3. In the novel Around the World in Eighty Days Jules Verne recounts the adventures of brave Phileas Fogg and his servent Passerpartout. They begin their journey when Phileas bets his friends that he can make a trip around the world in 80 days. If the diameter of the earth is 8000 miles, find the average speed in miles per hour Phileas Fogg needs to circumnavigate the earth about the equator in 80 days.

The equation of the circle with center (0, 0) and containing the point (53, -7) is x² + y² = 2858

The standard form equation of a circle with center (h, k) and radius r is:

(x - h)² + (y - k)² = r²

Given the center is (0, 0):

h = 0

k = 0

And given the point is (53, -7).

The distance between the center and the given point is equal to the radius of the circle.

Using the distance formula, we can calculate the radius:

[tex]r = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\\r = \sqrt{( 53 - 0 )^2+(-7 - 0)^2} \\\\r = \sqrt{( 53 )^2+(-7)^2} \\\\r = \sqrt{2809+ 49} \\\\r = \sqrt{2858}[/tex]

Substituting the values into the equation, we get:

(x - h)² + (y - k)² = r²

(x - 0)² + (y - 0)² = (√2858)²

Simplify

x² + y² = 2858

Therefore, the equation of the circle is x² + y² = 2858.

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The codewords of C are {[0 0 0 0 0], [1 0 1 1 0], [0 1 1 0 1], [1 1 0 1 1]}.

The given parity check matrix H has 3 rows and 5 columns, which implies that code C has length n = 5 and dimension k = n - rank(H). To find k, we need to row-reduce H and count the number of linearly independent rows:

[1 1 1 0 0]

[1 0 0 1 0]

[0 1 0 0 1]

R2 = R2 - R1:  [1 1 1 0 0]

               [0 -1 -1 1 0]

               [0 1 0 0 1]

R3 = R3 + R2:  [1 1 1 0 0]

               [0 -1 -1 1 0]

               [0 0 -1 1 1]

R2 = -R2:      [1 1 1 0 0]

               [0 1 1 -1 0]

               [0 0 -1 1 1]

R1 = R1 - R2:  [1 0 0 1 0]

               [0 1 1 -1 0]

               [0 0 -1 1 1]

R3 = -R3:      [1 0 0 1 0]

               [0 1 1 -1 0]

               [0 0 1 -1 -1]

The row-reduced form of H has 3 linearly independent rows, so k = n - rank(H) = 5 - 3 = 2.

To find the generator matrix G, we can use the method of systematic encoding. We first construct a matrix A consisting of k linearly independent columns of the identity matrix of size k:

[1 0]

[0 1]

Next, we compute the matrix B as the row-reduced form of the transpose of H:

[1 0 1]

[0 1 1]

We can then form the generator matrix G as:

[ A | B^T ] = [1 0 | 1 0 1]

             [0 1 | 0 1 1]

Therefore, the generator matrix of C is:

[1 0 1 1 0]

[0 1 1 0 1]

To list the codewords of C, we can use the generator matrix to encode all possible combinations of the message bits. Since k = 2, there are 2^2 = 4 possible message vectors:

[0 0]

[0 1]

[1 0]

[1 1]

Encoding each message vector with the generator matrix G, we obtain the corresponding codewords:

[0 0 0 0 0]

[1 0 1 1 0]

[0 1 1 0 1]

[1 1 0 1 1]

Therefore, the codewords of C are {[0 0 0 0 0], [1 0 1 1 0], [0 1 1 0 1], [1 1 0 1 1]}.

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The length of y and x in the given figure comes out to be [tex]4\frac{4}{9}[/tex] units and [tex]3\frac{5}{9}[/tex] units respectively.

According to the angle bisector theorem, an angle bisector divides the opposite side in equal proportions to the other two sides.

Given:

BC = 15 units

AC = 8 units

AB = 12 units

AC = x + y

8 = x + y ---- (1)

According to the angle bisector theorem,

x : y = 12 : 15

15x = 12y

5x = 4y

x = 0.8y

Put this in equation (1)

8 = 0.8y + y

1.8y = 8

y = 8/1.8

= 40/9 = [tex]4\frac{4}{9}[/tex] units

x = 32/9 = [tex]3\frac{5}{9}[/tex] units

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Answer:

-2 4 -4 3

Step-by-step explanation:

the answer is that

A list of dependent quantities from a table would include only those variables that are changing in response to the independent variable.

