A study was conducted in which rats showed compassion by freeing a trapped rat. In the study, all six of the six female rats showed compassion by freeing the trapped rat while 17 of the 24 male rats did so. We found a 95% confidence interval for the difference in proportion of rats showing compassion, using the proportion of female rats minus the proportion of male rats, to be 0.104 to 0.480. In testing whether there is a difference in these two proportions:

What are the null and alternative hypotheses?

Answer:

$6,200   i hope this helps!   :)

Step-by-step explanation:

the 4% interest of the $5000   4% of 5000 = 200

multiply by 6 for the 6 years   200 * 6 = 1200

add the 1200 to the 5000   5000 + 1200 = 6,200

Answer:

Shirt: $20

Trouser: $40

Step-by-step explanation:

5x + 3y = 220

6x + 2y = 200

3x + y = 100

y = 100 - 3x

5x + 3(100 - 3x) = 220

5x + 300 - 9x = 220

4x = 80

x = 20

y = 100 - 3(20)

y = 40

The cost of a shirt is $20 and the cost of pair of a jeans is $40.

Given that, five shirts and 3 pairs of jeans cost $220. Six shirts and 2 pairs of jeans cost $200.

We need to find the cost of one shirt and the cost of pair of jeans.

A linear equation is an equation in which the highest power of the variable is always 1.

A linear equation in two variables is of the form Ax + By + C = 0, in which A, B, and C are real numbers and x and y are the two variables, each with a degree of 1. If we consider two such linear equations, they are called simultaneous linear equations.

Let the cost of a shirt be x and the cost of pair of jeans be y.

Now, five shirts and 3 pairs of jeans cost $220.

That is, 5x+3y=220------(1)

Six shirts and 2 pairs of jeans cost $200.

6x+2y=200------(2)

Multiplying the equation (1) with 2, we get 10x+6y=440------(3)

Multiplying the equation (2) with 3, we get 18x+6y=600------(4)

Now, equation (4)-(3) is 8x=160

⇒x=$20

Substitute x=20 in equation (1), we get 5(20)+3y=220

⇒y=$40

Therefore, the cost of a shirt is $20 and the cost of pair of a jeans is $40.

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To test the claim that the mean difference between the prices of the two models is $10, we can use a t-test for dependent samples.

To test the claim that the mean difference between the prices of the two models is $10, we can use a t-test for dependent samples.

Answer:

B

Step-by-step explanation:

Take 2 points and use the slope formula

The 2 points: (0,0) and (5,4)

The slope formula is:

[tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{2} }[/tex]

We can say (0,0) is our first point, and (5,4) is our second, and substitute them in. y2 is 4, y1 is 0, x2 is 5, and x2 is 0.

[tex]m=\frac{4-0}{5-0}[/tex]

[tex]m=\frac{4}{5}[/tex]

So, the slope if 4/5, or choice B

Answer:

50 is more than 27

Step-by-step explanation:

27 comes before 50

Answer:

$6000

Step-by-step explanation:

so she made 72000 in a year, a year as 12 months so to find the monthly rate we just need to divide 72000 by 12 which gives 6000

Answer:

The Correct answer is 6000

Step-by-step explanation:

All you do is divide all the months in a year by how much she got paid to find salary.

Answer:

Test: [tex]\mu[/tex] < 20 with normal distⁿ

Hypothesis test:

H0:  [tex]\mu \ge[/tex] 20                         (Null Hypothesis, H₀ : [tex]\mu[/tex] = 20 is also correct)

H1: [tex]\mu[/tex] < 20                             (Alternative Hypothesis, also called H₁)

This is lower tailed test.

Since sample is large, sample standard deviation can be taken as an  approximation of population standard deviation.

x = 19.3

[tex]\sigma[/tex] = 11.1

n = 444

significance level, [tex]\alpha[/tex] = 0.05 (If no value is given, we take level of 0.05)

Test statistic [tex]z* = \frac{x-\mu}{\sigma/\sqrt{n}}[/tex]

                         [tex]= \frac{19.3-20}{11.1/\sqrt{444}}[/tex]

                       = - 1.33

The attached files contains additional information

Answer:    Step-by-step explanation:

Start by multiplying the ones: 6 times 28 is 168. Next, multiply the tens: 30 times 28 is 840. Add the products to get 1,008.

