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Answer:

90% confidence interval for the true proportion of air travelers who prefer the window seat is (0.575, 0.625)

Step-by-step explanation:

We have the following data:

Sample size = n = 1000

Proportion of travelers who prefer window seat = p = 60%

Standard Error = SE = 0.015

We need to construct a 90% confidence interval for the proportion of travelers who prefer window seat. Therefore, we will use One-sample z test about population proportion for constructing the confidence interval. The formula to calculate the confidence interval is:

[tex](p-z_{\frac{\alpha}{2}}\sqrt{\frac{p(1-p)}{n}}, p+z_{\frac{\alpha}{2}}\sqrt{\frac{p(1-p)}{n}})[/tex]

Since, standard error is calculated as:

[tex]SE=\sqrt{\frac{p(1-p)}{n} }[/tex]

Re-writing the formula of confidence interval:

[tex](p-z_{\frac{\alpha}{2}} \times SE, p+z_{\frac{\alpha}{2}} \times SE)[/tex]

Here, [tex]z_{\frac{\alpha}{2}}[/tex] is the critical value for 90% confidence interval. From the z-table this value comes out to be 1.645.

Substituting all the values in the formula gives us:

[tex](0.6 - 1.645 \times 0.015, 0.6 + 1.645 \times 0.015)\\\\ = (0.575, 0.625)[/tex]

Therefore, the 90% confidence interval for the true proportion of air travelers who prefer the window seat is (0.575, 0.625)

Answer: +/- 7

Step-by-step explanation:

3x² = 147

To solve for x divide through by three first.

3x² = 147

x² = 49, now we take the square root of both side by trying to apply laws of indices.

√x² = √49

The square root will neutralize the effect of the square because

√a = a¹/² so (x²)¹/², and (x²)¹/² =

x²×¹/² = x, therefore the solution is

x = +/- 7.

Answer:7^6

Step-by-step explanation:

Answer:

7^6

Step-by-step explanation:

Answer:

(a) The least-square regression line is: [tex]y=4.662+2.709x[/tex].

(b) The number of households using online banking at the beginning of 2007 is 31.8.

Step-by-step explanation:

The general form of a least square regression line is:

[tex]y=\alpha +\beta x[/tex]

Here,

y = dependent variable

x = independent variable

α = intercept

β = slope

(a)

The formula to compute intercept and slope is:

[tex]\begin{aligned} \alpha &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} \\\beta &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} \end{aligned}[/tex]

The values of ∑X, ∑Y, ∑XY and ∑X² are computed in the table below.

Compute the value of intercept and slope as follows:

[tex]\begin{aligned} \alpha &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 68.6 \cdot 55 - 15 \cdot 218.9}{ 6 \cdot 55 - 15^2} \approx 4.662 \\ \\\beta &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 6 \cdot 218.9 - 15 \cdot 68.6 }{ 6 \cdot 55 - \left( 15 \right)^2} \approx 2.709\end{aligned}[/tex]

The least-square regression line is:

[tex]y=4.662+2.709x[/tex]

(b)

For the year 2007 the value of x is 10.

Compute the value of y for x = 10 as follows:

[tex]y=4.662+2.709x[/tex]

  [tex]=4.662+(2.709\times10)\\=4.662+27.09\\=31.752\\\approx 31.8[/tex]

Thus, the number of households using online banking at the beginning of 2007 is 31.8.

Answer:

...

Step-by-step explanation:

...

Step-by-step explanation:

a) 24 / 250 = 0.096

b) Standard error for a proportion is:

σ = √(pq/n)

σ = √(0.096 × 0.904 / 250)

σ = 0.0186

c) At 98% confidence, the critical value is 2.326.  The margin of error is therefore:

2.326 × 0.0186 = 0.0433

d) At 95% confidence, the critical value is 1.960.  The margin of error is therefore:

1.960 × 0.0186 = 0.0365

So the confidence interval is:

(0.0960 − 0.0365, 0.0960 + 0.0365)

(0.0595, 0.1325)

e) 0.10 is within the 95% confidence interval, so the null hypothesis would not be rejected.

