An economist states that 10% of Champaign-Urbana’s labor force is unemployed. A random sample of 400 people in the labor force is obtained, of whom 28 are unemployed. What is the minimum sample size required in order to estimate the unemployment rate in Champaign-Urbana to within 2% of its true value with 95% confidence? (Use the economist’s guess as your initial assumed value for p.)

The probability of drawing a 7 followed by a 10 is (4/52) x (4/51) = 0.006 or 0.6%.

To calculate the probability of drawing a 7 first and then a 10 from a standard 52-card deck, you need to consider the number of 7s and 10s in the deck and the total number of cards.

There are 4 sevens and 4 tens in the deck. The probability of drawing a 7 first is 4/52 (since there are 4 sevens and 52 cards in total). After drawing a 7, there are now 51 cards left in the deck. The probability of drawing a 10 next is 4/51 (since there are still 4 tens but now only 51 cards).

To find the overall probability, multiply the probabilities of each event: (4/52) * (4/51) = 16/2652 ≈ 0.006 or 0.6%.

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Answer: 4976.28

Step-by-step explanation:

V=πr2h=π·122·11≈4976.28276

hope this helps!

There are 4,845 possible committees that can be formed from the 20-person Mathematics Department.

In this scenario, the Mathematics Department needs to form a committee of 4 people from a group of 20. To determine the number of possible committees, we need to use the concept of combinations, as the order of members within the committee does not matter.

A combination is a selection of items from a larger set, such that the order of the items does not matter. The formula for calculating combinations is:

C(n, k) = n! / (k! * (n - k)!)

Where:
- C(n, k) represents the number of combinations
- n is the total number of items in the set (in this case, the 20 people in the Mathematics Department)
- k is the number of items to be selected (in this case, the 4 members of the committee)
- n! (n factorial) means the product of all positive integers up to n
- k! (k factorial) means the product of all positive integers up to k

Applying the formula to your question:

C(20, 4) = 20! / (4! * (20 - 4)!)

C(20, 4) = 20! / (4! * 16!)

C(20, 4) = 2,432,902,008,176,640,000 / (24 * 20,922,789,888,000)

C(20, 4) = 4,845

So, there are 4,845 possible committees that can be formed from the 20-person Mathematics Department.

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The value of x in the circle is 10.75.

Option B is the correct answer.

We have,

In a circle, opposite angles are equal. So, we have:

m∠AOB = m∠COD (opposite angles)

Also, adjacent angles in a cyclic quadrilateral add up to 180 degrees.

m∠AOB + m∠BOD = 180°

Substituting the given values, we get:

(2x - 4)° + (14x + 12)° = 180°

Simplifying and solving for x, we get:

16x + 8 = 180

16x = 172

x = 10.75

Therefore,

The value of x in the circle is 10.75.

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To find the number of radios that had both digital tuners and CD players, we need to use the concept of overlapping sets. We know that there were 210 radios with digital tuners and 270 with CD players, but some of these radios had both features.

To find the number of radios that had both digital tuners and CD players, we need to subtract the number of radios that had only one of these features from the total number of radios.

Let X be the number of radios that had both digital tuners and CD players.

Then, the number of radios that had only digital tuners is 210 - X, and the number of radios that had only CD players is 270 - X.

The total number of radios is given as 300, so we can set up an equation:

X + (210 - X) + (270 - X) = 300

Simplifying this equation, we get:

X = 180

Therefore, there were 180 clock radios with both digital tuners and CD players.

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If the temperature of the turducken is 150° after half an hour, the temperature of the turducken after 45 minutes is 225 degrees.

To determine the temperature of the turducken after 45 minutes, we first need to establish the rate at which the temperature is changing.

Find the temperature change after half an hour (30 minutes)
The given temperature after 30 minutes is 150 degrees.

Calculate the rate of temperature change per minute
Temperature change / time = 150 degrees / 30 minutes = 5 degrees/minute

Determine the temperature after 45 minutes
Since the temperature increases by 5 degrees every minute, we need to find the temperature increase for an additional 15 minutes (45 minutes - 30 minutes = 15 minutes).

