There are 230 students enrolled in stat 155. suppose 127 of these students are majoring in computer science. The frequency for the number of computer science students enrolled in stat 155 is ____ and the relative frequency is ___ enter any decimal values to 3 places.

Data value is multiplied by a positive number, the shape and spread of the distribution change while the center remains the same.

Multiplying each data value by a number greater than 1 will stretch the distribution, making it wider, while multiplying each data value by a number between 0 and 1 will compress the distribution, making it narrower.

Data value in a distribution is transformed linearly by multiplying or dividing each value by a number, the shape and spread of the distribution may change, the center of the distribution remains unchanged.

This happens because multiplication by a number changes the scale of the data.

As a result, the range and variability of the data change in proportion to the scaling factor.

Similarly, if each data value is divided by a positive number, the shape and spread of the distribution change while the center remains the same. Dividing each data value by a number greater than 1 will compress the distribution, making it narrower, while dividing each data value by a number between 0 and 1 will stretch the distribution, making it wider. This happens because division by a number changes the scale of the data in the opposite direction to multiplication.

It's important to note that if the number by which each data value is multiplied or divided is negative, then the distribution will be reflected around the mean, making it mirror image of the original distribution.

Overall, transforming a distribution linearly by multiplying or dividing each data value by a number can change the shape and spread of the distribution while leaving the center unchanged.

It's important to consider the impact of such transformations when interpreting the data and drawing conclusions from the distribution.

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The value of the test statistic is 1.177.

What is test statistic?

A test statistic is a numerical summary of sample data that is used in hypothesis testing. It is used to assess the strength of evidence against a null hypothesis by comparing the observed data to what would be expected if the null hypothesis were true.

To find the value of the test statistic, we need to use the formula:

test statistic = (sample statistic - hypothesized parameter) / (standard error of the sample statistic)

In this case, the hypothesized parameter is the standard deviation of pulse rates of adult males, which is stated to be more than 12 bpm. So, we have:

hypothesized parameter: σ > 12 bpm

sample size: n = 141

sample standard deviation: s = 13.4 bpm

To calculate the standard error of the sample standard deviation, we use the formula:

standard error of s = σ / √n

Since we don't know the value of σ, we will use the sample standard deviation s as an estimate for it:

standard error of s = s / √n = 13.4 / √141 = 1.126

Now, we can plug in the values into the formula for the test statistic:

test statistic = (s - σ) / (standard error of s)

= (13.4 - 12) / 1.126

= 1.177

Therefore, the value of the test statistic is 1.177.

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Answer:

Line Segment KL is perpendicular to line segment LM.

Step-by-step explanation:

Notice how there is a right angle between line segments LM and KL. By the definition of perpendicular lines, they are perpendicular. If you have the chance, please answer my last question if this is helpful.

The equation is true for any value of x! This means that no matter how many tools Victor gives to Ilay, the ratio of their tools will never be 3:4. Therefore, there is no solution to this problem.

Let's start by using algebra to represent the given information. Let's say that the number of tools Victor has is represented by the variable "v" and the number of tools Ilay has is represented by the variable "i".

According to the problem, we know two things:

The ratio of Victor's tools to Ilay's tools is 5:2, which can be written as:

v/i = 5/2

Victor has 42 more tools than Ilay, which can be written as:

v = i + 42

Now, we want to find how many tools Victor should give to Ilay so that the ratio becomes 3:4. Let's say that the amount of tools Victor gives to Ilay is represented by the variable "x".

After giving x tools to Ilay, Victor will have v-x tools, and Ilay will have i+x tools. We want to find the value of x that makes the ratio of v-x to i+x equal to 3:4.

So, we can set up the following equation:

(v-x)/(i+x) = 3/4

Now we can substitute the expression for v and the ratio of v/i to get an equation in terms of i and x:

(i+42-x)/(i+x) = 3/4

Next, we can cross-multiply to get rid of the denominators:

4(i+42-x) = 3(i+x)

Simplifying this equation:

4i + 168 - 4x = 3i + 3x

Combining like terms:

i = 7x - 168

Now we have an equation that relates the number of tools Ilay has to the number of tools Victor gives him. We can substitute this into the equation v=i+42 to get an equation that only involves x:

v = 7x - 126

Finally, we can use this equation to find the value of x that makes the ratio 3:4.

