c. Is 247 a prime or composite number? Explain.

We assume that with a linear relationship between two variables, for any fixed value of x, the observed residuals follows a normal distribution.

This assumption is based on the Central Limit Theorem, which states that when the sample size is large enough, the distribution of sample means will be approximately normal, regardless of the shape of the underlying population distribution.

In the case of a linear relationship between two variables, we can assume that the residuals (the difference between the observed y values and the predicted values based on the linear regression model) follow a normal distribution with mean 0 and constant variance. This assumption is important because it allows us to use statistical methods that rely on normality, such as hypothesis testing and confidence intervals.

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Explanation

Step 1

2 lines are parallel if they have the same slope, so

a) let's check the slope of the given line

it is in the form

so, the slope of the line we are looking for is 8

Step 2

Now, to find the equation of the line, we can use this expression

then, Let

replace,

therefore, the answer is

I hope this helps you

The 95% confidence interval for the mean gas mileage of a 2012 Prius by all drivers who participate on fueleconomy.gov would depend on the sample size and the sample mean and standard deviation of the gas mileage data.

To calculate a 95% confidence interval for the mean gas mileage of a 2012 Prius by all drivers who participate on fueleconomy.gov, we would need to gather a sample of gas mileage data from the website. We would then calculate the sample mean and standard deviation of the gas mileage.
Assuming the sample follows a normal distribution and we have a sample size of at least 30, we can use the t-distribution to calculate the confidence interval. With a 95% confidence level and n degrees of freedom (n-1 = sample size - 1), we can look up the t-value using a t-distribution table or calculator.
Once we have the t-value, we can plug it into the following formula to calculate the confidence interval:
Confidence interval = sample mean ± (t-value * standard error)
The standard error is calculated by dividing the sample standard deviation by the square root of the sample size.

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9. A - Each person is assigned a three-digit number (from 000 to 999). On a Random Digit Table, numbers are read, three at a time. The first hundred three-digit numbers read will represent the people in the sample.

10. C - Every man in the sampling frame will be assigned 8 sequential 4-digit numbers and every woman in the sampling frame will be assigned 12 sequential 4-digit numbers. From a Random Digit Table, groupings of 4 numbers will be read and the first 100 subjects with their number read will be in the sample (duplicate selections will be ignored).

9. Method A is probability sampling because each individual in the sampling frame has an equal chance of being selected, and the selection is based on random digits.

10. Method C is stratified sampling because the sampling frame is divided into two strata based on gender, and each stratum is sampled separately using a random selection method. This allows for a more representative sample by ensuring that both men and women are adequately represented in the sample.

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9. A - Each person is assigned a three-digit number (from 000 to 999). On a Random Digit Table, numbers are read, three at a time. The first hundred three-digit numbers read will represent the people in the sample.

10. C - Every man in the sampling frame will be assigned 8 sequential 4-digit numbers and every woman in the sampling frame will be assigned 12 sequential 4-digit numbers. From a Random Digit Table, groupings of 4 numbers will be read and the first 100 subjects with their number read will be in the sample (duplicate selections will be ignored).

9. Method A is probability sampling because each individual in the sampling frame has an equal chance of being selected, and the selection is based on random digits.

10. Method C is stratified sampling because the sampling frame is divided into two strata based on gender, and each stratum is sampled separately using a random selection method. This allows for a more representative sample by ensuring that both men and women are adequately represented in the sample.

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Answer:

2^3

Step-by-step explanation:

you subtract the exponents if they have the same coefficient when dividing them.

9-6=3

The rate of the motorboat in still water is 49 km/hr. The rate of the current is 6 km/hr.

We have, A motorboat travels 258 km in 6 hours going upstream. It travels 330 km going downstream in the same amount of time. We have to calculate the rate of the boat in still water and the rate of the current. Let the speed of the boat in still water and rate of stream be "B" and "S" respectively.

Using the relative speed formula , the speed upstream is B - S and the speed downstream is B + S.

Use the distance , in speed/rate formula ,

Rate × Time = Distance

Upstream : (B-S)6 = 258

=> B - S = 43 --(1)

Downstream: (B+S)6 = 330

=> B + S = 55 --(2)

Solve the linear equations by elimination method. Add the two equations.

=> 2B = 98

=> B = 49 km/hr

Substitute this value of B in equation(2) and solve for S, B+S = 55

=> 49+S = 55

=> S = 6 km/hr

So, the rate of the current is 6 km/hr.

