Two different simple random samples are drawn from two different populations. The first sample consists of 20 people with 10 having a common attribute. The second sample consists of 1800 people with 1284 of them having the same common attribute. Compare the results from a hypothesis test of P = P2 (with a 0.01 significance level) and a 99% confidence interval estimate of p, - P2, What are the null and alternative hypotheses for the hypothesis test?

The solution is :

D. π < x < 2π, over this interval is the graph of y=cos(x) strictly increasing.

Given the function

y=cos(x)

Referring to the intervals [0, 2π].

It decreases from the interval [0, π ] and then starts increasing in the interval [π, 2π ]

Proving by taking derivative:

Taking derivative of the function, y=cos(x)

dy/dx = - sinx

In the interval [π, 2π ], sinx is negative i.e. sinx < 0.

Therefore

-sinx > 0

When, the derivative of a function is positive, then the function is strictly increasing.

So, the answer is:

D. π < x < 2π

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a) The critical value of t for a 95% confidence interval with df = 24 is approximately 2.064.

b) The critical value of t for a 98% confidence interval with df = 79 is approximately 2.626.

We have,

a) To find the critical value of t for a 95% confidence interval with

df = 24, we can use a t-table or a statistical calculator.

For a 95% confidence level and df = 24, we need to find the t-value corresponding to an alpha value of 0.05 (1 - confidence level).

Using a t-table or a statistical calculator, we find that the critical value of t for a 95% confidence interval with df = 24 is approximately 2.064.

b)

Similarly, for a 98% confidence interval with df = 79, we need to find the t-value corresponding to an alpha value of 0.02 (1 - confidence level).

Using a t-table or a statistical calculator, we find that the critical value of t for a 98% confidence interval with df = 79 is approximately 2.626.

Therefore,

a) The critical value of t for a 95% confidence interval with df = 24 is approximately 2.064.

b) The critical value of t for a 98% confidence interval with df = 79 is approximately 2.626.

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The mean of the stem leaf plot is 29.09, median is 29 , range is 46 and mode is 41.

The data from stem leaf plot is 19, 22,26, 29,30,31,41,41,43,52,6

Mean = (19 + 22 + 26 + 29 + 30 + 31 + 41 + 41 + 43 + 52 + 6) / 11

Mean = 320 / 11

Mean = 29.09

To find median let us arrange the data in ascending order

6, 19, 22, 26, 29, 30, 31, 41, 41, 43, 52

So the median of the data is 29.

To find the mode of the data, we need to find the value that appears most frequently.

Mode is 41
To find the range of the data, we need to subtract the smallest value from the largest value:

So the range of the data is 46.

The tennis players should report the median value to show they have practiced enough for the tournament, as it is a more robust measure of central tendency for this dataset.

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Therefore, using the linear approximation, we estimate that (2.001)⁵ ≈ 32.016.

We can use the linear approximation to estimate the given number by using the following formula:

f(x + Δx) ≈ f(x) + f'(x)Δx

where Δx is a small change in x, f'(x) is the derivative of the function f(x), and f(x + Δx) is the approximate value of the function for x + Δx.

In this case, we can let f(x) = x⁵, x = 2, and Δx = 0.001. Then,

f'(x) = 5x⁴

So,

f(2.001) ≈ f(2) + f'(2)Δx

f(2.001) ≈ 2⁵ + 5(2⁴)(0.001)

f(2.001) ≈ 32.016

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The explicit formula for the nth term of the sequence 8, 40, 200, ..., is:

[tex]a_n = 8 \times 5^{(n-1)}[/tex]

To find the explicit formula for the nth term of the sequence 8, 40, 200, ..., we first notice that each term is obtained by multiplying the previous term by 5. That is:

a₁ = 8

a₂ = 5a¹ = 40

a₃ = 5a² = 200

a₄ = 5a³= 1000

...

In general, we can write:

[tex]a_n = 5a_n-1[/tex]

where n is the index of the term in the sequence.