Final answer:

a) The point estimate of the proportion of components in the shipment that fail to meet the company's specifications is 9.6%. b) The standard error of the estimated proportion is 1.9%. c) The margin of error at the 98% confidence level is 4.4%. d) The 95% confidence interval estimate for the true proportion is approximately 5.9% to 13.3%. e) The null hypothesis that the proportion is 0.10 is rejected if the z-test statistic falls outside the range (-1.96, 1.96).

Explanation:

a) Point estimate:
The point estimate of the proportion of components in the shipment that fail to meet the company's specifications is the number of failed components divided by the total number of components tested. In this case, the point estimate is 24/250 = 0.096, or 9.6%.

b) Standard error:
The standard error of the estimated proportion is calculated using the formula SE = sqrt((phat * (1 - phat)) / n), where phat is the point estimate and n is the sample size. In this case, the standard error is sqrt((0.096 * (1 - 0.096)) / 250) = 0.019, or 1.9%.

c) Margin of error:
The margin of error is determined by multiplying the standard error by the appropriate critical value from the standard normal distribution. For a 98% confidence level, the critical value is approximately 2.33. Therefore, the margin of error is 2.33 * 0.019 = 0.044, or 4.4%.

d) Confidence interval:
The 95% confidence interval estimate for the true proportion of components that fail to meet the specifications is given by the formula phat +/- z * SE, where phat is the point estimate, z is the appropriate critical value from the standard normal distribution (for 95% confidence, z is approximately 1.96), and SE is the standard error. Therefore, the confidence interval is 0.096 +/- 1.96 * 0.019, or approximately 0.059 to 0.133.

e) Hypothesis test:
To test the null hypothesis H_0: p = 0.10 against the alternative hypothesis H_a: p != 0.10, we can use a two-tailed z-test. The test statistic is calculated as (phat - p_0) / sqrt((p_0 * (1 - p_0)) / n), where p_0 is the null hypothesis value (0.10), phat is the point estimate, and n is the sample size. The critical value for a significance level of 0.05 is approximately 1.96 from the standard normal distribution. If the test statistic is outside the range (-1.96, 1.96), we reject the null hypothesis. In this case, if the test statistic falls outside the range (-1.96, 1.96), we would reject the null hypothesis and conclude that the true proportion of components that fail to meet the specifications is not 0.10.

Answer:

  5.892×10^-2

Step-by-step explanation:

Scientific notation has one digit to the left of the decimal point. To write the number in scientific notation, it can work to start by writing the number with that as one of the factors:

  0.05891 = 5.891 × 0.01

  = 5.891 × 1/10^2

  = 5.891 × 10^-2

__

You can also enter this number into your calculator and change the display mode to SCI.

_____

It helps to understand the decimal place-value number system in terms of the power of 10 that multiplies each number place.

Answer:

[tex]y=x-2[/tex]

Step-by-step explanation:

So we are given the formula for the slope of a hyperbola in this form:

[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex].

That formula for the slope is [tex]m=\frac{b^2x}{a^2y}[/tex]

If we compare the following two equations, we will be able to find [tex]a^2[/tex] and [tex]b^2[/tex]:

[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex]

[tex]\frac{x^2}{8}-\frac{y^2}{4}=1[/tex]

We see that [tex]a^2=8[/tex] while [tex]b^2=4[/tex].

So the slope at [tex](x,y)=(4,2)[/tex] is:

[tex]m=\frac{b^2x}{a^2y}=\frac{4(4)}{8(2)}=\frac{16}{16}=1[/tex].

Recall: Slope-intercept form of a linear equation is [tex]y=mx+b[/tex].

We just found [tex]m=1[/tex]. Let's plug that in.

[tex]y=1x+b[/tex]

[tex]y=x+b[/tex]

To find [tex]b[/tex], the [tex]y[/tex]-intercept, we will need to use a point on our tangent line. We know that it is going through [tex](4,2)[/tex].

Let's enter this point in to find [tex]b[/tex].