(v-x)/(i+x) = 3/4

(7x-126-x)/(i+x) = 3/4

6x-126 = (3/4)(i+x)

6x-126 = (3/4)(7x-168+x)

6x-126 = (3/4)(8x-168)

6x-126 = 6x - 126

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So the probability distribution function for X is:

- P(X = 0) = 0.46

- P(X = 1) = 0.46

- P(X = 2) = 0.08

Probability is a measure of how likely an event is to occur. Many events are impossible to predict with absolute certainty.

(a) Using the tree diagram:

- P(RR) = (9/13) * (8/12) = 0.46

- P(RL) = (9/13) * (4/12) = 0.23

- P(LR) = (4/13) * (9/12) = 0.23

- P(LL) = (4/13) * (3/12) = 0.08

So the probabilities for the simple events are:

- P(RR) = 0.46

- P(RL) = 0.23

- P(LR) = 0.23

- P(LL) = 0.08

(b) The possible values for X are 0, 1, or 2.

- P(X = 0) = P(RR) = 0.46

- P(X = 1) = P(RL) + P(LR) = 0.23 + 0.23 = 0.46

- P(X = 2) = P(LL) = 0.08

So the probability distribution function for X is:

- P(X = 0) = 0.46

- P(X = 1) = 0.46

- P(X = 2) = 0.08

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The music box has a surface area of 1350 square cm.

A cube has six square faces that are all the same size. The length of each side of the cube is given as 15 cm. Therefore, the surface area of the cube can be found by calculating the area of one square face and then multiplying it by 6:

Area of one square face = (15 cm) x (15 cm) = 225 square cm

The surface area of the cube = 6 x (Area of one square face)

= 6 x 225 square cm

= 1350 square cm

As a result, the music box has a surface area of 1350 square cm.

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The missing lengths in the diagram are CU = 18 and UR = 6

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

QR = ST = 12

Also, we have

CU = 7x - 10

CV = 3x + 6

The length of the chords QR and ST have the same measure

This means that

CU = CV

Substitute the known values in the above equation, so, we have the following representation

7x - 10 = 3x + 6

Evaluate the like terms

So, we have

4x = 16

This gives

x = 4

Next, we have

UR = 1/2 * 12

UR = 6

And, we have

CU = 7(4) - 10

CU = 18

Hence, the missing lengths are CU = 18 and UR = 6

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Answer:

[tex]x \approx 60.4[/tex]

Step-by-step explanation:

We can solve for x using the trigonometric ratio cosine:

[tex]\cos(\theta) = \dfrac{\text{adjacent}}{\text{hypotenuse}}[/tex]

↓ plugging in the given values

[tex]\cos(22\°) = \dfrac{56}{x}[/tex]

↓ taking the reciprocal of (flipping) both sides

[tex]\dfrac{1}{\cos(22\°)} = \dfrac{x}{56}[/tex]

↓ multiplying both sides by 56

[tex]\dfrac{56}{\cos(22\°)} = x[/tex]

↓ plugging into a calculator

[tex]\boxed{x \approx 60.4}[/tex]

P is the centroid of triangle ABC, and we have AP = CP = BP, which is what we needed to prove.

Since â„“, m, and n are perpendicular bisectors of the sides of triangle ABC, they intersect at the circumcenter O of triangle ABC.

Since O is the circumcenter of triangle ABC, it lies on the perpendicular bisectors of all three sides. Therefore, OA = OB = OC.

Now, consider triangle AOC. Since OA = OC and â„“ is the perpendicular bisector of AC, â„“ passes through the midpoint of AC, which we will call D. Therefore, AD = CD.

Similarly, consider triangle BOC. Since OB = OC and n is the perpendicular bisector of BC, n passes through the midpoint of BC, which we will call E. Therefore, BE = CE.

We know that â„“, m, and n intersect at point P, so P is the intersection of lines AD, BE, and OC. Therefore, P is the centroid of triangle ABC, and we have AP = CP = BP, which is what we needed to prove.

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Only options I and III are (C)'s correct responses.

I. k-fold cross-validation requires fitting the model k times, whereas LOOCV requires fitting the model n times. Since k > n, k-fold cross-validation is more efficient computationally than LOOCV.

