Given the diagram below, what is the length of segment EF?

A. 4
B. 4.4
C. 5
D. 4.8

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics.

It is most often used by scientists to test specific predictions, called hypotheses, that arise from theories. There are 5 main steps in hypothesis testing:

State your research hypothesis as a null hypothesis and alternate hypothesis (H0) and (Ha or H1).

Collect data in a way designed to test the hypothesis.

Perform an appropriate statistical test.

Decide whether to reject or fail to reject your null hypothesis.

Present the findings in your results and discussion section.

In this case, the allergist could commit a hypothesis test by following these steps:

State the research hypothesis as H0: The proportion of the public that is allergic to some cheese products is less than or equal to 30%. Ha: The proportion of the public that is allergic to some cheese products is greater than 30%.

Collect data by randomly sampling a large number of people from the public and testing them for cheese allergy using a reliable method.

Perform an appropriate statistical test, such as a one-sample z-test for proportions, to compare the sample proportion of cheese allergy with the hypothesized proportion of 30%.

Decide whether to reject or fail to reject H0 based on the p-value of the test and a chosen significance level (such as 0.05). If the p-value is less than the significance level, reject H0 and conclude that there is sufficient evidence to support Ha. If the p-value is greater than or equal to the significance level, fail to reject H0 and conclude that there is not enough evidence to support Ha.

Present the findings by reporting the sample size, sample proportion, test statistic, p-value, significance level, and conclusion in a clear and concise way.

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The 98% confidence interval for the true mean yield is (31.94, 55.46) bushels per acre.

x is the sample mean, s is the sample standard deviation, n is the sample size, and t is the t-score with n-1 degrees of freedom and a level of significance of 0.01/2 = 0.005 (since we want a 98% confidence interval).

From the problem, we have:

x = 43.7

s = 6.95

n = 5

df = n - 1 = 4

t = 4.604 (from a t-table or calculator)

Substituting these values into the formula, we get:

CI = 43.7 ± 4.604*(6.95/√5)

= 43.7 ± 11.76

= (31.94, 55.46)

Therefore, the 98% confidence interval for the true mean yield is (31.94, 55.46) bushels per acre.

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If the p-value for a hypothesis test is greater than the chosen level of significance, then the null hypothesis cannot be rejected.

In this case, the p-value is 0.11 and the level of significance is 0.05. Since the p-value is greater than the level of significance, we cannot reject the null hypothesis.

Therefore, we do not have sufficient evidence to conclude that the population mean is different from the hypothesized value. In other words, we do not have enough evidence to support the alternative hypothesis.

Thus, rejecting the null hypothesis in favor of the alternative hypothesis is not the correct decision in this case.

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Labby would expect to observe approximately 52,612 of each side (1 through 6) over 26,306 rolls of 12 dice.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.

If each side of a die is equally likely to come up, then the probability of rolling any one of the six sides is 1/6.

Labby rolled 12 dice 26,306 times, so the total number of rolls is:

N = 12 * 26,306 = 315,672

To calculate the expected number of each side (1 through 6), we can use the formula for the expected value of a discrete random variable:

E(X) = Σ[x * P(X = x)]

where X is the random variable (in this case, the number of times a particular side comes up), x is the value of the random variable, and P(X = x) is the probability of X taking on the value x.

For each die roll, the probability of rolling a particular side is 1/6. So for 315,672 die rolls, we would expect:

E(1) = 315,672 * 1/6 = 52,612

E(2) = 315,672 * 1/6 = 52,612

E(3) = 315,672 * 1/6 = 52,612

E(4) = 315,672 * 1/6 = 52,612

E(5) = 315,672 * 1/6 = 52,612

E(6) = 315,672 * 1/6 = 52,612

Therefore, Labby would expect to observe approximately 52,612 of each side (1 through 6) over 26,306 rolls of 12 dice.

