The average time to serve a customer at a fast-food restaurant is 5 minutes. The standard deviation of the service time is 4 minutes. What is the coefficient of variation of the service time

The researcher is trying to reduce the cause of within-group variance related to individual differences or heterogeneity within the sample.

In statistics, within-group variance, also known as within-group variation or error variance, refers to the variability of data within a specific group or sample. It represents the differences among individuals within the same group or sample.

There are several causes of within-group variance, such as individual differences, measurement error, and uncontrolled extraneous variables.

In this scenario, the researcher is trying to limit who the findings will generalize to, which means that she wants to control or reduce the effect of individual differences or heterogeneity within the sample.

By limiting the sample to a specific population or subgroup, the researcher can reduce the within-group variance related to individual differences and increase the likelihood of finding significant results.

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There are 888 employees on The Game Shop's sales team. Last month, they sold a total of ggg games. Chris sold 171717 fewer games than the team averaged per employee, so the number of games he sold can be expressed as: (ggg/888) - 171717.

To find the average number of games sold per employee, we divide the total number of games sold by the total number of employees.

The problem gives us the total number of employees, which is 888, and the total number of games sold, which is ggg. So, the average number of games sold per employee is:

ggg games ÷ 888 employees = ggg/888 games per employee

Next, we're told that Chris sold 171717 fewer games than the team averaged per employee.

This means that the number of games he sold is equal to the average number of games sold per employee minus 171717.

Thus, the expression for the number of games Chris sold is: (ggg/888) - 171717.

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The height of the cylindrical water tank should be approximately 8.04 meters to hold 2000L of water with a radius of 500 cm.

The formula to calculate the volume of a cylinder is:

V = π[tex]r^2h[/tex]

where V is the volume, r is the radius, and h is the height.

We know that the manufacturer plans to make a cylindrical water tank that can hold 2000L of water. We also know that the radius of the tank is 500 cm.

First, we need to convert the volume from liters to cubic centimeters ([tex]cm^3[/tex]) because the units of radius and height are in centimeters:

2000L = 2,000,000[tex]cm^3[/tex]

Substituting these values into the formula, we get:

2,000,000 = π[tex](500)^2[/tex]h

Solving for h, we get:

h = 2,000,000 / (π[tex](500)^2[/tex])

h ≈ 8.04 cm

Therefore, the height of the cylindrical water tank should be approximately 8.04 meters to hold 2000L of water with a radius of 500 cm.

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Answer:13/24

Step-by-step explanation 1. the desired probability is the sum of the probabilities of two disjoint events. In the first event, an apple is selected from the first basket and an orange is selected from the second basket; the probability of this event is (4/6)(5/8)=20/48.                                                           2. In the second event, an orange is selected from the first basket and an apple is selected from the second basket; the probability of this event is (2/6)(3/8)=6/48. Therefore, the desired probability is 20/48+6/48=26/48=13/24.

The probability that the sample proportion will differ from the population proportion by less than 0.03 is 62%

To calculate the probability that the sample proportion will differ from the population proportion by less than 0.03, we first need to calculate the standard error of the sample proportion. The formula for the standard error is:

SE = [tex]\sqrt{[p(1-p)/n]}[/tex]

Where p is the population proportion (0.04), and n is the sample size (238). Plugging in these values, we get:

SE = [tex]\sqrt{[0.04(1-0.04)/238]}[/tex] = 0.028

Next, we need to calculate the margin of error, which is given by:

ME = z*SE

Where z is the z-score that corresponds to the desired level of confidence. Let's assume we want a 95% confidence level, which corresponds to a z-score of 1.96. Plugging in these values, we get:

ME = 1.96*0.028 = 0.055

Finally, we can calculate the probability that the sample proportion will differ from the population proportion by less than 0.03 by subtracting the margin of error from both sides of the true proportion (0.04) and adding it back on:

0.04 - 0.055 < p < 0.04 + 0.055

Simplifying, we get:

-0.015 < p - 0.04 < 0.015

Dividing by the standard error, we get:

-0.535 < z < 0.535

Looking up these z-scores in a standard normal distribution table, we find that the probability of getting a sample proportion within 0.03 of the population proportion is approximately 0.62, or 62%. This means that there is a 62% chance that the sample proportion will be within 0.03 of the population proportion if we were to sample 238 people from the city.

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The correct interpretation sentences for the TV problem above are:- A total of 500 TVs can be sold if the price is set at $190.

- When the price for the TV is $190, there are 500 TVs sold.

