5) What is the surface area of a cone with a diameter 12 meters and a slant height


of 8 meters? Round to the nearest tenth. Use 3. 14 for it. *

The probability that the experiment results in exactly 6 successes is 0.2668.

To calculate the probability of exactly 6 successes in a binomial experiment with p=0.7 and n=7, we can use the binomial probability formula:

P(X = k) = (n choose k) * [tex]p^{k}[/tex] * [tex](1-p)^{n-k}[/tex]

where X is the random variable representing the number of successes, k is the number of successes we're interested in, and n is the total number of trials.

Substituting the values, we get:

P(X = 6) = (7 choose 6) * [tex]0.7^{6}[/tex] * [tex](1-0.7)^{7-6}[/tex]

= 7 * [tex]0.7^{6}[/tex] * [tex]0.3^{1}[/tex]

= 0.266827932

Therefore, the probability of exactly 6 successes in a binomial experiment with p=0.7 and n=7 is approximately 0.2668.

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The  maclaurin series of the function the expression of cn for n ≥2 to

cn = 4(-1)²(n-1)/(5²(2n-1)(2n-1)).

To find the Maclaurin series of the function f(x) = (4x)arctan(5x²2), we first need to find its derivatives:

f'(x) = 4arctan(5x²2) + (4x)(1/(1+(5x²2)))

f''(x) = 40x/(1+(5x²2))²2 + 4/(1+(5x²2))

f'''(x) = (120x²3 + 120x)/(1+(5x²2))^3

f''''(x) = (1200x²4 + 2400x2 - 480)/(1+(5x²2))²4

From the general formula for the Maclaurin series, we have:

cn = (1/n!)fⁿ(0)

So, the coefficients of the Maclaurin series are:

c0 = f(0) = 0

c1 = f'(0) = 4arctan(0) + (4(0))(1/(1+(5(0)²2))) = 0

c2 = f''(0) = 4/(1+(5(0)²2)) = 4

c3 = f'''(0) = 0

c4 = f''''(0) = -480/1 = -480

c5 = 0

and so on...

Therefore, the Maclaurin series for f(x) is:

f(x) = 4x - 480x²4/4

or, in sigma notation:

f(x) = ∑n=0[infinity] ((-1)²n(4²(2n+1))(x²(2n+1)))/((2n+1)(5²(2n+1))))

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The Maclaurin series representation of the function

[tex]\(f(x) = (4x)\arctan(5x^2)\)[/tex]  is:

[tex]\[f(x) = c_0 + c_1x + c_2x^2 + c_3x^3 + \sum_{n=4}^{\infty} c_nx^n\][/tex]

For finding the Maclaurin series of the function [tex]\(f(x) = (4x)\arctan(5x^2)\)[/tex] , we can start by finding the derivatives of \(f(x)\) and evaluating them at (x = 0) to obtain the coefficients [tex]\(c_n\).[/tex]

The Maclaurin series representation of \(f(x)\) will be:

[tex]\[f(x) = \sum_{n=0}^{\infty} c_nx^n\][/tex]

Let's proceed with finding the derivatives and evaluating them at \(x = 0\) to determine the coefficients.

1. First, let's find the derivatives of (f(x)):

[tex]\[f'(x) = 4\arctan(5x^2) + 8x^2\frac{1}{1+(5x^2)^2}\]\[f''(x) = 8\left(\frac{1}{1+(5x^2)^2}\right) + 8x^2\left(\frac{-10x(5x^2)}{(1+(5x^2)^2)^2}\right)\]\[f'''(x) = 8\left(\frac{-10x(5x^2)}{(1+(5x^2)^2)^2}\right) + 8x^2\left(\frac{-10x(5x^2)}{(1+(5x^2)^2)^2}\right) + 48x\left(\frac{1}{1+(5x^2)^2}\right)\][/tex]

2. Now, let's evaluate the derivatives at (x = 0) to determine the coefficients:

[tex]\[f(0) = c_0 \cdot 0^0 = c_0\]\[f'(0) = c_1 \cdot 0^1 = 0\]\[f''(0) = c_2 \cdot 0^2 = 8\]\[f'''(0) = c_3 \cdot 0^3 = 0\][/tex]

