the area of the largest equilateral triangle that can be inscribed in a square of side length unit can be expressed in the form square units, where and are integers. what is the value of ?

the probability that a randomly selected customer uses coupons but did not bring their own bags is 0.13.

What is probability?

The probability formula enables us to determine the likelihood of an event by dividing the number of favorable outcomes by the total number of possible outcomes. The probability of an event can range from 0 to 1 because the number of favorable outcomes cannot exceed the total number of outcomes.

From the Venn diagram, we can see that the probability of using coupons but not bringing their own bags is the area inside circle C but outside the overlapping region. Therefore, the probability is:

P(C and not B) = P(C) - P(C and B) = 0.25 - 0.12 = 0.13

So, the probability that a randomly selected customer uses coupons but did not bring their own bags is 0.13.

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The image and the net that represents the solid figure is attached

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

rectangular prism

When the rectangular prism is splitted into nets, we have the following shapes

Shapes = 6 rectangular faces

This means that the net that represents the solid figure has 6 rectangular faces

Using the above as a guide, we have the following:

The net of the solid figure is the image 4

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Answer:

cubic meter (m³)

Step-by-step explanation:

N/A

The correct answer is option A, "smoothing constant".

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.

Exponential smoothing is a widely used forecasting technique that involves giving different weights to the past observations in a time series, with the most recent observation being given the highest weight. The parameter that determines the weight given to the most recent observation is known as the "smoothing constant".

The smoothing constant is a value between 0 and 1, and it represents the rate at which the influence of past observations on the forecast decreases over time. A larger value for the smoothing constant gives more weight to recent observations, while a smaller value gives more weight to older observations.

The parameter of the exponential smoothing model that provides the weight given to the most recent time series value in the calculation of the forecast value is known as the "smoothing constant".

Therefore, the correct answer is option A, "smoothing constant".

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Since 23² is less than 12² + 20², we can conclude that the values 12, 20, and 23 do not create a right triangle.

To determine if the values 12, 20, and 23 create a right triangle, we can use the Pythagorean theorem, which states that for any right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

So, we can calculate:

12² + 20² = 144 + 400 = 544

23² = 529

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According to the question the length of arc BC is approximately 1.69 feet.

The measurement of the circle's boundaries is called as the circumference or perimeter of the circle. whereas the circumference of a circle determines the space it occupies. The circumference of a circle is its length when it is opened up and drawn as a straight line. Units like cm or unit m are typically used to measure it. The circle's radius is considered while calculating the circumference of the circle using the formula. As a result, in order to calculate the circle's perimeter, we must know the radius or diameter value.

The circumference of a circle is given by the formula[tex]$C = 2\pi r$[/tex], where $r$ is the radius of the circle. In this case, the radius is 8 feet, so the circumference of the circle is: C=16π feet.

Since the angle BAC is one-third of a radian, we know that angle BOC (the angle at the center of the circle) is twice as large, or approximately $38.2^\circ$. This is because the angle at the center of the circle is twice as large as the angle on the circumference that it intercepts.

Now we can use this angle to find the length of arc BC. The formula for the length of an arc is: L = Ф/360 *C

L = 38.2/350 * 16π = 1.69 feet.

So the length of arc BC is approximately 1.69 feet.

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Note that the answers to the above transformation prompt is above as follows:

1. Angle PQR

2. Segment PS

3. Scale factor =  3/2 = 1.5

1. Angle PQR in the scaled copy corresponds to angle ABC in polygon ABCD in polygon PQRS. In the two separate figures, they are both in the same position. They complement each other.

2. In the scaled copy, segment PS is the section in polygon PQRS that corresponds to segment AD in polygon ABCD. They are similar in appearance and appear in the same location.

3. The scale factor is the ratio of any of the segment lengths.

Let's consider segments lengths of AD in ABCD, which corresponds to segment PS in PQRS.

