A researcher wants to test the claim that the average lifespan for florescent lights is 1600 hours. A random sample of 100 fluorescent lights has a mean lifespan of 1580 hours, and a standard deviation of 100 hours. Is there evidence to support the claim at 5% level of significance?

If one of the effects is substantial, it should be included in the analysis as a control variable.

If none of the effects are important, the analysis may need to be redone with a more comprehensive model or a bigger sample size.

If you conduct a two-way between-subjects ANOVA and discover that the interaction F-test is important, the next thing to do is to interpret the results.

You may be interested in estimating the main effects of each variable and the interaction effect.

In a two-way ANOVA, a statistical method is employed to identify the interactions between two variables.

ANOVA stands for analysis of variance.

It is a statistical method used to compare two or more populations by analyzing the variance between them.

F-test is a statistical method used to compare two variances or to test hypotheses about whether two population variances are equal.

It can be used to compare more than two variances in ANOVA.

When the interaction effect in a two-way between-subjects ANOVA is important, the interpretation of the main effects of each variable and the interaction effect must be done.

If one of the effects is substantial, it should be included in the analysis as a control variable.

If none of the effects are important, the analysis may need to be redone with a more comprehensive model or a bigger sample size.

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Answer: B, makes the most sence

Step-by-step explanation:

The composition relation (RS) of R with S is {(a, w), (b, z), (b, z), (c, z)}.

The composition relation (RS) of R with S is obtained by taking the pairs from R and S that have matching elements.

R = {(a, 2), (b, 3), (b, 4), (c, 3)}

S = {(1, y), (1, z), (2, w), (3, z)}

To obtain RS, we need to match the second element of each pair in R with the first element of each pair in S.

For the pair (a, 2) in R, we match the 2 with the second elements of pairs in S: (2, w). So we have (a, w).

For the pair (b, 3) in R, we match the 3 with the second elements of pairs in S: (3, z). So we have (b, z).

For the pair (b, 4) in R, we match the 4 with the second elements of pairs in S: (4, z). So we have (b, z).

For the pair (c, 3) in R, we match the 3 with the second elements of pairs in S: (3, z). So we have (c, z).

Putting it all together, the composition relation RS is:

RS = {(a, w), (b, z), (b, z), (c, z)}

Note that (b, z) appears twice in the composition relation because there are two pairs (b, 3) in R that match with (3, z) in S.

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Answer:

I cannot see pictures, so I will explain how to find slope, so you can do it on your own.

Step-by-step explanation:

Find 2 coordinates on the line.

Ex: (2,3) and (4,6)

Subtract the y-coords and x-coords from each other and divide.

6-3 = 3

4-2 = 2

3/2

So the example slope is 3/2.

The 3 represents the rise, and 2 represents the run.

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hope it helps

Answer:

63 degree

Step-by-step explanation:

Answer:

an = −1,171,875(1/5)^n-1

Step-by-step explanation:

The given sequence is geometric sequence since they have the same common ratio r. The nth term of a geometric sequence is expressed as;

an = ar^n-1

n is the number of terms

r is the common ratio

a is the first term

From the sequence;

a = −1,171,875

r = −234,375 /−1,171,875 = -46,875/−234,375 = 0.2

r = 1/5

Substitute the values in the formula;

an = −1,171,875(1/5)^n-1

Hence the required explicit formula is an = −1,171,875(1/5)^n-1

The explicit rule that describes the sequence is [tex]\rm a_n = -1,171,875 (\dfrac{1}{5})^{n - 1 }[/tex]. Then the correct option is C.

A sequence is a list of elements that have been ordered in a sequential manner, such that members come either before or after.

The sequence is {−1,171,875;−234,375;−46,875;−9375,…}

The given sequence is the geometric sequence since they have the same common ratio r. Then the nth term of the geometric sequence will be

[tex]\rm a_n = a\ r^{n-1}[/tex]

Where

Number of terms (n)

First-term (a) = -1,171,875

Common ratio (r) = 1/5

Then nth term will be

[tex]\rm a_n = -1,171,875 (\dfrac{1}{5})^{n - 1 }[/tex]

The explicit rule that describes the sequence is [tex]\rm a_n = -1,171,875 (\dfrac{1}{5})^{n - 1 }[/tex]. Then the correct option is C.