An explanation of independent and dependent variables in a table.

The independent variable is the variable that is changed or manipulated by the experimenter.

It is usually placed in the first column of the table.

The dependent variable on the other hand is the variable that changes in response to the independent variable.

It is usually placed in the second column of the table.

Let's say we are conducting an experiment to see how the time spent exercising affects the number of calories burned.

The independent variable would be the time spent exercising and the dependent variable would be the number of calories burned.

Our table might look something like this:

Time Spent Exercising (minutes) Calories Burned

10 100

20 200

30 300

40 400

"Time Spent Exercising" is the independent variable as it is the variable that we are changing.

"Calories Burned" is the dependent variable as it is the variable that is changing in response to the time spent exercising.

A list of dependent quantities from a table would include only those variables that are changing in response to the independent variable. Without seeing the specific table mentioned I cannot give an answer with complete accuracy but I hope this explanation helps clarify the concept of dependent and independent variables in a table.

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Answer: Slope = 3
y intercept (0,-3)

The function f(x) = 3x - 3 has a slope of 3 and a y-intercept of -3.

The graph of f(x) is given below.

We have,

f(x) = 3x - 3 ______(1)

The graph of this function is given below.

Now,

We can write the function in slope-intercept form.

y = mx + c ______(2)

So,

Comparing (1) and (2) we get,

m = 3

And,

y-intercept = -3

Thus,

The function f(x) = 3x - 3 has a slope of 3 and a y-intercept of -3.

The graph of f(x) is given below.

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Answer:

Step-by-step explanation:

A = 4,7,10,13,16
B = 10,20,40,80
C = 2,5,10,17,26

Next 3 no's

A = 19,22,25

B = 160,320,640

C = 37,50,65

The height of the pole would be 29.94 feet.

The scenario results in the formation of a right angle triangle.

The length of the support wire represents the hypotenuse of the right angle triangle.

The ground distance between the wire and the pole represents the adjacent side of the right angle triangle.

The height of the pole represents the opposite side of the right angle triangle.

To determine the height of the pole, h, we would apply Pythagoras theorem

Hypotenuse² = opposite side² + adjacent side²

18² = 10² + h²

324 = 100 + h²

h² = 324 - 100 = 224

h = √224 = 14.97

The wire meets the pole halfway up the pole.

The height of the pole would be

14.97 × 2 = 29.94 feet

Hence, The height of the pole would be 29.94 feet.

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complete question:

An 18 foot support wire is attached to a vertical pole. The wire is attached to the ground 10 feet away from the pole. If the wire meets the pole halfway up the pole, how y'all is the pole in feet?

Answer:

Step-by-step explanation:

The perimeter of a triangle is the sum of all its sides. The formula for the perimeter of a triangle is given by:

Perimeter = AB + BC + AC

Where AB, BC and AC are the lengths of its sides.

The initial perimeter of the triangle is:

12m + 20m + 27m = 59m

If all sides are increased by 10%, then the new sides would be:

12m + (12m * 0.1) = 13.2m 20m + (20m * 0.1) = 22m 27m + (27m * 0.1) = 29.7m

The new perimeter would be:

13.2m + 22m + 29.7m = 64.9m

The difference between the perimeters of the initial figure and the new figure would be:

64.9 - 59 = 5.9 meters.

The points on the given curve where the tangent line has slope 1 are (-107/54, 19/54) and (-25/27, -91/108).

To find the points on the given curve where the tangent line has slope 1, we need to find where dy/dx = 1.
Using implicit differentiation, we get:
dx/dt = [tex]6t^2[/tex]
dy/dt = 5/12 - 14t
dy/dx = (dy/dt) / (dx/dt) = (5/12 - 14t) / ([tex]6t^2[/tex])
Now we set dy/dx = 1:
1 = (5/12 - 14t) / ([tex]6t^2[/tex])
Simplifying, we get:
[tex]6t^2[/tex] = 5/12 - 14t
Rearranging, we get a quadratic equation:
[tex]6t^2[/tex] + 14t - 5/12 = 0
Using the quadratic formula, we get:
t = (-14 ± [tex]\sqrt{(14^2 - 4*6*(-5/12))}[/tex]) / (2*6)
Simplifying, we get:
t = (-7 ± [tex]\sqrt{(157)}[/tex])/12
Now we can find the corresponding values of x and y by plugging these values of t into the original equations:
When t = (-7 + [tex]\sqrt{(157)}[/tex])/12:
x = [tex]2t^3[/tex] = -107/54
y = 5/12 - 14t = 19/54
So the point is (-107/54, 19/54).
When t = (-7 - [tex]\sqrt{(157)}[/tex])/12:
x = [tex]2t^3[/tex] = -25/27
y = 5/12 - 14t = -91/108
So the point is (-25/27, -91/108).