AD = 2 units

PQ = 3 units

Scale factor from ABCD to PQRS = PQ/AD = 3/2 = 1.5

The whole number tells us that ABCD is scaled up or enlarged to given a bigger polygon, PQRS

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The surface area of each of the hemisphere's are:

1) S.A = 1520.5 cm²

2) S.A = 929.4 ft²

3) S.A = 706.9 m²

4) S.A = 615.8 in²

5) S.A = 804.2 in²

6) S.A = 380.1 yd²

The formula for the area of a sphere is expressed as:

S.A = 4πr²

1) The radius is given as r = 11 cm

S.A = 4 * π * 11²

S.A = 1520.5 cm²

2) The radius is given as r = 8.6 ft

S.A = 4 * π * 8.6²

S.A = 929.4 ft²

3) The diameter is given as d = 15 m

Thus, radius: r = 15/2 = 7.5 m

S.A = 4 * π * 7.5²

S.A = 706.9 m²

4) The radius is given as r = 7 in

S.A = 4 * π * 7²

S.A = 615.8 in²

5) The radius is given as r = 8 cm

S.A = 4 * π * 8²

S.A = 804.2 in²

6) The diameter is given as d = 11 yards

Thus, radius: r = 11/2 = 5.5 yards

S.A = 4 * π * 5.5²

S.A = 380.1 yd²

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The responses that must be included are the population is all high school students, the sample contains freshmen, sophomores, juniors, and seniors, and the sample is representative of students in the entire high school.

Hence, options A, B, and D are correct.

To ensure that a sample is representative of the population, it must be selected in a way that accurately reflects the characteristics of the population. In this case, the population is all high school students in the town, and the possible sample includes an equal number of students from each grade level - freshman, sophomores, juniors, and seniors.

This is a good approach to ensure that the sample is representative of the entire population, as it captures the diversity of the population by including students from each grade level. Additionally, by having an equal number of students from each grade level, the sample is not biased towards any particular group.

It is also important to ensure that the sample is not too small, as a small sample size may not accurately reflect the characteristics of the entire population. Finally, if the sample is truly representative of the entire high school, any conclusions drawn from the sample should be applicable to the population as a whole.

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Answer:

x = 100

y = 44

Step-by-step explanation:

The interior angles of a quadrilateral add up to 360 degrees, so we know that when all four angles are added together, they need to equal 360.

121 + 111 + x - 31 + 2y - 29 = 360

Additionally, the angles opposite each other equals 180 degrees. This means D + F = 180 degrees, and E + G = 180 degrees.

111 + (x - 31) = 180

Subtract 111 from both sides.

x - 31 = 69

Add 31 to each side

x = 100

Plug in the value for x to check the answer

111 + (100 - 31) = 180

Then, for y, we have the same set up

121 + (2y - 29) = 180

Subtract 121 from both sides

2y - 29 = 59

Add 29 to each side

2y = 88

Divide each side by 2

y = 44

Plug in the value for y to check the answer

121 + (2*44 - 29) = 180

This means that angle F equals 59 degrees and angle G equals 69 degrees.

x = 100

y = 44

The centroid is a point of concurrency of the medians of a triangle. The medians are the line segments that connect each vertex of the triangle to the midpoint of the opposite side. The centroid is located at the intersection of the three medians, and it is often denoted by the letter G.

Every triangle has a centroid, and it is one of the most important points in a triangle. The centroid divides each median into two segments, with the segment connecting the vertex to the centroid being twice as long as the segment connecting the midpoint to the centroid. Therefore, the centroid is located two-thirds of the distance from each vertex to the midpoint of the opposite side.

To illustrate a triangle with a centroid, we can take any triangle and draw its three medians. The centroid is the point at which these three medians intersect. Any type of triangle, whether it is acute, obtuse, or right, will have a centroid. Therefore, any triangle can illustrate a centroid, and it is a fundamental concept in geometry that is used to solve many problems and prove theorems related to triangles.

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This chart shows the number of moves required to solve the Towers of Hanoi puzzle for each specified number of disks.