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Answer:

[tex]0.64*y = 40[/tex]

Step-by-step explanation:

Answer:

64/100=40/y

Step-by-step explanation:

We use the simple equation of finding percentages, which would be the percentage (64) over 100 percent, as this is our total. If 64 percent of y equals 40, then the equation is 64/100=40/y. To solve for y, multiply 100 x 40= 4000, then divide by 64 to get the answer. Y=62.5

Answer:

Least Value: 16

Median: 26

Upper Quartile: 30

Lower Quartile: 20

Greatest Value: 34

Interquartile Range: 10

Range: 18

Answer:

18

Step-by-step explanation:

formula= length x width x height

3 x 3 x 2 = 18

Answer:

12

Step-by-step explanation:

V = Bh.

Base = b = length x width

length = 3

width = 3

height = 2

6 x 2

The statement "If f(x) is irreducible over R, then f(x²) is irreducible over R" is false. The irreducibility of f(x) does not guarantee the irreducibility of f(x²) over R.

The statement "If f(x) is irreducible over R, then f(x²) is irreducible over R" is actually false. In other words, just because a polynomial, f(x), is irreducible over the real numbers (R), it does not necessarily mean that its square, f(x²), will also be irreducible over R.

To understand why, let's first clarify the concept of irreducibility.

A polynomial is considered irreducible if it cannot be factored into a product of two or more non-constant polynomials with coefficients in the same field. In this case, we are considering the field of real numbers (R).

Now, when we square a polynomial, such as f(x)² or f(x²), it can lead to changes in its factorization.

The squared polynomial may introduce new factors or change the multiplicity of existing factors.

This means that the irreducibility of the original polynomial, f(x), does not necessarily carry over to the squared polynomial, f(x²).

To illustrate this, let's consider an example. Suppose we have a polynomial f(x) = x² + 1, which is irreducible over R. If we square this polynomial, we get f(x²) = (x² + 1)² = x⁴ + 2x² + 1.

The squared polynomial, in this case, is no longer irreducible over R because it can be factored as (x² + 1)(x² + 1).

This example shows that the irreducibility of f(x) does not imply the irreducibility of f(x²). It's important to carefully analyze the specific factors and properties of each polynomial to determine its irreducibility.

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Answer:

A right angle is neither Obtuse nor Acute

Step-by-step explanation:

Answer: Which angles are neither obtuse angles nor acute angles?

Answer:

Step-by-step explanation:

Remark

Cos(y) = adjacent Side / hypotenuse

y = 51 degrees

adjacent = 10

Solution

Cos(51) = 10/x              Multiply both sides by x

x cos(51) = 10               Divide by Cos(51)

x = 10 / cos(51)

Cos(51) = .6293

x = 10/0.6293

x = 15.89

Step-by-step explanation:

given,

[tex]2k \div 3 = 6 \\ 2k \div3 \times 3 = 6 \times 3 \\ 2k = 18 \\ k = 18 \div 2 \\ = 9[/tex]

Answer:  A

Step-by-step explanation:

The line and dots are closed circle, so B and D would not be the answer.

The line have passed through the point (-6,4) and (0,2); we uses to find the slope.

slope = m = (y2 - y1)/(x2 - x1) = (2 - 4)/(0 - (-6)) = -2 / 6 = -1/3

we plug in slope to the linear equation in form of y = mx + b, where m is the slope, and b is the y- intercept.

y = -1/3x + 2

So the answer is A.

Answer:

113.04

Step-by-step explanation:

Surface area for a sphere is 4*pi*radius^2

4*3*3*3.14

113.04

The surface area of the sphere with the given radius is 113.04cm².

A sphere is simply a 3-dimensional object with no vertices and edges.

The surface area of a sphere is expressed as;

Area = 4πr²

Given the data in the question;

To determine the surface area of the sphere, we substitute our given values into the expression above.

Area = 4πr²

Area = 4 × 3.14 × (3cm)²

Area = 4 × 3.14 × 9cm²

Area = 113.04cm²

Therefore, the surface area of the sphere with the given radius is 113.04cm².