II. k-fold cross-validation has an advantage over LOOCV in bias reduction since each training set is a random sample of the data and tends to reduce bias.

III. LOOCV has an advantage over k-fold cross-validation in variance reduction since LOOCV uses almost all the data to fit the model for each test observation, resulting in lower variance in the test error estimate. In contrast, k-fold cross-validation uses only a subset of the data for each training set, which can lead to higher variance in the test error estimate.

In conclusion, assertions I and III are valid, and the proper response is (C) I and III alone.

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The total FICA tax amount on the annual salary of $38,480 is given by  option d. $2,943.72

Annual salary is equals to $38,480.

FICA (Federal Insurance Contributions Act) tax includes two separate taxes.

Social Security tax and Medicare tax.

The Social Security tax rate is 6.2% and the Medicare tax rate is 1.45%, making the total FICA tax rate 7.65%.

To determine the total annual FICA tax for an annual salary of $38,480,

we need to multiply the salary by the FICA tax rate,

Total FICA tax = Annual salary × FICA tax rate

⇒ Total FICA tax = 0.0765 x $38,480

⇒ Total FICA tax = $2,943.72

Therefore, the total annual FICA tax is equal to option d) $2,943.72.

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Answer:

d

Step-by-step explanation:

To find the cost of one bottle of water, we need to divide the total cost of the case by the number of bottles in the case, which is 24.

So,

Cost of one bottle of water = Total cost of case / Number of bottles in case

= $2.99 / 24

= $0.1246

Rounding this to two decimal places, we get:

Cost of one bottle of water = $0.12

Therefore, one bottle of water costs $0.12.

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The integral evaluates to 1/15.

Let's evaluate the iterated integral:

[tex]\int _{x=0}^{ x=2y} \int _{y=0} ^{y=12xy} \int _{z=1} ^{z=xy}[/tex]dz dx dy

This is a triple integral, which means we will need to integrate three times, one for each variable. The order in which we integrate will depend on the shape of the region of integration. In this case, we can see that the limits of z depend on x and y, which means we will need to integrate with respect to z first.

So, let's begin by integrating with respect to z:

[tex]\int _{x=0}^{ x=2y} \int _{y=0} ^{y=12xy} \int _{z=1} ^{z=xy}[/tex] dz dx dy

= [tex]\int _{x=0}^{ x=2y} \int _{y=0} ^{y=12xy}[/tex] [xy - 1] dx dy

= [tex]\int _{x=0}^{ x=2y}[/tex] [x²y - x] dy

= [tex]\int _{x=0}^{ x=2y}[/tex] [2y⁴ - y²] dy

= 2/5 - 1/3

= 1/15

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Complete Question:

Evaluate the iterated integral.

[tex]\int _{x=0}^{ x=2y} \int _{y=0} ^{y=12xy} \int _{z=1} ^{z=xy}[/tex]dz dx dy

a) We would expect about 4 people in the sample to name chocolate as their favorite flavor of ice cream.

b) The probability of exactly six people naming chocolate is 0.20190.

c) The probability of six or more people naming chocolate is 0.1118.

a) We can use the expected value formula for a binomial distribution, where the probability of success is p = 0.3 and the number of trials is n = 14:

E(X) = np = 14 × 0.3 = 4.2

Rounding this to the nearest whole number, we would expect about 4 people in the sample to name chocolate as their favorite flavor of ice cream.

b) To find the probability that exactly six people name chocolate, we can use the binomial probability formula:

P(X = 6) = (14 choose 6) ÷ 0.3⁶ × 0.7⁸

Using a calculator, we can evaluate this expression as:

P(X = 6) = 0.2019

Rounding this to 5 decimal places, the probability of exactly six people naming chocolate is 0.20190.

c) To find the probability that six or more people name chocolate, we can use the cumulative binomial probability formula:

P(X ≥ 6) = 1 - P(X < 6) = 1 - P(X ≤ 5)

We can calculate P(X ≤ 5) using the binomial cumulative distribution function or by summing the probabilities for X = 0, 1, 2, 3, 4, and 5. Using the latter method, we get:

P(X ≤ 5) = (14 choose 0) × 0.3⁰ × 0.7¹⁴ + (14 choose 1) × 0.3¹ × 0.7¹³ + (14 choose 2) × 0.3² × 0.7¹² + (14 choose 3) × 0.3³ × 0.7¹¹ + (14 choose 4) × 0.3⁴ × 0.7¹⁰ + (14 choose 5) × 0.3⁵ × 0.7⁹

Using a calculator, we can evaluate this expression as:

P(X ≤ 5) = 0.8882

Therefore, the probability that six or more people name chocolate is:

P(X ≥ 6) = 1 - P(X ≤ 5) = 1 - 0.8882 = 0.1118

Rounding this to 4 decimal places, the probability of six or more people naming chocolate is 0.1118.

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The first step to conducting a statistical study is to clearly define the research question or problem.

This involves identifying the population of interest, the variables to be measured, and the hypothesis or objective of the study. Once the research question is clearly defined, the next step is to design the study, including selecting an appropriate sample size, choosing a sampling method, and determining the data collection method.

It is also important to consider potential sources of bias and confounding factors that may impact the study results. Overall, a well-designed statistical study should be able to produce reliable and accurate results that can be used to draw meaningful conclusions about the population of interest.

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After elimination of Smith from the votes  Russell will win the vacation package.

No, irrelevant alternative criterion does not violated the case because ranking of remaining candidates was not affected by Smith's removal.

To determine who will win the vacation package after eliminating Smith from consideration,

Conduct a pairwise comparison of the remaining candidates.

Comparing the number of times each candidate was ranked first, second, third, and fourth.

Comparing Evans, Russell, and Ford, we can see that,

Evans was ranked first 11 times, second 14 times, third 11 times, and fourth 9 times.

Russell was ranked first 14 times, second 11 times, third 9 times, and fourth 11 times.

Ford was ranked first 11 times, second 9 times, third 14 times, and fourth 11 times.

Based on these results, we can see that Russell was ranked first more often than the other candidates.

so Russell would be the winner of the vacation package.

As for the irrelevant alternative criterion, it is not violated in this case.

Smith was eliminated from consideration because they did not meet the original criteria.

So their removal from the voting does not change the fact that Evans, Russell, and Ford were the remaining candidates.

The ranking of the remaining candidates was not affected by Smith's removal, so the criterion is not violated.

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The above question is incomplete, the complete question is:

A county committee is trying to award a vacation package of a weekend at an Orlando resort to a deserving staff member, The votes are shown below:

                       11                  14                    11               9

1st Choice        Evans        Russell             Ford           Smith

2nd Choice      Russell      Ford                Smith          Evans

3rd Choice       Ford           Smith              Evans         Russell

4th Choice       Smith          Evans             Russell        Ford

The committee decides to use the Pairwise comparison method to determine the final winner. However, while finalizing the data, they find that Smith had won a significant prize during the last event and therefore did not meet the original criteria to be considered for the vacation package, so Smith is eliminated from the votes. Who actually will win the package? Is the irrelevant alternative criterion violated in this case? Why or why not?

Franco can read approximately 1.875 chapters of his history book in 1 hour, assuming his reading rate remains constant.

Franco read 3/8 of a chapter in 1/5 of an hour. To find out how many chapters he can read in 1 hour, we need to first determine his rate of reading.

To do this, we can set up a proportion:

3/8 of a chapter = x chapters
1/5 of an hour = 1 hour

Cross-multiplying, we get:

3/8 * 1 hour = x * 1/5

Simplifying:

3/8 = x/5

Cross-multiplying again:

15/8 = x

So Franco can read 15/8 or 1 7/8 chapters in 1 hour.

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The block will cover the distance 12m before it stops.

According to Newton's second law of motion, the acceleration a

of a body of mass m is determined by the net force [tex]F_n_e_t[/tex] acting on it:

[tex]F_n_e_t[/tex]  = ma.

The mass of a block, m = 8 kg

The initial speed of the block on rough horizontal surface , u = 6 m/s

The force of friction, F = 12N

We know that, the Newton's 2nd law: [tex]F_n_e_t[/tex]  = ma.

