Suppose that in a class of 10 stat majors and 10 engineers, 5 students are randomly chosen to present work at the board. What is the probability that exactly 4 of the students selected to present are stat majors

We must calculate the standard deviation of the differences between the values in the matched pairs in order to build a confidence interval using those values.

The 95% confidence interval is another frequently used measure of accuracy. In order to calculate it, a range of values that is 95% likely to contain the true population mean must be created using the standard deviation.

According to the 68-95-99.7 Rule, 95% of values are within two standard deviations of the mean, so to calculate the 95% confidence interval, one need only add and deduct two standard deviations from the mean.

Data dispersion in relation to the mean is quantified by a standard deviation, or σ. Data are said to be more closely clustered around the mean when the standard deviation is low and more dispersed when the standard deviation is high.

The difference between the values in the matched pairs' standard deviation is calculated.

The complete question is:

To construct a confidence interval using matched pairs, we must compute the standard deviation of the ___ between the values in the matched pairs.

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We must calculate the standard deviation of the differences between the values in the matched pairs in order to build a confidence interval using those values.

What is the difference between standard deviation and confidence interval?

The 95% confidence interval is another frequently used measure of accuracy. In order to calculate it, a range of values that is 95% likely to contain the true population mean must be created using the standard deviation.

According to the 68-95-99.7 Rule, 95% of values are within two standard deviations of the mean, so to calculate the 95% confidence interval, one need only add and deduct two standard deviations from the mean.

Data dispersion in relation to the mean is quantified by a standard deviation, or σ. Data are said to be more closely clustered around the mean when the standard deviation is low and more dispersed when the standard deviation is high.

The difference between the values in the matched pairs' standard deviation is calculated

To construct a confidence interval using matched pairs, we must compute the standard deviation of the ___ between the values in the matched pairs.

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Step-by-step explanation:

here,

x1=-7

x2=13

y1=-2

y2=-23

so

\(\boxed{\blue{ distance=\sqrt{(y2-y1)^2+(x2-x2)^2} }}\) ⠀

=\(\tt{\sqrt{(-23-(-2))^2+(13-(-7))^2}}\) ⠀

=\(\tt{\sqrt{(-21)^2+(20)^2} }\) ⠀

=\(\tt{\sqrt{ 441+400} }\) ⠀

=\(\tt{\sqrt{841} }\) ⠀

=\(\tt{ 29 }\) ⠀

So,

the distance between (-7, -2) and (13,-23)=29

The North American and European continents are moving apart at a rate of 3 cm/year. To drift 483 km farther apart than they are at present, it will take about 16,100,000 years, assuming a constant rate of drift.

To solve this problem, we can use the formula:

distance = rate x time

where distance is the distance that the continents will drift apart, rate is the rate of drift at which they are moving apart (3 cm/year), and time is the unknown time we need to find.

We need to convert the distance to the same unit as the rate, so let's convert 483 km to centimeters:

483 km = 483,000 m = 48,300,000 cm

Substituting the given value , we get:

48,300,000 cm = 3 cm/year x time

Solving for time, we get:

time = 48,300,000 cm / 3 cm/year

time = 16,100,000 years

Therefore, it will take about 16,100,000 years for the North American and European continents to drift 483 km farther apart than they are at present, assuming that the rate of drift remains constant.

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The North American and European continents drift apart at a rate of 3 cm/year. It will take about 16.1 million years for them to drift 483 km farther apart at this rate.

To solve this problem, we can use the following equation:

distance = rate * time

where distance is the distance the continents will have drifted apart after a certain amount of time, rate is the rate at which they are moving apart, and time is the time it takes for them to drift the given distance.

We want to find the time it takes for the continents to drift 483 km farther apart than they are at present, which is:

distance = 483 km = 483,000 m

The rate at which the continents are moving apart is:

rate = 3 cm/year = 0.03 m/year

Substituting the values, we get:

483,000 m = 0.03 m/year * time

Solving for time, we get: time = 483,000 m / 0.03 m/year = 16,100,000 years

Therefore, it will take approximately 16.1 million years for the North American and European continents to drift 483 km farther apart than they are at present, assuming the current rate of separation remains constant.