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After considering the given data we conclude that the evaluated limit of the given function is 35, which is option D

Here we have to apply the principle of evaluating function using a dedicated value.
Given [tex]f(x) = x^4 - 3x^3 x - 3,[/tex]we need to evaluate the limit of f(x) as x approaches negative 2.
To evaluate the limit, we can simply substitute x = -2 into the function:
[tex]f(-2) = (-2)^4 - 3(-2)^3(-2) - 3 = 16 + 24 - 2 - 3 = 35[/tex]
Therefore, the limit of f(x) as x approaches negative 2 is 35.
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Answer:

487

Step-by-step explanation:

We can use this formula to find the 60th term:

8n+7

Complete question :

Matthew asked 10 students how many pets and how many siblings each has. The line plots below show his data.

Which statement correctly describes Matthew’s data?

A. The median number of pets the students have is less than the median number of siblings the students have.

B. There is less variability in the number of pets the students have than in the number of siblings the students have.

C. The range in the number of siblings the students have is less than the range in the number of pets the students have.

D. The mean absolute deviation of the number of siblings the students have is less than the mean absolute deviation of the number of pets the students have.

Answer:

B. There is less variability in the number of pets the students have than in the number of siblings the students have.

Step-by-step explanation:

From the data:

Pets data:

3,3,4,4,4,4,5,5,5,5

Using calculator:

Median value = 4

Mean absolute deviation = 0.64

Range = 5 - 3 = 2

Siblings data:

Median value = 2

Mean absolute deviation = 1.52

Range = 5 - 0 = 5

Median value of pets > median value of siblings data

Range of siblings data > range of pets data

Mean absolute deviation of siblings data >Ean absolute deviation of pets data

Variability of pets data is lesser than that of siblings data ; as shown by the mean absolute deviation value

Answer: the formula is : β = 180° - α

A = 6 * a² * sin(α)

V = a³ * (1-cos(α)) * √1+2cos(α)

Sorry, i don't know any examples .

Step-by-step explanation:

The population parameter of interest is the proportion of all Greeks who would rate their lives poorly enough to be considered "suffering."b) The success-failure condition is met.c) The sampling distribution of p is a normal distribution with a mean equal to the population proportion and a standard deviation given by the formula σp = sqrt[p(1−p)/n]. If we assume that the claim is true, then p = 0.25, and the sample size is 1000, and hence the standard deviation of the sampling distribution of p is: sqrt[p(1−p)/n] = sqrt[(0.25)(0.75)/1000] ≈ 0.0144d) The probability that the sample proportion p is between 24% and 28% if the social science researcher's claim is correct is 0.6615 or 66.15% (approximately).

Population parameter of interest:The population parameter of interest is the proportion of all Greeks who would rate their lives poorly enough to be considered "suffering". The parameter of interest in this case is the percentage of Greeks who would be classified as "suffering."b) Check if the success-failure condition required for the Central Limit Theorem for the sample proportion is met.The success-failure condition is met when the number of successes and failures in the sample is both larger than 10. Let’s assume that the claim is true, thus the proportion p is equal to 0.25.

The sample size is 1,000. Therefore, the expected number of successes and failures arenp = 1,000 × 0.25 = 250n(1−p) = 1,000 × 0.75 = 750Both expected number of successes and failures are greater than 10, therefore, the success-failure condition is met.c) Sampling distribution of p if the social science researcher's claim is correct:The sampling distribution of p is a normal distribution with a mean equal to the population proportion and a standard deviation given by the formula σp = sqrt[p(1−p)/n]. If we assume that the claim is true, then p = 0.25, and the sample size is 1000, and hence the standard deviation of the sampling distribution of p is:sqrt[p(1−p)/n] = sqrt[(0.25)(0.75)/1000] ≈ 0.0144d) Probability that the sample proportion p is between 24% and 28% if the social science researcher's claim is correct:

The sample proportion, p, follows a normal distribution with mean 0.25 and standard deviation 0.0144. Therefore, the standardized value of 0.24 is(0.24−0.25)/0.0144 = -0.6944and the standardized value of 0.28 is(0.28−0.25)/0.0144 = 2.0833From standard normal distribution table, the probability of getting a value between -0.6944 and 2.0833 is approximately 0.6615. Thus, the probability that the sample proportion is between 24% and 28% is 0.6615 or 66.15% (approximately).