The other sentence "A total of 190 TVs can be sold if the price is set at $500. When the price for the TV is $500, there are 190 TVs sold" is not correct as it has the price and the quantity of TVs sold reversed.

In interpretation, it is important to pay attention to the context and the logic of the problem to ensure that the sentence accurately reflects the information provided. In this case, the correct interpretation sentences reflect the relationship between the price and the quantity of TVs sold. These sentences help to clarify the information and provide a clear understanding of the problem.

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The normal density curve is symmetric about its mean, with the highest point at the "mean."

The normal density curve is a continuous probability distribution that is widely used in statistics.

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The statements are inconsistent and cannot both be true.

To answer this question, we need to compare the exchange rate between the US dollar (USD) and the Canadian dollar (CAD) in 2006 and 2010.

In 2006, 1.00 USD bought 1.40 CAD. This can be expressed as:

1 USD = 1.40 CAD

In 2010, 1.00 USD bought 1.00 CAD. This can be expressed as:

1 USD = 1.00 CAD

To compare the two exchange rates, we can set them equal to each other and solve for CAD:

1 USD = 1.40 CAD

1 USD = 1.00 CAD

Setting the two equations equal to each other, we get:

1.40 CAD = 1.00 CAD

Subtracting 1.00 CAD from both sides, we get:

0.40 CAD = 0

This is a contradiction, which means that there is no consistent exchange rate that can explain both statements.

Therefore, the statements are inconsistent and cannot both be true.

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The critical numbers are 0 and 2, and the behavior of f at these numbers is At x = 0, the function has a local minimum.
At x = 2, the function has neither a local maximum nor a local minimum.

To find the critical numbers, we need to take the derivative of the function and set it equal to zero:
f'(x) = 6x^5(x-2)^5 + x^6(5)(x-2)^4(1) = 0
Simplifying this equation, we get:
x(x-2)^4(6x^4 + 5x^2(x-2)) = 0
The critical numbers are where the derivative equals zero, which are x = 0 and x = 2.
To describe the behavior of f at these critical numbers, we need to examine the sign of the derivative around each critical number. If the derivative is positive to the left and negative to the right of a critical number, then the function has a local maximum at that point. If the derivative is negative to the left and positive to the right, then the function has a local minimum at that point. If the derivative does not change sign at a critical number, then the function has neither a local maximum nor a local minimum at that point.
Let's examine each critical number:
At x = 0, we can see that the factor x is negative to the left of 0 and positive to the right of 0. The factor (x-2)^4 is positive everywhere. The factor 6x^4 + 5x^2(x-2) is positive at x = 0 (since the x^2 term is zero), which means the derivative is positive to the left and right of x = 0. Therefore, f has a local minimum at x = 0.
At x = 2, we can see that the factor (x-2)^4 is zero at x = 2, which means the derivative is zero at x = 2. To determine whether f has a local maximum or minimum at x = 2, we need to examine the sign of the derivative on either side of 2. If we plug in a value slightly less than 2 (e.g. x = 1.9), we get a positive derivative. If we plug in a value slightly greater than 2 (e.g. x = 2.1), we also get a positive derivative. Therefore, f has neither a local maximum nor a local minimum at x = 2.

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The foci of the ellipse are (4, 0) and (9, 0).

To find the foci of the ellipse, we first need to determine its standard form equation and identify the values of the major and minor axes. Given the endpoints of the major axis are (0,0) and (13,0), we can determine that the length of the major axis (2a) is 13 units. Thus, a = 6.5 units.

The minor axis has a length of 12 units, so the length of the minor axis (2b) is 12 units. Therefore, b = 6 units.

Next, we will find the value of c, which is the distance from the center of the ellipse to each focus. Using the relationship [tex]c^2 = a^2 - b^2[/tex], we get:

[tex]c^2 = (6.5)^2 - (6)^2[/tex]
[tex]c^2 = 42.25 - 36[/tex]
[tex]c^2 = 6.25[/tex]
c = √6.25
c ≈ 2.5 units

Now, we have all the necessary information to find the foci of the ellipse. Since the major axis is along the x-axis, the foci will be located at a distance of c units to the left and right of the center (which is the midpoint of the major axis). The center of the ellipse is (6.5, 0), so the foci will be at (6.5 - 2.5, 0) and (6.5 + 2.5, 0), which are (4, 0) and (9, 0).

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Moses is currently 3996 years old.

Let's denote Methuselah's current age as "M" and Moses's current age as "M2".

