2. Factor 12³ + 60x² + 75x.​

The probability of both events happening together is 2/18 or 1/9. To determine whether events A and B are independent, we need to first calculate their probabilities.

For event A, we can count the number of ways that the sum of the numbers showing is odd. There are 18 possible outcomes when two dice are rolled, and 9 of them result in an odd sum: (1,2), (1,4), (1,6), (2,1), (2,3), (2,5), (3,2), (3,4), and (4,1). Therefore, the probability of event A is 9/18 or 1/2.

For event B, we can count the number of ways that the sum of the numbers showing is 9, 11, or 12. There are 18 possible outcomes when two dice are rolled, and 4 of them result in a sum of 9, 2 of them result in a sum of 11, and 1 results in a sum of 12: (3,6), (4,5), (5,4), (6,3), (5,6), (6,5), and (6,6). Therefore, the probability of event B is 7/18.

To determine whether events A and B are independent, we need to see if the probability of both events happening together is equal to the product of their individual probabilities.

If events A and B were independent, then the probability of both events happening together would be the probability of event A multiplied by the probability of event B:

P(A and B) = P(A) * P(B)

Substituting in the values we calculated above:

P(A and B) = (1/2) * (7/18) = 7/36

To calculate the actual probability of both events happening together, we can count the number of outcomes where the sum of the numbers showing is both odd and 9, 11, or 12. There are only 2 such outcomes: (3,6) and (5,6). Therefore, the probability of both events happening together is 2/18 or 1/9.

Since P(A and B) does not equal P(A) * P(B), we can conclude that events A and B are not independent.

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Yes, when trying to find the p-value for a randomized distribution, you should include the sample means at the sample statistic. In this case, the sample statistic is 370, which represents the mean of the sample. The p-value is the proportion of simulated statistics that are less than or equal to the observed statistic in the left tail.

In a left-tailed test like the one you described (with null hypothesis H0: mu = 395 and alternative hypothesis Ha: mu < 395), the p-value is the probability of observing a sample mean as extreme or more extreme than the observed sample mean (in this case, 370) if the null hypothesis is true.  So, if the p-value is calculated to be 53/1000, it means that in 53 out of 1000 simulations (or randomized samples), the mean was less than or equal to 370. Therefore, the p-value is 0.053 or 5.3%. This suggests that there is some evidence to reject the null hypothesis in favor of the alternative hypothesis, as the observed sample mean is quite low compared to what would be expected if the true population mean were actually 395. However, the decision to reject or fail to reject the null hypothesis also depends on the significance level (alpha) chosen by the researcher.

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Answer:

The answer is 28

Step-by-step explanation:

5+1=6 ×2 =12 +16=28

a) The probability that none of the antennas is defective is 0.0498.

b) The probability that three or more of the antennas are defective is 0.0874.

Given data,

The probability of success (defective antenna) is 1.5% or 0.015, and the sample size is 200.

a)

Probability that none of the antennas is defective:

In this case, we want to find the probability of having zero defective antennas in the sample. The Poisson distribution formula for this scenario is given by:

P(X = 0) = (e^(-λ) * λ⁰) / 0!

Where λ is the mean of the Poisson distribution, which is equal to n * p, where n is the sample size and p is the probability of success.

λ = 200 * 0.015 = 3

P(X = 0) = (e⁻³ * 3⁰) / 0!

P(X = 0) ≈ 0.0498 (rounded to 4 decimal places)

Therefore, the probability that none of the antennas is defective is approximately 0.0498.

b)

Probability that three or more of the antennas are defective:

In this case, we want to find the probability of having three or more defective antennas in the sample. We can calculate this by finding the cumulative probability of having zero, one, and two defective antennas and subtracting it from 1.

P(X ≥ 3) = 1 - P(X = 0) - P(X = 1) - P(X = 2)

To calculate this, we can use the same Poisson formula with different values of λ:

λ = 200 * 0.015 = 3

P(X ≥ 3) = 1 - (e⁻³ * 3⁰) / 0! - (e⁻³ * 3¹) / 1! - (e⁻³ * 3²) / 2!

P(X ≥ 3) ≈ 0.0874 (rounded to 4 decimal places)

Hence , the probability that three or more of the antennas are defective is approximately 0.0874.