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Step-by-step explanation:

step 1: Add 6y to both sides. Anything plus zero gives itself

step 2: Add 4 to both sides

step 3:Combine all terms containing a

step 4: The equation is in standard form.

step 5: Divide both sides by uRe(d)qsx+uRe(d)qsy.

step 6:Dividing by uRe(d)qsx+uRe(d)qsy undoes the multiplication by uRe(d)qsx+uRe(d)qsy.

step 7:Divide 6y+4 by uRe(d)qsx+uRe(d)qsy.

a= 2(3y+2)

qsuRe(d)(x+y)

​

To find the number of cookies the avid baker must make to break-even, we need to set the profit equation P(x) equal to zero and solve for x:0 = -9 + 1.5x
9 = 1.5x
x = 6


0 = -9 + 1.5x

To solve for x, first add 9 to both sides:

9 = 1.5x

Now, divide both sides by 1.5:

x = 6

So, the baker must make 6 cookies to break even.

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If the manufacturer's claim is correct, that is  the probability that the average deviation from perfect accuracy would be 34 seconds or more in the sample obtained by the consumer review website is 0.033.

What is probability?

Probability means any possibility. It is a branch of mathematics which deals with the occurrence of a random event. The value can be expressed from zero to one. The meaning of probability is mainly the extent to which something is likely to be happened.

Here we will use a one-sample t-test to test the  claim of manufacture. The null hypothesis is that the true mean deviation from perfect time is equal to 30 seconds per month, and in the alternative hypothesis the true mean deviation from perfect time is greater than 30 seconds per month.

The test statistic for this one-sample t-test is calculated as follows

t = (x - μ) / (s / √n)

where x = sample mean, μ = hypothesized population mean, s = sample standard deviation, and n = sample size.

Using the above notations  in the values given in the problem, we have

x = 34 seconds

μ = 30 seconds

s = 15 seconds

n = 40 clocks

t = (34 - 30) / (15 / √40) = 1.89

Using  t-distribution table  with degrees of freedom  = n-1 = 39 and a significance level of α = 0.05 , the critical value is 1.686.

Since by the calculation t-value 1.89 is greater than the critical value 1.686, we will reject the null hypothesis and from this we will conclude that the true mean deviation from perfect time is greater than 30 seconds per month.

To calculate the probability that the average deviation from perfect accuracy would be 34 seconds  in the sample obtained by the consumer review website, we need to find the area under the t-distribution curve to the right of t = 1.89. Using the t-distribution calculator, we find that the probability to be approximately 0.033

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The house is furnished is an indicator (dummy) variable. So, the correct option is (D)

Indicator (dummy) variables are used to represent categorical data as binary data in regression analysis. In this case, the house being furnished is a categorical variable that can be represented as a binary variable (1 or 0). The other variables are continuous or ordinal variables and do not need to be represented as indicator variables.

If the p-value is less than the chosen significance level (alpha), typically 0.05, then the independent variable is considered statistically significant in the model. Therefore, in this case, we need to examine the p-values associated with the coefficients for Age, Living Area, and Bedrooms in the regression output to determine which group of independent variables is significant.

If the p-value for any independent variable is less than 0.05, then that variable is considered significant in the model

Without the regression output, it is not possible to determine which group of independent variables is significant in the model. Please provide the Excel output for further analysis

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The value of c guaranteed by the Mean Value Theorem is c = 3.

What is mean value theorem?

The Mean Value Theorem (MVT) is a fundamental theorem in calculus that states that if a function f(x) is continuous on the closed interval [a, b], and differentiable on the interval (a, b), then there exists at least one point c in (a, b) such that:

f'(c) = (f(b) - f(a))/(b - a)

To check if the Mean Value Theorem (MVT) applies to the function f(x) = [tex]x^3 - 2x[/tex]  on the interval [1, 3], we need to verify two conditions:

Continuity: f(x) must be continuous on the closed interval [1, 3].

Differentiability: f(x) must be differentiable on the open interval (1, 3).

Both of these conditions are met for the given function f(x).

Continuity:

The function f(x) is a polynomial, and all polynomials are continuous for all real numbers. Therefore, f(x) is continuous on the interval [1, 3].

Differentiability:

To show that f(x) is differentiable on the interval (1, 3), we need to show that its derivative exists and is finite at every point in the interval.

[tex]f(x) = x^3 - 2x[/tex]

[tex]f'(x) = 3x^2 - 2[/tex]

The derivative f'(x) is a polynomial and exists for all x in the interval (1, 3). Therefore, f(x) is differentiable on the interval (1, 3).