"Moses is twice as old as Methuselah was when Methuselah was one-third as old as Moses will be when Moses is as old as Methuselah is now." This can be written as:

M2 = 2 × (M - (1/3) × M2)

We can simplify this equation by multiplying both sides by 3:

3 × M2 = 6 × (M - (1/3) × M2)

3 × M2 = 6M - 2 × M2

5 × M2 = 6M

"If the difference of their ages is 666" can be written as:

M2 - M = 666

We can use equation (5) to substitute for M2 in equation (6):

5 × M2 = 6M

5 × (M + 666) = 6M

5M + 3330 = 6M

M = 3330

Therefore, Methuselah is currently 3330 years old. We can use equation (6) to find Moses's current age:

M2 - M = 666

M2 - 3330 = 666

M2 = 3996

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The time between buses is 10 minutes and the bus waits at the station for 3 minutes, so the time between the departure of one bus and the departure of the next bus is 10 + 3 = 13 minutes.

Since you arrive at a random time, the time you have to wait for the next bus can be any number from 0 to 13 minutes, with each value between 0 and 13 being equally likely.

The probability that you will have to wait more than 6 minutes to board a bus is the probability that you arrive at the station between 0 and 7 minutes after a bus has left.

This is because if you arrive at the station more than 7 minutes after a bus has left, you will have to wait less than 6 minutes for the next bus to arrival time.

The probability that you arrive at the station between 0 and 7 minutes after a bus has left is 7/13, or approximately 0.538.

Therefore, the probability that you will have to wait more than 6 minutes to board a bus is approximately 0.462 (1 - 0.538).

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Answer: A

Step-by-step explanation:

The critical number is also x = 4.To find the critical number(s) of a function, we need to first take the derivative of the function and then find where the derivative is equal to zero or undefined.

4. F(x) = x-1/x^2-x+2

To find the derivative, we can use the quotient rule:

F'(x) = [(x^2-x+2)(1) - (x-1)(2x-1)] / (x^2-x+2)^2

Next, we need to find where F'(x) is equal to zero or undefined.

Setting the numerator equal to zero gives:

(x^2-x+2) - (2x^2-3x+1) = 0

-x^2 + 4x - 1 = 0

Using the quadratic formula, we can solve for x:

x = (4 ± sqrt(16-4(-1)(-1))) / (-2)

x = (4 ± sqrt(20)) / (-2)

x = 1 ± sqrt(5)

So the critical numbers are 1 + sqrt(5) and 1 - sqrt(5).

5. F(x) = x^3/4 – 2x^1/4

To find the derivative, we can use the power rule:

F'(x) = (3/4)x^-1/4 - (1/2)x^-3/4

Next, we need to find where F'(x) is equal to zero or undefined.

Setting the numerator equal to zero gives:

3x^-1/4 - 2x^-3/4 = 0

Multiplying both sides by x^3/4 gives:

3 - 2x = 0

Solving for x gives:

x = 3/2

So the critical number is 3/2.

6. F(x) = x^4/5(x-4)^2

To find the derivative, we can use the quotient rule:

F'(x) = [(x-4)^2(4x^3/5) - x^4/5(2(x-4)(1))] / (x-4)^4

Simplifying gives:

F'(x) = (2x^3 + 16x^2 - 32x) / 5(x-4)^3

Next, we need to find where F'(x) is equal to zero or undefined.

Setting the numerator equal to zero gives:

2x(x^2 + 8x - 16) = 0

Using the quadratic formula, we can solve for x:

x = (-8 ± sqrt(64 + 8(16))) / 2

x = (-8 ± sqrt(192)) / 2

x = -4 ± 2sqrt(6)

So the critical numbers are -4 + 2sqrt(6) and -4 - 2sqrt(6). However, we also need to check if the derivative is undefined at x = 4.

Plugging in x = 4 gives:

F'(4) = (2(4)^3 + 16(4)^2 - 32(4)) / 5(4-4)^3

F'(4) = undefined

So the critical number is also x = 4.

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6 - 6 = 6 - 6 is the correct statement.

To complete the statement 6 - 6 = 6 + x, we need to find the value of x that makes the statement true.

Simplifying the left-hand side of the equation, we have:

6 - 6 = 0

On the right-hand side, we have:

6 + x

To make the statement true, we need to find the value of x that satisfies:

0 = 6 + x

We can solve for x by subtracting 6 from both sides:

0 - 6 = 6 + x - 6

-6 = x

Therefore, the completed statement is:

6 - 6 = 6 - 6

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Answer:

$11.10

Step-by-step explanation:

To calculate the price of the sno-cone machine after discount and sales tax, we need to first calculate the discount and then add sales tax.

