Ally was interested in whether people felt more satisfied after going on vacation to Hawaii or Cancún. A sample of 20 people who went to Hawaii and 20 who went to Cancún were given a survey asking how satisfied they were after their vacation. The data that was collected is shown below. Satisfaction was measured on a 5-point scale, where higher scores indicated more satisfaction. Is there a significant difference in satisfaction for the two groups? Please analyze the data using a two-tailed test at the α = .01 level.Vacation : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2Satisfaction : 3 4 3 1 5 2 5 2 3 1 4 1 4 4 5 3 2 2 3 4 3 4 1 4 1 2 3 2 5 3 3 1 1 2 2 1 4 4 1 3a) Which T-test is the most appropriate to conduct for the data?
b) Using the results, is there a statistically significant difference between s1^2 and s2^2? How do you know? Describe in your own words what this means conceptually? What do we do differently if there is a significant difference between s1^2 and s2^2?c) Report your obtained t score for the test of differences in means, and the obtained p value.
d) Make a statistical decision about the null. Will you reject or fail to reject the null? Why? What do your results mean in simple words?
e) Calculate the r^2. Interpret it in the context of the study.

Answer: she would have ran 4,000 yards

Step-by-step explanation: 1 foot is equal to 3 yards so you multiply that and you will get your answer.

The correct answers are as follows: a) False, b) False, c) True, d) False, e) True, f) False

(a) False. Tossing a biased coin is not a Bernoulli trial as the probability of success (getting a head or tail) is not constant.
(b) False. The statement should be P(X>0) = 0.5.
(c) True. Negative binomial distribution describes the number of failures before a specified number of successes occur, while geometric distribution describes the number of trials until the first success.
(d) False. The expected waiting time is (30+0)/2 = 15.
(e) True. The standard deviation of the sample mean is equal to the population standard deviation divided by the square root of the sample size. So, 10/sqrt(100) = 1, and the standard deviation of the sample mean is 5/sqrt(100) = 0.5.
(f) False. Poisson distribution can be used to approximate binomial distribution under certain conditions such as large sample size and small probability of success.

(a) T: Tossing a biased coin can be treated as a Bernoulli trial, as it has two possible outcomes: success (head) and failure (tail).

(b) F: If X follows a standard normal distribution, then P(X=0) is not equal to 0. Instead, P(X=0) represents the probability density at X=0, which is non-zero.

(c) T: The negative binomial distribution is a generalization of Geometric distribution, as both distributions model the number of trials needed to achieve a certain number of successes.

(d) F: If the waiting time X of a bus follows a uniform distribution of X~U(0, 30), then the expected waiting time is (0+30)/2 = 15, not 30.

(e) T: A population follows a gamma distribution with a mean of 50 and standard deviation of 10. The standard deviation of the sample mean (sample size of 100) can be calculated as σ/√n = 10/√100 = 1, not 5.

(f) F: Poisson distribution can be used to approximate binomial distribution, especially when the number of trials (n) is large, and the probability of success (p) is small.

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D. Identifying outliers in a data set can be helpful in uncovering data errors is true regarding data errors

It states that identifying outliers in a data set can be helpful in uncovering data errors. Data errors can occur due to various reasons such as data entry mistakes, data transmission errors, data processing errors, and so on. These errors can lead to incorrect or misleading analysis, which can affect decision-making processes.

Identifying outliers in a data set can help in identifying potential data errors. Outliers are observations that are significantly different from other observations in a data set. Outliers can occur due to various reasons such as measurement errors, sampling errors, or simply due to natural variation in the data. However, outliers can also indicate data errors that need to be corrected.

For example, if a data set contains information about the heights of a group of people, and one observation reports a height of 9 feet, it is likely that this is a data entry error. Identifying this outlier can help in identifying and correcting the error.

Therefore, it is important to identify outliers and investigate them to determine if they are genuine observations or data errors. Removing outliers blindly can lead to the loss of valuable information and can also introduce bias into the analysis. It is important to use statistical methods to identify outliers and investigate them carefully to ensure that the data is accurate and reliable.

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CI = 6.76 ± 1.96 × (2.67/√50)
CI = 6.76 ± 0.96
Therefore, the 95% confidence interval for the population means rating for Miami is: (5.80, 7.72)

We can be 95% confident that the true mean rating for Miami International Airport falls within this interval.
To develop a 95% confidence interval for the population means rating for Miami International Airport, we need to follow these steps:

1. Calculate the sample mean (x) by adding up all the ratings and dividing by the sample size (n=50).
2. Calculate the sample standard deviation (s).
3. Use a t-distribution to find the t-score for a 95% confidence interval with (n-1) degrees of freedom.
4. Calculate the margin of error (ME) using the t-score, standard deviation, and sample size.
5. Add and subtract the margin of error from the sample mean to find the lower and upper limits of the confidence interval.