Using the initial term a₁ = 8, we can use the recursive formula to find the value of any term in the sequence. However, to find an explicit formula for the nth term, we can use the formula for a geometric sequence, which is:

[tex]a_n = a_1 \times r^{(n-1)}[/tex]

where r is the common ratio. In this case, the common ratio is 5, so we can substitute it into the formula to get:

[tex]a_n = 8 \times 5^{(n-1)}[/tex]

The explicit formula for the nth term of the sequence 8, 40, 200, ..., is:

[tex]a_n = 8 \times 5^{(n-1)}[/tex]

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Work Shown:

Let's start things off by finding the slope.

[tex](x_1,y_1) = (-3,6) \text{ and } (x_2,y_2) = (-2,9)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1}}\\\\m = \frac{9 - 6}{-2 - (-3)}\\\\m = \frac{9 - 6}{-2 + 3}\\\\m = \frac{3}{1}\\\\m = 3\\\\[/tex]

The slope is 3.

Now use point-slope form to determine the equation.

[tex]\text{y}-\text{y}_1 = \text{m}(\text{x} - \text{x}_1)\\\\\text{y}-6 = 3(\text{x} - (-3))\\\\\boldsymbol{\textbf{y}-6 = 3(\text{x} + 3)}[/tex]

According to the Gallup poll, the proportion of American adults who believe in conspiracy theory has decreased significantly since 2001.

To test whether the proportion of Americans who believe in the conspiracy surrounding the death of President Kennedy has decreased, we need to conduct a hypothesis test. Let us assume that the null hypothesis is that the proportion of Americans who believe in the conspiracy theory has remained the same or increased, while the alternative hypothesis is that the proportion has decreased.
Let p be the true proportion of American adults who believe in the conspiracy theory, and let p0 be the proportion in 2001 (81%). The sample proportion in 2013 is 634/1039=0.61. The sample size is sufficiently large (1039>30), so we can use the z-test.
The test statistic is:
z = [tex](p - p0) / \sqrt{[p0*(1-p0)/n]}[/tex]
 = (0.61 - 0.81) / [tex]\sqrt{[0.81*(1-0.81)/1039]}[/tex]
 = -11.08
At the 1% level of significance, the critical value for a two-tailed test is z* = 2.58. Since the test statistic (z = -11.08) is much smaller than the critical value (z* = 2.58), we reject the null hypothesis in favour of the alternative hypothesis. Therefore, the data provide strong evidence that the proportion of Americans who believe in the conspiracy theory surrounding the death of President Kennedy has decreased since 2001.
In conclusion, according to the Gallup poll, the proportion of American adults who believe in conspiracy theory has decreased significantly since 2001. The sample size is sufficiently large, and the z-test was used to reach this conclusion at the 1% level of significance.

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Answer:

31

Step-by-step explanation:

Note: I'm assuming that the three values after your expression (49, 58, and 31) are the possible answers. Let me know if they're actually a part of the expression.

Following PEMDAS, we're going to have to start by evaluating the expression inside the parentheses. That expression is 16 - 9, which is equivalent to 7.

Now, we're left with this expression: 3 + 4(7). Still following PEMDAS, we're going to have to evaluate the multiplication next. 4(7) = 28, so we are now left with the simple addition problem 3 + 28, and this is equal to 31. The entire work with no explanation is shown below.

3 + 4(16 - 9) = 3 + 4(7) = 3 + 28 = 31

Hopefully, that's helpful. Let me know if you need further clarification. :)

The probability that the sample mean time taken is less than 85 minutes is 0.067 or 6.7%.

To answer this question, we can use the central limit theorem, which states that the distribution of sample means of a population with any distribution will approach a normal distribution as the sample size increases.

Given that the times taken to complete the tax form follow a normal distribution with a mean of 100 minutes and a standard deviation of 30 minutes, we can assume that the sample mean time taken also follows a normal distribution with a mean of 100 minutes and a standard deviation of 30 / sqrt(9) = 10 minutes (since the sample size is 9).

To find the probability that the sample mean time taken is less than 85 minutes, we need to standardize the sample mean using the formula z = (x - mu) / (sigma / sqrt(n)), where x is the sample mean, mu is the population mean, sigma is the population standard deviation, and n is the sample size.