A chart for the number of moves needed to solve the Towers of Hanoi puzzle with various numbers of disks. The formula to calculate the minimum number of moves is 2^n - 1, where n is the number of disks. Here's the chart:

| Number of Disks (n) | Number of Moves (2^n - 1) |
|---------------------|--------------------------|
|          2          |            3             |
|          3          |            7             |
|          4          |           15             |
|          5          |           31             |
|          6          |           63             |
|          7          |          127             |
|          8          |          255             |
|          9          |          511             |
|         10          |         1023             |
|         15          |        32767             |
|         20          |      1048575             |
|         25          |     33554431             |

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Answer:

C. f¹(x) = x² + 8; x ≥ 8

Explanation:

The given function is f(x) = √(x - 8), which can be rewritten as f(x) = (x - 8)^(1/2).

To find the inverse function, we need to solve for x:

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

y^2 = x - 8

x = y^2 + 8

Therefore, f¹(x) = x² + 8.

The domain of f(x) is all the values of x that make the expression inside the square root non-negative, that is, x - 8 ≥ 0. Solving for x, we get x ≥ 8. Therefore, the domain of f(x) is x ≥ 8.

Step-by-step explanation:

B. f¹(x) = (x+8)²; xz0

hope the answer is correct

The number that should be subtracted from thrice 13 by 5 to obtain 5 by 13 is 130.

The number that should be subtracted from thrice 13 by 5 to obtain 5 by 13 is calculated as follows;

let the number = n

thrice 13 by 5 = 3 (13) x 5 = 195

5 by 13 = 5 x 13 = 65

The value of the unknown number, n,  is calculated as;

195 - n = 65

n = 195 - 65

n = 130

Thus, when we subtract 130 from thrice 13 by 5, we will obtain 5 by 13 as shown in the calculation above.

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As we have proven both directions of the statement X = Y if and only if Xy = (X + Y)²/4.

Let's start with the "if" direction. This means we need to prove that if Xy = (X + Y)²/4, then X = Y. To do this, we can start by multiplying both sides of the equation by 4 to get rid of the fraction:

4Xy = (X + Y)²

Expanding the right-hand side of the equation gives:

4Xy = X² + 2XY + Y²

We can rearrange this equation by subtracting 2XY and Y² from both sides:

4Xy - 2XY - Y² = X²

Next, we can factor out X on the left-hand side:

X(4y - 2Y) = X² - Y²

If we assume X ≠ 0, we can divide both sides by X to get:

4y - 2Y = X - Y

Simplifying this expression gives:

2y = X + Y

Finally, we can substitute this equation back into the original equation Xy = (X + Y)²/4 to get:

Xy = (2y)²/4

Simplifying this expression gives:

Xy = y²

Since X ≠ 0 (as we assumed earlier), we can divide both sides by X to get:

y = X

Therefore, we have shown that if Xy = (X + Y)²/4, then X = Y.

Now, let's move on to the "only if" direction. This means we need to prove that if X = Y, then Xy = (X + Y)²/4. To do this, we can start with the equation X = Y and substitute Y for X in the equation Xy = (X + Y)²/4:

Yy = (Y + Y)²/4

Simplifying this expression gives:

Yy = Y²

Dividing both sides by Y (since Y ≠ 0), we get:

y = Y/1

Therefore, we have shown that if X = Y, then Xy = (X + Y)²/4.

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K-fold cross-validation generally produces an estimate with lower bias compared to leave-one-out cross-validation.(option b).

Cross-validation is a popular technique used in machine learning to estimate the performance of a model on unseen data. There are different methods of cross-validation, including leave-one-out and K-fold. In leave-one-out, only one data point is left out for testing, while in K-fold, a Kth portion of the data is held out.

Now, to answer the question of which method generally produces an estimate with higher bias, we need to look at the formula for bias in cross-validation. The bias is given by the difference between the expected value of the cross-validation estimate and the true performance of the model.