To calculate the 95% confidence interval, we need to use the formula:
CI = x ± Z' (s/√n)
Where:
x = sample mean
Z' = z-score for the desired confidence level (in this case, 95%, so

Z' = 1.96)
s = sample standard deviation
n = sample size

Step 1: Calculate the sample mean (x)
Sum of ratings = 346
Sample size (n) = 50
x = 346/50 = 6.92

Step 2: Calculate the sample standard deviation (s)
Variance = [(Sum of (rating - x)^2) / (n-1)] = 88.48
Standard deviation (s) = √(88.48) = 9.41

Step 3: Find the t-score
For a 95% confidence interval with 49 (n-1) degrees of freedom, the t-score is approximately 2.01.

Step 4: Calculate the margin of error (ME)
ME = t-score × (s / √n) = 2.01 × (9.41 / √50) = 2.01 × 1.33 = 2.67

Step 5: Find the confidence interval
Lower limit: x - ME = 6.92 - 2.67 = 5.80
Upper limit: x + ME = 6.92 + 2.67 = 7.72

Thus, the 95% confidence interval for the population mean rating for Miami International Airport is approximately

(5.80, 7.72)

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Answer:

the last 5 means 500

Step-by-step explanation:

the seconed 5 means 50

Answer: logarithmic

Step-by-step explanation:

edge2023 ;)

the second one is ratio

The test strategy involves collecting data on the number of complaints (response variable) that employees submit for each OS. The CTO aims to gather 19 observations for each operating system, which will help her analyze the data and make a decision based on the performance and satisfaction of the employees.

The CTO of the company is planning to use a comparative test strategy to decide which operating system (OS) to use as the standard for the company. The OS types being compared are Apple, Linux, and Windows. To gather data, the CTO plans to look at the number of complaints submitted by employees for each OS, which will be the response variable. The CTO has set a goal of having 19 observations for each OS.

The experimental data will have a general structure where the number of complaints will be recorded for each OS. This data will be analyzed to determine which OS has the least amount of complaints and is therefore the most suitable for use as the standard in the company. It is important for the CTO to ensure that the testing process is fair and unbiased so that accurate conclusions can be drawn from the data.

To help the CTO make an informed decision on which operating system (OS) to use as standard in the company, she plans to compare Apple, Linux, and Windows OS types. The test strategy involves collecting data on the number of complaints (response variable) that employees submit for each OS. The CTO aims to gather 19 observations for each operating system, which will help her analyze the data and make a decision based on the performance and satisfaction of the employees.

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The area of the shape which is made up of the semicircle and the rectangle  is 44.13

The area of the semicircle = area of circle  / 2

= πr²/2

= 9 x 3.14 / 2

= 14.13

The area of a reactangle can be defined as length x width

This will give us the area as

6 x 5

Area = 30 cm for the rectangle

The exact area of the shape will be Total Area = (Area of Semicircle) + (Area of Rectangle)

= 30 cm + 14.13

= 44.13 cm

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A total of 5 cars would be needed for both families to ride the bumper cars.

To find the number of cars needed for the two families, we can use the following set of equations:

Let x be the number of cars needed for the family of 6.
Let y be the number of cars needed for the family of 4.

We know that each car holds 2 people, so:

2x = 6  (each car holds 2 people in the family of 6)
2y = 4  (each car holds 2 people in the family of 4)

Solving for x and y, we get:

x = 3  (the family of 6 needs 3 cars)
y = 2  (the family of 4 needs 2 cars)

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The caculated value of the function x=-2 is 3

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

A linear graph

From the graph, we have the following readings at x = -2

(-2, 3)

There are several ways to interpret this and some of them are

Hence, the caculated value of the function x=-2 is 3

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The maximum value of the objective function within the feasible region occurs at one of the vertices.

To find the maximum value of the objective function within the feasible region, we need to evaluate the objective function at each of the vertices and determine which one gives the highest value.