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C. Both distributions are approximately normal with the same mean. The standard deviation for size 5 is greater than that for size 85.

Explanation:
When taking random samples from a population with a normal distribution, the sampling distributions of the sample mean will also be approximately normal. The mean of the sampling distributions will be the same as the population mean, which is 65 inches in this case.

However, the standard deviation of the sampling distributions will be different for the two sample sizes. The standard deviation of the sampling distribution is calculated as the population standard deviation divided by the square root of the sample size (σ/√n). In this case, the population standard deviation is 3.5 inches.

For the sample size of 5:
Standard deviation = 3.5/√5 ≈ 1.566

For the sample size of 85:
Standard deviation = 3.5/√85 ≈ 0.379

As you can see, the standard deviation for the sample size of 5 is greater than the standard deviation for the sample size of 85, which means that the sampling distribution for the smaller sample size will be more spread out than the one for the larger sample size.

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The probability that a shopper from this sample finds regifting socially acceptable is approximately 0.9938 (rounded to four decimal places).

To answer this question, we'll use the binomial probability formula, which is:

P(x) = (ⁿCₓ) × (pˣ) × (q^(n-x))

where:
- P(x) is the probability of x successes (in this case, x shoppers finding regifting socially acceptable)
- n is the number of trials (in this case, the sample size of 10 shoppers)
- x is the number of successes (the number of shoppers finding regifting acceptable)
- nCx is the number of combinations of n items taken x at a time
- p is the probability of success (68% or 0.68)
- q is the probability of failure (1 - p, or 32% or 0.32)

We want to find the probability that a shopper from the sample of 10 finds regifting socially acceptable. To do this, we can find the probability that any number of shoppers from the sample (1 to 10) find regifting socially acceptable, then sum these probabilities.

For example:
P(1 shopper finds regifting acceptable) = ¹⁰C₁ × (0.68¹) × (0.32⁹)
P(2 shoppers find regifting acceptable) = ¹⁰C₂ × (0.68²) × (0.32⁸)
...
P(10 shoppers find regifting acceptable) = ¹⁰C₁₀ ×  (0.68¹⁰) × (0.32⁰)

Sum these probabilities, and you get the total probability that a shopper from this sample finds regifting socially acceptable.
Therefore,  The probability that a shopper from this sample finds regifting socially acceptable is approximately 0.9938 (rounded to four decimal places).

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Step-by-step explanation:

If the bottle contains 500ml of water and the water fills half of the bottle, then the total capacity of the bottle must be 1000ml (since half of 1000ml is 500ml).

To convert this to liters, we can divide by 1000, since there are 1000 milliliters in one liter.

1000ml / 1000 = 1 liter

Therefore, the bottle holds 1 liter of water.

Riya earns $45 in commission for selling 15 newspaper ads at $50 each.

A commission is a charge or payment given to a person or group in exchange for a good or service. When selling goods or services on behalf of a corporation, sales representatives or agents are frequently compensated with commissions in the business world. For instance, a stockbroker may receive a fee for carrying out a trade on behalf of a customer, while a real estate agent may receive a commission depending on the sale price of a property they assist in selling.

Riya receives a 6% commission for selling newspaper ads, and if she sells 15 ads for $50 each, her total earnings can be calculated as follows:

Total earnings = Total sales x Commission rate

The total sales from selling 15 ads at $50 each are:

Total sales = 15 x $50 = $750

The commission rate is 6%, which can be written as 0.06 as a decimal.

Plugging these values into the formula, we get:

Total earnings = $750 x 0.06 = $45

Therefore, Riya earns $45 in commission for selling 15 newspaper ads at $50 each.

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The true statement is "A perfect cube represents the volume of a cube with equal integer side lengths." option c.

Option C says that a perfect cube represents the volume of a cube with equal integer side lengths.

This statement is true for all perfect cubes. In other words, if we have a cube with sides of length 3 units.

then the volume is simply the length times the width times the height, or 3 x 3 x 3 = 27 cubic units.

This applies to all perfect cubes, regardless of their size.

So to sum it up, option C is the correct statement about all perfect cubes. A perfect cube represents the volume of a cube with equal integer side lengths.

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The test of significance difference in average serotonin levels for the two groups of patients suggests that the antidepressant medication has an effect on serotonin levels in the brain.