Answer:

2900g

Step-by-step explanation:

1kg=1000g

2.9(1000)

=2900g

23.27

Use a calculator

Answer:

Hey Tamia,

          the answer is 0.4969564

Please rate me as brainiest as the answer explanation is in attached picture, which will clear every step.

Thanks

Step-by-step explanation:

To estimate the integral within an error rate, use the power series expansion of sin(x) to construct an equivalent series for sin(x²). Add terms until the error is less than  [tex]10^{-5}[/tex]. Integrate each term from 0 to 0.5.

To estimate the value of the integral ∫ from 0 to 0.5 sin(x²) dx with an error of magnitude less than 10^-5, we can use a power series expansion of sin(x). The power series expansion is given as sin(x) = x - x³/3! + x⁵/5! - x⁷/7! + .... Now since we are interested in sin(x²), we just replace x in the above series with x²: sin(x²) = x² - (x²)³/3! + (x²)⁵/5! - (x²)⁷/7! + .... This series can be truncated at any term, and the remaining terms would represent the error in your approximation. We keep adding terms until we reach an error less than [tex]10^{-5}[/tex]. Finally, integrate term by term from 0 to 0.5 to get the approximate value of the original integral.

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Answer:

A   -2 to -1

Step-by-step explanation:

Answer:

y+2 = 2(x+2)

Step-by-step explanation:

given point (a,b) and slope m, point slope form of a line is:

y-b = m(x-a)

Answer:

For this case we want to test that the true proportion of americans have experienced difficulty in making mortgage payments is higher than 0.28 (alternative hypothesis) and the sytem of hypotheis are:

NUll hypothesis: [tex]p \leq 0.28[/tex]

Alternative hypotheis: [tex] p >0.28[/tex]

Step-by-step explanation:

Previous concepts

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".  

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".  

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".  

Solution to the problem

For this case we want to test that the true proportion of americans have experienced difficulty in making mortgage payments is higher than 0.28 (alternative hypothesis) and the sytem of hypotheis are:

NUll hypothesis: [tex]p \leq 0.28[/tex]

Alternative hypotheis: [tex] p >0.28[/tex]

Answer:

The solutions listed from the smallest to the greatest are:

x:  [tex]-\sqrt{2}[/tex]   [tex]-\sqrt{2}[/tex]  [tex]\sqrt{2}[/tex]  [tex]\sqrt{2}[/tex]

y:      -1         1     -1     1

Step-by-step explanation:

The slope of the tangent line at a point of the curve is:

[tex]m = \frac{\frac{dy}{dt} }{\frac{dx}{dt} }[/tex]

[tex]m = -\frac{\cos 2\theta}{\sin \theta}[/tex]

The tangent line is horizontal when [tex]m = 0[/tex]. Then:

[tex]\cos 2\theta = 0[/tex]

[tex]2\theta = \cos^{-1}0[/tex]

[tex]\theta = \frac{1}{2}\cdot \cos^{-1} 0[/tex]

[tex]\theta = \frac{1}{2}\cdot \left(\frac{\pi}{2}+i\cdot \pi \right)[/tex], for all [tex]i \in \mathbb{N}_{O}[/tex]

[tex]\theta = \frac{\pi}{4} + i\cdot \frac{\pi}{2}[/tex], for all [tex]i \in \mathbb{N}_{O}[/tex]