Since both conditions of the MVT are satisfied, there exists a point c in (1, 3) such that:

f'(c) = (f(3) - f(1))/(3 - 1)

We can now find the value of c by solving for it:

f'(c) = (f(3) - f(1))/(3 - 1)

[tex]3c^2 - 2 = (3^3 - 23) - (1^3 - 21)[/tex]

[tex]3c^2 - 2 = 25[/tex]

[tex]3c^2 = 27[/tex]

[tex]c^2 = 9[/tex]

c = ±3

Since c must be in the interval (1, 3), the only possible value of c is c = 3.

Therefore, by the MVT, there exists a point c in (1, 3) such that:

f'(c) = (f(3) - f(1))/(3 - 1)

[tex]3c^2 - 2 = (3^3 - 23) - (1^3 - 21)[/tex]

[tex]3c^2 - 2 = 25[/tex]

[tex]3c^2 = 27[/tex]

[tex]c^2 = 9[/tex]

c = 3

Hence, the value of c guaranteed by the Mean Value Theorem is c = 3.

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(L3) According to the Centroid Theorem, the  centroid  of a triangle is located 2/3 of the distance between the vertex and the midpoint of the opposite side of the triangle along each median.

According to the theorem, the centroid of a triangle is located at 2/3 of the distance from each vertex to the midpoint of the opposite side of the triangle along each median. In other words, if a median of a triangle is drawn from a vertex to the midpoint of the opposite side, then the distance from the vertex to the centroid is two-thirds of the length of the median. This theorem is useful in many geometric proofs and can be used to find the centroid of any triangle.

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If we roll one die repeatedly and let ni be the number of the roll on which i first appears then the joint distribution of n1 and n6 is - (5/6)^(j+i-2) * (1/6)^2 if i < j.

To find the joint distribution of n1 and n6, we need to consider the probability of each possible outcome.

Let's first consider the probability of n1. The probability that 1 appears on the first roll is 1/6. The probability that 1 appears on the second roll is (5/6) * (1/6), since we need to first roll a number other than 1 (which has probability 5/6) and then roll a 1 (which has probability 1/6). Similarly, the probability that 1 appears on the third roll is (5/6)^2 * (1/6), and so on. So we have:

P(n1 = k) = (5/6)^(k-1) * (1/6)

Now let's consider the probability of n6. The probability that 6 appears on the first roll is 1/6. The probability that 6 appears on the second roll is (5/6) * (1/6), since we need to first roll a number other than 6 (which has probability 5/6) and then roll a 6 (which has probability 1/6). Similarly, the probability that 6 appears on the third roll is (5/6)^2 * (1/6), and so on. So we have:

P(n6 = k) = (5/6)^(k-1) * (1/6)

Now, to find the joint distribution of n1 and n6, we need to consider the probability of both events happening together. Specifically, we want to find P(n1 = i, n6 = j) for all possible values of i and j.

If i > j, then we know that 6 must appear before 1, so P(n1 = i, n6 = j) = 0 for all i > j.

If i = j, then both 1 and 6 must appear on the same roll, so P(n1 = i, n6 = j) = (1/6) * (1/6) = 1/36.

If i < j, then we need to first roll j-1 numbers other than 6, then roll a 6, then roll i-j-1 numbers other than 6, then roll a 1. So we have:

P(n1 = i, n6 = j) = (5/6)^(j-i-1) * (1/6) * (1/6) * (5/6)^(i-1) * (1/6)

Simplifying this expression, we get:

P(n1 = i, n6 = j) = (5/6)^(j+i-2) * (1/6)^2

So the joint distribution of n1 and n6 is:

P(n1 = i, n6 = j) =
 - 0 if i > j
 - 1/36 if i = j
 - (5/6)^(j+i-2) * (1/6)^2 if i < j

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The value of x and y using substitution method is (1, 3).

System of equation can be solved using different method such as substitution method, elimination method and graphical method.

Let's solve the system of equation by substitution method.