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The required probability that the total number of spots showing is less than 7 is 9.26%

The probability of an event is found by considering all possibilities that follow the given condition. The probability value cannot exceed the interval [0,1].

Three six-sided dice are rolled at the same time.

It is asked to calculate the probability that the total number of spots showing is less than 7.

If the die is rolled, possible outcomes are as given below.

S: {1, 2, 3, 4, 5, 6}

Number of elements in sample space, n(S) = 6.

Probability of any specific outcome from S = 1/6

If the three dice are rolled together, the total number of elements in the sample space will be [tex](6^3)[/tex]

Then, the probability of getting any of any specific outcome from this sample will be given by: [tex]\frac{1}{6^3} =\frac{1}{216}[/tex]

Find the total possibilities for which the total of outcomes of all three dice is less than 7. It is possible when we get the following outcomes.

The minimum total that we get is 3 with outcomes (1,1,1) on three dice.

For a total of 3:

Possible outcomes: [1, 1, 1]

The number of possibilities [tex]A_1=1[/tex]

For total 4:

Possible outcomes: [1,1,2], [1,2,1], [2, 1, 1]

Number of possibilities [tex]A_2=3[/tex]

For a total of 5:

Possible outcomes:  [1,1,3], [1,3,1], [3, 1, 1],  [1,2,2], [2,2,1], [2, 1, 2]

The number of possibilities [tex]A_3=6[/tex]

For a total of 6:

Possible outcomes :  [1,1,4], [1,4,1], [4, 1, 1],[1, 2, 3] ,[1,3,2],[2, 3, 1], [3,2,1], [3, 1, 2],[2,1,3], [2, ,2 ,2]

The number of possibilities : [tex]A_4=10[/tex]

The number of possibilities for which the total number of spots showing is less than 7 is given by,

[tex]A_1+A_2+A_3+A_4[/tex]

=> 1+ 3+ 6+ 10

=> 20

The probability that the total number of spots showing are less than 7 is calculated below.

P = 20/216

P = 0.0926

P = 9.26%

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The given question is incomplete, complete question is:

Explain how to solve this problem:

You have three six-sided dice. When all three dice are rolled at the same time, calculate the probability of the following outcomes:

a. The total number of spots showing is less than 7

(a) The monopolist's profit-maximizing quantity is 50 units, and the price is $100 per unit.

(b) To achieve the allocatively efficient quantity, the government should set the price at $60 per unit.

(c) Producing the allocatively efficient quantity may not be economically feasible for the monopolist as the price is lower than the average total cost of production.

(d) To have the monopolist earn zero economic profit, the government should set the price at $80 per unit.

(e) The deadweight loss will decrease compared to that of the unregulated monopolist.

(a) The profit-maximizing quantity is where marginal revenue equals marginal cost, which occurs at 50 units, and the corresponding price is $100 per unit. At this quantity, the monopolist's total revenue is $5000, and its total cost is $2500, resulting in a profit of $2500.

(b) To achieve allocative efficiency, the government should set the price at the point where the demand curve intersects the marginal cost curve, which is at 70 units and a price of $60 per unit. At this quantity, the price is equal to the marginal cost, and society maximizes its total surplus.

(c) Producing the allocatively efficient quantity may not be economically feasible for the monopolist because the price of $60 per unit is lower than the average total cost of production, which is $75 per unit. Thus, the monopolist will incur losses if it produces at this quantity.

(d) To regulate the monopolist to earn zero economic profit, the government should set the price at the point where the demand curve intersects the average total cost curve, which is at 80 units and a price of $80 per unit. At this quantity, the price is equal to the average total cost, and the monopolist earns zero economic profit.

(e) The deadweight loss will decrease compared to that of the unregulated monopolist because the allocatively efficient quantity is being produced. However, there may still be some deadweight loss due to the difference between the price and the average total cost.