In statistical hypothesis testing, a statistically significant difference is a result that is unlikely to occur by chance alone. In other words, it suggests that there is a real difference between two groups or conditions being compared, rather than the difference being due to random variation or error.

In this case, the two groups of patients being compared are those who received the antidepressant medication and those who did not. The average serotonin levels were measured for both groups, and the statistical analysis showed that there is a significant difference between the two groups.

However, further analysis and study would be necessary to determine the magnitude and clinical significance of this effect, as well as to rule out any other potential factors that may have influenced the results.

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Friends A and D have the highest percent error (16.67%), while friends B and C have the lowest percent error (8.33%).

To find the percent error for each friend, we need to compare their estimate with the actual time it takes to get to the concert, and then calculate the percentage difference:

Friend A: Estimated time = 50 min. Percent error = |50 - 60|/60 x 100% = 16.67%

Friend B: Estimated time = 55 min. Percent error = |55 - 60|/60 x 100% = 8.33%

Friend C: Estimated time = 65 min. Percent error = |65 - 60|/60 x 100% = 8.33%

Friend D: Estimated time = 70 min. Percent error = |70 - 60|/60 x 100% = 16.67%

Therefore, friends A and D have the highest percent error (16.67%), while friends B and C have the lowest percent error (8.33%).

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The probability that a randomly selected junior biology major has taken either a statistics or a computer course is 0.68

To find the probability that a randomly selected junior biology major has taken either a statistics or a computer course (or both), we'll use the formula:

P(A or B) = P(A) + P(B) - P(A and B)

Where:
- P(A) is the probability of having taken a statistics course (52% or 0.52)
- P(B) is the probability of having taken a computer course (23% or 0.23)
- P(A and B) is the probability of having taken both courses (7% or 0.07)

Now, plug in the values:

P(A or B) = 0.52 + 0.23 - 0.07
P(A or B) = 0.68

So, the probability that a randomly selected junior biology major has taken either a statistics or a computer course (or both) is 0.68, or 68%.

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Answer:

2

Step-by-step explanation:

i did the quiz

Option 1 is true. The mean of the sample provides sufficient information to construct the confidence interval. We can use the sample mean and standard deviation to estimate the population mean and construct a confidence interval around it.

However, we need to assume that the sample is random and representative of the population, and that the population follows a normal distribution or that the sample size is large enough for the central limit theorem to apply.
Even though our parameter of interest is the mean, we need to estimate the population variance in the procedure. This is because the confidence interval is calculated using the sample mean, the sample size, and the estimated population standard deviation (derived from the sample variance). The sample mean alone (option 1) is not sufficient, and it is possible to construct a confidence interval using only one sample (option 2 is incorrect).

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The expected payoff from playing the final round of the game show is -$25,000. This is a negative value. Therefore, you should not play the final round of the game. The lowest probability of a correct guess that would make the guessing in the final round profitable (in expected value) is 11.1111%. This is the probability at which playing the final round yields an expected value of zero.

To calculate the expected payoff from playing the final round of the game show, we can use the formula:
Expected payoff = (Probability of winning × Payoff for winning) + (Probability of losing × Payoff for losing)

In this case, you have a 10% chance of answering the question correctly and increasing your winnings to $3 million, and a 90% chance of answering incorrectly and decreasing your winnings to $750,000. Ignoring your current winnings, the expected payoff is:
Expected payoff = (0.10 × $2 million) + (0.90 × -$250,000) = $200,000 - $225,000 = -$25,000

Given that this is negative, you should not play the final round of the game.

To find the lowest probability of a correct guess that would make guessing in the final round profitable (in expected value), we can set the expected payoff to zero:
0 = (P × $2 million) + ((1-P) × -$250,000)

Solving for P:

$250,000(1-P) = $2 million × P
$250,000 - $250,000P = $2 million × P
$250,000 = $2,250,000 × P

P = 0.111111 (11.1111%)

So, the lowest probability of a correct guess that would make guessing in the final round profitable (in expected value) is 11.1111%.