The sno-cone machine is priced at $13 and is on sale for 20% off. To calculate the discount, we can multiply the original price by the discount rate:

Discount = Original Price x Discount Rate

Discount = $13 x 0.20

Discount = $2.60

Therefore, the discount is $2.60.

The sale price of the sno-cone machine after discount can be calculated by subtracting the discount from the original price:

Sale Price = Original Price - Discount

Sale Price = $13 - $2.60

Sale Price = $10.40

Therefore, the sale price of the sno-cone machine after discount is $10.40.

To calculate the sales tax, we can multiply the sale price by the sales tax rate:

Sales Tax = Sale Price x Sales Tax Rate

Sales Tax = $10.40 x 0.0675

Sales Tax = $0.70

Therefore, the sales tax is $0.70.

Finally, to calculate the final price of the sno-cone machine after discount and sales tax, we can add the sale price and sales tax:

Final Price = Sale Price + Sales Tax

Final Price = $10.40 + $0.70

Final Price = $11.10

Therefore, the final price of the sno-cone machine after discount and sales tax is $11.10 1.

I hope this helps!

The correct answer is (c) normal distribution.

When comparing two proportions, the difference between them can be calculated, and its sampling distribution can be approximated by a normal distribution when the sample sizes are sufficiently large.

The mean of the sampling distribution is the difference between the true population proportions, and the standard deviation of the sampling distribution is calculated as:

[tex]sqrt[(p1*(1-p1)/n1) + (p2*(1-p2)/n2)][/tex]

where p1 and p2 are the population proportions, and n1 and n2 are the sample sizes.

Therefore, the sampling distribution of the difference between two proportions is approximated by a normal distribution with mean (p1-p2) and standard deviation given by the above formula.

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The measure of angle B is m∠B = 157°

Given Quadrilateral ABCD is inscribed in a circle. That means its four vertices lie on the edge of the circle

∠B and ∠D are opposite angles in the quadrilateral ABCD

m∠B + m∠D = 180°

The opposite ∠s in a cyclic quadrilateral,

∵ m∠B = (6x + 19)°

∵ m∠D = x°

Substitute them in the rule;

(6x + 19) + x = 180

Add the like terms in the left-hand side

(6x + x) + 19 = 180

7x + 19 = 180

Subtract 19 from both sides;

7x = 161

Divide both sides by 7

x = 23

m∠B = 6(23) + 19

m∠B = 138 + 19

m∠B = 157°

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The solutions to the equations are

From the question, we have the following parameters that can be used in our computation:

Set of linear equations

Next, we solve the equations as follows:

5x + 2(x − 1) = 6(x+1) + x

This gives

5x + 2x - 2 = 6x + 6 + x

Evaluate the like terms

-2 = 6 ---- No solution

Next, we have

5x + 2(x − 1) = 6(x – 1) − x

This gives

5x + 2x - 2 = 6x - 6 - x

Evaluate the like terms

2x = -2

Divide

x = -1

Next, we have

5x + 2(x − 3) = 6(x − 1) − x

This gives

5x + 2x - 6 = 6x - 6 - x

Evaluate the like terms

2x = 0

Divide

x = 0

Lastly, we have

5x + 2(x – 3) = 6(x − 1) +x

This gives

5x + 2x - 6 = 6x - 6 + x

Evaluate the like terms

0 = 0 ---- All real numbers

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The number of 3-digit positive integers whose middle digit is equal to the sum of the first and last digits is 55 such numbers

Let's first consider the possible values for the middle digit, which is the sum of the first and last digits:

If the first digit is 1, then the middle digit can only be 2, and the last digit can be any digit from 0 to 8.

There are 9 possible numbers in this case.

If the first digit is 2, then the middle digit can be 2 or 4, and the last digit can be any digit from 0 to 6.

There are 14 possible numbers in this case.

If the first digit is 3, then the middle digit can be 2, 4, or 6, and the last digit can be any digit from 0 to 4.

There are 15 possible numbers in this case.

If the first digit is 4, then the middle digit can be 2, 4, 6, or 8, and the last digit can be any digit from 0 to 2.

There are 13 possible numbers in this case.

If the first digit is 5, then the middle digit can be 4, 6, or 8, and the last digit can only be 0.

There are 3 possible numbers in this case.

If the first digit is 6, then the middle digit can only be 6, and the last digit can only be 0.

There is only 1 possible number in this case.