Plugging in the values, we get z = (85 - 100) / (10) = -1.5.

We can then look up the probability of getting a z-score of -1.5 or lower in a standard normal distribution table or using a calculator. The probability is approximately 0.067 or 6.7%.

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Using the knowledge of similar triangles for the figure the value of x would be

The value of x is solved in a two column table as shown

Statement                        Reason

EF || RS                               given

EA / SA = FA / RA               proportions of  similar triangles are equal

24/16 = (7 + (x + 2)) / (x+2)  substitution property of equality

24(x + 2) = 16(x + 9)             simplifying

24x - 16x = 144 - 48             gathering like terms

8x = 96                                 division property of equality

x = 12                                

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Answer:

To compare the balances of the two loans at the time of repayment, we need to calculate the future value of the loan amount for each loan option after 12 months of compounding.

For the Unsubsidized Stafford Loan:

Principal (P) = $9,529

Annual interest rate (r) = 5.95%

Compounding period (n) = 12 (monthly compounding)

Time period (t) = 1 year

Using the formula for future value of a loan (FV), we get:

The formula is:

FV = P * (1 + r/n)^(nt) = $9,529 * (1 + 0.0595/12)^(121) = $10,087.14

For the PLUS Loan:

Principal (P) = $10,172.23

Annual interest rate (r) = 6.55%

Compounding period (n) = 12 (monthly compounding)

Time period (t) = 1 year

Using the same formula, we get:

FV = P * (1 + r/n)^(nt) = $10,172.23 * (1 + 0.0655/12)^(121) = $10,774.71

Therefore, the Unsubsidized Stafford Loan will have a lower balance at the time of repayment, by $687.57 ($10,087.14 - $10,774.71).

Answer:

To calculate the edge length, take the cube root of the total volume of the cube.

Step-by-step explanation:

hope this helps ! :)

The formula that shows the dependence of the edge length 'a' on volume V of a cube will be a = ∛V.

All the edges of the cube are congruent with each other. Suppose that: The side length of the considered cube is 'a' units. Then, we get:

Volume of that cube = a³ cubic units.

Solve the equation for 'a', then we have

V = a³

a³ = V

a = ∛V

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Therefore, we can conclude that the changing cultural values have resulted in more Hispanic men grocery shopping by  -3.81 percent.

To determine if a lower proportion of Hispanic grocery shoppers are women, we need to perform a hypothesis test using the given sample data.

Let p be the true proportion of Hispanic grocery shoppers who are women. The null hypothesis is that p = 0.94, while the alternative hypothesis is that p < 0.94. We will use a one-tailed test with a significance level of α = 0.05.

The test statistic is calculated as:

z = (x - np) / √(np(1-p))

where x is the number of women in the sample (606), n is the sample size (689), and p is the null hypothesis value (0.94).

z = (606 - 6890.94) / √(6890.94*0.06)

z = -3.81

The critical value for a one-tailed test with α = 0.05 and degrees of freedom of 688 is -1.645. Since the calculated z value of -3.81 is less than the critical value of -1.645, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that a lower proportion of Hispanic grocery shoppers are women.

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The key feature that is different for the two functions is (d) the slope

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

Linear functions on a graph and a table

As a general rule

All linear functions have the same domain, the same range

The slope of the table is

Slope = (8 - 6)/(-8 + 4) = -1/2

The slope of the graph is

Slope = (2 + 1)/(0 - 1) = -3

This means that their slopes are different

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Therefore, further research would be needed to determine if the relationship between the price of gasoline and gasoline consumption holds at higher prices.

A linear correlation coefficient of 0.7 indicates a strong positive linear relationship between the price of gasoline and gasoline consumption. In other words, as the price of gasoline increases, gasoline consumption also tends to increase. However, correlation does not necessarily imply causation, and there may be other factors at play that influence gasoline consumption.

It is not necessarily reliable to apply the results of this study to prices of gasoline higher than $5.30 per gallon because the study only included gasoline prices within that range. Extrapolating the results beyond the range of data may lead to inaccurate predictions or conclusions. Additionally, there may be other factors at play at higher prices that were not present within the range of prices studied.