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Complete question:

A motorboat travels 258 km in 6 hours going upstream. It travels 330 km going downstream in same amount of time. What is the rate of the boat in still water and what is the rate of the current.

When a four-digit number is divisible by nine and is written as 3AA1, the digit A stands for 7.

A number is itself divisible by nine if the total of its digits is also nine digits.

Multiples in mathematics are the outcomes of multiplying an integer by a certain number. a multiple of 9 is a number that divides by nine.

By utilizing the aforementioned attribute, we can

3 + A +A +1 = 9, OR 18, OR 27

4 + 2A = 9, OR 18, OR 27

using 18

2A = 18 - 4

2A = 14

A = 7

therefore we can say that the number is  3771

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Answer:

Step-by-step explanation:

Test score = Time x 10 + 50

Hope that helps!

after 3 trips, the probabilities for the driver's locations are approximately 0.524 for airport A, 0.274 for hotel B, and 0.202 for hotel C. If the driver starts at hotel B, after 3 trips, we expect them to be at hotel B with a probability of approximately 0.46. The stationary distribution of the chain indicates that, in the long run, the driver is most likely to be found at the airport (state A) with a probability of approximately 0.4167.

(a) To find the transition probability matrix, we assign the values A = 0, B = 1, and C = 2. The matrix will have dimensions 3x3, with each entry representing the probability of transitioning from one state to another.

Let's denote the transition probability matrix as P. The entries of P are given by:

P = [[0, 1/4, 3/4],

[4/5, 0, 1/5],

[4/5, 1/5, 0]]

(b) If the driver is initially at the airport (state A), we can find the probability of their location after 3 trips by multiplying the initial state vector [1, 0, 0] by the transition probability matrix P three times:

[1, 0, 0] * \(P^3\)= [0.524, 0.274, 0.202]

Therefore, after 3 trips, the probabilities for the driver's locations are approximately 0.524 for airport A, 0.274 for hotel B, and 0.202 for hotel C.

(c) If the driver is initially in hotel B (state B), we can calculate the probability of their location after 3 trips by multiplying the initial state vector [0, 1, 0] by the transition probability matrix P three times:

[0, 1, 0] *\(P^3\)= [0.46, 0.46, 0.08]

Therefore, after 3 trips, we expect the Uber driver to be at hotel B with a probability of approximately 0.46.

(d) To find the stationary distribution of the chain, we need to solve the equation π = π * P, where π is the stationary distribution vector. This equation represents the balance between entering and leaving each state in the long run. Solving this equation yields the following vector:

π = [0.4167, 0.2778, 0.3056]

Interpretation: The stationary distribution indicates the long-term probabilities of the Uber driver's location in the Markov chain. In this case, the Uber driver is most likely to be found at the airport (state A) with a probability of approximately 0.4167. Hotel C has the second highest probability of approximately 0.3056, while hotel B has the lowest probability of approximately 0.2778. This suggests that, on average, the Uber driver spends the most time at the airport, followed by hotel C, and the least time at hotel B.

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Answer:

The slope of the line is 0.1.

Answer:

See below

Step-by-step explanation:

a) Using the first two lines to get the equation:

Since t = 0 represents a start point, the y-intercept is 163488

Slope is:

And the equation:

b) Prediction of the population in 2012 using the function:

As we see the number we got is less than the one on the line 3 of the table. So the model underestimated the actual population.

Answer:

12

Step-by-step explanation:

The proportion is equal to \(\frac{x}{10}=\frac{42}{35}\)

We can simplify the right side by dividing by 7/7 to get the right side equal to 6/5. Now we can cross-multiply to get

\(60=5x\)

Dividing both sides by 5, we have the answer as

\(x=12\)

Answer:

The price per unit of chocolate bars is £0.3.

Step-by-step explanation:

The cost of 4 chocolates bars is  £1.20.

The cost of 1 chocolate bars is \(\frac{1.20}{4}\)

The cost of 1 chocolate bars is £0.3.