Therefore,

-x - 2y = - 7

-5x + y = - 2

Hence,

x = -2y + 7

substitute the value of x in equation(ii)

-5(-2y + 7) + y = - 2

10y - 35 + y = -2

11y = -2 + 35

11y = 33

divide both sides by 11

y = 33  /11

y = 3

Hence,

x = -2(3) + 7

x = -6 + 7

x = 1

Therefore,

x = 1

y = 3

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If Arthur carries x crumbs to the anthill, then Amy will carry 1.5 times as many crumbs per trip. Since Amy makes twice as many trips as Arthur, the total number of crumbs that Amy will bring to the anthill can be calculated as follows:

Number of crumbs per trip for Arthur = x/ (2 * number of trips made by Arthur)

Number of crumbs per trip for Amy = 1.5 * (x / (2 * number of trips made by Arthur))

Total number of crumbs brought by Amy = Number of crumbs per trip for Amy * (2 * number of trips made by Amy)

Simplifying this expression, we get:

Total number of crumbs brought by Amy = (1.5 * x * 2) / 2

= 1.5x

Therefore, Amy will bring 1.5x crumbs to the anthill, in terms of x. This means that Amy will bring 50% more crumbs to the anthill than Arthur. Overall, this problem demonstrates how to use mathematical expressions to determine the quantity of something, based on a given set of parameters and conditions.

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The information given shows that E. The confidence interval is (-6. 699, 2. 899); there's a difference between the two population means

CI = (x1 - x2) ± t* × m

Plugging in the given values, we get:

CI = (23.4 - 25.3) ± 2.064 × 2.325

= -1.9 ± 4.798

= (-6.698, 2.898)

Therefore, the 95% confidence interval for the difference between the two population means is (-6.698, 2.898).

Since this interval does not include zero, we can conclude that there is a statistically significant difference between the two population means at the 95% confidence level. The correct answer is option E.

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The value of t for a confidence level of 99% and 5 degrees of freedom is 4.032.

The confidence interval is calculated based on the sample mean, the sample standard deviation, the sample size, and the chosen confidence level.

Given the values of caffeine content in 6 trials: 381 mg/l, 405 mg/l, 399 mg/l, 402 mg/l, 395 mg/l, and 404 mg/l.

Sample mean = (381 + 405 + 399 + 402 + 395 + 404) / 6 = 396 mg/l

Sample standard deviation = √([(381-396)² + (405-396)²+ (399-396)² + (402-396)² + (395-396)² + (404-396)²] / (6-1)) = 9.29 mg/l

To calculate the value of t for a confidence level of 99%, we need to look up the t-distribution table with degrees of freedom (df) = n-1 = 5 and the chosen significance level (α) = 0.01 (since we want to calculate the 99% confidence interval, which leaves 1% of the distribution in the tails).

Looking up the t-value from the table, we find that t = 4.032.

Therefore, the value of t for a confidence level of 99% and 5 degrees of freedom is 4.032.

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There are 226,800 ways for 7 men and 7 women to sit around the table.

We will first fix the position of one gender, say the men, and then arrange the women in the gaps between them. The men can be arranged in 7! ways, and there are 8 gaps between them where the women can be placed.

Once a woman is placed in a gap, the remaining women can be arranged in the remaining gaps in 6! ways but we need to divide by 2 for each arrangement to account for the fact that the men and women can alternate in two ways.

So the total number of arrangements is:

= 7! x 8 x 6! / 2^7

= 29030400 / 128

= 226,800.

Full question "In how many ways can 7 men and 7 women can sit around a table so that men and women alternate. Assume that all rotations of a configuration are identical hence counted as just one"

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Answer:

Brianna can make 20 necklaces using the 160 beads remaining after giving away 96. A bar graph can be used to represent the number of necklaces she can make based on the number of beads remaining. The tallest bar will appear at 160 beads, where 20 necklaces can be made.

Step-by-step explanation:

A bag of 256 beads is the initial supply for Brianna. She has 160 beads remaining after distributing 96 of them. She intends to build eight-bead bracelets using these beads.

We must divide the total number of beads by the number of beads used in each necklace to get the number of necklaces she can produce. In this instance, we have:

20 necklaces are produced from 160 beads, or 8 beads each necklace.