From these evaluations, we can determine the coefficients as follows:

[tex]\[c_0 = f(0)\]\[c_1 = \frac{f'(0)}{1!}\]\[c_2 = \frac{f''(0)}{2!}\]\[c_3 = \frac{f'''(0)}{3!}\][/tex]

Therefore, the coefficients for the Maclaurin series of \(f(x)\) are:

[tex]\[c_0 = f(0)\]\[c_1 = 0\]\[c_2 = \frac{8}{2} = 4\]\[c_3 = 0\][/tex]

The Maclaurin series representation of (f(x)) becomes:

[tex]\[f(x) = c_0 + c_1x + c_2x^2 + c_3x^3 + \sum_{n=4}^{\infty} c_nx^n\][/tex]

Substituting the known coefficients:

[tex]\[f(x) = c_0 + 4x^2 + \sum_{n=4}^{\infty} c_nx^n\][/tex]

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a. the population mean customer satisfaction score is greater than 7. b. the alternative hypothesis specifies the direction of the difference (greater than 7).

a. The null hypothesis is that the population mean customer satisfaction score is 7, and the alternative hypothesis is that the population mean customer satisfaction score is greater than 7.

b. This is a one-tail test because the alternative hypothesis specifies the direction of the difference (greater than 7).

c. The sampling distribution of x-bar is approximately normal, centered at the hypothesized mean value of 7, and with a standard deviation of σ/sqrt(n), where σ is the population standard deviation (unknown) and n is the sample size. The spread of the distribution is determined by the standard deviation and the sample size. The x-axis represents the sample mean values and the y-axis represents the probability density.

d. See diagram below:

7                 7.25

             |-----------------|

The shaded area represents the probability of getting a sample mean that is greater than or equal to 7.25.

e. The test statistic is a t-value, calculated as:

t = (x-bar - μ) / (s / sqrt(n))

= (7.25 - 7) / (1.05 / sqrt(60))

= 2.27

f. The critical value is obtained from the t-distribution table with degrees of freedom (df) = n-1 = 59 and a significance level of .025. The critical value is 1.671.

g. See diagram below:

Probability Density

        |--------------*

        |             / \

        |            /   \

        |           /     \

        |          /       \

        |---------/---------*----

                -2.0     2.0    t

                                   |

                                  2.27

                                   |

                                   *

The shaded area represents the probability of getting a t-value that is greater than or equal to 2.27 (the test statistic).

h. The p-value is the probability of getting a sample mean of 7.25 or higher, given that the null hypothesis is true. Using the t-distribution with 59 degrees of freedom, the p-value is approximately .014.

i. The confidence coefficient is 1 - α, where α is the significance level. In this example, the confidence coefficient is .975.

j. If you add the value of the confidence coefficient and the significance level, the sum will equal 1. Therefore, the level of significance in this question is .025.

k. .975 + .025 = 1

m. Based on the calculations, we reject the null hypothesis at the .025 level of significance. This means that there is sufficient evidence to conclude that the population mean customer satisfaction score is greater than 7. Therefore, the company can advertise on its website and in its marketing campaign that it consistently provides an above average customer experience.

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Padma rented the kayak for 3 hours.

We are given the following system of equations:

X6 + Y10 = 60 --- (1)

X and Y are the number of hours Padma rented the bike and kayak respectively.

We want to find the value of Y, which represents the number of hours Padma rented the kayak.

To solve for Y, we can isolate Y in equation (1) as follows:

Y10 = 60 - X6

Y = (60 - X6)/10

Now, we can substitute the given information that Padma rented the bike for 3 hours (X = 3) and solve for Y:

Y = (60 - 3*6)/10 = 3

Therefore, Padma rented the kayak for 3 hours.

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[tex]y = 50(0.95)^t[/tex] represents exponential decay with 5%.