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The hierarchical database model is based on a tree structure, where data is organized in a parent-child relationship. Each parent segment can have multiple child segments, but each child segment has only one parent.

In this model, data access is typically navigated from the top-level parent segment to its child segments in a hierarchical manner. The parent-child relationships provide a clear structure for organizing and representing data. However, it also means that a lack of a parent segment or a child segment is not allowed in this model.

Compared to a matrix structure, where segments can have relationships with multiple other segments, the hierarchical model is more rigid in its one-to-many relationship between parent and child segments.

However, it may pose challenges when dealing with complex or interrelated data that doesn't fit neatly into a hierarchical structure.

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The missing coordinates of the three vectors form which makes them an orthonormal basis for R³ are as follow,

v₁ = [-0.8, -0.6, 0]

v₂ = [-0.6, -1, 0.45]

v₃ =[-0.27, -0.36, -0.8].

To form an orthonormal basis for R³, the three vectors must be orthogonal  that is perpendicular to each other.

And have unit length norm equal to 1.

Two of the vectors, find the missing coordinates to satisfy these conditions.

Let us consider the two given vectors,

v₁ = [-0.8, -0.6, 0]

v₂ = [?, -1, ?]

To find the missing coordinates of v₂,

Find a vector that is orthogonal to v₁.

One way to do this is by taking the cross product of v₁ and v₂, which will give us a vector orthogonal to both.

Cross product formula: v₁ × v₂ = [a₁b₂ - a₂b₁, a₂b₀ - a₀b₂, a₀b₁ - a₁b₀]

Using the cross product formula, find the missing coordinates of v₂,

v₂ = [?, -1, ?] = v₁ × [?, -1, ?]

Let us calculate the cross product,

v₂

= [?, -1, ?]

= [-0.8 × ?, -0.6 × (-1) - 0 × ?, 0 × ? - (-0.6 × ?)]

To satisfy the orthogonality condition, the dot product of v₁ and v₂ must be zero,

v₁ · v₂ = -0.8 × ? + (-0.6) × (-1) + 0 × ?

⇒ -0.8 × ? + (-0.6) × (-1) + 0 × ? = 0

Simplifying the equation,

⇒-0.8 × ? + 0.6 + 0 = 0

⇒ -0.8 × ? = -0.6

Dividing both sides by -0.8,

⇒ ? = -0.6 / -0.8

⇒ ? = 0.75

Now substitute this value back into the cross product equation to find the missing coordinates of v₂,

v₂ = [-0.8 × 0.75, -1, 0.6 × 0.75]

   = [-0.6, -1, 0.45]

The missing coordinates for the vector v₂ are [-0.6, -1, 0.45].

To find the missing coordinates for the third vector,

Use the same process.

Let us consider the two given vectors,

v₁ = [-0.8, -0.6, 0]

v₂ = [-0.6, -1, 0.45]

v₃ = [?, ?, ?]

Again, find a vector that is orthogonal to both v₁ and v₂.

Use the cross product to determine the missing coordinates,

v₃ = [?, ?, ?]

   = v₁ × v₂

Calculating the cross product,

⇒ v₃  = [?, ?, ?]

        = [-0.6 × 0.45 - 0 × (-1), 0 × (-0.6) - (-0.8 × 0.45), (-0.8) × (-1) - (-0.6) × 0]

Simplifying the equation,

⇒v₃ = [?, ?, ?]

      = [-0.27, -0.36, -0.8]

The missing coordinates for the vector v₃ are [-0.27, -0.36, -0.8].

Therefore, the missing coordinates that would make the three vectors form an orthonormal basis for R³ are,

v₁ = [-0.8, -0.6, 0]

v₂ = [-0.6, -1, 0.45]

v₃ =[-0.27, -0.36, -0.8].

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The probability distribution of the number of successful repairs among the next three breakdowns is a binomial distribution with parameters n=3 and p=0.90.

The probability of a successful repair within one hour is 0.90, which implies that the probability of an unsuccessful repair is 0.10. The question asks for the probability distribution of the number of successes among the next three repairs, which is a binomial distribution since there are a fixed number of trials (3) and each trial has two possible outcomes (success or failure).

Let X be the number of successful repairs among the next three. Then, the possible values of X are 0, 1, 2, and 3. The probability of X successes out of 3 repairs is given by the binomial distribution formula:

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

where n is the number of trials, k is the number of successes, p is the probability of success, and (n choose k) is the binomial coefficient.