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There are 8! (factorial) ways for the eight students to stand next to each other. However, since no two professors can stand next to each other, we need to alternate professors and students. We can start with a professor, then a student, then a professor, and so on.

There are 5! ways to arrange the five professors among the eight spaces where a professor can stand. Once the professors are arranged, there are 8 - 5 = 3 spaces left for students to stand. There are 8P3 (permutations) ways to arrange the three students among the three spaces.

Therefore, the total number of ways for eight students and five professors to stand next to each other such that no two professors are standing next to each other is 5! * 8P3 = 5,760 ways.

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The four points that the homebuyers are purchasing to lower their rate from 5.05% to 4.81% will cost them D. $5,480.

The points purchased for loans are charges that the borrower pays upfront to lower their interest rates.

Each point equals a percentage of the loan amount.

For example, four points on a $137,000 loan are 4 percent of the loan amount, or $5,480.

The loan amount for the purchase of the condominium = $137,000

Fixed interest rate = 5.05%

Loan period = 15 years

Loan option rate = 4.81%

Four points = $5,480 ($137,000 x 4%)

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The graph of the piecewise function is attached accordingly.

A piecewise-defined function in mathematics is one that is composed of several smaller functions, each of which has a certain interval of the domain it applies to.

Instead of being a property of the function itself, piecewise definition is a means to represent the function.

There are several configurations for piecewise specified functions. Their "pieces" might be entirely linear or comprise a variety of functional forms, including constant, linear, quadratic, cubic, square-root, cube-root, exponential, etc. There is no "parent function" for piecewise defined functions because of this variety.

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Full Question:

Although part of your question is missing, you might be referring to this full question: See the attached image.

We can see that the experimental probability is smaller than the theoretical one.

The theoretical probability is equal to the quotient between the number of yellow marbles and the total number, so here we have:

T = 3/8 = 0.375

The experimental probability is equal to the quotient between the number of times that Mel got a yellow marble and the total number of trials, so here we have:

E = 12/40 = 0.3

So the experimental probability is smaller than the theoretical one.

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The transformation to create the pattern is 180° rotation

Given data ,

Let the pattern be represented as figure A

Now , the figure A has footprints of the left leg

when rotating by 180° in the clockwise or anticlockwise direction , the sign only changes and it will be up side down

Hence , the transformation is 180° rotation

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The best unit of measurement to represent the diameters of Mars and the Sun is millimeters.

1 kilometer = 1,000,000 millimeters

Therefore, the Sun's diameter in millimeters can be calculated as:

1.391 × 10⁶ km × 1,000,000 mm/km = 1.391 × 10¹² mm

Sun's diameter / Mars's diameter = (1.391 × 10¹² mm) / (6.794 × 10⁹ mm)

This simplifies to:

Sun's diameter / Mars's diameter ≈ 204,474

Therefore, the Sun's diameter is approximately 204,474 times greater than Mars's diameter.

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The money that will be in the account at the end of six years is $8,404.5

The initial deposit = P = $7200

Rate = r = 5.5% per year

Time = 6 years ( Compounded Quarterly)

As per the question, the compound interest calculation can be used to determine how much money will be in the account after six years. Compound interest may be thought of as the addition of the loan's interest to the deposit's principal amount. As a result, it is computed using the Principal plus any prior interest.

Using, the formula for compound interest is:

A = [tex]P(1 + r/n)^(nt)[/tex]

Substituting the values -

A = [tex]7200(1 + 0.055/4)^(4 x 6)[/tex]

A = [tex]7200(1.01375)^24[/tex]

A = 7200 x 1.1657

A ≈ 8,404.5

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Mr. Tuyen uses 25/8 or 3 1/8 (or 3 1/64) tanks of gas in five weeks.

As per the question,

Multiply the amount of gas used in one week (5/8 tank) by the number of weeks (5):

5/8 x 5 = 25/8 tanks of gas.

Simplify the fraction 25/8 by dividing the numerator and denominator by 8: 25/8 ÷ 8/8 = 25/64.