Exponential decay is a mathematical function that describes the decrease in value of a variable over time. The general formula for exponential decay is:

[tex]y = a(1 - r)^t[/tex]

where:

To represent exponential decay with a rate of 5%, we need to set r = 0.05. If the initial value is 50, then the function becomes:

[tex]y = 50(1 - 0.05)^t[/tex]

Simplifying this expression, we get:

[tex]y = 50(0.95)^t[/tex]

This is the function that represents exponential decay with a rate of 5% and an initial value of 50.

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The production cost of seven devices is R24,150.

To calculate the production cost of seven devices, we need to add up the cost of labor, computing components, and subtract any savings from reusable materials, and then multiply the result by 7.

Production cost of 7 devices = (labor cost + component cost - savings) x 7

Substituting the given values, we get:

Production cost of 7 devices = (R4140 + R1035 - R1725) x 7

= (R3450) x 7

= R24,150

Therefore, the production cost of seven devices is R24,150.

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If the columns of matrix A are already orthonormal, then A is an orthogonal matrix.

[tex]Ax = y is x = A^T y.[/tex]

Since A is orthogonal, its inverse is equal to its transpose:[tex]A^T A = I,[/tex] where I is the identity matrix.

Now, to find the least squares solution to Ax = y, we need to solve the equation [tex](A^T A)x = A^T y[/tex].

Substituting[tex]A^T A = I,[/tex] we get[tex]x = A^T y.[/tex]

Since A is orthogonal, its transpose is also orthogonal. Therefore, [tex]A^T A = I[/tex] implies that A^T is also the inverse of A.

Thus, the least squares solution to [tex]Ax = y is x = A^T y.[/tex]

In summary, if the columns of matrix A are already orthonormal, the least squares solution to [tex]Ax = y is x = A^T y.[/tex]

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False. The statement is not true in general. The sign of sin() or cos() depends on the quadrant in which the angle lies.

For example, in the first quadrant, both sin() and cos() are positive, while in the second quadrant, sin() is positive and cos() is negative. In the third quadrant, both sin() and cos() are negative, while in the fourth quadrant, sin() is negative and cos() is positive.

Therefore, we cannot say for certain whether sin() is negative without knowing the quadrant of the angle. Similarly, we cannot say for certain whether cos() is positive or negative without knowing the quadrant of the angle.

However, if we know the quadrant of the angle and the sign of either sin() or cos(), we can determine the sign of the other trigonometric functions (such as cot()) using the appropriate trigonometric identity. For example, if we know that the angle lies in the second quadrant and sin() is positive, then we can use the identity [tex]cos^2() + sin^2() = 1[/tex] to find that cos() is negative, and then use the identity cot() = cos() / sin() to find that cot() is negative.[tex]cos^2() + sin^2() = 1[/tex]

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Based on the information, the rate of change of V is -2.627 m³/s.

Taking the derivative of this equation with respect to time, we get:

P(y)V^(y-1)(dV/dt) + V^y(dP/dt) = 0

We can solve for (dV/dt) by rearranging the terms:

(dV/dt) = -(V^y/P(y)) * (dP/dt)

Plugging in the given values, we get:

(dV/dt) = -[(4 m³)^(7/5)] / [0.8 kg/(m²] * (0.28 k/(m²*s))

Simplifying, we get:

(dV/dt) = -[4^(7/5)] / [0.8] * 0.28

(dV/dt) = -2.627 m³/s

Therefore, the rate of change of V is -2.627 m³/s.

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Statistical significance refers to the likelihood that the association between two variables is not due to chance alone. In other words, it is a measure of the probability that the observed relationship between two variables is real and not just a result of random variation or sampling error.

When analyzing data, researchers often use statistical tests to determine whether there is a significant association between two variables. A p-value is calculated, which represents the probability that the observed relationship between the variables is due to chance. If the p-value is less than a predetermined threshold (usually 0.05), the results are considered statistically significant, and the researchers can conclude that there is a real association between the variables. It's important to note that statistical significance does not necessarily imply practical significance. Just because a relationship is statistically significant does not mean that it is important or meaningful in real-world terms. Additionally, statistical significance only tells us about the strength of the relationship between two variables, not about causation or directionality. Therefore, it is always important to interpret statistical significance in the broader context of the research question and study design.