Answer: $4.80 (us dollars)

Step-by-step explanation:

Answer:

A=439.82 or A=439

Step-by-step explanation:

~~~~~~~~:)

Answer:

sin20°

Step-by-step explanation:

Using the cofunction identity

cosx = sin(90 - x) , thus

cos70° = sin(90 - 70)° = sin20°

I can help you with that problem i just did that on my own.

you can go for option g cause ans is 14:5

The basic unit of mass of the ball in the metric system is the gram.

The base units of length (distance), capacity (volume), and weight (mass) in the metric system are the meter, liter, and gram, respectively. We utilize units that are derived from metric units to measure smaller or greater quantities.

Mass is a physical body's total amount of matter. Inertia, or the body's resistance to acceleration when a net force is applied, is also measured by this term. The strength of an object's gravitational pull to other bodies is also influenced by its mass.

Therefore, the basic unit of mass of the ball in the metric system is the gram.

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Answer:

y=2x-5

Step-by-step explanation:

Given the following expression:

You can find an equivalent expression by simplifying it.

Remember the Sign Rules for Multiplication:

Then, you can rewrite the expression as follows:

And finally, you have to add the like terms (by definition, like terms have the same variables and the same exponents). Then, you get:

Therefore, the answer is: Second option.

Answer:-4

Step-by-step explanation:

11,7,3,-1,-5,......they have a difference of -4

11-4=7

7-4=3

3-4=-1

-1-4=-5

Recursive formula for the given sequence is \(a_{n}=a_{n-1}-4\)

A recursive formula is a formula that defines any term of a sequence in terms of its preceding term(s).

Consider

The first term \(a_{1} =11\)

second term \(a_{2}=7\)

Common difference = 7-11 = -4

Third term \(a_{3}=3\)

Common difference = 3-7 =- 4

Fourth term \(a_{4}=-1\)

Common difference = -1-3= -4

Then the formula for the sequence is \(a_{n}=a_{n-1}-4\)

Hence, the Recursive formula for the give sequence is \(a_{n}=a_{n-1}-4\)

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Answer:

Your answer is -6 just count down with negatives

The conclusion that can be made at the 0.05 significance level is that we reject the null hypothesis and conclude that there is enough evidence at the 0.05 significance level to conclude that participation in Greek life has increased since 2005, option b.

Based on the given information, we conducted a hypothesis test to determine if the percentage of students who participate in Greek life has increased since 2005. The significance level is given as 0.05. The p-value obtained from the study is 0.0031.
To interpret the results, we compare the p-value with the significance level. If the p-value is less than the significance level, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
In this case, the obtained p-value (0.0031) is less than the significance level (0.05). Therefore, we reject the null hypothesis and conclude that there is enough evidence at the 0.05 significance level to conclude that participation in Greek life has increased since 2005.
Therefore, the correct answer to the question is option b.  "We reject the null hypothesis and conclude that there is enough evidence at the 0.05 significance level to conclude that participation in Greek life has increased since 2005."

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Because it only considers the worst possible outcomes, the maximin decision criterion has the least downside risk.

Wald's maximin model is a non-probabilistic decision-making model in game theory and decision theory.

It says that while choosing a course of action, the decision-maker should choose the one whose greatest (highest) loss is better than the least (minimum) loss of all other options that are feasible under the current conditions. The approach that maximizes one's own lowest payout is referred to as "maximin" in non-zero-sum games.

When given a choice between numerous options, the maximin approach instructs managers to consider each option's worst-case outcome. This presupposes that each choice has a number of possible outcomes.

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These standardization methods are crucial in chromatography to ensure accurate quantification and comparability of results.

In chromatography, standardization methods are used to ensure accurate and reliable results by establishing reference points or calibration standards. Here are three common methods of standardization in chromatography: External Standardization: In this method, a set of known standard samples with known concentrations or properties is prepared separately from the sample being analyzed. These standards are then analyzed using the same chromatographic conditions as the sample. By comparing the response of the sample to that of the standards, the concentration or properties of the sample can be determined. Internal Standardization: This method involves the addition of a known compound (internal standard) to both the standard solutions and the sample. The internal standard should ideally have similar properties to the analyte of interest but be different enough to be easily distinguished. The response of the internal standard is used as a reference to correct for variations in sample preparation, injection volume, and instrumental response. Internal standardization helps improve the accuracy and precision of the analysis. Standard Addition: This method is useful when the matrix of the sample interferes with the analysis or when the analyte concentration is unknown. It involves adding known amounts of the analyte of interest to different aliquots of the sample. The response of the analyte is then measured, and the concentration is determined by comparing the response with that of the standards. The difference in response between the sample and the standards allows for the determination of the analyte concentration in the original sample.

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