All F tests compare variances by ___________________.
a. dividing them
b. multiplying them
c. subtracting them
d. dividing, multiplying, AND dividing them.

(g) and Theorem 5 are not equivalent.

Are (g) and Theorem 5 equivalent?

You are correct. Statement (g) in Theorem 8, which states that the equation Ax = b has at least one solution for each b in R", includes both the case of a unique solution and the case of infinitely many solutions.

Therefore, (g) is not equivalent to Theorem 5, which specifically states that the equation Ax = b has a unique solution x = A^(-1)b when A is an invertible matrix. The equivalence mentioned in the text seems to be an error or a misinterpretation.

The correct interpretation is that Theorem 5 implies statement (g) in Theorem 8, but the converse is not necessarily true.

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The level of significance chosen for this hypothesis testing is 5%. In this hypothesis testing scenario, the null hypothesis (H0) is that the population proportion (P) is equal to 0.25 and the alternative hypothesis (Ha) is that P is not equal to 0.25.

The P-value is 0.094, which is the probability of observing a sample proportion at least as extreme as the one obtained if the null hypothesis were true.

Since the test rejected the null hypothesis, it means that the P-value is less than the chosen level of significance (alpha), indicating that the data provides enough evidence to reject the null hypothesis. Therefore, the alpha level chosen for this test must be greater than 0.094.

The only answer choice that satisfies this condition is C, where alpha = 5%. This means that there is a 5% chance of rejecting the null hypothesis when it is actually true. In other words, the level of significance chosen for this hypothesis testing is 5%.

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Answer:

you are correct but

the 11th is not 90-71 = 19°

The formula for finding the number of permutations of n objects with identical items is n! / (n1! * n2! * ... * nr!).

To find the number of permutations of n objects where n1, n2, ..., nr items are identical, we can use the formula:
n! / (n1! * n2! * ... * nr!)
Here, n is the total number of objects and n1, n2, ..., nr are the number of identical items in each group.
This formula works by first finding the total number of permutations of all n objects, which is n!.

However, we need to adjust for the fact that some objects are identical. We divide by the factorial of the number of identical objects in each group, to avoid overcounting.For example, if we have 6 objects and 2 pairs of identical objects (n1 = n2 = 2), the formula gives:
6! / (2! * 2! * 2!) = 15 permutations
This means there are 15 different ways to arrange the 6 objects, taking into account the identical pairs.

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Answer:

Step-by-step explanation:

false

Greenhouse- Geisser correction required when you do not have sphericity.

The Greenhouse-Geisser correction is a statistical method used to adjust for violations of sphericity in repeated measures ANOVA.

Sphericity assumes that the variances of the differences between all possible pairs of repeated measures are equal. When this assumption is violated, the Greenhouse-Geisser correction can be used to adjust the degrees of freedom to account for the non-sphericity and provide more accurate p-values.

Therefore, the correction is required when you do not have sphericity.

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The height of the parallelogram is equal to 20 meters.

In Mathematics and Geometry, the area of a parallelogram can be calculated by using the following formula:

Area of a parallelogram, A = b × h

Where:

By substituting the given parameters into the formula for the area of a parallelogram, we have the following;

Area of a parallelogram, A = b × h

1000 = 50 × h

Height, h = 1000/50

Height, h = 20 meters.

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There are 6,158,592 ways to place the passengers into the vans.

Since each van has 9 passenger seats and there are a total of 10 people, it is not possible to place all of them in one van.

Thus, we need to consider two cases:

9 people in the blue van, 1 person in the red van.

There are 10 ways to choose the person who will ride in the red van, and the remaining 9 people will go in the blue van.

There is only 1 way to arrange the passengers in the red van, and 9! ways to arrange the passengers in the blue van.

The total number of ways for this case is:

10 x 9! = 3,628,800

8 people in the blue van, 2 people in the red van.

There are 45 ways to choose the two people who will ride in the red van, and the remaining 8 people will go in the blue van.

There are 2 ways to choose which person will sit in which seat in the red van, and 8!/(2!6!) ways to arrange the passengers in the blue van.

The total number of ways for this case is:

45 × 2 × (8!/2!6!) = 45 × 2 × 28 × 7! = 2,529,792

The total number of ways to place the passengers into the vans is:

3,628,800 + 2,529,792 = 6,158,592

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At Woodbridge Middle School's annual concert, 6 classical tunes were played.