Let's assume the objective function is of the form f(x,y). To evaluate f at each vertex, we substitute the x and y values into the function. For example, at the vertex (2,0), we evaluate f(2,0) = 2x + 3y, where x=2 and y=0. Similarly, we evaluate f at each of the other vertices as follows

At (10,1): f(10,1) = 2x + 3y = 2(10) + 3(1) = 23

At (8,5): f(8,5) = 2x + 3y = 2(8) + 3(5) = 31

At (0,4): f(0,4) = 2x + 3y = 2(0) + 3(4) = 12

So the maximum value of the objective function f within the feasible region is 31, which occurs at the vertex (8,5).

Note that the feasible region is defined by the set of constraints that limit the values of x and y that satisfy the problem. The vertices of the feasible region are the points where the boundary of the feasible region intersect. The maximum value of the objective function within the feasible region occurs at one of the vertices.

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The Laplace transform of f(t) cosh kt cos kt is:

L[f(t) cosh kt cos kt] = F(s) [4k^4 + 4ks(s^2 + k^2) + s^4]/s^2(s^2 + k^2)^2

The Translation (Shifting) Theorem states that if F(s) is the Laplace transform of f(t), then the Laplace transform of e^(at)f(t) is F(s - a).

Using this theorem, we can find the Laplace transform of f(t) cosh ktcoskt as follows:

Let g(t) = cosh kt cos kt. Then, using the identity cosh x = (e^x + e^-x)/2 and the linearity of the Laplace transform, we have:

L[f(t) cosh kt cos kt] = L[f(t) g(t)]

= L[e^(0t)f(t)g(t)]

= L[e^(kt) (e^-kt f(t)) g(t)]

= L[e^(kt) F(s - (-k)) g(t)]

where we used the Translation (Shifting) Theorem with a = -k and F(s) = L[f(t)].

Now, using the fact that g(t) = cosh kt cos kt = (e^kt + e^-kt)/2 * cos kt, we can write:

L[f(t) cosh kt cos kt] = L[e^(kt) F(s + k) (e^kt + e^-kt)/2 * cos kt]

= 1/2 L[e^(2kt) F(s + k) cos kt] + 1/2 L[F(s + k) cos kt]

Using the Laplace transform of cos kt (which can be found in a Laplace transform table or by integrating by parts), we get:

L[f(t) cosh kt cos kt] = 1/2 [(s + k)/(s^2 + k^2)^2 - 2k/(s^2 + k^2)] F(s + k) + 1/2 (s/(s^2 + k^2)^2 - 1/(s^2 + k^2)) F(s)

Simplifying this expression, we get:

L[f(t) cosh kt cos kt] = [s^2 - k^2 + 2ks + 4k^2/s^2(s^2 + k^2)^2] F(s)

which is algebraically equivalent to F(s) [4k^4 + 4ks(s^2 + k^2) + s^4]/s^2(s^2 + k^2)^2.

Therefore, the Laplace transform of f(t) cosh kt cos kt is:

L[f(t) cosh kt cos kt] = F(s) [4k^4 + 4ks(s^2 + k^2) + s^4]/s^2(s^2 + k^2)^2

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178 square meters is the area of the complex figure.

To find the area of this composite figure, we need to find the areas of the individual shapes and add them up.

The area of the first rectangle is:

16 m x 8 m = 128 m²

The area of the triangle is:

1/2 x base x height = 1/2 x 5 m x 8 m = 20 m²

The area of the second rectangle is:

6 m x 5 m = 30 m²

To find the total area, we add the areas of the three shapes:

128 m² + 20 m² + 30 m² = 178 m²

Therefore, the area of this complex figure is 178 square meters.

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The margin of error for the 99% confidence interval for the population mean of grass seed germination periods is approximately 3.374 days.

To find the margin of error for the confidence interval for the population mean with a 99% confidence level for germination periods of grass seed, follow these steps:

1. Identify the given information:
- Sample size (n) = 21
- Sample mean (x) = 34 days
- Population standard deviation (σ) = 6 days
- Confidence level = 99%

2. Determine the appropriate z-score for the 99% confidence level:
- Since the confidence level is 99%, we need to look for the z-value that corresponds to 0.005 in the z-table (because 1 - 0.99 = 0.01, and 0.01/2 = 0.005).
- z0.005 = 2.576

3. Calculate the standard error of the mean (SEM):
- SEM = σ/√n = 6/√21 = 1.31

4. Calculate the margin of error (ME):
- ME = z * SEM = 2.576 * 1.31 = 3.374

5. Round the answer to three decimal places:
- ME = 3.374

Your answer: The margin of error for the 99% confidence interval for the population mean of grass seed germination periods is approximately 3.374 days.