Substituting the values for this problem, we get:

[tex]$P(X=0) = {3\choose 0} \cdot 0.10^0 \cdot 0.90^3 = 0.729$[/tex]

[tex]$P(X=1) = \binom{3}{1} \cdot 0.10^1 \cdot 0.90^2 = 0.243$[/tex]

[tex]$P(X=2) = \binom{3}{2} \cdot 0.10^2 \cdot 0.90^1 = 0.027$[/tex]

[tex]$P(X=3) = \binom{3}{3} \cdot 0.10^3 \cdot 0.90^0 = 0.001$[/tex]

Therefore, the probability distribution of the number of successes among the next three repairs is:

X | P(X)

0 | 0.729

1 | 0.243

2 | 0.027

3 | 0.001

This means that the probability of having no successful repairs in the next three breakdowns is 0.729, the probability of having exactly one successful repair is 0.243, the probability of having exactly two successful repairs is 0.027, and the probability of having all three successful repairs is 0.001.

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Based on the information, the measure of angle A is 97° and B is 83 degrees.

Let's represent the measure of angle A as 'x'.

According to the problem, angle B is the measure of angle A minus 14, which can be written as:

B = A - 14

Since angles A and B are supplementary, their sum is equal to 180 degrees:

A + B = 180

Substituting the expression for B, we have:

x + (x - 14) = 180

Simplifying the equation:

2x - 14 = 180

Adding 14 to both sides:

2x = 194

Dividing both sides by 2:

x = 97

Therefore, the measure of angle A is 97 degrees.

Substituting this value back into the expression for B:

B = A - 14 = 97 - 14 = 83

So, the measure of angle B is 83 degrees.

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. Angle A and B are supplementary angles. The measure of angle B is the measure of angle A minus 14. Find the measure of the angle A and B.

The type of measurement scale used by the ice festival committee to measure the depth of the ice during the month of February is the ratio scale. Here option A is the correct answer.

A ratio scale is a type of measurement scale that possesses all the properties of an interval scale with an additional feature of a true zero point. This means that the measurements on a ratio scale have a meaningful zero point, indicating the complete absence of the measured quantity. For example, in the case of measuring the depth of the ice, a ratio scale would allow us to say that the depth of the ice is zero when there is no ice present.

In contrast, interval scales, which are commonly used in temperature measurements, do not have a true zero point. While zero on an interval scale represents the absence of a particular value, it does not imply that the quantity being measured is absent altogether.

Nominal scales, on the other hand, are used to categorize data into distinct and separate groups without any inherent order or numerical value. These scales are used to measure qualitative variables, such as gender or race.

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Complete question:

During the winter, the ice festival committee measures the depth of the ice during the month of February. what is the type of measurement scale? multiple choice

A - ratio

B - interval

C - nominal

D - numerical

The angle values that satisfy sin x = -0.39 are

In the question we were given that

sin x = -0.39

we find the angle by using the inverse sine function or arc sin on a calculator:

arc sin -0.39 = -23.45 degrees

sin functions are negative in the fourth and third quadrant hence we move the angle to these quadrants

Third quadrant: 180 + 23.45 = 203.45 degrees

fourth quadrant: 270 + 23.45 = 293.45 degrees

Therefore, the two angle values that satisfy sin x = -0.39 are approximately 203.45 degrees and 293.45 degrees

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The given vectors h1, 2, 4, 3i, h1, 1, 0, 1i, and h2, 1, 1, 3i in R4 are linearly dependent, as determined by creating a matrix with the vectors as columns and row reducing it. The row-reduced matrix has a row of zeros, indicating that one of the vectors can be expressed as a linear combination of the other two.

The given vectors are h1, 2, 4, 3i, h1, 1, 0, 1i, and h2, 1, 1, 3i in R4. To determine whether these vectors are linearly independent or linearly dependent, we can create a matrix with the vectors as columns and row reduce it. If the row-reduced matrix has a row of zeros, then the vectors are linearly dependent. Otherwise, they are linearly independent.