Temperature increase for 15 minutes = 5 degrees/minute * 15 minutes = 75 degrees

Add the temperature increase to the initial temperature
Temperature after 45 minutes = 150 degrees (initial temperature) + 75 degrees (increase) = 225 degrees

Therefore, the temperature of the turducken after 45 minutes is 225 degrees.

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The work done in moving the expression from the origin to a distance of 3 feet is 99.25 pounds-feet.

To find the work done in moving the particle from the origin to a distance of 3 feet, we first need to find the expression for the force exerted on the particle. According to the given information, the force exerted on the particle is given by 3x^3 + 6 pounds at a point x feet from the origin.
To calculate the work done, we need to use the formula W = ∫F(x)dx where F(x) is the force function and dx is the displacement of the particle.
In this case, we are moving the particle from the origin (x = 0) to a distance of 3 feet (x = 3). Therefore, the work done can be calculated as:
W = ∫(3x^3 + 6) dx from 0 to 3
Simplifying the integral, we get:
W = [(3/4)x^4 + 6x] from 0 to 3
W = [(3/4)(3^4) + 6(3)] - [(3/4)(0^4) + 6(0)]
W = 81/4 + 18
W = 99.25 pounds-feet
Therefore, the work done in moving the expression from the origin to a distance of 3 feet is 99.25 pounds-feet.

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Yoplait yogurt's support of the breast cancer research (donating 10 cents for each pink Yoplait lid customers send in) is a form of Corporate Social Responsibility (CSR), specifically cause-related marketing.

CSR refers to a company's voluntary actions that go beyond legal

requirements to address social and environmental issues.

Cause-related marketing is a type of CSR where a company associates

itself with a social cause and promotes it through its marketing efforts.

In this case, Yoplait is supporting breast cancer research by donating 10

cents for every pink Yoplait lid that customers send in, which is a form of

cause-related marketing.

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Answer:

The length of side x is 9√2.

Step-by-step explanation:

In an isosceles right triangle, the length of the hypotenuse is √2 times the length of each leg. So x = 9√2.

The probability of getting someone in the 18-21 age bracket or someone who refused to respond is approximately 0.34 or 34%.

To find the probability of getting someone in the 18-21 age bracket or someone who refused to respond, we need to add the probabilities of these two events happening.

First, let's find the probability of getting someone in the 18-21 age bracket. Out of the total 374 people contacted, 88 are in this age bracket. So the probability of getting someone in this age bracket is 88/374.

Next, let's find the probability of getting someone who refused to respond. Out of the total 374 people contacted, 13 in the 18-21 age bracket and 26 in the 22-29 age bracket refused to respond. So the total number of people who refused to respond is 13+26=39. Therefore, the probability of getting someone who refused to respond is 39/374.

Finally, we add these two probabilities to get the probability of getting someone in the 18-21 age bracket or someone who refused to respond:

88/374 + 39/374 = 127/374

total is 0.34% or 34%

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Answer:

c

Step-by-step explanation:

I did the test and got it correct

The correct for the new member's score will affect center and spread of the bowling team is,

⇒ The new member's score will increase the center and spread of the bowling team.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The members of a bowling team score from 159 to 221. Their average score is 172.

And, A new member with an outlying score of 279 joins the team.

We know that;

When we add new member with an outlying score of 279 joins the team, the value of average is increase.

Thus, The correct for the new member's score will affect center and spread of the bowling team is,

⇒ The new member's score will increase the center and spread of the bowling team.