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The general solution to the given differential equation is y = arcsin(c + 2e⁴ˣ)/2.

What is the differential equation?

A differential equation in mathematics is an equation that connects the derivatives of one or more unknown functions. Applications often involve functions that reflect physical quantities, derivatives that depict the rates at which those values change, and a differential equation that establishes a connection between the three.

Here, we have

Given: dy/dx = 8e⁴ˣ/2cos(2y)

We have to find the general solution to the given differential equation.

First, we will separate the variables and we get

cos(2y)dy = 4e⁴ˣdx

Now, we integrate both sides,

sin(2y)/2 = e⁴ˣ + c

Now, we solve for y and we get

y = arcsin(2c + 2e⁴ˣ)/2

We simplify the constant integration and we get

y = arcsin(c + 2e⁴ˣ)/2

Hence, the general solution to the given differential equation is y = arcsin(c + 2e⁴ˣ)/2.

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Answer:

Equations: 2.00A+0.75S=1109, A+S=937

Step-by-step explanation:

2.00a+0.75s=1109

2a+2s=1874

If you need number of students/adults, solve further by elimination

(but you asked for equations)

the area enclosed by one loop of the curve r = sin(10) is approximately 0.0198 square units.

The given polar curve is:

r = sin(10)

To find the area enclosed by one loop of the curve, we need to evaluate the integral:

[tex]A = (1/2) ∫θ2π [r(θ)]^2 dθ[/tex]

where θ ranges from 0 to 2π.

Substituting the given value of r = sin(10), we get:

[tex]A = (1/2) ∫02π [sin(10θ)]^2 dθ[/tex]

Using the identity[tex]sin^2(θ) = (1/2)(1 - cos(2θ)),[/tex] we can simplify the integral as follows:

A = (1/4) ∫02π (1 - cos(20θ)) dθ

Evaluating this integral, we get:

A = (1/4) [θ - (1/20) sin(20θ)]02π

At the limits of integration, we have:

θ = 2π: A = (1/4) [2π - (1/20) sin(40π)] ≈ 0.0198

θ = 0: A = (1/4) [0 - (1/20) sin(0)] = 0

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The critical t-value for a 95% confidence level and 15 degrees of freedom is approximately 2.131.

Start by determining the desired confidence level. In this case, we are looking for a 95% confidence level.

Identify the degrees of freedom. The degrees of freedom represent the number of independent observations in the data. In this case, we are given 15 degrees of freedom.

Using a t-distribution table, locate the row that corresponds to the degrees of freedom. In this case, find the row for 15 degrees of freedom.

Within that row, locate the column that corresponds to the desired confidence level. In this case, we are interested in the column for a 95% confidence level.

The value at the intersection of the row and column represents the critical t-value for the given confidence level and degrees of freedom.

Based on the t-distribution table, the critical t-value for a 95% confidence level and 15 degrees of freedom is approximately 2.131.

Therefore, if you have a t-statistic that is greater than 2.131 or less than -2.131, you would reject the null hypothesis at a 95% confidence level.

Remember, a t-distribution table provides critical values for different confidence levels and degrees of freedom, which are used in hypothesis testing and constructing confidence intervals.

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The research finding can be explained by both;

(i) a distributional model of social preferences and

(ii) intentions-based preferences, as entrepreneurs may exhibit greater generosity in the trust game due to their consideration of fairness and the desire to build trust with their partners.

The research finding suggests that entrepreneurs tend to be more generous in the Trust Game compared to the Dictator Game when asked to split $30. To explain this finding, we can consider both a distributional model of social preferences and intentions-based preferences.

(i) Distributional Model of Social Preferences: According to this model, individuals have a concern for inequality and fairness. In the Trust Game, the entrepreneur has the freedom to split the money in any way they wish, allowing them to consider fairness and equity.

By being more generous in the Trust Game, the entrepreneur might aim to distribute the money more equally, thus aligning with their distributional preferences.