Constructing the matrix with the given vectors as columns, we get:

\begin{bmatrix} 1 & 1 & 2 \\ 2 & 0 & 4 \\ 4 & 1 & 0 \\ 3 & 1 & 1 \end{bmatrix}

Row reducing this matrix, we get:

\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \end{bmatrix}

Since the row-reduced matrix has a row of zeros, the given vectors are linearly dependent. Specifically, the fourth vector can be expressed as a linear combination of the first three vectors. Therefore, we can conclude that the vectors h1, 2, 4, 3i, h1, 1, 0, 1i, and h2, 1, 1, 3i in R4 are linearly dependent.

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The source of error is computed in the denominator of the test statistic for the between-subjects design, but not the within-subjects design is Option (c) between-groups.

The test statistic is a numerical value that measures the difference between groups, and it is typically derived from the data collected in the experiment. In a between-subjects design, the test statistic is computed by comparing the means of two or more groups of participants on a given variable. This means that the test statistic reflects the difference between groups, rather than within groups.

In contrast, in a within-subjects design, the test statistic is computed by comparing the scores of the same group of participants on a given variable, before and after some intervention or treatment. This means that the test statistic reflects the difference within groups, rather than between groups.

The Given question States, which source of error is computed in the denominator of the test statistic for the between-subjects design but not the within-subjects design?  In a between-subjects design, the test statistic is typically computed using an analysis of variance (ANOVA), which involves partitioning the total variability in the data into two components: the variability between groups and the variability within groups. The denominator of the test statistic in a between-subjects ANOVA reflects the variability within groups, which is a measure of the random error in the data. This error arises from individual differences between participants that are not related to the experimental manipulation. By contrast, the variability between groups reflects the systematic effects of the experimental manipulation, and is used to estimate the effect size or the degree of association between the independent and dependent variables.

In a within-subjects design, the variability between groups is not relevant, because there is only one group of participants that is measured twice (or more) on the same variable. Instead, the denominator of the test statistic in a within-subjects design reflects the variability within subjects, which is a measure of the random error in the data. This error arises from factors such as measurement error, natural variability in the participants' responses, and other sources of noise that are not related to the experimental manipulation.

The source of error computed in the denominator of the test statistic depends on the type of experimental design used. In a between-subjects design, the denominator reflects the variability within groups, while in a within-subjects design, it reflects the variability within subjects. The choice of design depends on the research question, the nature of the variables being measured, and other practical considerations.

Therefore, the source of error is computed in the denominator of the test statistic for the between-subjects design, but not the within-subjects design is Option (c) between-groups.

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Complete Question

Which source of error is computed in the denominator of the test statistic for the between-subjects design, but not the within-subjects design?

a. Between-persons

b. Within-groups

c. Between-groups

d. Within-persons

Therefore, the total cost of the first 25 units of production is 200.

To find the total cost of the first 25 units of production, we need to integrate the marginal cost function over the range of units from 0 to 25.

The marginal cost function is given as 8√x, where x represents the number of units. To find the total cost, we integrate this marginal cost function with respect to x over the range of 0 to 25:

∫(8√x)dx from 0 to 25

To integrate 8√x, we can use the power rule of integration, which states that ∫x^n dx = (1/(n+1))x^(n+1) + C.

Applying the power rule, we integrate 8√x as follows:

∫(8√x)dx = 8 * ∫x^(1/2)dx = 8 * (2/3)x^(3/2) + C

Now, we can evaluate this integral over the range of 0 to 25:

[8 * (2/3)x^(3/2)] evaluated from 0 to 25

Substituting the upper limit of 25:

[8 * (2/3)(25)^(3/2)] - [8 * (2/3)(0)^(3/2)]

Simplifying:

[8 * (2/3)(25)^(3/2)] - 0

Calculating the expression within brackets:

[8 * (2/3)(25)^(3/2)] = 200

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The diagonal of the given rectangle is 18.6 units.

As per the question, the length of the rectangle is 15 units and the width is 11 units.

Therefore, we can consider the length as one side of the right triangle and the width as the other side.

As we know that Pythagoras's theorem states that in a right-angled triangle, the square of one side is equal to the sum of the squares of the other two sides.

Using the Pythagorean theorem:

diagonal² = length² + width²

diagonal² = 15² + 11²

diagonal² = 225 + 121

diagonal² = 346

To find the length of the diagonal, we take the square root of both sides:

diagonal = √346

diagonal = 18.6

Hence, the diagonal is approximately 18.6 units.

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Answer: Nominal Scale Level

Step-by-step explanation:

Data that is measured using a nominal scale is qualitative.

colors, names, labels and favorite foods along with yes or no responses are examples of nominal level data.