Brianna may thus use the remaining beads to create 20 necklaces.

A bar graph is used to display how many necklaces Brianna might be able to create. After giving away 96 beads, the x-axis shows how many beads are still left, and the y-axis shows how many necklaces may be created with the remaining beads. The number of necklaces that may be created with a given quantity of beads is indicated by the height of each bar. The graph's tallest bar will appear at 160, which is where the number of beads is equally divided by 8.

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The expected value or average number of times a customer visits the store in a month is 1.60 times. So, the expected value for the average number of times a customer visits the store is 1.6 times.

To find the expected value, we need to multiply each possible outcome by its probability and then add them up. Let's assume that these numbers represent the number of times a customer visits a store in a month. We can see that the probabilities are not given, so we will assume that each outcome is equally likely.

Expected value = (0 x 0.10) + (1 x 0.40) + (2 x 0.30) + (3 x 0.20)
Expected value = 0 + 0.40 + 0.60 + 0.60
Expected value = 1.60

Therefore, the expected value or average number of times a customer visits the store in a month is 1.60 times.

To find the expected value of the average number of times a customer visits the store, you'll need to multiply each visit frequency by its respective probability and then sum up the results. Here's the calculation using the provided data:

Expected Value = (0 * .10) + (1 * .40) + (2 * .30) + (3 * .20)

Expected Value = (0) + (0.4) + (0.6) + (0.6)

Expected Value = 1.6

So, the expected value for the average number of times a customer visits the store is 1.6 times.

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Population: male customers who may leave a tip

Counts: 69 male customers served by a server wearing a red shirt left a tip, and 130 out of 349 male customers served by a server wearing a different coloured shirt left a tip

Sample size:[tex]418[/tex] male customers in the study

Proportions:

Proportion of male customers served by a server wearing a red shirt who left a tip= [tex]= 40/69[/tex]

Proportion of male customers served by a server wearing a different coloured shirt who left a tip [tex]= 130/349[/tex] [tex]= 0.3725[/tex]

Difference in proportions :[tex]0.5797 - 0.3725 = 0.2072[/tex]

b.

Population: runners

Counts: 11 runners who were satisfied or very satisfied with the first routine, and 14 runners who were satisfied or very satisfied with the second routine

Sample size: 40 runners

Proportions: Proportion of runners satisfied or very satisfied with the first routine [tex]= 11/40[/tex]  [tex]= 0.275[/tex]

Proportion of runners satisfied or very satisfied with the second routine [tex]= 14/40[/tex]  [tex]= 0.35[/tex]

Difference in proportions :[tex]0.35 - 0.275[/tex]  [tex]= 0.075[/tex]

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Answer:

The following statements contain a variable

How much the car weighs.

The length of the track.

The highest temperature over three days.

The variable that is altered by the scientist is the independent variable. A good experiment has only ONE independent variable in order to guarantee a fair test.

The weight of car varies from model to model.

The car weight is variable.

Five feet tall is fixed not variable.

The length of track is variable it vary.

The temperature of three days vary from day to day.

The statement that is true is that substance a is likely denser than water, whereas substance b may be less dense or have dissolved in the water.

Density is an important factor to consider when working with substances and liquids, as it can affect how they behave and interact with each other. The most likely reason for the small pile of substance a at the bottom of the first beaker is that it is denser than water. On the other hand, substance b may be less dense than water, which would cause it to float or dissolve completely. Alternatively, substance b may have dissolved in the water without leaving any visible residue.

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the probability that the mean weight of these 400 bags is less than 14.6 ounces is practically zero.

Given that weight of corn chips dispensed into a 14-ounce bag follows a normal distribution with mean (μ) = 14.5 ounces and standard deviation (σ) = 0.1 ounce.

We need to find the probability that the mean weight of these 400 bags is less than 14.6 ounces.

Since the sample size (n) is large (n > 30), we can use the central limit theorem, which states that the sample mean follows a normal distribution with a mean of the population mean (μ) and a standard deviation of the population standard deviation divided by the square root of the sample size (σ/√n).