For K-fold cross-validation, the expected value of the estimate is computed as the average of the estimates obtained in each of the K folds. This means that the bias is dependent on the number of folds used. The more folds used, the lower the bias is likely to be.

Hence the correct option is (b).

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Blindness and eyesight are two different physical conditions that affect an individual's ability to see.

Even with good eyesight, there are limitations to our perception that can cause us to miss important details or fail to see what is right in front of us.

The narrator feels that people with good eyesight fail to see what is right in front of them because of the limitations of their perception. Our eyesight only allows us to see a limited portion of the electromagnetic spectrum, which means that there are many things in the world that we cannot see.

In mathematical terms, we can think of eyesight as a function that maps the input of light waves to the output of an image in our brain. However, this function has limitations in terms of the range of inputs it can handle and the accuracy of the output it produces.

This means that even with good eyesight, there are certain inputs that our eyes cannot handle and certain details that our brain cannot fully process.

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Complete Question:

How are blind people different from people with eyesight? Why does the narrator feel that people with good eye sight fail to see what is right in front of them?

The hypothesis test is right-tailed and direction is specified, and the given population parameter is greater than the specified value (more than $500). So, the correct answer from given options is B).

The hypothesis test is right-tailed because a direction is specified. The null hypothesis assumes that the average tax refund is equal to or less than $500, while the alternative hypothesis assumes that the average tax refund is greater than $500.

Therefore, the test is designed to detect if the population parameter is greater than the specified value, making it a right-tailed test. So, the correct option is B).

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After performing the calculations, you'll find that the probability of less than 3 households having board games out of 10 households is approximately 0.0038 or 0.38%.

To find the probability that less than 3 households have board games, we can use the binomial probability formula. The terms involved in this problem are:

1. n: number of trials (households)
2. k: number of successful outcomes (households with board games)
3. p: probability of success (having board games)
4. q: probability of failure (not having board games)

Given that 75% of households have board games, p = 0.75, and q = 1 - p = 0.25. In this case, n = 10 households. We need to find the probability of k = 0, 1, or 2 households having board games.

The binomial probability formula is:
P(X = k) = C(n, k) * p^k * q^(n-k)

Step 1: Calculate the probability for k = 0, 1, and 2 separately:
P(X = 0) = C(10, 0) * 0.75^0 * 0.25^10
P(X = 1) = C(10, 1) * 0.75^1 * 0.25^9
P(X = 2) = C(10, 2) * 0.75^2 * 0.25^8

Step 2: Add the probabilities for k = 0, 1, and 2 to get the total probability:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

After performing the calculations, you'll find that the probability of less than 3 households having board games out of 10 households is approximately 0.0038 or 0.38%.

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Answer:

Sqrt 49 = 7

Sqrt 136 = 11.6619037896906

Sqrt 181 = 13.45362404707371

Sqrt 100 = 10

Sqrt -64 = Not a real number (invalid input)

In this scenario, a computer software magazine compares the rates of malware infection for computers protected by security software A and B.

To construct a 98% confidence interval for the difference between the proportions of infection for the two types of security software packages, follow these steps:

1. Calculate the proportions of infection for each security software (pA and pB):
  pA = 80/800 = 0.1
  pB = 45/900 = 0.05

2. Calculate the combined proportion (pC) and the standard error (SE) for the difference between proportions:
  pC = (80 + 45) / (800 + 900) = 125/1700 = 0.0735
  SE = sqrt((pC * (1 - pC)) * ((1/800) + (1/900))) = 0.0204

3. Find the z-score for a 98% confidence interval (z = 2.33 for a 98% CI).

4. Calculate the margin of error (ME) using the z-score and standard error:
  ME = z * SE = 2.33 * 0.0204 = 0.0475

5. Calculate the confidence interval for the difference between proportions:
  CI = (pA - pB) ± ME = (0.1 - 0.05) ± 0.0475 = 0.05 ± 0.0475 = (0.0025, 0.0975)

The 98% confidence interval is (0.0025, 0.0975), which can be rounded to (0.002, 0.098). This interval does not contain zero, which means it contradicts the claim that the proportion of infections is the same for the two types of security software. Therefore, the answer is (0.02, 0.098); yes.