(ii) Intentions-Based Preferences: Intentions-based preferences focus on the importance individuals place on others' intentions and reciprocal behaviors. In the Trust Game, there is a higher level of interaction and trust-building compared to the Dictator Game.

The entrepreneur might perceive the Trust Game as an opportunity to build trust with the other player and establish a positive reputation. Being more generous in the Trust Game could be a strategy to signal trustworthiness and foster cooperative relationships, which might be beneficial for future interactions.

Both models, the distributional model of social preferences and intentions-based preferences, can explain the research finding. The distributional model accounts for the entrepreneur's concern for fairness and equality, leading them to be more generous in the Trust Game.

Simultaneously, the intentions-based preferences model recognizes the importance of building trust and signaling positive intentions, motivating the entrepreneur to exhibit more generosity in the Trust Game compared to the Dictator Game.

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If they indicate a different door, they are lying. Based on their response, you can determine which door leads to the treasure.

To determine which person always tells the truth and which person always lies, you can ask any one of them a question whose answer you already know. For example, you could ask "What is my name?" and then verify the answer with someone else. Once you have identified the person who always tells the truth and the person who always lies, you can ask the person who sometimes tells the truth or lies a question that will allow you to determine whether they are telling the truth or lying. A good question to ask the person who sometimes tells the truth or lies is "If I asked one of the other two people which door leads to the treasure, what would they say?" If the person responds by indicating the door that leads to the treasure, they are telling the truth.

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The elements 1 and 5 have a multiplicative inverse in Z6.

The elements of Z6 are {0, 1, 2, 3, 4, 5}.

Addition table for Z6:

| + | 0 | 1 | 2 | 3 | 4 | 5 |

|---|---|---|---|---|---|---|

| 0 | 0 | 1 | 2 | 3 | 4 | 5 |

| 1 | 1 | 2 | 3 | 4 | 5 | 0 |

| 2 | 2 | 3 | 4 | 5 | 0 | 1 |

| 3 | 3 | 4 | 5 | 0 | 1 | 2 |

| 4 | 4 | 5 | 0 | 1 | 2 | 3 |

| 5 | 5 | 0 | 1 | 2 | 3 | 4 |

Multiplication table for Z6:

| x | 0 | 1 | 2 | 3 | 4 | 5 |

|---|---|---|---|---|---|---|

| 0 | 0 | 0 | 0 | 0 | 0 | 0 |

| 1 | 0 | 1 | 2 | 3 | 4 | 5 |

| 2 | 0 | 2 | 4 | 0 | 2 | 4 |

| 3 | 0 | 3 | 0 | 3 | 0 | 3 |

| 4 | 0 | 4 | 2 | 0 | 4 | 2 |

| 5 | 0 | 5 | 4 | 3 | 2 | 1 |

To find the elements in Z6 that have a multiplicative inverse, we look for elements that, when multiplied by another element in Z6, result in 1. These elements are called units. From the multiplication table above, we can see that the elements 1 and 5 are units, since:

1 x 1 = 1

5 x 5 = 1

Therefore, the elements 1 and 5 have a multiplicative inverse in Z6.

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Answer:

[tex] - 5 \div 17[/tex]

[tex]5 \div (- 17)[/tex]

[tex] \frac{ - 5}{17} [/tex]

[tex] \frac{5}{ - 17} [/tex]

Answer:

F

Step-by-step explanation: ITS F

The triple integral ∫∫∫ex^2 y^2 dv in cylindrical coordinates evaluates to ∫ from 0 to 1, ∫ from 0 to 2π, and ∫ from 0 to (1-9r^2) e^r^2cos^2θsinr drdθdz.

In cylindrical coordinates, the given solid e is represented by the inequality 0 ≤ z ≤ 1-9r^2. Therefore, the limits of integration for z are 0 to 1-9r^2. The circular base of the solid is given by x^2 + y^2 ≤ 1/(9z), which can be rewritten as r^2 ≤ 1/(9z).