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Instantaneous voltage equation: v = X(1 - e^(-t/Y))
X = 11
Y = 1

a) Differentiate v with respect to t to give an equation for dv/dt:

Using the chain rule and the fact that the derivative of e^(ax) is a*e^(ax), we get:

dv/dt = X * (-1/Y) * e^(-t/Y) = -11/Y * e^(-t/Y)

Since Y = 1:

dv/dt = -11 * e^(-t)

b) Calculate the value of dv/dt at t = 2s and t = 4s:

For t = 2s:
dv/dt = -11 * e^(-2) ≈ -11 * 0.135 = -1.485

For t = 4s:
dv/dt = -11 * e^(-4) ≈ -11 * 0.018 = -0.198

c) Find the second derivative (d^2v/dt^2):

To find the second derivative, we differentiate dv/dt once more:

d^2v/dt^2 = d/dt(-11 * e^(-t)) = 11 * e^(-t)

In summary:

a) dv/dt = -11 * e^(-t)
b) At t = 2s, dv/dt ≈ -1.485; at t = 4s, dv/dt ≈ -0.198
c) d^2v/dt^2 = 11 * e^(-t)

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For a simple random sample with size 22 and mean of 129, the computed value the standard error of the mean is equals to the 0.6396.

The standard error is a statistical term that measures the accuracy for which a sample distribution represents a population by using standard deviation. The deviation of sample mean from population mean is called the standard error of mean. SEM is calculated by the standard deviation divided by the square root of the sample size, [tex]SEM = \frac{ \sigma}{\sqrt{n}}[/tex]

We have a simple random sample from a population that has a normal distribution. Also, Mean of sample = 129

Sample size, n = 22

Standard deviations of sample, σ = 3

Using the formula of standard error of mean is, SEM [tex]= \frac{ 3}{\sqrt{22}}[/tex]

= 0.63960

Hence, required value is 0.6396.

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In ANOVA, a main effect occurs when a factor significantly affects the outcome variable. This means that there is a statistically significant difference in the outcome variable across the different levels or categories of the factor being tested. For example, in a study comparing the effectiveness of different types of medication for a particular condition, a main effect would be present if the type of medication significantly affected the outcome (e.g. reduction in symptoms).

It is important to note that a main effect does not necessarily indicate the presence of an interaction between factors or outcomes. An interaction occurs when the effect of one factor on the outcome variable differs depending on the level or category of another factor. For example, in a study comparing the effectiveness of medication for a particular condition, an interaction might occur if the effect of the medication was different for men and women.

In summary, a main effect in ANOVA occurs when there is a significant difference in the outcome variable across the levels or categories of a factor being tested, while an interaction occurs when the effect of one factor on the outcome variable differs depending on the level or category of another factor.
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If Ed wants to determine whether there is a statistically significant difference in performance between two related groups, in this case, the same group of students taking the test twice, he can use a paired samples t-test.

The paired samples t-test is a hypothesis test that compares the means of two related groups to determine whether there is a statistically significant difference between them. It is appropriate when the data are paired or matched, such as when the same group of individuals is measured twice.

In this case, Ed can use the paired samples t-test to compare the scores of the same group of students on the two tests. He can calculate the difference between the scores of each student on the two tests and then use the t-test to determine whether the mean difference is statistically significant.

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The rate of change of the area when the radius is 2 centimeters is approximately 100.5 square centimeters per minute.

To find the rate of change of the area of a circle when the radius is 2 centimeters, we need to use the formula for the area of a circle, which is [tex]A = πr^2.[/tex]

We know that the radius is increasing at a rate of 8 centimeters per minute, so we can use this information to find the rate of change of the area.

We can start by finding the area of the circle when the radius is 2 centimeters. Substituting r = 2 into the formula, we get:

A = π(2)^2
A = 4π

So the area of the circle is 4π square centimeters when the radius is 2 centimeters.

Now, let's find the derivative of the area with respect to time. Using the power rule of differentiation, we get:

dA/dt = 2πr (dr/dt)

Substituting r = 2 and dr/dt = 8, we get:

dA/dt = 2π(2)(8)
dA/dt = 32π

So the rate of change of the area when the radius is 2 centimeters is 32π square centimeters per minute. To round this to one decimal place, we can use a calculator to get:

dA/dt ≈ 100.5

Therefore, the rate of change of the area when the radius is 2 centimeters is approximately 100.5 square centimeters per minute.