Answer: a) The population parameter of interest is the proportion of all Greeks who would rate their lives poorly enough to be considered "suffering."b) The success-failure condition is met.c) The sampling distribution of p is a normal distribution with a mean equal to the population proportion and a standard deviation given by the formula σp = sqrt[p(1−p)/n]. If we assume that the claim is true, then p = 0.25, and the sample size is 1000, and hence the standard deviation of the sampling distribution of p is: sqrt[p(1−p)/n] = sqrt[(0.25)(0.75)/1000] ≈ 0.0144d) The probability that the sample proportion p is between 24% and 28% if the social science researcher's claim is correct is 0.6615 or 66.15% (approximately).

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Comparing the observed and expected distributions can help detect peculiarities in the data in cases where there is an expectation or a known pattern that can be used for comparison.

A newly discovered secret novel from a deceased prolific author: In this case, comparing the observed distribution of the writing style, themes, or language in the novel with the expected distribution based on the author's previous works can help identify any peculiarities or deviations from the author's typical style.

The reported ages of users on a popular social networking site: Comparing the observed distribution of ages with the expected distribution based on demographic data or population statistics can reveal any anomalies or discrepancies, such as an unusually high or low frequency of certain age groups, which may indicate data inaccuracies or biases.

Both of the above: Both scenarios involve comparing observed and expected distributions to identify peculiarities or deviations in the data.

None of the above: If there is no expectation or known pattern to compare the observed distribution against, comparing the observed and expected distributions may not be applicable for detecting peculiarities in the data.

In conclusion, comparing observed and expected distributions can be helpful in detecting peculiarities in the data when there is an expectation or known pattern to use for comparison. It can be useful in scenarios such as analyzing a newly discovered novel from a deceased author or examining reported ages on a social networking site. However, if there is no expectation or known pattern, this method may not be applicable.

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Answer:

4/18

Step-by-step explanation:

Answer:

3.666667

Step-by-step explanation:

You can do long division, or you can use a calculator.

Answer:

door?

Step-by-step explanation:

Or is it 2 windows?

The follow-ups to the Window Equation don't as a rule utilize the a additionally image and rises to sign, and are drawn by flipping one of the numbers.

1 + 1 = window

2 + 2 = fish

3 + 3 = eight

4 + 4 = arrow

5 + 5 = apple

6 + 6 = cherry

7 + 7 = triangle

8 + 8 = butterfly

Hope this helps!

Picture below: The steps and associated words showing how to complete the window symbol.

Answer:

if its not a fraction or a number that can be written as a fraction, its an irrational

Answer:

the answer is 8

Step-by-step explanation:

8x6=48

Answer:

8

Step-by-step explanation:

its 8 because the multiples of 6 are 6, 12, 18, 24, 30, 36, 48 then the multiples of 8 are 8, 16, 24, 32, 40, 48

In the absence of the blonde turning down everyone, the pure strategy Nash equilibrium is for all men to choose brunettes. If the blonde turns down everyone, the pure strategy Nash equilibrium remains the same: all men choosing brunettes.

In this case, all four men choose brunettes. Since no man is going for the blonde, their payoff is b if they are the only man going for a brunette. This scenario is a pure strategy Nash equilibrium because no man has an incentive to deviate.

If one man goes for the blonde, his payoff is c. The other three men choose brunettes, resulting in a payoff of b. This situation is not a Nash equilibrium because the man going for the blonde has an incentive to deviate and choose a brunette instead, increasing his payoff to b.

Since the payoffs are the same for any number of men going for the blonde, the pure strategy Nash equilibrium is for all men to choose brunettes. Each man's payoff will be b, regardless of whether they choose the blonde or a brunette.

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Answer:

x = -51

Step-by-step explanation:

Do I need to explain oorrrrrrrrr.....

Answer:

I believe it would be 5.

Step-by-step explanation:

I'm not completely sure, but this seems quite easy, so I hope I'm right :D

There are 6 different numbers on the number cube so x = 6

The 1/x means you have a 1 in x ( total choices) of getting a certain number.

The total choices would be the total numbers in the cube which is 6.

The answer is 6