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Answer:

  g(x) = 24(2^(x-1)) +16

Step-by-step explanation:

A function is stretched vertically by a factor of 'a' by multiplying by 'a'.

  g(x) = 4·f(x) = 4(6(2^(x-1) +4)

  g(x) = 24(2^(x-1)) +16

Answer:

Step-by-step explanation:

Let X represent the total amount of money you need to pay.

X= $1.99 x 3.33

  = $6.6267

  = $6.60 (rounded)

You need to pay $6.60 for the book in Overtaxia.

Answer:

length L = \(\sqrt[2]{18}\) or \(3\sqrt{2}\)

slope = 45 degree

neither

Step-by-step explanation:

The height of the cylinder is 10.81 cm and the radius of the cylinder is 5.41 cm

The volume of the cylinder can = 1000 cubic cm

Consider the height of the cylinder as h and the radius of the base is r

Volume of the cylinder = π\(r^2\)h = 1000

h = 1000 / π\(r^2\)

The surface area of the cylinder

A = 2π\(r^2\) + 2πrh

A = 2π\(r^2\) + 2πr(1000 / π\(r^2\) )

A = 2π ( \(r^2\) + 1000 / π\(r^2\))

Differentiate the terms

A' =  2π (2r + 1000 / π\(r^3\))

When the minimum surface area

2π (2r + 1000 / π\(r^3\)) = 0

r = \((1000/2\pi )^\frac{1}{3}\)

r = 5.41 cm

Then,

h =  1000 / π\(r^2\)

= 1000 / (π × 5.41 × 5.41)

= 1000 / 91.94

= 10.87 cm

Hence, the height of the cylinder is 10.81 cm and the radius of the cylinder is 5.41 cm

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The equation of the line that passes through the point (8,2) and is parallel to the line x+4y = 28 is y = -x/4+4.

According to the question,

We have the following information;

Point thorough which line is passing = (8,2)

Equation of the line:

x+4y = 28

Now, we will convert this equation into the slope-intercept form:

4y = -x+28

Dividing by 4 on both sides of the equation:

y = -x/4+28/4

y = -x/4+7

Slope of the line = -1/4

We know that the following formula is used to find the equation of the line:

(y-y') = m(x-x')

(y-2) = -1/4(x-8)

y-2 = -x/4+2

Adding 2 on both sides:

y = -x/4+4

Hence, the equation of the line that passes through the point (8,2) and is parallel to the line x+4y = 28 is y = -x/4+4.

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The average of the table is 4 and the standard deviation is 1.1547.

The average of the table is calculated using the formula (Sum of all data points) / (Number of data points). In the given table, the average is (2 + 5 + 3 + 4 + 6 + 4 + 3) / 7 = 4.

The standard deviation is calculated using the formula (Sum of Squared Differences / (Number of Data Points -1))1/2. In the given table, the standard deviation is ((\(2-4^{2}\)+ \(5-4^{2}\) +\(3-4^{2}\) + \(4-4^{2}\) + \(6-4^{2}\) + \(4-4^{2}\) + \((3-4)^{2}\) / (7-1))1/2 = 1.1547.

Therefore, the average of the table is 4 and the standard deviation is 1.1547.

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Answer:

As X increases, Y decreases in a perfectly linear fashion. This means that as one variable increases, the other variable decreases in exact proportion. In this example, X and Y have a perfect negative correlation with a correlation coefficient of -1.0.

Using mathematical operations, the greatest number of songs Aerabella can play at her Sweet 16 party is 106.

The number of songs Aerabella can play is determined by subtracting the fixed charge for the day from her spending budget and dividing the difference by the unit charge per song.

Subtraction and division operations are two of the four basic mathematical operations, including addition and multiplication.