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A sequence starts with a LS of a child seated at a desk coloring. There is a cut to a MS of that same scene, but the child is now drinking from a glass is Jump cut, option C.

In film editing, a jump cut is a split that separates a single continuous sequential shot of a subject into two sections, with a section of the video edited out to create the illusion of a temporal leap. To accomplish the effect, the subject's camera position in the remaining clips in the sequence need only be slightly altered. It is a manipulation of temporal space that uses a single shot's length and fractures it to advance the viewer.

Jump cuts are therefore viewed as a breach of traditional continuity editing, which tries to de-emphasize editing and create the illusion of continuous time and space in the story-world. Nevertheless, jump cuts are occasionally utilised for artistic reasons. Jump cuts frequently highlight how carefully the movie was put together. Occasionally, more than one jump cut is used in a single sequence.

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Complete question:

A sequence starts with a LS of a child seated at a desk coloring. There is a cut to a MS of that same scene, but the child is now drinking from a glass. This represents: Group of answer choices:

Editing

Continuity

Jump cut

Cutaway

This represents transition from the scene of coloring to drinking.

The sequence represents a transition from coloring to drinking. The initial LS (long shot) shows a child seated at a desk, engaged in the activity of coloring. This establishes the starting point of the sequence.

But in the subsequent MS (medium shot), the same scene is depicted but now the child is seen drinking from a glass instead of coloring. This transition from coloring to drinking indicates a change in activity within the sequence. The shift from the LS to the MS with the child's change in action from coloring to drinking signifies progression of time or a shift in focus.

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To find the height of the new rectangular box, we first need to determine the volume of the original can. The can has a height of 6 inches and a diameter of 4 inches, which means it has a radius of 2 inches. The volume of a cylinder (can) is calculated using the formula V = πr²h.

In this case, V = π(2²)(6) = 24π cubic inches.

Now, we need to find the height of the new rectangular box that has a width of 4 inches and a depth of 2 inches. To maintain the same volume, the formula for the volume of a rectangular prism (box) is V = lwh.

Since we know the volume (24π cubic inches), width (4 inches), and depth (2 inches), we can solve for the height (h):

24π = (4)(2)(h)
24π = 8h

Now, divide both sides by 8:

h = 3π inches

So, the height of the new rectangular box would be 3π inches to maintain the same volume as the original can.

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Ultimately, the best approach will depend on the specific circumstances and needs of the company. A combination of these strategies may be necessary to effectively address the issue of machine breakdowns and ensure reliable production.

less reliable, which is causing delays in production and increasing the cost of maintenance. The president has asked for your advice on how to address this issue.

Here are some suggestions on how to address the issue of machine breakdowns:

Invest in new machines: The most straightforward solution is to invest in new machines that are more reliable and efficient. While this option may involve a significant upfront cost, it can help reduce long-term expenses related to maintenance and delays caused by machine breakdowns.

Implement a preventive maintenance program: A preventive maintenance program can help reduce the likelihood of machine breakdowns by regularly inspecting and servicing the machines. This can include tasks such as lubrication, cleaning, and replacing worn-out parts.

Train machine operators: Proper training of machine operators can help prevent breakdowns caused by human error. This includes training on how to operate the machines safely and efficiently, as well as how to identify and report potential issues before they become major problems.

Implement a predictive maintenance program: Predictive maintenance involves using sensors and data analysis to monitor the condition of machines and predict when maintenance is needed. This can help identify potential issues before they lead to a breakdown, reducing downtime and maintenance costs.

Outsource maintenance: If maintaining machines is not the company's core competency, it may be more cost-effective to outsource maintenance to a specialized service provider. This can help ensure that machines are properly maintained without requiring the company to invest in additional resources or expertise.

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There were 20 questions on the quiz.

Let's start by using algebra to solve the problem.

Let x be the total number of questions on the quiz.

If Jianna got 87.5% of the questions correct, then she got 0.875x questions

correct.

We also know that Jianna got 17.5 questions correct.