The given ratio of popular to classical tunes played is 2:3, which means that for every 2 popular tunes played, 3 classical tunes were played. Let's assume that the number of popular tunes played is '2x' (since the ratio of popular to classical tunes is 2:3) and the number of classical tunes played is '3x'. Therefore, the total number of tunes played is:

2x + 3x = 5x

We are given that the total number of popular and classical tunes played is 10, so we can write:

5x = 10

Dividing both sides by 5, we get:

x = 2

Therefore, the number of popular tunes played is:

2x = 2 x 2 = 4

And the number of classical tunes played is:

3x = 3 x 2 = 6

So, at Woodbridge Middle School's annual concert, 6 classical tunes were played.

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Answer:

--------------------

Perimeter is the sum of three side lengths.

Use the sum and known sides to find the missing side:

Substitute sides for P and solve for ?:

The missing side is x² + 3x + 5 units.

Systematic sampling and cluster sampling are examples of probability sampling methods used in human research. These methods are employed to ensure that each participant in the population has a known, non-zero chance of being selected, which helps in obtaining representative samples and drawing more accurate conclusions.

Systematic sampling and cluster sampling are both examples of probability sampling methods used in human research.

Probability sampling methods involve randomly selecting participants from a larger population, giving each individual an equal chance of being selected.

Systematic sampling involves selecting every nth participant from a list of the population, while cluster sampling involves dividing the population into clusters or groups and then randomly selecting entire clusters to include in the study.

These methods are considered to be more representative and unbiased than non-probability sampling methods, which do not involve random selection and may not accurately reflect the characteristics of the population.

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Step-by-step explanation:

35 %   means you pay 65%   or  .65

if x is the original price   the discounted price is  $  .65 x

Answer:

i think its 18

Step-by-step explanation:

Answer:

Yes, it would be appropriate to find a confidence interval for the proportion of voters choosing Kennedy since we have the necessary information (number of people who voted for Kennedy, number of people who voted for Nixon, and number of third-party votes) and the sample size (total number of voters) is large enough to assume a normal distribution. A confidence interval can provide an estimate of the true proportion of voters who chose Kennedy and the level of uncertainty around that estimate.

To solve the system of equations the value of k must be:

x = k

Here we have the system of equations:

x + 3y = k

x - k = y

We want to solve the equation for x in terms of k, so let's do that.

We can see that y is isolated in the second equation, so let's replace that in the first equation:

x + 3*(x - k) = k

Now we need to isolate x.

x + 3x - 3k = k

4x = k + 3k

4x = 4k

x = 4k/4 = k

x = k

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Answer:

K.

Step-by-step explanation:

To find the value of x, we can substitute x-k for y in the first equation: x + 3(x-k) = k. Simplifying, we get 4x - 3k = k. Adding 3k to both sides, we get 4x = 4k, or x = k. Therefore, x is equal to k.

The equation that represents the situation is y = 2x + 1062

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

x     y

3   1032

5   1072

7   1112

9   1152

A linear equation is represented as

y = mx + c

Using the points, we have

3m + c = 1032

5m + c = 1072

So, we have

2m = 40

Divide

m = 2

Next, we have

5(2) + c = 1072

This gives

c = 1062

So, the equation is

y = 2x + 1062

Hence, the equation that represents the situation is y = 2x + 1062

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Each cross street is 500 m far apart from each other.

Given that a scenario of three streets, Washington Street and N. South St. is 3.2 km long from the north.

There are no cross streets for the first 1.2 km then there are four cross streets each an equal distance apart,

So,

We need to find the distance between each street,

3.2-1.2 = 2 km

Therefore, all the 4 streets collectively are of length 2 km,

Since, each of them have equal distance so,

4s = 20 [say s is the length of one street]

s = 0.5 km

s = 500 meters

Hence, each cross street is 500 m far apart from each other.

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Conducting multiple t-tests on the same DV inflates the  experiment wise alpha.

When conducting multiple t-tests on the same dependent variable, there is an increased probability of committing a Type I error, which is rejecting the null hypothesis when it is actually true. This is because the more tests that are performed, the more likely it is that one or more of them will produce a significant result by chance alone.