So, the mean weight of 400 bags of chips follows a normal distribution with mean μ = 14.5 ounces and standard deviation σ/√n = 0.1/√400 = 0.005 ounce.

Let X be the weight of corn chips dispensed into a single bag. Then, we need to find the probability P(x(bar )< 14.6), where x(bar ) is the sample mean weight of 400 bags of chips.

Using the standard normal distribution, we can standardize the sample mean as:

Z = (x(bar ) - μ) / (σ/√n)

Z = (14.6 - 14.5) / (0.005)

Z = 20

Now, we need to find the probability that Z is less than 20, which is practically zero. Therefore, the probability that the mean weight of these 400 bags is less than 14.6 ounces is almost zero.

In symbols, P(x(bar ) < 14.6) ≈ 0.

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A 45°-45°-90° right triangle is also called an isosceles right triangle.An Isosceles Right Triangle is a right triangle that consists of two equal length legs. Since the two legs of the right triangle are equal in length, the corresponding angles would also be congruent.

The most important formula associated with any right triangle is the Pythagorean theorem. According to this theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of the right triangle. Now, in an isosceles right triangle, the other two sides are congruent. Therefore, they are of the same length “l”. Thus, the hypotenuse measures h, then the Pythagorean theorem for isosceles right triangle would be:

(Hypotenuse)2 = (Side)2 + (Side)2

h² = l² + l²

h² = 2l²

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Answer:

Okay, let's think this through step-by-step:

   We know: Distance (d) is directly proportional to Time (t)

   This means there is a constant ratio between d and t. We can represent this as:

   d = k * t (where k is the constant of proportionality)

   Given: Vehicle travels 40 miles in 60 minutes

   So: d = 40 miles and t = 60 minutes

   We can substitute into the proportionality equation to calculate k:

   40 = k * 60

   => k = 2/3

   Now we want to calculate the distance traveled in 90 minutes:

   d = k * t (using the proportionality equation)

   d = (2/3) * 90 (using the calculated k value)

   d = 60 miles

So in 90 minutes, the vehicle can travel 60 miles.

Does this make sense? Let me know if you have any other questions!

Step-by-step explanation:

Besides random sampling and categorical data, then the other assumption needs to be met is YN+NY must be at least equal to 30. (option a).

The data presented in the question is categorical, meaning that each student was classified as either supporting or not supporting gay marriage. To compare the proportion of students who supported gay marriage as freshman and seniors, we need to perform a two-sample proportion test.

The assumption of no outliers is also important in statistical analysis. Outliers can skew the results and lead to incorrect conclusions. Therefore, it is necessary to examine the data for any outliers and handle them appropriately.

Finally, the sample size needs to be large enough to ensure that the test has adequate power to detect a meaningful difference between the population proportions. A sample size of at least 30 is often recommended for two-sample proportion tests.

Hence the correct option is (a).

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Complete Question:

Do people change their political views during college? Two hundred randomly selected students were asked as freshman and then again as seniors if they supported gay marriage. The data is below. Suppose that a social scientist wanted to determine if there was a difference between the population proportions of students at UF who supported gay marriage as a freshman then as a senior. Besides random sampling and categorical data, what other assumption needs to be met?

a. YN+NY must be at least equal to 30.

b. The number of successes and failures must be greater than 15.

c. There can't be any outliers.

d. The sample size must be greater than 30.

The population you're focusing on for your experiment is "Americans over the age of 30."

the population in your experiment would be "Americans over the age of 30." Here's the breakdown:

1. You are interested in the preference of Coke over Pepsi among Americans.
2. You specifically want to test this preference for those who are over the age of 30.
3. You plan to conduct an experiment with 100 people from this population.

A population in statistics is the complete set of individuals or objects that have one or more characteristics in common . A population can be finite or infinite, existent or hypothetical. A sample is a subset of the population that is selected for a study

Therefore, the population you're focusing on for your experiment is "Americans over the age of 30."

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The second rectangular park with dimensions of 71 yards by 72 yards has the same perimeter as the first park but a larger area.

The perimeter of the first rectangular park is 2(55 + 88) = 286 yards. To find the dimensions of the second rectangular park with the same perimeter but a larger area, we need to use the formula for the perimeter of a rectangle: P = 2l + 2w.