25/64 is an improper fraction, so we can convert it to a mixed number:

3 1/64 tanks of gas.

Alternative method:

In one week, Mr. Tuyen uses 5/8 of a tank of gas.

In five weeks, he uses 5/8 x 5 = 25/8 tanks of gas.

25/8 is an improper fraction, so we can convert it to a mixed number: 3 1/8 tanks of gas.

Therefore, Mr. Tuyen uses 25/8 or 3 1/8 (or 3 1/64) tanks of gas in five weeks.

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The product of two rational numbers can always be written as a fraction. The Option D is correct.

The product of 2 rational numbers can not be written as either irrational or whole number. This is because it will be expressed as the ratio of two integers and the product of two ratios of integers will always result in another ratio of integers.

For example, if we multiply  3/5 & 2/7 (rational numbers), we get (3/5) x (2/7) = 6/35 which is also a rational number. Therefore, the product of two rational numbers will always be a rational number or a fraction.

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The given scenario describes an example of a cluster sampling technique.

The responses given by the players can be considered representative of the opinions held by the entire team.

The action taken by the football coach in selecting either the varsity or junior varsity team and asking for the opinion of all players on a new logo constitutes a randomly selected sample.

This means that the coach did not specifically choose certain players or a particular group to provide feedback, but rather included all members of one of the two teams.

Therefore, the responses given by the players can be considered representative of the opinions held by the entire team.

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Answer:

D

Step-by-step explanation:

x + y = [tex]\frac{z}{2}[/tex]

multiply through by 2 to clear the fraction

2x + 2y = z ( subtract 2y from both sides )

2x = z - 2y

The relationship between the figure number and the number of circle is

Each figure represents the number of circles as in the pattern shown in figures 1 , 2, and 3

The pattern used in the getting the number of circles is twice the figure number minus 1. This is expressed mathematically as

2n - 1

where

n = figure number

hence we have that: figure 1, that is n = 1, such that

2n - 1

= 2 x 1 - 1

= 2 - 1

= 1

figure 2, n = 2, such that

2n - 1

= 2 x 2 - 1

= 4 - 1

= 3

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(D) If many random samples of size 15 are taken from this population, then 95% of the confidence intervals will contain the population mean.

The best interpretation of the 95% confidence interval (64.06, 66.96) for the population mean, based on a random sample of size 15, is choice (B). This interpretation correctly states that if many random samples of size 15 are taken from the same population, then 95% of the time the population mean will lie within the interval. In other words, we can be 95% confident that the true population mean falls within this range based on the sample data. It is important to note that this does not mean that 95% of the population measurements lie within the interval (choice A), nor does it mean that 95% of the sample means will lie within the interval (choice C) or that 95% of the confidence intervals will contain the population mean (choice D) or the sample mean (choice E). These options are incorrect because they either misinterpret or generalize the confidence interval beyond its intended scope. Therefore, the best interpretation is the one that accurately reflects the meaning and purpose of a confidence interval.
(D) If many random samples of size 15 are taken from this population, then 95% of the confidence intervals will contain the population mean.

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The Factor monomials of the -15[tex]y^4[/tex] = (D)(3y²) is -15[tex]y^4[/tex] = -5y² × 3y² or -15[tex]y^4[/tex] = -15y² × y², and the value of D could be 5 or -15 depending on simplification.

To factor the monomial -15[tex]y^4[/tex] as the product of two monomials, one of which is D and the other is 3y², we need to determine what constant D is.

To do this, we can divide -15[tex]y^4[/tex] by 3y², which gives us -5y². Therefore, we can write:

-15[tex]y^4[/tex] = (D)(3y²)

-5y^2 = D

So, the factored form of -15[tex]y^4[/tex] is:

-15[tex]y^4[/tex] = -5y² × 3y²

or

-15[tex]y^4[/tex] = -15y² × y²

Note that either way of writing the factored form is correct, as the order of the factors in a multiplication does not matter.

We divide the monomial by one of the factors, then use the quotient as the constant in the other factor to factor the monomial as the product of two monomials.

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