The total spending budget = $130

The fixed rental charge for a DJ = $50

The charge per song (unit rate) = $0.75

The variable cost for the party = $80 ($130 - $50)

The number of songs Aerabella can play = 106.67 ($80 ÷ $0.75)

= 106

Thus, based on the mathematical operations of subtraction and division, and given the fixed cost of hiring a DJ, the highest number of songs Aerabella can play for her Sweet 16 party is 106.

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Answer: To determine if the series –128 + 96 – 72 + 54 – ... is a geometric series, we need to check if the ratio between consecutive terms is constant.

Let's calculate the ratio between the second and first terms:

96 / (-128) = -3/4

Now let's calculate the ratio between the third and second terms:

-72 / 96 = -3/4

The ratio between the fourth and third terms is:

54 / (-72) = -3/4

We can see that the ratio between consecutive terms is always the same: -3/4. Therefore, the series –128 + 96 – 72 + 54 – ... is a geometric series with a common ratio of -3/4.

So the answer is r equals negative three fourths.

Step-by-step explanation:

The series provided is a geometric series because each term after the first is found by multiplying the previous term by -3/4. Therefore, the common ratio 'r' equals -3/4.

In a geometric series, each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. In the series given –128 + 96 – 72 + 54 – …, the second term (96) divided by the first term (-128) equals -3/4, the third term (-72) divided by the second term (96) also equals -3/4, and so on. This constant ratio between successive terms demonstrates that this is indeed a geometric series. Therefore, the statement that proves this is a geometric series is 'r equals negative three fourths' where r represents the common ratio.

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Answer: Choice B) Investment decreases by 3% each month

=====================================================

Explanation:

We won't use the value 2500 at all.

The base of the exponential is 0.97

Set this equal to 1+r and solve for r

1+r = 0.97

r = 0.97-1

r = -0.03

The negative r value indicates we have exponential decay, so the value of the investment decreases by 3% each month.

Let's say you had $100 to start off. This would mean the investment would be worth $97 after one month is up.

The five large cities in India are:

The population of large cities in India are:

The distance between the large cities in India are:

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A minimum sample size of 62 is needed to be 95% confident that the sample mean is within 2 words of the true population mean, assuming a normal distribution of the number of words per sentence in the book and a population standard deviation of 4 words.

To determine the minimum sample size needed to be 95% confident that the sample mean is within 2 words of the true population mean, we can use the formula for the margin of error:

Margin of error = z * (standard deviation / sqrt(n))

Where z is the z-score for the desired confidence level, standard deviation is the population standard deviation (given as 4 words), and n is the sample size.

We want the margin of error to be no more than 2 words, so we can set up the inequality:

z * (4 / √n) ≤ 2

To find the value of z for 95% confidence level, we can use a z-table or calculator and find that z = 1.96.

Substituting this value into the inequality and solving for n, we get:

1.96 * (4 / √n) ≤ 2

Simplifying and solving for n, we get:

n >= 61.05

Since we can't have a fractional sample size, we can round up to the nearest whole number and conclude that a minimum sample size of 62 is needed to be 95% confident that the sample mean is within 2 words of the true population mean.

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The given information is as follows:A random sample of 150 teachers in an​ inner-city school district found that​ 72% of them had volunteered time to a local charitable cause within the past 12 months.

The formula for calculating the standard error of sample proportion is given as:$$Standard\(\ error=\frac{\sqrt{pq}}{n}$$\)where:p = proportion of success in the sampleq = proportion of failure in the samplen = sample sizeGiven:Sample proportion, p = 72% or 0.72Sample size, n = 150

The proportion of failure in the sample can be calculated as:q = 1 - p= 1 - 0.72= 0.28Substituting the known values in the above formula, we get:\($$Standard \ error=\frac{\sqrt{pq}}{n}$$$$=\frac{\sqrt{0.72(0.28)}}{150}$$$$=0.0372$$\)Rounding off to the nearest thousandth, we get the standard error of sample proportion as 0.037

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The answer to the question is 5 units up.