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Answer:

12

Step-by-step explanation:

60% is the same as 0.6

So, we simply multiply:

20 * 0.6 = 12

Therfore, the answer is 12

~~~Harsha~~~

The probability that a woman is less than 70 inches tall is 0.9332, or approximately 93.32%.

To find the probability that a woman is less than 70 inches tall, we need to use the normal distribution and standard normal distribution tables.

First, we need to convert the given measurements into standard units by using the formula:

z = (x - μ) / σ

where z is the standard score, x is the height we want to find the probability for (70 inches), μ is the mean (64.3 inches), and σ is the standard deviation (3.8 inches).

Plugging in the values, we get:

z = (70 - 64.3) / 3.8 = 1.50

Next, we can look up the probability of getting a z-score of 1.50 or less from the standard normal distribution table. This probability is 0.9332.

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If the null hypothesis is not rejected, we cannot conclude that there is a significant difference between the two time periods.

Assuming that the question is "Has real gross domestic product per capita significantly increased between 1988 and 1990?" We can use a paired-sample t-test to answer this question.

Here are the steps to conduct the paired-sample t-test:

Null hypothesis: The mean difference between the real gross domestic product per capita in 1988 and 1990 is zero. In other words, there is no significant difference between the two time periods.

Alternative hypothesis: The mean difference between the real gross domestic product per capita in 1988 and 1990 is not zero. In other words, there is a significant difference between the two time periods.

Determine the level of significance, alpha (α). Let's assume α = 0.05.

Calculate the difference between the two time periods (1990 - 1988) for each observation.

Calculate the mean and standard deviation of the differences.

Calculate the standard error of the mean difference (SEd) by dividing the standard deviation of the differences by the square root of the sample size.

Calculate the t-statistic by dividing the mean difference by the SEd.

Calculate the degrees of freedom (df) using the formula: df = n - 1, where n is the sample size.

Determine the critical t-value from the t-distribution table with df = n - 1 and α = 0.05.

Compare the calculated t-value with the critical t-value. If the calculated t-value is greater than the critical t-value, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.

Interpret the results. If we reject the null hypothesis, we can conclude that there is a significant difference between the two time periods, and the direction of the difference can be determined by the sign of the mean difference.

Note: In order to conduct the paired-sample t-test, we need to assume that the differences are normally distributed and the variances of the two populations are equal.

After conducting the test, we can conclude whether there is a significant difference in real gross domestic product per capita between 1988 and 1990. If the null hypothesis is rejected, we can conclude that there is a significant difference between the two time periods. If the null hypothesis is not rejected, we cannot conclude that there is a significant difference between the two time periods.

Complete question: Two of the variables in this file ( rgdpch and rgdp88) measure real Gross Domestic Product (GDP) per capita in 1990 and 1988. Please conduct the appropriate t-test to answer the following question:

Is there statistically significant evidence that per capita GDP in 1988 is different from that of 1990? Please show your results and reasoning to justify your answer.

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The behavior of the graph of the function is that it crosses the x-axis at at each zero

The equationn of the function is given as

f(x) = (x-5)(x-1)(x+4)

Express properly

So, we have

f(x) = (x - 5)(x - 1)(x + 4)

The multiplicities of the factors of the above equation are 1

This means that the graph would cross the x-axis at at each zero

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Therefore, the total area of the region that satisfies the two inequalities is 14.5 square units.

The two inequalities given are:

y >= x

y <= |x - 3|

The region that satisfies both inequalities is the shaded area in the graph.

We can find the area of this region by splitting it into two parts: the triangle formed by the points (0, 0), (3, 0), and (3, 3), and the trapezoid formed by the points (3, 3), (2, 1), (-1, 3), and (-3, 3).

The area of the triangle is (1/2)33 = 4.5 square units.

To find the area of the trapezoid, we need to find the lengths of its two bases and its height. The height is the distance between the x-axis and the line y = |x - 3|. This line intersects the x-axis at x = 3 and at x = -1. At x = 3, the height is 0. At x = -1, the height is |-1 - 3| = 4. So the height of the trapezoid is 4 units.

The lengths of the two bases of the trapezoid are the distances between the y-axis and the lines x = 2 and x = -3. These distances are 2 and 3 units, respectively. So the area of the trapezoid is (1/2)*(2 + 3)*4 = 10 square units.

Therefore, the total area of the region that satisfies the two inequalities is 4.5 + 10 = 14.5 square units.

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Complete question:

How many square units are in the region satisfying the inequalities y>=(x) and y<=-(x)+3? Express your answer as a decimal. * the () are absolute value signs.

The function of the “whiskers” in a box and whisker plot include the following: C. They compare the lower quartile to the upper quartile.

In Mathematics and Statistics, a box plot is sometimes referred to as box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.