The first four solutions are:

x:   [tex]\sqrt{2}[/tex]   [tex]-\sqrt{2}[/tex]  [tex]-\sqrt{2}[/tex]  [tex]\sqrt{2}[/tex]

y:     1        -1        1     -1

The solutions listed from the smallest to the greatest are:

x:  [tex]-\sqrt{2}[/tex]   [tex]-\sqrt{2}[/tex]  [tex]\sqrt{2}[/tex]  [tex]\sqrt{2}[/tex]

y:      -1         1     -1     1

Using derivatives of the parametric curves and the solving a trigonometric equation, it is found that the points (x,y) are:

[tex]x = 2\cos{\left(\frac{k\pi}{4}\right)}, k = 1, 3, 5, \cdots[/tex]

[tex]y = \sin{\left(\frac{k\pi}{2}\right)}, k = 1, 3, 5, \cdots[/tex]

Given two parametric curves x(t) and y(t), the slope of the tangent line is given by:

[tex]m = \frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}[/tex]

The tangent line is horizontal for:

[tex]\frac{dy}{dt} = 0, \frac{dx}{dt} \neq 0[/tex]

In this problem, since we are working with trigonometric functions sine and cosine, they will never be simultaneously 0, hence, the equation of interest is:

[tex]\frac{dy}{dt} = 0[/tex]

Then:

[tex]y(t) = \sin{2\theta}[/tex]

[tex]\frac{dy}{d\theta} = 2cos{2\theta}[/tex]

Hence:

[tex]2\cos{2\theta} = 0[/tex]

[tex]\cos{2\theta} = 0[/tex]

[tex]\cos{2\theta} = \cos{\left(\frac{k\pi}{2}\right)}, k = 1, 3, 5, \cdots[/tex]

[tex]2\theta = \frac{k\pi}{2}[/tex]

[tex]\theta = \frac{k\pi}{4}, k = 1, 3, 5, \cdots[/tex]

Hence, the points (x,y) are:

[tex]x = 2\cos{\left(\frac{k\pi}{4}\right)}, k = 1, 3, 5, \cdots[/tex]

[tex]y = \sin{\left(\frac{k\pi}{2}\right)}, k = 1, 3, 5, \cdots[/tex]

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Answer:

It takes approximately 13.737 hours for the 200 degree water to cool down to 125 degrees.

Step-by-step explanation:

Recall Newton's Law of heating and cooling for an object of initial temperature [tex]T_0[/tex], in an ambient temperature [tex]T_a[/tex]:

[tex]T(t)=T_a+(T_0-T_a)\,e^{-kt}[/tex]

where t is the time elapsed.

We know the ambient temperature and the initial temperature of the object, but we don't know the value of the constant "k" that describes the cooling process. We can obtain such value (k) by using the information that the 200 degrees water cooled 10 degrees in 1.25 hours.

In such case we have:

[tex]T(t)=T_a+(T_0-T_a)\,e^{-kt}\\200-10=75+(200-75)\,e^{-k(1.25)}\\190=75+125\,e^{-k(1.25)}\\190-75=125\,e^{-k(1.25)}\\115=125\,e^{-k(1.25)}\\\frac{115}{125}= e^{-k(1.25)}\\0.92=e^{-k(1.25)}\\ln(0.92)=-k\,(1.25)\\k=\frac{ln(0.92)}{-1.25} \\k=0.0667[/tex]

Therefore, we have now the complete expression for the cooling process:

[tex]T(t)=75+125\,e^{-0.0667\,t}[/tex]

To find the time it takes to cool the 200 degree water down to 125 degrees, we use:

[tex]125=75+125\,e^{-0.0667\,t}\\125-75=125\,e^{-0.0667\,t}\\50=125\,e^{-0.0667\,t}\\\frac{50}{125} =e^{-0.0667\,t}\\0.4=e^{-0.0667\,t}\\ln(0.4)=-0.0667\,\,t\\t=\frac{ln(0.4)}{-0.0667} \\t=13.737\,\,hours[/tex]

Answer:

see the explanation

Step-by-step explanation:

we know that

The equation of a exponential growth function is given by

[tex]f(x)=a(b^x)[/tex]

where

a is the initial value or y-intercept

b is the factor growth (b>0)

In this problem

a=1

so

[tex]f(x)=b^x[/tex]

we know that

The graph of the function has no x-intercept

Remember that the x-intercept of a function is the value of x when the value of the function is equal to zero

That means ----> The output of the function can NEVER be equal to zero

Verify

For f(x)=0

[tex]0=b^x[/tex]

Apply log both sides

[tex]log(0)=xlog(b)[/tex]

Remember that

log 0 is undefined. It's not a real number, because you can never get zero by raising anything to the power of anything else.