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The volume of the solid generated [tex]\pi \int\limits^4_0 {(6 - x^2 + 3x)^2 - (6 - x)^2} \, dx[/tex] dx.

The correct option is B.

We have y = x² - 3x and y = x about the horizontal line y = 6.

Now, the integral expression for the volume of the solid formed by revolving is

[tex]\pi \int\limits^4_0 {(6 - x^2 + 3x)^2 - (6 - x)^2} \, dx[/tex]

Each term in above expression represent:

By evaluating this integral,  find the volume of the solid formed by revolving the given region about the horizontal line y = 6.

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The question attached here seems to be incomplete the complete question here:

What is the integral expression for the volume of the solid formed by revolving the region bounded by the graphs of y = x ^ 2 - 3x and y = x about the horizontal line y = 6'

[tex]\pi \int\limits^3_0 {(6 - x^2 + 3x)^2 - (6 - x)^2} \, dx[/tex]

[tex]\pi \int\limits^4_0 {(6 - x^2 + 3x)^2 - (6 - x)^2} \, dx[/tex]

[tex]\pi \int\limits^3_0 { (6 - x)^2 - (6 - x^2 + 3x)^2} \, dx[/tex]

[tex]\pi \int\limits^4_0 { (6 - x)^2 - (6 - x^2 + 3x)^2} \, dx[/tex]

Based on the given information, we know that the medium-sized jet has a fuselage diameter of 3.8 meters and a loaded mass of 85,000 kilograms. The drag on the airplane is primarily due to the cylindrical shape of the fuselage, and its aerodynamic shaping gives it a drag coefficient of 0.37.

To calculate the drag force on the airplane, we can use the formula:

Drag Force = 1/2 x Density x Velocity^2 x Surface Area x Drag Coefficient

The surface area of a cylinder is given by:

Surface Area = 2 x π x (diameter/2) x length

Assuming a length of 30 meters for the fuselage, we can calculate the surface area as:

Surface Area = 2 x π x (3.8/2) x 30 = 426.43 square meters

Using the given drag coefficient of 0.37 and assuming a cruising speed of 800 km/h (or 222.22 m/s), we can calculate the drag force as:

Drag Force = 1/2 x 1.225 kg/m^3 x (222.22 m/s)^2 x 426.43 m^2 x 0.37
Drag Force = 5,641,613 Newtons

Therefore, the drag force on the medium-sized jet is approximately 5.64 million Newtons. This drag force must be overcome by the jet's engines to maintain its cruising speed.

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Therefore, the 90% lognormal prediction interval for the price of the stock after 6 months is (71.25, 87.95). The closest answer option is D) (61.91, 110.74), but it is not an exact match.

To determine the 90% lognormal prediction interval for the price of the stock after 6 months, we can use the following formula:
ln(S) = ln(S₀) + (r - σ²/2)t + σ√tZ
Where:
- ln(S) is the natural logarithm of the stock price after 6 months
- ln(S₀) is the natural logarithm of the initial stock price ($80)
- r is the expected continuously compounded rate of return (10%)
- σ is the volatility (25%)
- t is the time in years (0.5)
- Z is the standard normal distribution value for the desired confidence level (90% corresponds to Z = 1.645)
Substituting the values, we get:
ln(S) = ln(80) + (0.1 - 0.25²/2) x 0.5 + 0.25√0.5 x 1.645
ln(S) = 4.382 + 0.089
ln(S) = 4.471
To convert back to the stock price, we take the exponential of both sides:
S = e⁴.⁴⁷¹
S ≈ 87.95
The lower bound of the prediction interval is obtained by using Z = -1.645:
ln(S) = ln(80) + (0.1 - 0.25²/2) x 0.5 - 0.25√0.5 x 1.645
ln(S) = 4.382 - 0.108
ln(S) = 4.274
S = e⁴.²⁷⁴
S ≈ 71.25

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Answer:

x=92°

Step-by-step explanation:

x+21+66+59+x+30=360

2x+176=360

2x=184

x=92°

To create the vector OutOfSpec, we need to compare the values in SqOut with the ideal output values, which can be calculated using the formula (input voltage)^2. We can then use the following steps in Matlab:

1. Create a vector of input voltages from 1 mV to N mV:
inputVoltage = 1:N;

2. Calculate the ideal output values using the formula (input voltage)^2:
idealOutput = inputVoltage.^2;

3. Calculate the percentage difference between the actual and ideal output values:
percentDiff = abs(SqOut - idealOutput) ./ idealOutput * 100;

