Sara bought a pair of jeans for $75. If the jeans were on sale for $25 off, calculate the discount.

The desired significance level (usually 0.05), the researcher can determine whether to reject or fail to reject the null hypothesis.

What is the sample proportion of respondents who prefer to live somewhere other than where they currently live?

The sample proportion of respondents who prefer to live somewhere else can be calculated by dividing the number of respondents who indicated a preference for a different location by the total number of respondents.

To make confidence intervals and perform hypothesis testing in this scenario, the researcher can use formulas based on proportions. Since the question asks respondents about their preference (either yes or no), it involves a binomial distribution.

1.Confidence Interval Formula (Proportions): To construct a confidence interval for the proportion of people who prefer to live somewhere other than their current location, the researcher can use the following formula:

Confidence Interval=p​±Z×\(\sqrt{\frac{p(1-p)}{n} }\)

where:

2.Hypothesis Testing Formula (Proportions): To perform a hypothesis test to determine if the proportion of people who prefer to live elsewhere is significantly different from a particular value (null hypothesis), the researcher can use the following formula:

\(Z=\frac{p-p_{0} }{\sqrt{\frac{p_{0}(p_{0} -1)}{n} } }\)

​​where:

By comparing the calculated Z-value with the critical value(s) for the desired significance level (usually 0.05), the researcher can determine whether to reject or fail to reject the null hypothesis.

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The decimal expansion of the given fraction is 0.0208. Therefore, the correct answer is option D.

The given fraction is 13/625.

Decimals are one of the types of numbers, which has a whole number and the fractional part separated by a decimal point.

Here, the decimal expansion is 13/625 = 0.0208

So, the number of places of decimal are 4.

Therefore, the correct answer is option D.

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Answer:

Step-by-step explanation:

Row with x:

The last row:

Answer:

4 cars fit for 12 students. and

2 vans fit for 16 students.

Answer:

6 students in each van.

Step-by-step explanation:

Having van as x variable and car as y variable.

3x + y = 22

2x + 4y = 28

Step 1: Solve for y in 3x + y =22

y = 22 - 3x

Step 2: Substitute y = 22 - 3x into 2x + 4y =28

2x + 4(22-3x) = 28

2x + 88 - 12x = 28

=> -10x + 88 = 28

Step 3: Solve for x (which is one van) in -10x + 88 = 28,

-10x = 28 - 88

-10x = -60

=> x = 6  

Thus, we have 6 students that can fit in each van.  

A congruent polygon refers to two or more polygons that have the same shape and size. There must be an equal number of sides between two polygons for them to be congruent.

Congruent polygons have parallel sides of equal length and parallel angles of similar magnitude. When two polygons are congruent, they can be superimposed on one another using translations, rotations, and reflections without affecting their appearance or dimensions. Concluding about the matching sides, shapes, angles, and other geometric properties of congruent polygons allows us to draw conclusions about them.

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To find the variances of the random variables V and W, we need to apply the properties of variances and the given information about X, Y, and their correlation coefficient. The variances σV2 and σW2 can be determined using the formulas for the variances of linear combinations of random variables.

Given that X and Y have means E[X] = 1 and E[Y] = 1, variances σX2 = 4 and σY2 = 9, and a correlation coefficient ρXY = 0.5, we can calculate the means E[V] and E[W] using the given definitions: V = -X + 2Y and W = X + Y.

The mean of V, E[V], can be found by applying the linearity property of expectations:

E[V] = E[-X + 2Y] = -E[X] + 2E[Y] = -1 + 2 = 1.

Similarly, the mean of W, E[W], can be calculated as:

E[W] = E[X + Y] = E[X] + E[Y] = 1 + 1 = 2.

To find the variances σV2 and σW2, we utilize the formulas for the variances of linear combinations of random variables:

σV2 = Cov(-X + 2Y, -X + 2Y) = Var(-X) + 4Var(Y) + 2Cov(-X, 2Y)

    = Var(X) + 4Var(Y) - 4Cov(X, Y),

and

σW2 = Cov(X + Y, X + Y) = Var(X) + Var(Y) + 2Cov(X, Y).