Final answer:

Exponential functions with a positive base can never output zero due to their growth pattern.

Explanation:

Exponential functions of the form f(x) = b^x, where b is greater than 0, never output zero.

To verify this, consider that any positive number raised to any power will never result in zero, as it will approach zero but never reach it. For example, 2^x will grow rapidly but never touch zero. This property holds true for all exponential functions with a positive base.

Answer:

B=22.348 Inches per minutes

Step-by-step explanation:

A snail is traveling along a straight path. The snail’s velocity can be modeled by [tex]v(t)=1.4ln(1+t^2)[/tex] inches per minute for 0 ≤ t ≤ 15 minutes.

If the snail's velocity is [tex]v(t)=1.4ln(1+t^2)[/tex] per minute, its displacement for 0 ≤ t ≤ 15 minutes is given by the integral:

[tex]\int_{0}^{15}1.4ln(1+t^2)dt=76.04307[/tex]

The ant travels with a constant acceleration of 2 Inches per minute.

Therefore, the velocity of the ant will be:

[tex] \int 2 dt=2t+c,[/tex] inches per minutes, for some constant c.

For the interval, 12≤t≤15, the displacement of the ant is:

[tex] \int_{12}^{15}(2t+c)dt=t^2+ct|_{12}^{15}=81+3c[/tex]

Since the snails displacement and that of the ant are equal in 12≤t≤15.

81+3c=76.04307

3c=76.04307-81

3c=-4.95693

c=-1.65231

The velocity of the ant at t=12 is therefore:

2t+c=2(12)-1.65231=22.348 Inches per minutes

B=22.348 Inches per minutes

The value of B to the nearest whole number, given all of the factors enumerated above, is 22.4 inches/Min. (For the full answer, please see the attached.)

This simply refers to the pace or rate at which an object or a person changes their position in relation to a frame of reference. It is also a function of time.

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Answer:

0.9%

Step-by-step explanation:

To determine the percentage of Earth's surface affected by a meteor strike, we calculate the surface area of Earth and the area of impact, then divide the area of impact by Earth's total surface area and multiply by 100 to get a percentage. Using the given Earth's radius of 3959 miles and the meteor's diameter of 750 miles, the affected area is approximately 0.224% of Earth's surface.

To calculate the percentage of the Earth's surface affected by a meteor strike, we can use the formula for the surface area of a sphere and the formula for the surface area of a circle, which represents the affected area.

The total surface area of the Earth (AEarth) is given by 4πr2, where r is the radius of the Earth. The radius of the Earth is 3959 miles.

The surface area affected by the meteor (AMeteor) can be approximated by the surface area of a circle, πd2/4, where d is the diameter of the meteor. The diameter of the meteor is 750 miles. Therefore, the affected area is approximately π * (7502)/4.

Now we can calculate both the total surface area of the Earth and the affected area:

To find the percentage of the surface affected, we divide the affected area by the total surface area and then multiply by 100:

Percentage = (AMeteor / AEarth) * 100

Percentage = (441,963 / 197,000,000) * 100 = 0.224% of the Earth's surface is affected by the meteor strike.