Therefore, the average value of the function f(x) = 25 - x^2 on the interval [0, 5] is 50/3.

To find the average value of the function f(x) = 25 - x^2 on the interval [0, 5], we need to calculate the definite integral of the function over the interval and divide it by the length of the interval.

The average value (AV) is given by the formula:

AV = (1 / (b - a)) * ∫[a to b] f(x) dx

In this case, a = 0 and b = 5, so the average value becomes:

AV = (1 / (5 - 0)) * ∫[0 to 5] (25 - x^2) dx

Simplifying, we have:

AV = (1/5) * ∫[0 to 5] (25 - x^2) dx

To evaluate the integral, we integrate term by term:

AV = (1/5) * [25x - (x^3 / 3)] evaluated from 0 to 5

AV = (1/5) * [(255 - (5^3 / 3)) - (250 - (0^3 / 3))]

AV = (1/5) * [(125 - (125 / 3)) - 0]

AV = (1/5) * [(375/3 - 125/3)]

AV = (1/5) * (250/3)

AV = 250/15

AV = 50/3

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The probability that the sample mean exceeds 45 is approximately 0.

By the central limit theorem, the sample mean of a large sample size from any distribution with a finite mean and variance is approximately normally distributed.

Since the exponential distribution has a mean of 4 and a variance of 16, we can approximate the distribution of the sample mean as a normal distribution with mean 4 and standard deviation 4/sqrt(225) = 4/15.

To find the probability that the sample mean exceeds 45, we can standardize the distribution using the z-score formula:

z = (45 - 4) / (4/15) = 10.625

Using a standard normal distribution table or a calculator, we can find the probability that a standard normal random variable exceeds 10.625:

P(Z > 10.625) ≈ 0

Therefore, the probability that the sample mean exceeds 45 is approximately 0.

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The z-values that correspond to the middle 72% of the normal distribution are given as follows:

-1.08 < Z < 1.08.

The z-score of a measure X of a normally distributed variable that has mean symbolized by the symbol [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Considering the symmetry of the normal distribution, the middle 72% is composed between the 14th percentile and the 76th percentile, hence the z-scores are given as follows:

-1.08 < Z < 1.08.

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To find a polynomial function f(x) with integer coefficients and leading coefficient 1, such that f(x) has x= 30 as one of its roots, we can use the factor theorem.

The factor theorem states that if x-a is a factor of a polynomial function f(x), then f(a) = 0.

Therefore, we can say that (x-30) is a factor of f(x) since x=30 is one of its roots.

Now, we can use long division or synthetic division to find the other factors of f(x) and write it in factored form. However, since we want a polynomial function with integer coefficients, we can simply multiply (x-30) by another factor such that all coefficients are integers.

For example, we can choose (x+2) as the other factor. Therefore,

f(x) = (x-30)(x+2)

Expanding this gives us:

f(x) = x^2 - 28x - 60

This is a polynomial function with integer coefficients and leading coefficient 1, such that f(x) has x=30 as one of its roots.

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Answer:

24cm

Step-by-step explanation:

its a right triangle so you use the Pythagorean theorem of [tex]a^{2}+b^{2}=c^{2}[/tex]

you plug in the numbers and get [tex]10^{2}+b^{2} =26^{2}[/tex]

you than do 100+[tex]b^{2}[/tex]=676

[tex]b^{2}[/tex]=576

b=[tex]\sqrt{576\\}[/tex]

b=24

The sides of the similar triangle are 10, 18.75, and 337.5.

What is the triangle?

A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.

If two triangles are similar, then their corresponding sides are in proportion. That is, the ratio of the length of corresponding sides is the same for both triangles.

Let the sides of the similar triangle be a, b, and c. We know that the shortest side of the original triangle is 8, and the corresponding side in the similar triangle is 10. So, we can set up the proportion:

8/10 = 15/b = 18/c

We can solve for b and c by cross-multiplying:

8c = 10(15) = 150

c = 18(150/8) = 337.5

and

8b = 15(10) = 150

b = 18.75

Therefore, the sides of the similar triangle are 10, 18.75, and 337.5.

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Answer:

x = 48

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

sum the 3 angles and equate to 180

x + 105 + 27 = 180

x + 132 = 180 ( subtract 132 from both sides )

x = 48