In total, the number of 3-digit positive integers whose middle digit is equal to the sum of the first and last digits is:

9 + 14 + 15 + 13 + 3 + 1 = 55

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The probability that exactly 4 of the students selected to present are stat majors is 0.219, or about 22%.

The total number of ways to choose 5 students from a class of 20 is:

C(20,5) = (20!)/[(5!)(15!)] = 15504

To find the probability that exactly 4 of the students selected are stat majors, we need to count the number of ways to choose 4 stat majors and 1 engineer, and divide by the total number of ways to choose 5 students:

[C(10,4) * C(10,1)] / C(20,5) = [(10!)/[(4!)(6!)]] * [(10!)/[(1!)(9!)]] / [(20!)/[(5!)(15!)]] = 0.219

Therefore, the probability that exactly 4 of the students selected to present are stat majors is 0.219, or about 22%.

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The researchers monitored the same children's consumption of sugar-sweetened beverages and obesity over the course of two years using a longitudinal quasi-experimental methodology.

The researchers used a longitudinal quasi-experimental design in this study, as they measured the same children's sugared-beverage consumption and obesity for two years.

This design allows the researchers to observe changes over time and make causal inferences about the relationship between the variables.

By comparing the same group of children's obesity rates before and after the addition of one sugared drink per day, the researchers were able to establish a causal link between the consumption of sugared drinks and increased risk of obesity.

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The dimensions of the corral that will minimize the cost of the fencing are x = 4 yards (width) and y = 325 yards (length).

To begin solving this problem, we need to use the given information to set up an equation that represents the cost of the fencing. Let's start by defining the dimensions of the rectangular corral. We can use x to represent the width and y to represent the length.

Since the area of the corral is 1300 square yards, we know that:

xy = 1300

Now, let's think about the fencing. We need to divide the corral in half with a fence down the middle, which means we have two equal sections with a width of x/2. The length of each section is still y.

To find the perimeter of each section, we add up all the sides. For the top and bottom, we have two lengths of y and two widths of x/2. For the sides, we have two lengths of x/2 and two widths of y. This gives us a perimeter of:

2y + x + 2x + 2y = 4y + 2x

Since we have two sections, the total perimeter is:

2(4y + 2x) = 8y + 4x

We can now set up an equation for the cost of the fencing:

Cost = (8y + 4x)($5) + (x)($3)

The first part of the equation represents the cost of the perimeter fence, while the second part represents the cost of the fence down the middle.

Now, we want to find the dimensions of the corral that will minimize the cost of the fencing. To do this, we can use calculus. We take the derivative of the cost equation with respect to x and set it equal to zero:

dCost/dx = 20y + 3 = 0

Solving for y, we get:

y = -3/20

Since we can't have a negative length, this solution is not valid. However, we can find the minimum cost by plugging in the value of y that makes the derivative equal to zero into the original equation for the cost of the fencing. This gives us:

Cost = (8y + 4x)($5) + (x)($3)
Cost = (8(-3/20) + 4x)($5) + (x)($3)
Cost = (-(12/5) + 4x)($5) + (x)($3)
Cost = -24x + 3x^2 + 3900

To minimize the cost, we take the derivative with respect to x and set it equal to zero:

dCost/dx = -24 + 6x = 0
x = 4

Plugging this value of x back into the equation for the cost of the fencing gives us:

Cost = -24(4) + 3(4^2) + 3900
Cost = $3892

Therefore, the dimensions of the corral that will minimize the cost of the fencing are x = 4 yards (width) and y = 325 yards (length).

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The amount of all angles within every quadrilateral adds up to a cumulative 360°.

All triangles exhibit angles that total 180°, and since the diagonal is shared between both of these triangles, we shall add up their angles only once when totaling the quadrilateral.

Consequently, the sum of all four angles in the quadrilateral is twice the angle degree of one triangle plus 180° (for the connecting diagonal), which equates to:

(180°) + 180° = 360°

Therefore, the amount of all angles within every quadrilateral adds up to a cumulative 360°.

This justification holds true for all types of quadrilaterals, for instance the one illustrated in the representation at the right, due to it being divided into two parts through the extention of a diagonal.

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Using the order, we can evaluate the expression, the answer is 0.

To evaluate this expression, we need to follow the order of operations, which is a set of rules that dictate the order in which mathematical operations should be performed. The order of operations is:

1. Perform any calculations inside parentheses first.

2. Exponents (ie powers and square roots, etc.)

3. Multiplication and Division (from left to right)

4. Addition and Subtraction (from left to right)

Using this order, we can evaluate the expression as follows:

-31÷(-30)+(-1)

= 1 + (-1)    [since -31 ÷ (-30) = 1]

= 0

Therefore, the answer is 0.