Answer:

[tex]3.786-2.262\frac{0.187}{\sqrt{10}}=3.652[/tex]    

[tex]3.786+2.262\frac{0.187}{\sqrt{10}}=3.920[/tex]    

So on this case the 95% confidence interval would be given by (3.652;3.920)    

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

[tex]\bar X[/tex] represent the sample mean for the sample  

[tex]\mu[/tex] population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

In order to calculate the mean and the sample deviation we can use the following formulas:  

[tex]\bar X= \sum_{i=1}^n \frac{x_i}{n}[/tex] (2)  

[tex]s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}[/tex] (3)  

The mean calculated for this case is [tex]\bar X=3.786[/tex]

The sample deviation calculated [tex]s=0.187[/tex]

In order to calculate the critical value [tex]t_{\alpha/2}[/tex] we need to find first the degrees of freedom, given by:

[tex]df=n-1=10-1=9[/tex]

Since the Confidence is 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,9)".And we see that [tex]t_{\alpha/2}=2.262[/tex]

Now we have everything in order to replace into formula (1):

[tex]3.786-2.262\frac{0.187}{\sqrt{10}}=3.652[/tex]    

[tex]3.786+2.262\frac{0.187}{\sqrt{10}}=3.920[/tex]    

So on this case the 95% confidence interval would be given by (3.652;3.920)    

To estimate the mean grams of acetanilide that can be recovered from an initial amount of 4.85 g of aniline, calculate the sample mean and the 95% confidence interval.

To estimate the mean grams of acetanilide that can be recovered from an initial amount of 4.85 g of aniline, we can calculate the sample mean and the 95% confidence interval.

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To solve the equation -2/7x=-1/3 for x, you would divide both sides by -2/7. This translates to multiplication of -1/3 by the reciprocal of -2/7 which is -7/2. By performing this multiplication, x equals to 7/6.

The equation at question here is -2/7x=-1/3. To solve for x, we need to isolate x on one side of the equation. To do this, we can divide both sides of the equation by -2/7, which is the coefficient of x in the equation. Performing this operation (also known as the division property of equality), we get:

When we divide by a fraction, it's the same as multiplying by its reciprocal, so:

Performing this multiplication gives x = 7/6.

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Answer:

The calculated chi -square  value =5.7356 Is less than12.01 at 0.1level of significance .

The null hypothesis is accepted.

The past 5 years, a driver has tracked the gas mileage of his car and found that the variance from fill-up to fill-up was σ2 = 23 mpg^2.

Step-by-step explanation:

Step:-(1)

Given data 28 25 29 25 32 36 27 24

Sample size 'n' = 8

mean of the sample (x⁻) = ∑x /n = [tex]\frac{28+ 25+ 29 +25 +32 +36 + 27 + 24}{8}[/tex]

mean of the sample (x⁻) =  28.25

x                           x- x⁻                         (x-x⁻ )²

28              28 - 28.25  = -0.25       0.0625    

25             25 -28.25   = -3.25       10.56

29             29-28.25    = 0.75        0.5625

25             25-28.25    = -3.25      10.56

32             32-28.25    =   3.75      14.06

36            36-28.25    =   7.75      60.06

27            27-28.25    = -1.25      1.5625

24            24-28.25    = -4.25      18.06

                                          ∑(x-x⁻)² =   115.4875    

Step:-(2)

The sample standard deviation

           S² = ∑(x-x⁻)²/n-1 = [tex]\frac{115.4875 }{7}[/tex]  = 16.49

   By using χ² distribution

                           χ²  = [tex]\frac{ns^2 }{variance}[/tex]

By above test can be applied only if the population from which sample is drawn normal.

Given data For the past 5 years, a driver has tracked the gas mileage of his car and found that the variance from fill-up to fill-up was σ2 = 23 mpg^2.

Population variance σ² = 23

Step:-(3)

Null hypothesis :H₀:σ² = 23

Alternative hypothesis :H₁:≠23

[tex]X^{2} = \frac{8 (16.49)}{23}=5.7356[/tex]

The calculated chi -square  value =5.7356

The degrees of freedom γ=n-1 =8-1=7

The tabulated value of chi -square = 12.01 at 0.1level of significance (check table)

The calculated chi -square  value =5.7356 Is less than12.01 at 0.1level of significance .

The null hypothesis is accepted.