[tex]2=4+b[/tex]

Subtract 4 on both sides:

[tex]2-4=b[/tex]

Simplify:

[tex]-2=b[/tex]

The equation for the tangent line at [tex](4,2)[/tex] on the given equation is:

[tex]y=x-2[/tex]

Answer: y = x - 2

Step-by-step explanation:

First you take the derivative of each term. d/dx(x²/8) - d/dx(y²/4) = d/dx(1)

x/4 - (y/2)dy/dx = 0

Then you solve for dy/dx: dy/dx = x/2y

Plug in the values: dy/dx = 1

To find the y-intercept, plug in values for y = mx+ b. 2 = 4 + b, b = -2

The equation is y = x - 2

The equation we've developed to represent the rabbit population over time, where 't' is the number of months since January, is P(t) = 19sin((2π/12)t - π/2) + (160t/12) + 650. This equation covers the oscillations in the population and the steady yearly increase.

The subject matter falls under the discipline of Mathematics, particularly in the topics involving functions. We can create a sinusoidal (sine or cosine) function to represent the oscillation of the population of rabbits.

Given that the population fluctuates 19 above and below the average, and the average increases by 160 each year, this suggests a sinusoidal period of 12 months (a year) with a vertical shift (midline) that increases linearly.

Considering t as the number of months since January, the equation for the population P in terms of the months since January t would be:

P(t) = 19sin((2π/12)t - π/2) + (160t/12) + 650

The 19 is the amplitude, (2π/12)t - π/2 represents the sinusoidal oscillation adjusted to start at the minimum in January, (160t/12) is the yearly change in population that increases per month, and 650 is the average population at the start.

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To find the population equation in terms of months since January considering oscillations and growth, use the formula p(t) = 650 + 160t + 19sin(2πt/12).

Population Equation: The equation for the population p in terms of the months since January t can be written as p(t) = 650 + 160t + 19sin(2πt/12). This equation takes into account the initial population of 650 rabbits, an increase of 160 rabbits per year, and the oscillation of 19 above and below the average population.

Answer:

   look for the x-intercepts

Step-by-step explanation:

A "zero" is a value of x where the function value is zero. On a graph, that point is where the graph meets the x-axis. Every x-intercept is a zero of the function.

__

If there are no x-intercepts, then there are no real zeros. The roots (zeros) will be complex.

Answer:

You can use the graph of a trigonometry function to show sales amounts over a given period of time. Here’s an example: Even though people in many parts of the world play soccer year-round, certain times of the year show an increase in the sales of outdoor soccer shoes.

Step-by-step explanation:

Answer:

The probability of students scored less than 60 = .0768

Step-by-step explanation:

Given -

Mean score [tex](\nu )[/tex] = 70

standard deviation [tex](\sigma )[/tex] = 7

Let X be the score of students

the probability that students scored less than 60 =

[tex]P(X< 60)[/tex]  = [tex]P(\frac{X - \nu }{\sigma}< \frac{60 - 70}{7})[/tex]

                  =  [tex]P(z < \frac{60 - 70}{7})[/tex]   put[ Z= [tex]\frac{X - \nu }{\sigma}[/tex]]

                   =  [tex]P(z < -1.428)[/tex]  using z table

                    =  .0768

Answer:

Step-by-step explanation:

So, we do not have enough evidence to conclude that the number of adolescent relationships is equal between those with an older sibling and those without.

check the attached file for explanation and solution

Answer:

a) y-intercept = 2.59

b) Therefore, we can say that when the penguin is not diving, the mean dive duration is 2.59 minutes.

Step-by-step explanation:

(a) What is the y-intercept of the regression line? (Use 2 decimal places)

The given regression equation is

y = 2.59 + 0.0126x

The standard form of the regression equation is given by

y = a + bx

Where a is the y-intercept of the regression line and b is the slope of the regression line.

Comparing the given equation with the standard form,

y-intercept = 2.59

(b) What is the correct interpretation of the y-intercept?

The y-intercept is the value we get when x = 0

y = 2.59 + 0.0126(0)

y = 2.59 + 0

y = 2.59 minutes

Therefore, we can say that when the penguin is not diving, the mean dive duration is 2.59 minutes.