In this context, we can reasonably infer ad logically deduce that the function of the “whiskers” in a box-and-whisker plot is to indicate or show any form of variability that exist outside the lower quartile and upper quartile.

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Complete Question:

What is the function of the “whiskers” in a box and whisker plot?

A

They represent the interquartile range.

B

They link the interquartile range to the minimum and maximum.

C

They compare the lower quartile to the upper quartile.

D

They compare the median to the interquartile range.

To add or subtract radical expressions, put each in simplest form and apply the distributive property, if possible.

We can add only like radicals, which are radicals with the same index and the same radicand. We must write each expression in simplified form for radicals before we can tell if the radicals are similar.
To add or subtract radical expressions, put each in simplified form and apply the distributive property, if possible. We can add only like radicals, which are radicals with the same index and the same radicand. We must write each expression in simplified form for radicals before we can tell if the terms are similar.

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Answer: Larry spends a total of 54 days traveling to Japan in one year for business.

Step-by-step explanation: Assuming each round trip takes 18 hours in both directions, Larry spends a total of 36 hours for each round trip to Japan.

To calculate the total number of days he spends traveling to Japan in one year, you can use the following steps:

Calculate the total number of hours Larry spends traveling to Japan in one year:

Total hours = 3 round trips/month * 12 months/year * 36 hours/round trip

Total hours = 3 * 12 * 36 = 1,296 hours

Convert the total number of hours to days:

1 day = 24 hours

Total days = Total hours / 24 hours/day

Total days = 1,296 hours / 24 hours/day

Total days = 54 days

Therefore, Larry spends a total of 54 days traveling to Japan in one year for business.

Answer:

The practice of using brass rings to stretch the neck, also known as neck elongation or neck stretching, is traditionally associated with the Padaung ethnic group from Myanmar (formerly known as Burma).

From a sociological perspective, the use of brass rings to stretch the neck can be seen as an example of deviance, which refers to behavior that violates social norms and expectations. Deviance can be either criminal or non-criminal, depending on the specific behavior in question and the cultural context in which it occurs.

In the case of Padaung women, the use of brass rings to elongate the neck is a form of non-criminal deviance, as it does not violate any laws. However, it does violate cultural norms and expectations in many other societies, where elongated necks are not seen as desirable or attractive.

Therefore, the practice of neck elongation among Padaung women can be seen as a form of cultural deviance, in which members of a particular group engage in behavior that is not considered acceptable or desirable by the larger society in which they live. At the same time, it can also be seen as an expression of cultural identity and tradition, as the practice has been passed down through generations and is an important part of Padaung culture and heritage.

The relative fitness of red birds is 1, not 0.5.

To determine the relative fitness of each bird type, we need to compare the average number of offspring each type produces in the next generation.

For red birds, the average number of offspring is 10.

For orange birds, the average number of offspring is 8.

For yellow birds, the average number of offspring is 2.

To calculate the relative fitness of each bird type, we divide each average number of offspring by the highest average number of offspring (which is 10):

- Redbirds: 10/10 = 1
- Orange birds: 8/10 = 0.8
- Yellow birds: 2/10 = 0.2

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To solve this problem, we need to use the transition matrix P50 provided in the file data6.mat. This matrix tells us the probabilities of moving from one state to another, where each state represents a different number of coins that you and your friend have.

First, we need to define the initial state vector Xo as [0, ...,1,...,0], where 1 is at index 26 to represent the starting state where both you and your friend have 25 coins. We can use this vector to calculate the probability distribution after 201 rolls of the dice.

To do this, we can use the formula Xn = P^n * Xo, where P^n is the transition matrix raised to the power of n, and Xn is the resulting state vector after n rolls of the dice.

Using MATLAB, we can calculate X201 as follows:

load data6.mat
P = P50;
Xo = zeros(1,50);
Xo(26) = 1;
X201 = (P^201)*Xo;

We can store the resulting vector as Ex1Avec and visualize it as a bar plot using the following code:

Ex1Avec = X201;
bar(Ex1Avec)
xlabel('State')
ylabel('Probability')
title('State Vector: 201 Rolls')

This will give us a bar plot showing the probability distribution for each state after 201 rolls of the dice. We can see which state has the highest probability of occurring, which will tell us the most likely outcome of the game after 201 rolls.
To find the probability distribution after 201 rolls of the dice, you can follow these steps:

1. Load the transition matrix P50 from the data6.mat file.
2. Initialize the initial state vector X0 with 1 at index 26 (representing you and your friend having 25 coins each) and all other entries 0.
3. Raise the transition matrix P50 to the power of 201 (the number of turns).
4. Multiply the initial state vector X0 by the raised matrix to obtain the state vector X201.
5. Store the vector X201 as Ex1Avec and visualize it using the provided bar plot code.

Here's the MATLAB code for these steps:

```MATLAB
load('data6.mat'); % Load the transition matrix P50
X0 = zeros(1, 51); % Initialize the initial state vector X0
X0(26) = 1; % Set the initial state with you and your friend having 25 coins each

P201 = P50^201; % Raise the transition matrix P50 to the power of 201
Ex1Avec = X0 * P201; % Multiply the initial state vector X0 by the raised matrix to obtain X201

% Visualize the state vector as a bar plot
bar(Ex1Avec);
xlabel('State');
ylabel('Probability');
title('State Vector: 201 Rolls');
```

The output will be a bar plot of the state vector after 201 rolls of the dice, representing the probability distribution of the game at that point.

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Answer:

B

Step-by-step explanation:

The line should be solid because it is greater than or equal to. B also has the line [tex]\frac{-6}{5} x - 5[/tex] graphed correctly.

1) Hypothesis 2) Not a hypothesis 3) Hypothesis 4) Hypothesis.

1) The statement "The more a person sits, the more weight a person gains" is likely to be a Hypothesis, as it proposes a relationship between daily sitting times and weight gain that can be tested with the data collected.

2) The statement "Data on the daily sitting times and weights for 1000 people indicates that the mean sitting time is 5 hours a day" is Not a hypothesis, as it presents a factual observation rather than a testable prediction or relationship.

3) The statement "Men sit longer than women each day" is likely to be a Hypothesis, as it proposes a testable relationship between gender and daily sitting times using the collected data.

4) The statement "People should stand more to gain health benefits" is Not a hypothesis, as it presents a recommendation or opinion rather than a testable prediction or relationship.

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Answer: El producto notable de (x + 2y) (x - 2y) es x^2 - (2y)^2, que se puede simplificar a x^2 - 4y^2.

Step-by-step explanation:

The treatment mean square can be calculated by dividing the sum of squares for treatment by the degrees of freedom for treatment. In this case, the sum of squares for treatment is 1,122 and the degrees of freedom for treatment is 2. Therefore, the treatment mean square is 1,122/2 = 561. Therefore, the correct answer is: 561.

Based on the ANOVA table you've provided, you're interested in determining the treatment mean square. The treatment mean square (also called mean square between) is calculated by dividing the treatment sum of squares by the treatment degrees of freedom (df). Unfortunately, the ANOVA table appears to be incomplete, and I am unable to give you the specific numbers for the calculations.

However, I can guide you on how to calculate the treatment mean square. Once you have the treatment sum of squares and treatment df, simply follow this formula:

Treatment Mean Square = Treatment Sum of Squares / Treatment df

After applying this formula, you'll be able to choose the correct answer from the multiple-choice options you've mentioned: 71.6, 71.8, 561, or 537.

The treatment mean square can be calculated by dividing the sum of squares for treatment by the degrees of freedom for treatment. In this case, the sum of squares for treatment is 1,122 and the degrees of freedom for treatment is 2. Therefore, the treatment mean square is 1,122/2 = 561. Therefore, the correct answer is: 561.

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the measure of the smallest exterior angle is 13. 846 degrees

It is important to note that the sum of the exterior angles of a polygon is expressed with the formula;

Sum of exterior angles = 360

Note that are hexagon is defined as a polygon with 6 sides and six vertices.

Now, substitute the measure of the angles

x + 2x + 6x + 8x + 9x = 360

collect the like terms, we have;

26x = 360

Divide both sides by the coefficient of x, we have;

26x/26 = 360/x

x = 13. 846 degrees

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