Given the variances σX2 = 4 and σY2 = 9, and the correlation coefficient ρXY = 0.5, we can substitute these values into the formulas and calculate the variances σV2 and σW2.

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Answer:

Positive correlation

Step-by-step explanation:

From the scatter plot shown in the graph above, we can observe that the data points that are clustered in a band run upwards from left of the graph to the right.

In simple terms, both variables move along the same direction, which means, as variable on one axis increases, the variable on the other axis increases as well.

This shows that the variables depicted on the scatter plot are positively correlated. It shows a positive correlation between the variables.

The relationship between the variables on the scatter plot it a positive correlation

From the graph, we have the following highlights

When the x and the y values increase or decrease in the same direction, then the correlation of the graph is positive.

Hence, the relationship between the variables on the scatter plot it a positive correlation

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Answer:

Decrement

Step-by-step explanation:

Answer:

Answer:I think A is the answer sorry if I’m wrong

Step-by-step explanation:

The equivalent decimal have 1 places right after the decimal point, if

the denominator of the fraction is 10.

And, The equivalent decimal have 2 places right after the decimal point, if

the denominator of the fraction is 100.

Here,

We have to determine places after the decimal point does the equivalent decimal have,

The denominator of the fraction is 10 and the denominator of the fraction is 100.

What is Decimal representation?

A decimal number is a number where the integer part is separated from the fractional part with the help of a decimal point.

Now,

Let the number 2 in numerator,

Denominator = 10

Then, Fraction = 2/10 = 0.2

Hence, The equivalent decimal have 1 places right after the decimal point.

Let the number 3 in numerator,

Denominator = 100

Then, Fraction = 3/100 = 0.03

Hence, The equivalent decimal have 2 places right after the decimal point.

So, The equivalent decimal have 1 places right after the decimal point, if

the denominator of the fraction is 10.

And, The equivalent decimal have 2 places right after the decimal point, if

the denominator of the fraction is 100.

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Replace y = -4x into y = 3x + 28

-4x = 3x + 28

Minus both side by 3x

-7x = 28

x = -4

Recheck : - 4 x (-4) = 3 x (-4) + 28
16 = -12 +28 = 16 (t)

Answer:

(- 4, 16 )

Step-by-step explanation:

y = 3x + 28 → (1)

y = - 4x → (2)

substitute y = 3x + 28 into (2)

3x + 28 = - 4x ( add 4x to both sides )

7x + 28 = 0 ( subtract 28 from both sides )

7x = - 28 ( divide both sides by 7 )

x = - 4

substitute x = - 4 into (2)

y = - 4(- 4) = 16

solution is (- 4, 16 )

sqrt(-49) is not a real number

Square root of any negative number is not a real number

The solution to the equation (1 - tan² x)/(1 + tan² x) = cos x is all values of x in the domain 0 < x ≤ π.

Given equation: (1 - tan²x)/(1 + tan²x) = cos x

Using the Pythagorean Identity: 1 + tan²x= sec²x

Substituting sec²x into the equation:

(1 - tan²x)/(sec²x) = cos x

Simplifying the equation:

sec²x - tan²x = cos x

Substituting sin² x with 1 - cos² x (from the Pythagorean Identity: sin² x + cos² x = 1):

cos² x + 4 = 4 + cos² x

The equation simplifies to 4 = 4, which is always true.

Therefore, the solution to the equation (1 - tan² x)/(1 + tan² x) = cos x on the domain 0 < x ≤ 2πis all values of x in the domain 0 < x ≤ 2π.

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The interval of completion times containing the middle 95% of test-takers is approximately [40, 74].

We are given the mean μ = 57 and the standard deviation σ = 8 of the length of time needed to complete a certain test, which is normally distributed.A) We need to find the percent of people that take between 49 and 65 minutes to complete the exam.To find this, we can use the z-score formula as follows;z = (x - μ) / σ, where x = completion time= 49 minutesz1 = (49 - 57) / 8= -1z2 = (65 - 57) / 8= 1

Now, we need to find the area under the normal curve between these z-scores as shown in the figure below;z1 = -1, z2 = 1We can see that the area under the normal curve between -1 and 1 is approximately 0.6826. Therefore, the percent of people that take between 49 and 65 minutes to complete the exam is 68.26%.B) We need to find the interval of completion times containing the middle 95% of test-takers.To find this, we need to find the z-scores corresponding to the middle 95% of test-takers from the normal distribution table or calculator.