The solutions to 9x² + 4 = 0 are imaginary, there are no real solutions.

To find the solutions to the equation 9x² + 4 = 0, we need to solve for x. However, when we attempt to solve this equation using traditional methods such as factoring or isolating the variable, we encounter a problem. The equation has no real solutions because there are no real numbers that can be squared to give a negative value.

We can see this by attempting to solve the equation:

9x² + 4 = 0

Subtracting 4 from both sides:

9x² = -4

Dividing by 9:

x² = -4/9Taking the square root of both sides:

x = ±√(-4/9)

Here, we encounter the issue of taking the square root of a negative number. The square root of a negative number is not a real number, but rather an imaginary number. In this case, the solutions to the equation are ±√(-4/9), which can be written as ±(2/3)i, where i is the imaginary unit.

Therefore, the correct answer is not provided among the options listed. The solutions to the equation 9x² + 4 = 0 are imaginary, there are no real solutions.

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Answer:

9

Step-by-step explanation:

divide 24 by 8 and multiply what you got by 3

24/8=3

3*3=9

Answer:

9

Step-by-step explanation:

\( \frac{3}{8} \times \frac{24}{1} \)

\( \frac{3 \times 24}{8 \times 1} \)

\( \frac{72}{8} \)

\(72 \div 8\)

\( = 9\)

Answer:

the given picture is not clear

\( \large \mathfrak{Solution : }\)

let the total time taken to paint the bookcase be x

now ,

the required equation is :

Answer:

bruce has spent 45.45 percent of his money

The different 5 card hands can be dealt from a standard deck that contains 2 hearts and the rest other cards is 712,842, for all diamonds is 1,287, for 3 black and 2 hearts is 202,800, for at least 3 clubs and the rest being other cards is 241,098.

The standard deck will contain 13 diamond cards, 13 heart cards, 13 club cards, and 13 spade cards, or 26 black cards and 26 red cards.

The combination can be used to calculate how many different 5 card hands can be dealt because the order of cards dealt is not important. So,

For 2 hearts and the rest other cards is,

\(C_{(13,2)}\) * \(C_{(39,3)}\) = 78 * 9,139 = 712,842.

For all diamonds is,

\(C_{(13,5)}\) = 1,287.

For 3 black and 2 hearts is,

\(C_{(26,3)}\) * \(C_{(13,2)}\) = 2,600 * 78 = 202,800.

For at least 3 clubs and the rest being other cards is,

\(C_{(13,3)}\) * \(C_{(39,2)}\) + \(C_{(13,4)}\) * \(C_{(39,1)}\) + \(C_{(13,5)}\)

= 286 * 741 + 715 * 39 + 1,287

= 241,098

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\(\qquad\qquad\huge\underline{{\sf Answer}}♨\)

Let's write the equation of line in slope point form ~

\(\qquad \sf  \dashrightarrow \:y - y1 = m(x - x1)\)

\(\qquad \sf  \dashrightarrow \:y -2 = 3(x -1)\)

\(\qquad \sf  \dashrightarrow \:y -2 = 3x - 3\)

\(\qquad \sf  \dashrightarrow \:y = 3x -1\)

Now, let's use this equation of line to plot two points ~

Now, plot these points on graph ~

Answer:

4x

Step-by-step explanation:

P = S + S + S

P = x + x + 3 + 2x - 3

P = 4x

Answer:

3x + 15

Step-by-step explanation:

when distributing, multiply the number outside of the parentheses by the numbers inside the parentheses.

Hey there!

3(x + 5)

DISTRIBUTE 3 WITHIN the PARENTHESES

= 3(x) + 3(5)

= 3x + 15

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

305 R 5

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Answer:

D

Step-by-step explanation:

- ÷ + = -

AND 64/4 IS 16

SOO -16 IS THE CORRECT ANSWER