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The nitrogen level that gives the best yield function is where the optimal nitrogen level is 6 units.

To find the nitrogen level that gives the best yield, we need to find the maximum value of the yield function Y. To do this, we can take the derivative of Y with respect to N, set it equal to zero, and solve for N.

dy/dN = k(36 - N²)/(36 + N²)²

Setting dy/dN equal to zero, we get:

0 = k(36 - N²)/(36 + N²)²

Solving for N, we get:

N = ±6

Since N has to be a positive value, the optimal nitrogen level is N = 6 units.

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Our confidence interval is only representative of the sample that we selected, and there could be variation in the true population proportion.

To construct a confidence interval for the population proportion of all pregnant women who gave birth the week of their due date

the following steps can be taken:

1. Determine the sample size: The sample size can be determined based on the desired level of confidence and margin of error. Let's say we want a 95% confidence level and a margin of error of 5%, which means we want to be 95% confident that the true proportion falls within 5% of the sample proportion. Using a confidence interval calculator, the required sample size would be 385.

2. Select a random sample of women who have recently given birth: The sample should be selected randomly to ensure that it is representative of the population of all pregnant women.

3. Calculate the sample proportion: Determine the proportion of women in the sample who gave birth the week of their due date.

4. Calculate the standard error: The standard error can be calculated using the formula SE = √((p*(1-p))/n), where p is the sample proportion and n is the sample size.

5. Calculate the confidence interval: Using a confidence interval calculator, the confidence interval for the population proportion can be calculated. For our example, the confidence interval would be 0.404 to 0.556.

The confidence interval we constructed (0.404 to 0.556) does not contradict the study's claim that a certain proportion of pregnant women give birth the week of their due date, as the interval includes the possibility of this proportion being within the range of 0.40 to 0.56.

Our confidence interval is only representative of the sample that we selected, and there could be variation in the true population proportion.

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Suppose that the correlation between educational level attained and yearly income is +0.68. This indicates that there is a positive and strong relationship between educational level and yearly income.

It means that as the level of education attained increases, the yearly income also tends to increase. However, it is important to note that correlation does not imply causation, and there could be other factors that contribute to the relationship between education and income.

Based on the provided correlation coefficient of +0.68 between educational level attained and yearly income, we know that there is a positive and moderately strong relationship between the two variables. As a person's education level increases, their yearly income is also likely to increase.

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Step-by-step explanation:

The product of the form method is a technique used to factorize a quadratic expression of the form ax^2 + bx + c. Here are the steps to follow:

1. Write down the quadratic expression in the standard form ax^2 + bx + c, where a, b, and c are constants.

2. Multiply the coefficient a by the constant c to get the product ac.

3. Find two factors of ac that add up to the coefficient b. In other words, find two numbers p and q such that pq = ac and p + q = b.

4. Rewrite the quadratic expression by replacing the middle term bx with the two terms px and qx. This is done by splitting the middle term of the quadratic expression using the two numbers p and q found in step 3. So the quadratic expression becomes ax^2 + px + qx + c.

5. Factor the first two terms of the expression ax^2 + px using the greatest common factor (GCF). This gives us a(x + p/a)x + qx + c.

6. Factor the last two terms qx + c using the GCF. This gives us a(x + p/a)(x + c/q).

7. Simplify the expression by combining any like terms and check that the factors obtained in step 6 can be expanded back into the original quadratic expression.

8. Write down the factored form of the quadratic expression, which is (x + p/a)(x + c/q).

These are the steps of the product of the form method.

The degree of the expression 12x+5x²-99x⁵ is

The degree of an algebraic expression is the highest power of the variable in the expression. An expression can have a variable or more.

For example, the degree of the expression 5y⁷+ 6y⁴+ 3y² is 7 because 7 is the highest exponent of the variable y in the expression.