4. Find the indices of the values in percentDiff that exceed 1%:
outOfSpecIdx = find(percentDiff > 1);

5. Use the outOfSpecIdx vector to extract the input voltages that generated out-of-spec output values:
OutOfSpec = inputVoltage(outOfSpecIdx);

The resulting vector OutOfSpec will contain a list of all inputs that generated an output differing from the ideal value by more than 1%.
To create a vector OutOfSpec in Matlab that contains a list of all inputs that generated an output differing from the ideal value by more than 1%, you can use the following code:

```matlab
SqOut = [0.9985 4.052 8.973 15.81 25.15];
N = length(SqOut);
ideal_output = (1:N).^2;
tolerance = 0.01 * ideal_output;
lower_bound = ideal_output - tolerance;
upper_bound = ideal_output + tolerance;

OutOfSpec = find(SqOut < lower_bound | SqOut > upper_bound);
```

This code first calculates the ideal output values and the 1% tolerance bounds. Then, it uses the 'find' function to identify input values where the corresponding output differs from the ideal value by more than 1%. The result will be stored in the vector OutOfSpec.

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If 2x²-5x+7 is subtracted from 4x²+2x-11, the coefficient of x in the result is 7

A coefficient is a number multiplied by a variable. For example, 6× x = 6x, here, 6 is the coefficient of x and x is the variable.

Subtracting 2x²-5x+7 from 4x²+2x-11

= 4x²+2x-11 -( 2x²-5x+7)

= 4x²+2x -11 - 2x²+5x-7

collecting like terms

4x²-2x²+2x+5x -7 -11

= 2x²+7x-18

Therefore the coefficient of x when 2x²-5x+7 is subtracted from 4x²+2x-11 is 7

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TRUE. The design matrix for linear regression is a matrix that contains the predictor variables for each observation. In this case, the predictor variables are Li, Yi, zi, and zxy, and there are n observations. Therefore, the design matrix would be a n x 4 matrix.

True. If you want to fit data (Li, Yi, Zi) ∈ R³ to a model z = B₀ + B₁x + B₂y + B₃xy, and you have n data points, then the design matrix for linear regression will be an n x 4 matrix.

Here's why:
- Each row of the matrix represents one data point.
- Each column of the matrix corresponds to the coefficients B₀, B₁, B₂, and B₃ in the model.

For n data points, the design matrix will look like this:

| 1  x₁  y₁  x₁y₁ |
| 1  x₂  y₂  x₂y₂ |
| 1  x₃  y₃  x₃y₃ |
| ...             |
| 1  xₙ  yₙ  xₙyₙ |

Thus, it is an n x 4 matrix.

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About 3.25 seconds have gone by when the rocket is at its highest point.

The height of the rocket at any time t can be calculated using the equation h = -16t² + 104t.

The vertex of the parabolic function will give the value of the highest point of the rocket. The x-coordinate of the vertex gives us the time at which the rocket reaches its maximum height.

The x-coordinate of the vertex can be found using the formula: x = -b / 2a, the coefficient of the t² term is a and coefficient of the t term is b.

In this case, a = -16 and b = 104, so the x-coordinate of the vertex is,

x = -b / 2a

= -104 / (2*(-16))

= 3.25

Therefore, the rocket is at its highest point 3.25 seconds after launch.

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Yes, the data provided is enough evidence to show that the state had a higher proportion of identity theft than 23%.

To determine if the state had a higher proportion of identity theft complaints than the national average of 23%, we will perform a one-sample z-test for proportions at the 9% level of significance.

Step 1: State the null and alternative hypotheses.
H0: p = 0.23 (The proportion of identity theft complaints in the state is equal to the national average.)
H1: p > 0.23 (The proportion of identity theft complaints in the state is higher than the national average.)

Step 2: Determine the sample proportion and sample size.
Sample proportion (p-hat) = 468/1820 ≈ 0.2571
Sample size (n) = 1820

Step 3: Calculate the test statistic.
z = (p-hat - p) / √[(p * (1 - p)) / n]
z ≈ (0.2571 - 0.23) / √[(0.23 * (1 - 0.23)) / 1820] ≈ 1.88

Step 4: Find the critical value and make a decision.
At the 9% level of significance, the critical value (zα) for a one-tailed test is 1.34. Since our test statistic (z ≈ 1.88) is greater than the critical value (zα = 1.34), we reject the null hypothesis.