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The monthly payment if the interest rate was 11% will be $45.63.

The remaining amount is calculated as,

P = (1 - 0.20) x $925

P = 0.80 x $925

P = $740

The monthly payment is calculated as,

MP = [$740 + ($740 x 0.11)] / 18

MP = $821.4 / 18

MP = $45.63

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The monthly payment is $49.69.

We have,

The amount of the down payment is:

0.20 x $925 = $185

So the amount financed is:

$925 - $185 = $740

Using the formula for the monthly payment on a loan:

= (Pr(1+r)^n) / ((1+r)^n - 1)

where:

P = principal or amount financed = $740

r = monthly interest rate = 11%/12 = 0.0091667

n = total number of payments = 18

Plugging in the values, we get:

Monthly payment

= ($7400.0091667 x (1+0.0091667)^18) / ((1 + 0.0091667)^18 - 1)

= $49.69 (rounded to the nearest cent)

Therefore,

The monthly payment is $49.69.

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The standard deviation of the population affects the width of the confidence interval for the population mean. A larger standard deviation results in a wider confidence interval, while a smaller standard deviation results in a narrower confidence interval.

The standard deviation of the population plays a crucial role in determining the width of the confidence interval for the population mean. The formula for the confidence interval for the population mean is:

CI = X ± Z × (σ / sqrt(n))

where:

CI is the confidence interval

X is the sample mean

Z is the Z-score corresponding to the desired level of confidence

σ is the standard deviation of the population

n is the sample size

As you can see from the formula, the width of the confidence interval is directly proportional to the standard deviation of the population. The larger the standard deviation, the wider the confidence interval. This means that if the standard deviation of the population is large, then we need a larger sample size or a lower confidence level to obtain a narrower confidence interval. On the other hand, if the standard deviation of the population is small, we can obtain a narrower confidence interval with a smaller sample size or a higher confidence level.

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The probability of rolling double ones or double sixes at least once in three rolls is 1 - 0.701 = 0.299, or approximately 29.9%.

There are a total of 6 x 6 = 36 possible outcomes when rolling a pair of dice, assuming the dice are fair and unbiased.

The probability of rolling double ones or double sixes on any one roll is 2/36 = 1/18. So, the probability of NOT rolling double ones or double sixes on any one roll is 1 - 1/18 = 17/18.

The probability of not rolling double ones or double sixes on all three rolls is [tex](17/18) \times (17/18) \times (17/18) = (17/18)^3 = 0.701.[/tex]

Therefore, the probability of rolling double ones or double sixes at least once in three rolls is 1 - 0.701 = 0.299, or approximately 29.9%.

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The US Crime Commission needs to take a sample of at least 1068 crimes to estimate the proportion of crimes in which firearms are used with a margin of error of 3% and a 95% confidence level, assuming no preliminary estimate is available.

To calculate the minimum required sample size, we can use the formula:

[tex]n = [(Z^2) \times p \times q] / E^2[/tex]

where:

n is the sample size

Z is the Z-score corresponding to the desired confidence level (95% in this case), which is 1.96

p is the estimated proportion of crimes in which firearms are used (since no preliminary estimate is available, we can use 0.5 as a conservative estimate to get the maximum sample size)

q is the complement of p, which is 1 - p

E is the margin of error, which is 3% or 0.03

Substituting the values, we get:

[tex]n = [(1.96^2) \times 0.5 \times 0.5] / 0.03^2[/tex]

n = 1067.11

Rounding up to the nearest integer, the minimum required sample size is 1068. Therefore, the US Crime Commission needs to take a sample of at least 1068 crimes to estimate the proportion of crimes in which firearms are used with a margin of error of 3% and a 95% confidence level, assuming no preliminary estimate is available.

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The purchase price in dollars of the television that has been marked up 25% of the retail price of $4,500 would be $5,625.

To find the purchase price of the television in dollars, follow these steps:

1. Determine the markup amount: 25% of the retail price ($4,500).
2. Subtract the markup amount from the retail price to find the purchase price.

Step 1: Calculate the markup amount:
25% of $4,500 = 0.25 × 4,500 = $1,125

Step 2: Subtract the markup amount from the retail price:
$4,500 (retail price) - $1,125 (markup) = $3,375

The purchase price of the television in dollars is $3,375.

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