos 160°

Substituting this into the original equation gives:

-3(-cos 160°) - 6 = 19 cos θ

Simplifying this expression gives:

3 cos 160° - 6 = 19 cos θ

Using the fact that cos 160° = cos(-20°), we can rewrite this as:

3 cos (-20°) - 6 = 19 cos θ

Now, using the identity cos(-θ) = cosθ, we get:

3 cos 20° - 6 = 19 cos θ

Adding 6 to both sides and dividing by 19, we obtain:

cos θ = (-3 cos 20° + 6)/19

Using a table of trigonometric values, we can find that cos 20° is approximately 0.9397. Substituting this value into the equation above, we get:

cos θ ≈ (-3 × 0.9397 + 6)/19

cos θ ≈ -0.628

Since -1 ≤ cos θ ≤ 1, there are no angles between 0° and 360° that satisfy the equation to the nearest 10th of a degree. Therefore, the answer is that there are no solutions.

There were 29 individuals in the study. The sample size can be calculated by adding 1 to the degrees of freedom (df) represented in the t-statistic.

In this case, df = 28, so 28 + 1 = 29. The report should state that p < .05, which means that the difference between treatments is statistically significant at the 5% level of significance. This indicates that there is less than a 5% chance of observing such a large difference between treatments by chance alone.

However, it is important to note that statistical significance does not necessarily imply practical significance, and the effect size should also be considered when interpreting the results of the study.

Additionally, the report should provide more information about the study design, measures, and variables to give readers a better understanding of the findings and their implications.

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The length of the line drawn between points A and B is 13.454 unit length. Thus, the option C is the most appropriate answer to the given question.

The length of the line AB is described by the distance formula:

d = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²

Coordinates of point A = (0, 10)

Coordinates of point B = (9, 0)

x₁ = 0

x₂ = 9

y₁ = 10

y₂ = 0

d = √ (9 - 0)² + (0 - 10)²

d = √ 81 + 100

d = √ 181

d = 13.45 unit length

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The bottom right graph shows the line of best fit for the data.

For a data-set, the definition of a residual is that it is the difference of the actual output value by the predicted output value, that is:

Residual = Observed - Predicted.

Hence the graph of the line of best fit should have the smallest possible residual values, meaning that the points on the scatter plot are the closest possible to the line.

For this problem, we have that the bottom right graph has the smaller residuals, hence it shows the line of best fit for the data.

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The constant of proportionality is 1.25

The variables of hours worked, x, and wages earned y are proportional

when they can be expressed in the form;

y = c·x

Such that we have; Δy = c·Δx

Where;

Δy = Change in the y variable

Δx = Change in x variable

Therefore;

C = Δy / Δx

The constant of proportionality is therefore given by the rate of change of the graph which is found as follows;

C = 1/2 ÷ 2/5

C = 5/4

C = 1.25

Hence the constant of proportionality is 1.25.

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Answer:

1654 yd²

Step-by-step explanation:

Break the shape up into a rectangle and 2 triangles, find the area of each, then add together to get the total area.

A-rectangle = l x w = 45 x 25 = 1125

A-triangle1 = 1/2bh = 1/2(14)(25 + 12) = 259

A-triangle2 = 1/2(45)(12) = 270

Total area = 1125 + 259 + 270 = 1654 yd²