So we can set up the equation:

0.875x = 17.5

To solve for x, we can divide both sides by 0.875:

x = 20

Therefore, there were 20 questions on the quiz.

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This format had 144 possible telephone area codes in the United States and Canada.

We can calculate the number of possible area codes based on the given information by multiplying the number of options for each digit.

There are 8 options for the first digit (2 through 9), 2 options for the second digit (0 or 1), and 9 options for the third digit (1 through 9).

So, the total number of possible area codes is:

8 x 2 x 9 = 144

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The most likely action that the researcher will take will depend on the specific details of the experiment, the resources available, and the scientific objectives of the study. However, the researcher should aim to address the sources of uncertainty and variability in the data to obtain a more accurate estimate of the response time that can be of practical use.

The wide confidence interval indicates that there is a large amount of uncertainty in the estimate of the average response time. To obtain a more precise estimate, the researcher may need to increase the sample size or use a different experimental design to reduce variability and improve the accuracy of the estimate.

Alternatively, the researcher may need to revise the methodology or protocol to identify potential sources of error or bias in the data collection process. For instance, if the stimulus is poorly calibrated, or if the mice are not acclimated to the testing environment, this could contribute to variability in the response time.

Another possibility is to explore alternative statistical methods that may provide a more precise estimate of the response time. For instance, if the distribution of response times is known to be skewed, the researcher could use a nonparametric method to estimate the median response time instead of the mean.

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The median from A meets BC at D is  (2.5, 3)

The coordinates of the point D is (4,2).

(i) To find the coordinates of the point D, we first need to find the midpoint of BC.

Midpoint of BC = ( (1+6)/2 , (4+5)/2 ) = (3.5, 4.5)

Now, we can find the slope of AD as follows:

Slope of AD = (5-2) / (6-4) = 1.5

Using the point-slope form of a line, we can write the equation of AD as:

y - 2 = 1.5(x - 4)

Simplifying this equation, we get:

y = 1.5x - 4

To find the coordinates of D, we need to solve for the intersection of AD and BC.

Substituting y = 1.5x - 4 into the equation of BC (y - 4 = (5-4)/(6-1)(x-1)), we get:

1.5x - 4 = 0.2x + 3.6

Solving for x, we get:

x = 4

Substituting x = 4 into the equation of AD, we get:

y = 1.5(4) - 4 = 2


(ii) To find the coordinates of the midpoint of AB, we can simply use the midpoint formula:

Midpoint of AB = ( (4+6)/2 , (2+5)/2 ) = (5, 3.5)

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The probability that at least one household has their TV set tuned to the game is 1 - (1-0.22)^33, which is approximately 0.993.

To solve this problem using the direct method, we can use the fact that 22% of TV sets were tuned to the game. This means that the probability of a randomly selected TV set being tuned to the game is 0.22.

To find the probability that at least one of the 33 households surveyed had their TV set tuned to the game, we can use the complement method. The complement of the event "at least one household has their TV set tuned to the game" is "none of the households have their TV set tuned to the game".

Using the complement method, we can find the probability of this event by taking the probability that no households have their TV set tuned to the game, which is (1-0.22)^33.

So, the probability that at least one household has their TV set tuned to the game is 1 - (1-0.22)^33, which is approximately 0.993.

If I had to do this by hand, I would use the complement method, as it involves simpler calculations.

To find the probability that at least one TV set among the 33 households surveyed is tuned to NBC Sunday Night Football, we can use either the direct method or the complement method.

1. Direct Method:
The direct method requires calculating the probabilities of 1, 2, 3, ..., 33 households watching the game, and then summing up these probabilities. This method can be tedious and time-consuming, especially when done by hand.

2. Complement Method:
The complement method is generally easier and quicker, as it involves calculating the probability that none of the 33 households is watching the game and then subtracting this probability from 1.

Given that 22% (0.22) of the TV sets in use were tuned to the game, the probability that a household is not watching the game is 1 - 0.22 = 0.78.

For all 33 households not to be watching the game, the probability is (0.78)^33 ≈ 0.00038.