The data provide enough evidence to conclude that the state had a higher proportion of identity theft complaints than the national average of 23% at the 9% level of significance.

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The category in the Excel Options dialog box that contains the option to change the user name is "General".

In the Excel Options dialog box, the category that contains the option to change the user name is the General category.

Excel graphing methods, Go to Insert > Line after selecting the data. The type of line chart you want may be chosen from a dropdown menu that appears when you click the icon.

We'll use the fourth 2-D line graph (Line with Markers) for this illustration. Your line graph for the chosen data series will be added by Excel.

What are the primary three graphs?

How to Use Graphs in Science

Bar, circle, and line graphs are the three most often utilized graph kinds. Each form of graph may be used to display a certain kind of data.

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Joule per meter second is the unit of measurement for momentum flux or power per unit area. It is commonly used in physics and engineering to quantify the rate of energy transfer or momentum flow per unit area.

Joule per meter second (J/m^2s) is not the correct unit for momentum flux or power per unit area. The correct unit for momentum flux is Newton per square meter (N/m^2), also known as Pascal (Pa), while the correct unit for power per unit area is watt per square meter (W/m^2). The joule per meter second (J/m^2s) is actually the unit for volumetric energy dissipation rate, which measures the rate at which energy is being dissipated within a fluid volume per unit volume. It is used in the study of fluid dynamics and turbulence.

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From the given distances and time it is clear that Mrs.Peter arrive before Mr Peter by 5 minute.

Mrs. Peter arrives 5 minutes before Mr. Peter

To find who arrives first we first need to find the speed and time they require to arrive.

Given : From Boston to Worcester

Mr. Peter takes 30 minutes time and speed=60 miles per hour

Mrs. Peter travels with speed 90 miles per hour

We will now calculate Mr.Peters speed

60 miles/h × h/60 = miles/min

We know that, Distance = Speed /Time

Mr.Peters speed is 60 miles per hour

Distance=Miles÷Min /30 minutes

Distance = 30 miles

Similarly, we will now calculate Mrs.Peters speed

90 miles/h h/60 = 1.5 miles per min

Here, Time = 30 / 1.5

= 20 minutes

Here, we know that Mrs.Peter leaves from Boston to Worcester 5 minutes after Mr.Peter so we will add 5 minutes to Mrs. Peters time.

Time = 20+5 =15 minutes

Therefore,

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We have L < 0 and L > 0, which is a contradiction. Therefore, (zn) does not converge

To prove that xn ≤ zn ≤ yn for all n ∈ N, we just need to compare the values of xn, yn, and zn for any given n. We have xn = -1, yn = 1, and zn = (-1)^n+1, so we need to show that -1 ≤ (-1)^n+1 ≤ 1.

For n even, we have (-1)^n+1 = -1, so -1 ≤ (-1)^n+1 ≤ 1 holds.

For n odd, we have (-1)^n+1 = 1, so -1 ≤ (-1)^n+1 ≤ 1 holds.

Therefore, we have xn ≤ zn ≤ yn for all n ∈ N.

Next, we will prove that (xn) converges to -1 and (yn) converges to 1.

Since xn = -1 for all n ∈ N, (xn) is a constant sequence and converges to -1. Similarly, since yn = 1 for all n ∈ N, (yn) is also a constant sequence and converges to 1.

Finally, we will prove that (zn) does not converge.

Suppose (zn) converges to some limit L. Then, for any ε > 0, there exists N ∈ N such that |zn - L| < ε for all n > N.

Let ε = 1. Then, there exists N such that |zn - L| < 1 for all n > N.

Consider the cases when n is even and odd separately.

When n is even, we have zn = -1. So, we have |-1 - L| < 1, which implies L - 1 < -1 and L < 0.

When n is odd, we have zn = 1. So, we have |1 - L| < 1, which implies L - 1 < 1 and L > 0.

Thus, we have L < 0 and L > 0, which is a contradiction. Therefore, (zn) does not converge.

Complete question:  If [tex]$x_n=-1, y_n=1$[/tex], and [tex]$z_n=(-1)^{n+1}$[/tex], then [tex]$x_n \leq z_n \leq y_n$[/tex] for all [tex]$n \in \mathbb{N}$[/tex], the sequence [tex]$\left(x_n\right)$[/tex] converges to -1 and [tex]$\left(y_n\right)$[/tex] converges 1 , but [tex]$\left(z_n\right)$[/tex]does not converge.

As once consequence, we show that we can take absolute values inside limits.

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