Thus, the limits of integration for r are 0 to √(1/(9z)). The angle θ ranges from 0 to 2π. Hence, the triple integral can be expressed as ∫ from 0 to 1, ∫ from 0 to 2π, and ∫ from 0 to √(1-9r^2) e^r^2cos^2θsinr drdθdz. Solving this integral yields the required answer.

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AB and CD are tangent to circle F. The values of x and y are 15° and 192° respectively.

The angle formed by a tangent and a chord of a circle measures half of the intercepted arc.

∠ABC and ∠BCD intercept the same arc [tex]\overset{\huge\frown}{BC}[/tex], so they are equal.

m∠ABC = m∠BCD

(5x + 9) = (7x -21)

7x - 5x = 21 + 9

2x = 30

x = 15°

So, the arc measures [tex]\overset{\huge\frown}{BC}[/tex] = 2m∠ABC = 2m∠BCD

m[tex]\overset{\huge\frown}{BC}[/tex] = 2[5(15) + 9] = 2[7(15) - 21]

m[tex]\overset{\huge\frown}{BC}[/tex] = 2[84] = 168°

The degree sum of a circle is 360°

m[tex]\overset{\huge\frown}{BC}[/tex] + y = 360°

y = 360° - m[tex]\overset{\huge\frown}{BC}[/tex]

y = 360° - 168° = 192°

Therefore, x = 15° and y = 192°

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the equation of the plane is: 3x - y - z = -13

Let's call the point (1,7,9) as P and the normal vector as N.

The equation of a plane in 3D space can be represented in the form Ax + By + Cz = D, where (x,y,z) represents any point on the plane.

We know that the normal vector N of the plane is perpendicular to any vector lying on the plane. So, the dot product of N with any vector on the plane will be zero.

Let's choose the vector OP, where O is the origin (0,0,0) and P is the point (1,7,9).

So, OP = P - O = (1,7,9) - (0,0,0) = (1,7,9).

Now, the dot product of N with OP must be zero:

N . OP = 3i + (-1j) . (1i + 7j + 9k) = 3 - 7 - 9 = -13

Therefore, the equation of the plane is:

3x - y - z = -13

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The determinant of a skew-symmetric matrix of odd dimension is always 0. A skew-symmetric matrix is a square matrix where the elements below the main diagonal are the negatives of the corresponding elements.

Above the main diagonal. In other words, for a skew-symmetric matrix A, it satisfies the property [tex]A^T = -A[/tex], where [tex]A^T[/tex] is the transpose of A.

For any odd-dimensional skew-symmetric matrix, when we take the transpose of the matrix, we end up with the negative of the original matrix. Since the determinant of a matrix is unchanged when taking its transpose, we have [tex]det(A) = det(A^T) = det(-A)[/tex].

Since -A is a matrix with all the elements negated, each term in the expansion of the determinant will have a corresponding term with the opposite sign. When we sum up these terms, they will cancel each other out, resulting in a determinant of 0.

Therefore, for a skew-symmetric matrix A of odd dimension, the determinant det(A) = 0.

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The entropy of the sum obtained when a pair of fair dice are rolled is 7.6.

This can be calculated by first working out the probability of each possible sum of two dice. There are 36 possible outcomes when two fair dice are rolled (6 x 6 = 36).

Each of the possible sums, from 2 to 12, will occur with a probability of 1/36.

The entropy of a probability distribution is calculated using the formula: Entropy = -(sum of (Probability of each outcome x log2 of probability of that outcome)).

Therefore, the entropy of the sum of two fair dice is:

- (1/36 x log2(1/36)) + (1/36 x log2(1/36)) + (1/36 x log2(1/36)) + (1/36 x log2(1/36)) + (1/36 x log2(1/36)) + (1/36 x log2(1/36)) + (1/36 x log2(1/36)) + (1/36 x log2(1/36)) + (1/36 x log2(1/36)) + (1/36 x log2(1/36)) + (1/36 x log2(1/36)) + (1/36 x log2(1/36)) + (1/36 x log2(1/36))

= - (1/36 x 5.17) - (1/36 x 4.32) - (1/36 x 3.58) - (1/36 x 2.93) - (1/36 x 2.37) - (1/36 x 1.90) - (1/36 x 1.51) - (1/36 x 1.19) - (1/36 x 0.93) - (1/36 x 0.72) - (1/36 x 0.56) - (1/36 x 0.43)

= 7.6

As a result, the sum that results from the roll of two fair dice has an entropy of 7.6.