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Answer:

w^3(4 + u^2)(2 + u)(2 - u)

Step-by-step explanation:

6w^3 – u^4w^3

w^3(16 – u^4)

w^3(42 - ((u^2)^2)

w^3(4 + u^2)(4 - u^2)

w^3(4 + u^2)(22 - u^2)

w^3(4 + u^2)(2 + u)(2 - u)

Answer:

looks delicious

Step-by-step explanation:

Answer:

Man looks so good!

Step-by-step explanation:

Send me some in the mail. lol ☺☻♥

Yes, this sample of the trees in the county likely to be representative if each forest is the same size.

Representative sample, the sample must accurately reflect the population studied in demographics and characteristics of the chosen subjects.

For example, a representative sample will reflect only those within the study population and should not extend to those outside the study. If Jose is interested in studying the exercise habits of college athletes, only the population of college athletes should be considered for the selection of a representative sample. Jose will not choose athletes from high school or career athletes as part of his representative sample.

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Answer:

steps below

Step-by-step explanation:

a,b in 2nd quadrant: sine is positive and cosine is negative

sin a = 3/4      cos a = -√7/4

cos b = -12/13    sin b = 5/12

sin(a+b) = sin a cos b + cos a sin b

             = 3/4*(-12/13) + (-√7/4)*(5/12)

             = - 9/13 - (5√7/48)

             = -0.9679

cos(a-b) = cos a cos b + sin a sin b   (can you try yourself?)

The most effective way to use her 4 hours of study time to get the highest possibility or probability of test scores would be to spend 4 hours working on multiple-choice problems and 0 hours reviewing lecture notes.

From the information given, it is clear that working on multiple-choice problems is the most effective way to improve her test score. Therefore, the highest possibility or probability of test scores would be achieved by spending the most time working on multiple-choice problems.

The available time for studying is 4 hours, so the maximum time that can be spent working on multiple-choice problems is 4 hours. If she spends 4 hours working on multiple-choice problems, she will not have any time left to review lecture notes.

So, the most effective way to use her 4 hours of study time to get the highest possible test score would be to spend 4 hours working on multiple-choice problems and 0 hours reviewing lecture notes.

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Answer:

20

Step-by-step explanation:

Triangle inequality says that the third side can only be 18-3...15, that is bigger than 15.

And 18+3... 21, that is smaller than 21.

If the third side is 21, the 18 and the 3 will just lay right on top of the 21 and not make a triangle. So it has to be 20 in order to be a whole number.

The obtained value must be compared against the critical value. Hence, the correct option is b.

In hypothesis testing, the critical value is a threshold or cutoff point that is determined based on the chosen significance level (alpha level) and the distribution of the test statistic. It helps in determining whether to reject or fail to reject the null hypothesis.

After calculating the test statistic (such as z-score or t-statistic) from the observed data, it is compared to the critical value associated with the chosen significance level.

If the test statistic exceeds the critical value, it falls into the critical region, leading to the rejection of the null hypothesis.

If the test statistic is less than or equal to the critical value, it falls into the non-critical region, resulting in a failure to reject the null hypothesis.

Therefore, the obtained value must be compared against the critical value to make a decision in hypothesis testing. Hence, the correct answer is option b.

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Answer:

There's no A so I'm going to assume you meant X

X = 23

Step-by-step explanation:

X is equal to 23, because 23 - 18 = 5

or 5 + 18 = 23

a) The given series converges.

b) The series ∑(n=1 to infinity) ne^(-2n) converges.

c) The series ∑(n=1 to infinity) (2n^2+6)/(3n^4+4) converges.

d) The series ∑(n=1 to infinity) n/(n+1) diverges.

(a) To determine the convergence or divergence of the series ∑(n=0 to infinity) 9n/π^2, we can use the comparison test.