Answer:

Heather rode the farthest

She rode 0.1km farther than Hailey.

Step-by-step explanation:

This is a conversion of units question.

Heather rode her horse 2 kilometers.

Hailey rode 1900 meters on her horse.

Each km has 1000 meters.

So 1900 meters = 1900/1000 = 1.9 km

This means that Hailey rode for 1.9 km.

Heather rode the farthest(2km is greather than 1.9km)

2 - 1.9 = 0.1km

She rode 0.1km farther than Hailey.

Answer:

160°

Step-by-step explanation:

∠C and ∠D are both inscribed angles of arc AB.  Therefore, they are equal.

5w + 20 = 7w − 4

24 = 2w

w = 12

Therefore, ∠C = ∠D = 80°.

Inscribed angles are half the central angle, so mAB = 2 × 80° = 160°.

Answer:

Required results are [tex]\nabla .\vec{F}[/tex]=8\cos(8x+5z)-8ye^x[/tex]  and  [tex]\nabla\times \vec{F}=-8e^xz\uvec{i}+(8ye^xz+5\sin(8x+5z))\uvec{j}[/tex]

Step-by-step explanation:

Given vector function is,

[tex]\vec{F}=\sin(8x+5z)\uvec{i}-8ye^xz\uvec{k}[/tex]

To find [tex]\nabla .\vec{F}[/tex] and [tex]\nabla \times \vec{F}[/tex] .

[tex]\nabla .\vec{F}[/tex]

[tex]=(\frac{\partial}{\partial x}\uvec{i}+\frac{\partial}{\partial y} \uvec{j}+\frac{\partial}{\partial z} \uvec{k})(\sin(8x+5z)\uvec{i}-8ye^xz\uvec{k})[/tex]

[tex]=\frac{\partial}{\partial x}(\sin(8x+5z))-\frac{\partial}{\partial z}(8ye^xz)[/tex]

[tex]=8\cos(8x+5z)-8ye^x[/tex]

And,

[tex]\nabla \times \vec{F}[/tex]

[tex]=(\frac{\partial}{\partial x}\uvec{i}+\frac{\partial}{\partial y} \uvec{j}+\frac{\partial}{\partial z} \uvec{k})\times(\sin(8x+5z)\uvec{i}-8ye^xz\uvec{k})[/tex]

[tex]\end{Vmatrix}[/tex]

[tex]=\uvec{i}\Big[\frac{\partial}{\partial y}(-8ye^xz)\Big]-\uvec{j}\Big[\frac{\partial}{\partial x}(-8ye^xz)-\frac{\partial}{\partial z}(\sin(8x+5z))\Big]+\uvec{k}\Big[-\frac{\partial}{\partial y}(-\sin(8x+5z))\Big][/tex]

[tex]=-8e^xz\uvec{i}+(8ye^xz+5\sin(8x+5z))\uvec{j}[/tex]

Hence the result.

Answer:

40

Step-by-step explanation:

8*5

Answer:

This would be -9 to the 5th power. (-9^5)

Step-by-step explanation:

-9 to the 5th power when put in a calculator equals -59,049.

The exponent is how many times the number is multiplied by itself.

Answer:

-59049

Step-by-step explanation:

(-9).(-9).(-9).(-9).(-9)

=81.(-9).(-9).(-9)

= -729.(-9).(-9)

= 6561.(-9)

= -59049

Answer:

4x+5y = 320

x+y = 70

Step-by-step explanation:

We need one equation for the total number of shirts, and one for the total cost.

Total number = 70

So that means medium shirts + large shirts = 70

So our first equation is x+y = 70

Total cost = $320

So that means $4 times medium shirts + $5 times large shirts = 320

So our second equation is 4x+5y = 320

Answer:

330+77= 407

Step-by-step explanation:

*Danganronpa flashbacks*

Answer:

24 guppies

Step-by-step explanation:

Assuming a linear relationship,  the volume required per guppy is given by:

[tex]g=\frac{576\ in^3}{3\ guppies}\\ g= 192\ in^3/guppy[/tex]

The volume of the fish tank is given by the product of its length, by its width and its height:

[tex]V = 24*12*16\\V=4,608\ in^3[/tex]

The number of guppies that this tank can safely hold is:

[tex]n=\frac{V}{g}=\frac{4,608}{192} \\n=24\ guppies[/tex]

The tank can safely hold 24 guppies.