Therefore, its final velocity is zero, v = 0

Since the only force that is acting on the body along the horizontal direction is the kinetic frictional force

[tex]F_n_e_t[/tex]  = ma. ([tex]F_n_e_t[/tex]  is acting in opposite direction to that of object motion)

a = [tex]\frac{f_n_e_t}{m}[/tex] = [tex]\frac{-12}{8} = -1.5m/s^2[/tex]

Negative sign shows that it is in the opposite direction to that of initial velocity.

By using the third kinematic equation, we get:

[tex]v^2=u^2+2as\\\\= > s = \frac{0-6^2}{2(-1.5)}\\ \\s = \frac{36}{3} = 12m[/tex]

Therefore, the block will cover the distance 12m before it stops.

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The area between the curves x = 28 − 7y² and x = 7y² − 28 is 0.

By counting the number of squares on a piece of paper with grids (square shaped), and using basic formulas, it is possible to determine the area of shapes like quadrilaterals and circles, which are 2D shapes.

To find the area between the curves x = 28 − 7y² and x = 7y² − 28, we need to first find the points of intersection.

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

28 - 7y² = 7y² - 28

Simplifying and solving for y, we get:

y = ±2

So, the two curves intersect at y = 2 and y = -2.

Next, we need to determine which curve is on top in each interval. To do this, we can evaluate the y-values for each curve at y = 0 and y = 2:

For x = 28 − 7y²:

- At y = 0, x = 28

- At y = 2, x = 0

For x = 7y² − 28:

- At y = 0, x = -28

- At y = 2, x = 28

So, the curve x = 28 − 7y² is on top for y between 0 and 2, and the curve x = 7y² − 28 is on top for y between -2 and 0.

Using the formula for finding the area between two curves, we can now calculate the total area:

A = ∫(-2)²[28 - 7y² - (7y² - 28)] dy + ∫02[(7y² - 28) - (28 - 7y²)] dy

Simplifying, we get:

A = 2∫02(14y² - 28) dy

A = 2[[tex]14y^{3/3[/tex] - 28y]0²

A = 2(0 - 0)

A = 0

Therefore, the area between the curves x = 28 − 7y² and x = 7y² − 28 is 0.

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Answer:

Step-by-step explanation:

The expression represents the median benefit for this insurance policy is x = [250 - √(62500 + 4/c)] / 2

To determine the median benefit for this policy, we need to first understand the probability density function (PDF) associated with the policy. The PDF is a mathematical function that describes the probability of a random variable taking on a specific value. In this case, the random variable is the benefit amount provided by the insurance policy.

The cumulative distribution function (CDF) for this PDF is F(x) = cx(250 - x)/2. To find the value of x that corresponds to a cumulative probability of 0.5, we set F(x) = 0.5 and solve for x:

0.5 = cx(250 - x)/2

1 = cx(250 - x)

1/c = x(250 - x)

1/c = -x² + 250x

0 = -x² + 250x - 1/c

We can solve this quadratic equation using the quadratic formula, which gives us:

x = [250 ± √(250² - 4(-1/c)(-1))] / 2

Simplifying this expression gives us:

x = [250 ± √(62500 + 4/c)] / 2

Since we know that x cannot exceed 250, we take the negative root of the expression to get:

x = [250 - √(62500 + 4/c)] / 2

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To find the number that maximizes the product, we need to use calculus. Let's start by setting up the problem. Let x be the first number and y be the second number. We know that: x + y^3 = 864. We want to find the maximum value of xy.

Now, substitute this expression for x into our product function:
P(y) = (864 - y^3) * y

To find the maximum, we need to take the derivative of P(y) with respect to y and set it equal to 0:
dP/dy = -3y^4 + 864y - y^3(dy/dy)

dP/dy = -3y^4 + 864y - y^3(1)

Now, set dP/dy = 0 and solve for y:
0 = -3y^4 + 864y - y^3

It's a challenging polynomial to solve, but we can use numerical methods or technology to find the critical points of y.

Once we have the value(s) of y, we can plug it back into the equation x = 864 - y^3 to find the corresponding value(s) of x.

Finally, determine whether the critical points result in a maximum by checking the second derivative or analyzing the function's behavior around the critical points. The pair of numbers (x, y) will yield the maximum product.

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The 80% confidence interval estimate of the population mean rating for DFW airport can be calculated using the formula:

Margin of error = (Z-score)*(standard deviation/sqrt(sample size))

where the Z-score for 80% confidence level is 1.28.