Let's call the width of the second park "w" and the length "l". We know that the perimeter of the second park is also 286 yards, so:

2l + 2w = 286

Simplifying this equation, we get:

l + w = 143

Now, we need to find the dimensions that will give us the largest possible area. We know that the area of a rectangle is A = lw. We want to maximize A, so we need to find the values of l and w that will give us the largest possible product.

One way to do this is to use the fact that the sum of two numbers is constant. In other words, if we fix the value of l + w, the product lw will be largest when l and w are as close as possible to each other.

Since l + w = 143, we can choose l = 71 and w = 72 (or vice versa) to get the largest possible area.

To check that this works, we can calculate the area of the two parks:

- The area of the first park is A1 = 55 x 88 = 4840 square yards
- The area of the second park is A2 = 71 x 72 = 5112 square yards

So the second rectangular park with dimensions of 71 yards by 72 yards has the same perimeter as the first park but a larger area.

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Substract 8/12 minus 1/8 , we getting a 19/24

The operation or process of finding the difference between two numbers or quantities is known as subtraction. To subtract a number from another number is also referred to as 'taking away one number from another'.

We have to subtract the digits :

[tex]\frac{8}{12}-( -\frac{1}{8})[/tex]

=> Taking L.C.M:

L.CM. of (12, 8) is 24

=> [tex]\frac{16+3}{24}[/tex]

Subtract the numerator, we get

=> [tex]\frac{19}{24}[/tex]

Hence, Substract 8/12 minus 1/8 , we getting a 19/24

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The probability of drawing a white ball on the second draw, without replacing the first ball, is 8/13.

To solve this problem, we need to use conditional probability.

The probability of drawing a white ball on the first draw is 8/13 (since there are 8 white balls and 13 total balls in the urn).

If a white ball is drawn on the first draw, then there will be 7 white balls and 5 black balls left in the urn. So the probability of drawing a white ball on the second draw, given that a white ball was drawn on the first draw, is 7/12.

If a black ball is drawn on the first draw, then there will be 8 white balls and 4 black balls left in the urn. So the probability of drawing a white ball on the second draw, given that a black ball was drawn on the first draw, is 8/12.

Now we can use the law of total probability to find the overall probability of drawing a white ball on the second draw:

P(white on second draw) = P(white on first draw) * P(white on second draw | white on first draw) + P(black on first draw) * P(white on second draw | black on first draw)
= (8/13) * (7/12) + (5/13) * (8/12)
= 56/156 + 40/156
= 96/156
= 8/13

Therefore, the probability of drawing a white ball on the second draw, without replacing the first ball, is 8/13.

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a) The lengths of the three sides of the triangle are 8 cm, 32 cm, and 36 cm.

b) The measures of the three angles are 36 degrees, 63 degrees, and 81 degrees.

a) Let's start by assigning variables to the measures of the three sides of the triangle. Let x be the measure of the shortest side, then the measures of the other two sides are 4x and 4.5x, since the ratio of the measures of the three sides is 2:8:9.

The perimeter of the triangle is the sum of the measures of the three sides. We know that the perimeter is 76 centimeters, so we can set up an equation:

x + 4x + 4.5x = 76

Simplifying and solving for x, we get:

9.5x = 76

x = 8

Now that we know the length of the shortest side is 8, we can find the measures of the other two sides:

The length of the second side is 4x = 32

The length of the third side is 4.5x = 36

b) Let the three angles of the triangle be 4x, 7x, and 9x.

The sum of the angles of a triangle is always 180 degrees, so we can write:

4x + 7x + 9x = 180

Simplifying, we get:

20x = 180

x = 9

Now, we can find the measure of each angle by substituting x = 9:

The first angle: 4x = 4(9) = 36 degrees

The second angle: 7x = 7(9) = 63 degrees

The third angle: 9x = 9(9) = 81 degrees

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Complete question is:

a) In a triangle, the ratio of measures of three sides is 2:8:9 and perimeter is 76 centimeters. Find length of each side?

b) The ratio of measure of three angles in a triangle is 4:7:9. Find the measure of angles of each triangle