Similarly the expression 12x+5x²-99x⁵ has 3 terms with x has the variable. The highest power of x in the expression is 5. Therefore the degree of the expression is 5.

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This right rectangular prism, which measures 6 by 6 by 15 cm, has a surface area of 432 square centimetres.

The sum of the areas of the six faces of a right rectangular prism gives the prism's surface area. The prism in this instance is 6 centimetres x 6 centimetres by 15 centimetres in size.

We must first determine the size of each face's area before adding them all up to determine the surface area. Each of the top and bottom faces measures 6 cm by 6 cm, giving them a combined area of 6 cm by 6 cm, or [tex]36 cm^2[/tex].

The front and back faces each have an area of [tex]90 cm^2[/tex] because they are each 6 cm by 15 cm in size.

Last but not least, the left and right faces have a combined area of 6 cm by 15 cm, or [tex]90 cm^2[/tex], each.

The total area of all six faces is as follows:

[tex]36 cm^2 +90 cm^2 +90 cm^2 +90 cm^2 = 432 cm^2[/tex].

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The value of P(not yellow) if the spinner is spun once is 75%

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

Spinner with repeated colors numbered from 1 to 8

The sample space of a eight-sided number cube is

S = {8 colors}

Where, the sections that are not yellow are

not yellow = 6 sections

Using the above as a guide, we have the following:

P(not yellow) = n(not yellow)/n(S)

So, we have

P(not yellow) = 6/8

Evaluate

P(not yellow) = 75%

Hence, the value of P(not yellow) is 75%

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The exact value of y is [tex]\sqrt{3}[/tex]

The correct answer is an option (c)

Let us assume that in the attached diagram of right triangle the angle A measures 45 degrees.

Here, the hypotenuse measures [tex]\sqrt{6}[/tex]

We know that in right triangle, the sine of angle θ is nothing but the ratio of opposite side of angle θ to the hypotenuse.

Consider the sine of angle A

sin(A) = opposite side of angle A / hypotenuse

sin(45°) = y / ( [tex]\sqrt{6}[/tex])

We know that from the standard trigonometric table the value of sin(45°) is [tex]\frac{1}{\sqrt{2} }[/tex]

Substitute this value in above equation we get,

[tex]\frac{1}{\sqrt{2} }[/tex] =  y / ( [tex]\sqrt{6}[/tex])

We solve this equation to find the value of y.

y =  [tex]\sqrt{6}[/tex] ×  [tex]\frac{1}{\sqrt{2} }[/tex]

y = [tex]\frac{\sqrt{3}\sqrt{2} }{\sqrt{2} }[/tex]

y = [tex]\sqrt{3}[/tex]

Therefore, the correct answer is an option (c)

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Based on the given information, we know that the arrival rate is 9 customers per hour and the service rate is 14 customers per hour. Since the arrival and service distributions are not known, we cannot use the m/m/1 formulas to calculate the average waiting time and total time spent in the system.

However, we can still use the Little's Law formula to relate the average number of customers in the system to the average waiting time. Little's Law states that the average number of customers in the system (N) is equal to the product of the arrival rate (λ) and the average time spent in the system (T), or N = λT.

Since we want to find the total time spent in the system, we can rearrange the formula to solve for T. Thus, T = N / λ.

We know from the given information that the average waiting time in the line is 18 minutes. Therefore, the average time spent in the system for a customer is T = 18 minutes + (1/14 hour), which is equal to 1.9 hours.

To calculate the total time spent in the system, we need to add the waiting time to the service time. Since the service rate is 14 customers per hour, the service time per customer is 1/14 hour or approximately 4.3 minutes. Thus, the total time spent in the system is approximately 22.3 minutes or 0.37 hours.

In summary, the average time spent in the system for a customer is 1.9 hours, and the total time spent in the system is approximately 22.3 minutes or 0.37 hours.

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brainly.com/question/30036732

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