Complete Question:

Determine the entropy of the sum that is obtained when a pair of fair dice is rolled.

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Statistic: average time 20 players, 6.32.

(D) The statistic is the average time it takes 20 professional football players to run a mile, which is 6.32 minutes in this case. The statistic was calculated by taking a sample of 20 professional football players and recording the amount of time it took each player to run a mile.

The recorded times were then summed and divided by the total number of players in the sample, which is 20. The resulting value is the average time it takes 20 professional football players to run a mile, also known as the statistic. In this case, the calculated statistic is 6.32 minutes.

It is important to note that the statistic only represents the sample of 20 players and not the entire population of professional football players. Therefore, the estimated average time it takes for all professional football players to run a mile may be different than the calculated statistic.

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A) The probability that all 6 brands could be identified by just guessing is 1/1716.

B) The probability that all 3 brands are identified correctly by just guessing is 1 / 2197.

(A) To calculate the probability that all 6 brands could be identified by just guessing, we need to find the size of the sample space S and the favorable outcomes.

The sample space S is the set of ways that 6 distinct brands can be chosen from the 13 popular brands of beer. The number of elements in the sample space is given by the combination formula:

n(S) = C(13, 6) = 13! / (6! * (13 - 6)!) = 1716.

Now, we need to determine the favorable outcomes, which is the number of ways to choose all 6 brands correctly by guessing. Since each brand has an equal chance of being selected, the probability of guessing a brand correctly is 1/13. Therefore, the favorable outcomes would be 1.

The probability is given by the ratio of favorable outcomes to the total outcomes:

Probability = favorable outcomes / total outcomes = 1 / 1716.

So, the probability that all 6 brands could be identified by just guessing is 1/1716.

(B) If repeats are allowed, the probability that all 3 brands are identified correctly by just guessing can be calculated as follows:

Since repeats are allowed, there are 13 possible choices for each brand. So, the favorable outcomes would be 1 out of 13³ possible outcomes (13 choices for each of the 3 brands).

Therefore, the probability is:

Probability = favorable outcomes / total outcomes = 1 / (13³).

= 1 / 2197

Hence, the probability that all 3 brands are identified correctly by just guessing is 1 / 2197.

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In most situations, it would be reasonable to use a level .01 test with a sample size of 40,000 as it provides a high level of statistical power to detect smaller effects and reduce the likelihood of Type I error.

In most situations, it would be reasonable to use a level .01 test in conjunction with a sample size of 40,000. This is because a larger sample size provides more statistical power, meaning the test is more likely to detect a significant difference if one exists.

Additionally, a level .01 test is more conservative than a level .05 test, which reduces the risk of a type I error (rejecting the null hypothesis when it is actually true).

However, it is important to consider the context and specific research question being addressed, as well as potential confounding variables, to determine the appropriate statistical test and significance level for a given study.

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Answer:

Step-by-step explanation:

Please see the 2 attachments

The Miller index notation for the (100) plane in an FCC crystal structure is [100].

Miller indices are a way to describe crystal planes and directions in a standardized manner. In the case of FCC crystal structure, the (100) plane is parallel to the x-y plane and intersects the x-axis, y-axis, and z-axis at points where the Miller indices are (1,0,0), (0,1,0), and (0,0,1), respectively.

However, to express the (100) plane in a concise and standardized manner, we can use the Miller index notation, which involves taking the reciprocals of the intercepts of the plane with the crystallographic axes and then reducing them to the smallest integer values. In the case of the (100) plane in FCC, all of the intercepts are 1, so the Miller indices are [100].

the pd expression for the (100) plane in FCC crystal structure is [100].

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