Conclusion:-

The null hypothesis is accepted.

The past 5 years, a driver has tracked the gas mileage of his car and found that the variance from fill-up to fill-up was σ2 = 23 mpg^2.

Answer: 5/13

Step-by-step explanation:

I got it correct

Answer:

(0, –5)

Step-by-step explanation:

If you don't see this option there is another option, (0 , 11) is also correct.

Answer:

x = -6,1

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

The 95% confidence interval is between 26.5 ng/ml and 40.3 ng/ml

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.96*\frac{19.6}{\sqrt{31}} = 6.9[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 33.4 - 6.9 = 26.5 ng/ml

The upper end of the interval is the sample mean added to M. So it is 6.4 + 33.4 + 6.9 = 40.3 ng/ml

The 95% confidence interval is between 26.5 ng/ml and 40.3 ng/ml

The 95% confidence interval for the mean measurement of the biomarker osteocalcin (OC) is approximately 26.64 ng/ml to 40.16 ng/ml.

To calculate the 95% confidence interval for the mean measurement of the biomarker osteocalcin (OC), we can use the formula:

CI = Mean ± Z * (SD / sqrt(n))

Where CI is the confidence interval, Mean is the sample mean, SD is the known standard deviation, Z is the Z-score corresponding to the desired confidence level, and n is the sample size.

In this case, the sample mean is 33.4 ng/ml, the known standard deviation is 19.6 ng/ml, and the sample size is 31. The Z-score for a 95% confidence level is approximately 1.96. Plugging these values into the formula:

CI = 33.4 ± 1.96 * (19.6 / sqrt(31))

Simplifying the formula:

CI = 33.4 ± 6.76

Therefore, the 95% confidence interval for the mean measurement of osteocalcin is approximately 26.64 ng/ml to 40.16 ng/ml.

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Answer:

(1) True / False: (a) To reduce the margin of error in a stratified sample, we must design strata so that the units within each stratum are as similar as possible.

R = True, since to have a more exact margin you have to eliminate the errors, and as we do it by running error by error, in order to obtain a point on the graph where the products are within the positive margin and you can obtain a graph less error than the beginning.

(b) To reduce the margin of error in a group sample, we must design groups so that the units within each group are as similar as possible.

R = if this type of procedure is reliable because it helps you to correct the errors of the procedure, but to be able to do it you have to have very well accounted for, each piece of information, whether negative or positive, of the study being carried out and from there to create data that help reduce the margin of error.

Step-by-step explanation:

cosB=4/5

B=36.86°

Hope it helps u

Answer:

the answer is C. 3(2k + 7)   i hope this helps!   :)

Step-by-step explanation:

trying to find 6k + 21

given 3(2k + 6)

distribute the 3 to both inside the parenthesis 6k + 18

given 3(k + 6)

distribute the 3 to both inside the parenthesis 3k + 18

given 3(2k + 7)

distribute the 3 again to both inside of the parenthesis 6k + 21

Answer:

C. 3(2k+7)

Step-by-step explanation:

you should mark me brainliest lol

The given 95% confidence interval of (1.6, 7.0) for the difference between the average weekly study times (mu_1 - mu_2) means we are 95% confident that students planning to attend graduate school study between 1.6 to 7 hours more per week on average than those who do not.

The teaching assistant is comparing the average weekly study times between students intending to go to graduate school and those who are not with the use of data. The relevant statistical concept in this context is the confidence interval for the difference in population means.

The given 95% confidence interval for the difference between the average weekly study times (mu_1 - mu_2) is (1.6, 7.0). This interval was calculated from the provided data, and it provides a statistical estimation that, in this context, means we are 95% sure that students who plan to attend graduate school study between 1.6 to 7 hours more per week on average compared to those who do not plan to go to graduate school.

To interpret this, you can say that we are 95% confident that the true difference in average weekly study times between the two groups falls within this interval. As the entire interval is positive, we may infer that those planning for graduate school likely study more on average than their peers not planning for graduate school.

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