Answer:

18.86 feet

Step-by-step explanation:

The circumference of the inner circle is 88 ft.

Circumference of a Circle[tex]=2\pi r[/tex]

Therefore:

[tex]2\pi r =88\\r=88 \div (2*\frac{22}{7})=14 ft[/tex]

Radius of the inner circle=14 feet

If the distance between the inner circle and the outer circle is 3 ft, the radius of the outer circle=14+3 =17 feet.

Therefore. circumference of the outer Circle[tex]=2\pi r[/tex]

[tex]=2*\frac{22}{7}*17=106.86 ft[/tex]

Difference in Circumference=106.86-88 =18.86 feet

The circumference of the outer circle is greater than that of the inner circle by 18.86 feet.

18.9

Step-by-step explanation:

Answer:

720

Step-by-step explanation:

96 * 7.5

Answer: 300

We know that 5×3=15. Since we are trying to get 1500 we Multiply 300×5 and get 1500.

How do we know?

As you see when you still multiply either of those problems you have 15 in it. So we should know 300×5=1500.

Note: We can also multiply 500×3 and get 1500. You still get the same answer but just switched numbers.

Answer:

[tex]300[/tex]

Step-by-step explanation:

[tex] \frac{1500}{5} = 300[/tex]

It's very easy to find if you use a calculator.

To know whether that the answer is correct or wrong you can do like this.

[tex]300 \times 5 = 1500[/tex]

hope this helps

thanks.

By calculating the average speed of Tomos in the 525-meter race, we can estimate that he would take about 3 minutes 12 seconds to complete an 800-meter race if he maintains the same average speed.

To solve this problem, we first need to figure out Tomos's average speed in the 525-meter ski race that he completed in 2 minutes and 6 seconds. We convert the time to seconds for ease of calculation. So, 2 minutes 6 seconds equals 126 seconds. Now, we calculate his average speed by dividing the length of the race by the time he took to complete it:

Average speed = Distance / Time
Average speed = 525m / 126s
Average speed = 4.17 m/s

Now to calculate how long Tomos should take to complete an 800 m race, we rearrange the formula to solve for time. Time = Distance / Average Speed:

Time = 800m / 4.17 m/s
Time = 191.84 seconds

Learn more about Average Speed here:

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Answer:

[tex]9797-1.67\frac{2313}{\sqrt{61}}=9302.43[/tex]    

[tex]9797+1.67\frac{2313}{\sqrt{61}}=10291.57[/tex]    

And we can conclude that at 90% of confidence the true mean for the number of steps taken on a typical workday for all people working in New York City who wear an activity tracker is between 9302.43 and 10291.57

Step-by-step explanation:

Data provided

[tex]\bar X=9797[/tex] represent the sample mean for the steps

[tex]\mu[/tex] population mean

s=2313 represent the sample standard deviation

n=61 represent the sample size  

Solution

The confidence interval for the true population mean is given by :

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

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

[tex]df=n-1=61-1=60[/tex]

The Confidence is 0.90 or 90%, the value for the significance is [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,60)".And we see that [tex]t_{\alpha/2}=1.67[/tex]

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

[tex]9797-1.67\frac{2313}{\sqrt{61}}=9302.43[/tex]    

[tex]9797+1.67\frac{2313}{\sqrt{61}}=10291.57[/tex]    

And we can conclude that at 90% of confidence the true mean for the number of steps taken on a typical workday for all people working in New York City who wear an activity tracker is between 9302.43 and 10291.57

90% confident that the true mean number of steps taken on a typical workday for all people working in New York City who wear activity trackers is between approximately 9,302.94 steps and 10,291.06 steps.