The per comparison alpha is the probability of committing a Type I error on a single test, which is typically set at 0.05 (or 0.01) level of significance. When multiple tests are conducted, the probability of committing a Type I error across all tests, known as the experiment-wise alpha, increases. This means that the overall likelihood of falsely rejecting at least one null hypothesis increases with each additional test.

Therefore, it is important to adjust the alpha level for multiple comparisons using appropriate statistical techniques, such as Bonferroni correction or False Discovery Rate (FDR) control. These methods help to maintain a desirable experiment-wise error rate and control the risk of falsely rejecting the null hypothesis.

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Answer:

Step-by-step explanation:

Using the inclusion-exclusion principle, we can find the number of students who play at least one of the games as follows:

Number of students who play at least one of the games = number of students who play football + number of students who play table tennis - number of students who play both games

= 16 + 12 - 5

= 23

Therefore, 23 students play at least one of the games.

To find the number of students who play none of the games, we can subtract the number of students who play at least one of the games from the total number of students:

Number of students who play none of the games = total number of students - number of students who play at least one of the games

= 31 - 23

= 8

Therefore, 8 students play none of the games.

The number of home runs that Homer would need to hit next season to have a 12-year mean of 60 is given as follows:

98.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.

The sum of the observations, considering next year's amount as x, is given as follows:

25 + 49 + 51 + 52 + 56 + 58 + 62 + 64 + 65 + 68 + 72 + x = 622 + x.

Hence, for a mean of 60, the value of x is obtained as follows:

(622 + x)/12 = 60

622 + x = 720

x = 98.

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The equation of the quadratic function is:

f(x) = 4(x + 2)^2 - 3

To determine the equation of a quadratic function, we can start with the general form of a quadratic equation:

f(x) = ax^2 + bx + c

Given that the quadratic function has a minimum at (-2, -3), we know that the vertex of the parabola is at (-2, -3). The x-coordinate of the vertex gives us the value of the line of symmetry, which is also the value of the x-coordinate at the minimum point. Thus, we have:

x = -2

To find the coefficient "a" of the quadratic function, we can use the fact that the vertex form of a quadratic function is given by:

f(x) = a(x - h)^2 + k

where (h, k) is the vertex. Substituting the values of the vertex (-2, -3) into the vertex form, we get:

f(x) = a(x - (-2))^2 + (-3)

f(x) = a(x + 2)^2 - 3

Now, we can use the fact that the quadratic function passes through the point (-1, 1). Substituting these coordinates into the equation, we get:

1 = a(-1 + 2)^2 - 3

1 = a(1)^2 - 3

1 = a - 3

a = 4

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The solution for the equation AB=BC is A = B(CB⁻¹), given that B is invertible.To solve the equation AB=BC for A, assuming that A, B, and C are square matrices and B is invertible, follow these steps:

1. Since B is invertible, it means it has an inverse matrix, denoted as B⁻¹.
2. To isolate A, you can multiply both sides of the equation by the inverse of B.
3. Multiply B⁻¹ to the right side of both equations: (AB)B⁻¹= (BC)B⁻¹.

4. Remember that matrix multiplication is associative, so you can rearrange the parentheses: A(BB⁻¹) = B(CB⁻¹).
5. Since the product of a matrix and its inverse is the identity matrix (I), we have AI = B(CB⁻¹).
6. As multiplying by the identity matrix doesn't change the original matrix, we can simplify the equation to A = B(CB⁻¹).
Now, you have isolated A, and the solution for the equation AB=BC is A = B(CB⁻¹).

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The output for the given inputs 6, 8, and 9 is 1, 3, and 4 respectively.

Based on the given input-output relationship, we can see that the output is obtained by subtracting 5 from the input. Let's apply this rule to the given inputs:

Input: 6

Output: 6 - 5 = 1

Input: 8

Output: 8 - 5 = 3

Input: 9

Output: 9 - 5 = 4

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So Simon has [tex]7/10[/tex] of the original cakes left.

Simon gives 1/5 of the cakes to Sali:

= 30 * 1/5

= 6 cakes.

Simon gives 10% of the cakes to Jane:

= 10% * 30

= 3 cakes.

The total number of cakes Simon gives away is:

=  6 + 3

= 9 cakes.

So, Simon is left with 30 - 9 = 21 cakes.

To express this as a fraction of the original 30 cakes, we will simplify as:

= 21/30

= 7/10.