So, the margin of error = (1.28)*(0.55/sqrt(25)) = 0.28.

Therefore, the confidence interval estimate can be calculated by subtracting and adding the margin of error to the sample mean:

Confidence interval = sample mean ± margin of error
Confidence interval = 3.84 ± 0.28
Confidence interval = (3.56, 4.12)

The question requires us to find an 80% confidence interval estimate for the population mean rating of DFW airport using a sample of 25 travelers. The formula for the margin of error is used to calculate the range of values within which the population mean is likely to fall. The Z-score for the 80% confidence level is used in the formula. We then use this margin of error to calculate the confidence interval estimate by adding and subtracting it from the sample mean. This gives us a range of values within which we can be confident that the population mean rating falls.

The 80% confidence interval estimate for the population mean rating of DFW airport is (3.56, 4.12). This means that we can be 80% confident that the population mean rating falls within this range of values. The sample mean of 3.84 is the best estimate of the population mean rating, and the margin of error of 0.28 indicates the level of uncertainty in this estimate.

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The median test score is 90.5.

What is the median?

The median is defined as the middle value of a sorted list of numbers. The middle number is found by ordering the numbers. The numbers are ordered in ascending order. Once the numbers are ordered, the middle number is called the median of the given data set.

In this case, the best measure of central tendency would be the median. The reason is that there is one outlier (13) that is significantly lower than the rest of the scores.

If we calculate the mean, the outlier would have a significant effect on the result, pulling it down.

The median, on the other hand, would be less affected by the outlier and provide a more representative measure of the typical score in the class.

To calculate the median, we need to order the scores from lowest to highest:

13, 83, 85, 87, 90, 91, 93, 97, 98, 99, 100, 100

The median is the middle score. Since there are 12 scores, the median would be the average of the sixth and seventh scores:

Median = (90 + 91) / 2 = 90.5

Therefore, the median test score is 90.5.

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The equation represents the proportional relationship between the number of bag and cost of cereal bag is y = 7.25x

Number of bags = 3

Cost of three bags of cereal = 21.75

Let the number of bags of cereal bought = x

The cost paid for the bag = y

They both are directly proportional

3/x = 21.75/y

3y = 21.75x

on dividing both side with 3 we will get cost of one bag of cereals

3y/3 = 21.75x/3

y = 7.25x

The proportional relationship between a number of bags of cereal and the cost of cereal is y = 7.25

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Step-by-step explanation:

A. 1/6 + 1/2 = 4/6 = 2/3 (between 0 and 1)

B. 1/6 + 1/6 = 2/6 = 1/3 (between 0 and 1)

C. 1/6 (between 0 and 1)

D. 1/6 * 1/6 = 1/36 (between 0 and 1)

So, all of the options A, B, C, and D could represent the probability of a simple event as they are between 0 and 1?

The average speed of the eagle who traveled 6km in 400 seconds in meters per second is 15.

Average speed of the eagle = total distance / total time taken

Total distance traveled by the eagle = 6km

Total time taken by an eagle to travel 6 km = 400 s

To convert 6 km into m

1 km = 1000 m

6 km = 6 × 1000m

6 km = 6000 m

Average speed of the eagle = 6000/400

Average speed of the eagle = 15 meter per second

Hence, the average speed of the eagle is 15 meter per second .

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Answer: x=-7 y=7

Step-by-step explanation:

The answer is that regression analysis is the most appropriate method.

The most appropriate statistical method to justify building a new elementary school in the district would be regression analysis. This method can be used to examine the relationship between the expected number of students and the capacity of the schools in the district.



Regression analysis is a statistical method that helps to determine the relationship between two or more variables. In this case, the expected number of students would be the independent variable, while the capacity of the schools in the district would be the dependent variable. By analyzing the relationship between these variables, the school district can make predictions about how many students will need to be accommodated in the future and whether a new elementary school is necessary.

In contrast, binomial distribution is a statistical method that is used to calculate the probability of a specific number of successes in a set of trials, which would not be suitable for this situation. Confidence intervals and hypothesis tests are statistical methods used to draw conclusions about populations based on sample data, but may not be the most appropriate method for this situation.

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