Let's compare the given series with the series ∑(n=0 to infinity) 1/2^n, which is a geometric series with a common ratio of 1/2.

By comparing the terms, we have 9n/π^2 > 1/2^n for all n ≥ 0.

Since the series ∑(n=0 to infinity) 1/2^n converges (it is a convergent geometric series with a common ratio less than 1), and the given series is always larger than this convergent series, we can conclude that the given series ∑(n=0 to infinity) 9n/π^2 also converges.

(b) To determine the convergence or divergence of the series ∑(n=1 to infinity) ne^(-2n), we can use the ratio test.

Applying the ratio test, we calculate the limit:

lim (n→∞) |(n+1)e^(-2(n+1))/(ne^(-2n))| = lim (n→∞) |(n+1)/(n)e^(-2)|

Taking the limit, we have:

lim (n→∞) |(n+1)/(n)e^(-2)| = e^(-2)

Since e^(-2) is a constant less than 1, the limit is less than 1.

According to the ratio test, if the limit is less than 1, the series converges. Therefore, the series ∑(n=1 to infinity) ne^(-2n) converges.

(c) To determine the convergence or divergence of the series ∑(n=1 to infinity) (2n^2+6)/(3n^4+4), we can use the limit comparison test.

Comparing the given series with the series ∑(n=1 to infinity) 1/n^2, which is a convergent p-series with p = 2, we calculate the limit:

lim (n→∞) |((2n^2+6)/(3n^4+4))/(1/n^2)| = lim (n→∞) |(2n^2+6)/(3n^4+4)| * |n^2|

Taking the limit, we have:

lim (n→∞) |(2n^2+6)/(3n^4+4)| * |n^2| = 2/3

Since 2/3 is a finite non-zero value, the limit is finite and non-zero.

According to the limit comparison test, if the limit is finite and non-zero, and the series used for comparison (in this case, 1/n^2) converges, then the given series also converges.

Therefore, the series ∑(n=1 to infinity) (2n^2+6)/(3n^4+4) converges.

(d) To determine the convergence or divergence of the series ∑(n=1 to infinity) n/(n+1), we can use the limit test.

Taking the limit as n approaches infinity:

lim (n→∞) n/(n+1) = 1

Since the limit is equal to 1, which is not zero, the series fails the limit test.

According to the limit test, if the limit is not equal to zero, the series diverges.

Therefore, the series ∑(n=1 to infinity) n/(n+1) diverges.

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Answer:

$27,072.88

Step-by-step explanation:

$3,307,673,720,131 ÷ $122,176,626

The greatest number of groups he can display them in is 4.

To find the greatest number of groups that Edward can display his stamps in, we need to find the greatest common divisor (GCD) of the numbers of U.S. and international stamps he has.

In this case, the GCD of 12 and 8 is 4. This means that Edward can display his stamps in groups of 4, with each group consisting of 2 U.S. stamps and 2 international stamps, since 4 is a factor of both 12 and 8.

If he were to try to make groups of any larger size, he would have leftover stamps that could not be paired up.

Therefore, the greatest number of groups he can display them in is 4.

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If testing shows that there is less than a 5% chance the results were random, the study is considered statistically significant.

In statistical hypothesis testing, researchers often set a significance level, denoted as α (alpha), which is typically 0.05 or 5%. This significance level represents the threshold below which the researchers consider the results to be statistically significant. If the p-value, which is a measure of the evidence against the null hypothesis, is less than the chosen significance level, it indicates that the results are unlikely to have occurred by chance alone.

When testing shows that there is less than a 5% chance (or any chosen significance level) that the results were random, the study is considered statistically significant. This means that the observed data provides evidence to reject the null hypothesis in favor of the alternative hypothesis. The results are deemed significant because the probability of obtaining such extreme or more extreme results under the assumption of randomness is very low.

Statistical significance is an important criterion in research as it helps researchers draw valid conclusions and make inferences from their data. However, it is essential to note that statistical significance does not imply practical significance or the magnitude of the effect observed. Additional considerations, such as effect size and contextual relevance, are necessary to fully interpret the implications of a statistically significant result in practical terms.

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