To construct a 90% confidence interval for the mean number of steps taken on a typical workday for people working in New York City who wear activity trackers, you can use the following formula:

Confidence Interval = X ± Z * (σ/√n)

Where:

X is the sample mean (9,797 steps).

Z is the Z-score corresponding to the desired confidence level (90% confidence level corresponds to a Z-score of 1.645, but you can use a Z-table or calculator to get the exact value).

σ is the population standard deviation (2,313 steps).

n is the sample size (61).

Now, let's plug in the values and calculate the confidence interval:

Z for a 90% confidence level is approximately 1.645.

Confidence Interval = 9,797 ± 1.645 * (2,313/√61)

Confidence Interval = 9,797 ± 1.645 * (299.98)

Confidence Interval ≈ 9,797 ± 494.06

Now, calculate the lower and upper bounds of the confidence interval

Lower Bound = 9,797 - 494.06 ≈ 9,302.94

Upper Bound = 9,797 + 494.06 ≈ 10,291.06

Interpretation:

We are 90% confident that the true mean number of steps taken on a typical workday for all people working in New York City who wear activity trackers is between approximately 9,302.94 steps and 10,291.06 steps. This means that if we were to take many random samples and calculate a 90% confidence interval for each sample, we would expect about 90% of those intervals to contain the true population mean.

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Answer:1968ft^2

Step-by-step explanation:

Perimeter(p)=178feet

P=2L+2w

178=2L+2w

178=2(L+w)

L+w=178 ➗ 2

L+w=89.............(1)

W+7=L

L-w=7...................(11)

L+w=89... ..........(1)

L-w=7...................(11)

Subtract (11) from (1)

2w=89-7

2w=82

w=82 ➗ 2

w=41 width=41feet

Substitute w=41 in (11)

L-w=7

L-41=7

L=7+41

L=48feet

Area= length x width

Area=48 x 41

Area=1968ft^2

The area of the garden is 1968 square feet by setting up and solving equations based on the information about the garden's length, width, and perimeter.

The problem is asking for the area of a rectangular garden where the length is 7 feet longer than its width. We also know the perimeter of the garden is 178 feet. Normally in a rectangle, the formula for the perimeter is P = 2(length + width).

Since the length is 7 feet longer, let's denote the width as 'w' and therefore the length as 'w+7'. Substituting in the perimeter formula we get: 178 = 2(w + w + 7).

By simplifying and solving the equation we find that the width, w = 41 feet. Therefore, the length is w+7 = 48 feet.

Lastly, the area of a rectangle is calculated as length * width, so substituting the values we found we get the area = 48 feet * 41 feet = 1968 square feet.

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B alone can empty the pool in 5.744 hours, if A alone can empty the pool in 4.75 hours and  it takes 2.6 hours when both drains are turned on.

Step-by-step explanation:

The given is,

                   A alone can empty the pool in 4.75 hours.

                   It takes 2.6 hours when both drains are turned on.

Step:1

            One hour work drains A and B =

                  One hour work of drain A + One hour work of Drain B.........(1)

            One hour work of Drain A = [tex]\frac{1}{4.75}[/tex]

                     One hour of ( A + B ) = [tex]\frac{1}{2.6}[/tex]

            Equation (1) becomes,

                     One hour work of B = One hour work of ( A + B )

                                                                  - One hour work of A

            Substitute the values,

                     One hour work of B =  [tex]\frac{1}{2.6} - \frac{1}{4.75}[/tex]

                                                       = [tex]\frac{4.75-2.6}{(4.75)(2.6)}[/tex]

                                                       = [tex]\frac{2.15}{12.35}[/tex]

                                                       = [tex]\frac{1}{5.744}[/tex]

                    One hour work of B  = [tex]\frac{1}{5.744}[/tex]

             B alone can empty the pool in 5.744 hours

Result:

           B alone can empty the pool in 5.744 hours, if A alone can empty the pool in 4.75 hours and  it takes 2.6 hours when both drains are turned on.

Answer:

the correct graph is pictured below

Step-by-step explanation:

the graph is below