Now, to find the probability that at least one household is watching the game, we subtract this probability from 1:

1 - 0.00038 ≈ 0.99962.

So, the probability that at least one of the 33 households is tuned to NBC Sunday Night Football is approximately 0.99962.

If you had to do this by hand, the complement method would be the preferred approach, as it requires fewer calculations and is more straightforward.

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Answer:

Step-by-step explanation:

To calculate the total length of crepe paper Katie needs to buy, we first need to find the length of each diagonal of the ceiling.

Since the ceiling is a square, the length of each diagonal can be found using the Pythagorean theorem:

diagonal^2 = side^2 + side^2

diagonal^2 = 2 * side^2

diagonal = sqrt(2 * side^2)

diagonal = sqrt(2 * 20^2) = sqrt(800) = 20 * sqrt(2)

So the length of each diagonal is 20 * sqrt(2) ft.

Katie needs to hang crepe paper around the perimeter of the ceiling, which is 4 * 20 = 80 ft long.

She also needs to hang crepe paper from each corner to the opposite corner, which means she needs to cover the length of each diagonal twice. So the total length of crepe paper she needs is:

2 * 20 * sqrt(2) + 80 = 40 * sqrt(2) + 80 ≈ 131.31 ft

Therefore, Katie needs to buy at least 6 rolls of crepe paper (since each roll contains 25 ft of crepe paper).

As the number of degrees of freedom for a t-distribution increases, the difference between the t-distribution and the standard normal distribution (b) becomes smaller.

As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution becomes smaller. This is because as the degrees of freedom increase, the t distribution approaches the normal distribution in shape and becomes more concentrated around the mean. Therefore, the t distribution becomes more similar to the standard normal distribution, which has a mean of 0 and a standard deviation of 1. So, the correct answer is b. becomes smaller.

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option c) "When revenue is more than cost" is correct.

option c) "f'(x) = 180x^29 - 30x^14 + 12x^2 - 2" is correct.

Problem 1: The best approximation for finding the price of an individual product is the marginal cost. Marginal cost is the cost of producing one additional unit of a product, and it takes into account the incremental costs associated with producing each additional unit. This information can be used to determine the optimal price point for a product that maximizes profit.

Problem 2: Profit is earned when revenue is more than cost. In other words, when the total revenue generated by a product or service is greater than the total cost of producing and selling it, a profit is earned. Therefore, option c) "When revenue is more than cost" is correct.

Problem 3: There is no problem statement provided for this question.

Problem 4: The derivative of f(x) = 6x^30 – 2x^15 + 4x^3 – 2x +1 is f'(x) = 180x^29 - 30x^14 + 12x^2 - 2. To find the derivative of a polynomial function, we use the power rule, which states that the derivative of x^n is nx^(n-1), where n is a constant. We apply this rule to each term of the function and simplify to obtain the answer. Therefore, option c) "f'(x) = 180x^29 - 30x^14 + 12x^2 - 2" is correct.

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The statement "r of 1 means that all variability is shared" is FALSE regarding the calculation of the correlation coefficient, r.

The correlation coefficient, r, ranges from -1 to 1, with a value of 1 indicating a perfect positive correlation and a value of -1 indicating a perfect negative correlation. A value of 0 indicates no correlation between the variables.

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To solve this problem, we can use the binomial probability formula:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

Where:
- P(X=k) is the probability of getting k nonconforming washing machines in the sample
- n is the sample size, which is 10 in this case
- p is the probability of getting a nonconforming washing machine, which is 0.08
- (n choose k) is the binomial coefficient, which is the number of ways to choose k items from n without replacement, and is calculated as n! / (k! * (n-k)!)

So, to find the probability of getting 1 nonconforming washing machine in the sample, we plug in k=1:

P(X=1) = (10 choose 1) * 0.08^1 * (1-0.08)^(10-1)
P(X=1) = 10 * 0.08 * 0.9227
P(X=1) = 0.0738

Therefore, the probability of getting 1 nonconforming washing machine in the sample is approximately 0.0738, or 7.38%.

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