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To solve this problem, we can use the Poisson distribution, which models the number of events that occur in a fixed period of time, given the average rate of occurrence.

a. To find the probability that at most 425 people are struck by lightning in a year, we can use the Poisson distribution with a mean of 400. The formula for the Poisson distribution is:
P(X ≤ k) = e^-λ ∑_(i=0)^k (λ^i/i!)
where X is the random variable (the number of people struck by lightning in a year), λ is the mean (400), and k is the maximum number of people we're interested in (425). Plugging in the values, we get:
P(X ≤ 425) = e^-400 ∑_(i=0)^425 (400^i/i!) = 0.8855
So the probability that at most 425 people are struck by lightning in a year is 0.8855, or about 88.55%.
b. To find the probability that at least 375 people are struck by lightning in a year, we can use the complement rule: the probability of an event happening is 1 minus the probability of the event not happening. So in this case, we want to find the probability that fewer than 375 people are struck by lightning, and subtract that from 1 to get the probability of at least 375 people being struck.
P(X ≥ 375) = 1 - P(X < 375) = 1 - e^-400 ∑_(i=0)^374 (400^i/i!) = 0.9369
So the probability that at least 375 people are struck by lightning in a year is 0.9369, or about 93.69%.
It's important to note that these probabilities are based on the assumption that the number of people struck by lightning in a year follows a Poisson distribution with a mean of 400. This may not be a perfect model, but it's a reasonable approximation based on the available data. Additionally, the chances of being struck by lightning are still relatively low - even at the high end of our estimates, only about 0.1% of the US population would be affected.

Based on the given information of 400 people being struck by lightning in the United States on average each year, we can calculate the probabilities for the scenarios you mentioned.
a. The probability that at most 425 people are struck by lightning in a year:
To calculate this, we'll need to know the distribution of people being struck by lightning, which isn't provided. However, let's assume it follows a normal distribution with a mean of 400 and some standard deviation. In this case, we would calculate the z-score for 425 people and find the corresponding probability from the z-table. Unfortunately, without the standard deviation, we cannot compute the exact probability.
b. The probability that at least 375 people are struck by lightning in a year:
Similarly, to calculate this probability, we'd need the standard deviation to find the z-score for 375 people and then find the corresponding probability from the z-table. Again, without the standard deviation, we cannot compute the exact probability.
In conclusion, without knowing the standard deviation or the distribution of people being struck by lightning, we cannot provide a precise probability for the given scenarios.

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Area of small sector is 1620 square meters and Area of large sector  is 12960 square meters

Area of sector = 1/2r²θ

r is the radius of the circle which is 9cm

The area of small and large sectors we have to find

Small sector has θ value of 40 degrees

and large sector has 320 degrees

Area of small sector = 1/2(9)²×40

=1/2×81×40

=1620 square meters

Area of large sector = 1/2(9)²×320

=81×160

=12960 square meters

Hence, area of small sector is 1620 square meters and Area of large sector  is 12960 square meters

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For ð inputs, there can be an infinite number of subsets of those features. This is because a subset is a collection of some or all of the features within the inputs. Therefore, the number of possible subsets is determined by the number of possible ways in which we can choose from the available features.

For instance, if we have three features within an input, we can create subsets of one, two, or all three features. This gives us a total of seven possible subsets. However, this is not the only way in which we can create subsets. We can also create subsets that contain no features or any combination of features, which increases the number of possible subsets even further.

Therefore, the total number of possible subsets for ð inputs is limitless. It is important to note that not all subsets will be relevant or useful, but the more subsets we have, the more options we have for creating effective models or making informed decisions based on the inputs and features.

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For ð inputs, there can be an infinite number of subsets of those features. This is because a subset is a collection of some or all of the features within the inputs. Therefore, the number of possible subsets is determined by the number of possible ways in which we can choose from the available features.

For instance, if we have three features within an input, we can create subsets of one, two, or all three features. This gives us a total of seven possible subsets. However, this is not the only way in which we can create subsets. We can also create subsets that contain no features or any combination of features, which increases the number of possible subsets even further.

Therefore, the total number of possible subsets for ð inputs is limitless. It is important to note that not all subsets will be relevant or useful, but the more subsets we have, the more options we have for creating effective models or making informed decisions based on the inputs and features.

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