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Mobius Strip The surface shown in the figure is called a Mobius strip and can the represented by the parametric equations

 where  Try to graph other Mobius strips for different values of using a computer algebra system.

 

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Priyanshu Patel
Priyanshu PatelLv10
15 Mar 2021

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Related textbook solutions

Introductory Statistics
OER Edition, 2013
Openstax
ISBN: 9781938168208

Related questions

Since Thorndike “Graph-Pro” racquetball racquets were introduced several years ago, no attempt has ever been made to offer a lightweight version. Ted has done some research and found that some of the other manufacturers offer a lighter version of their standard racquet. In addition, some of the racquetball players he has talked to have said a lighter racquet would probably improve their game.

Talking with production engineers, Ted learns that the racquets coming off the line don’t all weigh the same anyway. According to the chief engineer, the racquets weigh an av- erage of 240 grams, but the weights “vary all over the lot,” and he takes advantage of the situation to press for a high-tech $700,000 machine that would produce racquets of equal quality while holding this variation within narrower limits.

Old Luke isn’t too keen on buying a $700,000 machine, especially since Ted might have a better solution. Ted has dusted off the literature that accompanied the racquet-production machine and found that the machine generates output that is approximately normally distributed, with a standard deviation of 10 grams. This is a little sloppy these days, but maybe Thorndike Sports Equipment can turn this weakness into a strength.

Conversing further with Luke, talking to three sporting goods retailers, and interviewing players at five different racquetball facilities, Ted comes back to the office with a terrific idea. Asking Luke to sit down, and bringing him some coffee, Ted begins his pitch: “Say, grandfather, why don’t we take the racquets at the lighter end of the range and label them ‘Graph-Pro Light,’ with the ones more in the middle being ‘Graph-Pro Regular,’ and the ones at the heavier end can be ‘Graph-Pro Stout’?”

Luke responds that just because this works for the beer companies, this doesn’t mean it will work for Thorndike Sports Equipment. However, he’s willing to give it a try. Af- ter accompanying Ted on another round of conversations with retailers and players, the elder Thorndike tells Ted that for now, he’d like to see 15% of the production consist of “Graph-Pro Light,” with 80% “Graph-Pro Regular,” and 5% “Graph-Pro Stout.”

Ted’s next task is to tell the production people how to go about selecting which racquets are to be put into these three different categories.

(a) What is the weight below which racquets classify as Graph-Pro Light? (b) What is the weight above which racquets classify as Graph-Pro Stout?

 

A random sample of soil specimens was taken from a large geographic area. The specimens can be assumed to be independent. The amount of organic matter, as a percent, was determined for each specimen. The data are below:
0.14, 0.32, 1.17, 1.45, 3.5, 5.02, 5.09, 5.22
A soil scientist wants to know whether the population mean percent organic matter is different than 4%. A
significance level of α = 0.05 is chosen.

    1. (a)  State hypotheses appropriate to the research question.
    2. (b)  Graph the data as you see fit. Why did you choose the graph(s) that you did and what does it (do they) tell you?
    3. (c)  Regardless of your conclusion from (b), use the bootstrap to perform a test of the hypotheses you stated in (a). Use B = 8000 resamplings. Compute the p-value, and make a reject or not reject conclusion. Then state the conclusion in the context of the problem. In other words, does it seem the mean organic matter level is different than 4%?
    4. (d)  Regardless of your conclusion from part (b), use a T -test to perform a test of the hypotheses you stated in (a). Compute the p-value, and make a reject or not reject conclusion. Then state the conclusion in the context of the problem. In other words, does it seem the mean organic matter level is different than 4%?. (I recommend doing this part with a hand calculator and statistical tables as practice for exam conditions, but you may check your answers using R if you wish.)
    5. (e)  Compare your answers from parts (c) and (d). Which method do you think is better? Are you surprised at the similarity or dissimilarity? What do you think explains this?

EX16_XL_CH05_GRADER_CAP_AS - Travel Expenses 1.3

Project Description:

You are the manager of an information technology (IT) team. Your employees go to training workshops and national conferences to keep up-to-date in the field. You created a list of expenses by category for each employee for the last six months. Now you want to subtotal the data to review total costs by employee and then create a PivotTable to look at the data from different perspectives.

Instructions:

For the purpose of grading the project you are required to perform the following tasks:

Step

Instructions

Points Possible

1

Start Excel. Open the downloaded Excel file named exploring_e05_grader_a1_Expenses.xlsx. Save the workbook as exploring_e05_grader_a1_Expenses_LastFirst, replacing LastFirst with your own name.

0.000

2

On the Subtotals worksheet, sort the data by Employee and further sort by Category, both in alphabetical order.

4.000

3

Use the Subtotals feature to insert subtotal rows by Employee to calculate the total expense by employee.

5.000

4

Collapse the Donaldson and Hart sections to show only their totals. Leave the other employees’ individual rows displayed.

5.000

5

Use the Expenses worksheet to create a blank PivotTable on a new worksheet named Summary. Name the PivotTable Categories.

8.000

6

Use the Category and Expense fields, enabling Excel to determine where the fields go in the PivotTable.

5.000

7

Modify the Values field to determine the average expense by category. Change the custom name to Average Expense.

4.000

8

Format the Values field with Accounting number type.

3.000

9

Type Category in cell A3 and change the Grand Totals layout option to On for Rows Only.

5.000

10

Apply Pivot Style Dark 2 and display banded rows.

Note, depending upon the version of Office being used, the style name may be Light Blue, Pivot Style Dark 2.

5.000

11

Insert a slicer for the Employee field, change the slicer height to 2 inches and apply the Slicer Style Dark 5. Move the slicer below the PivotTable.

Note, depending upon the version of Office being used, the style name may be Light Blue, Slicer Style Dark 5.

5.000

12

Use the Expenses worksheet to create another blank PivotTable on a sheet named Totals. Add the Employee to the Rows and add the Expense field to the Values area. Sort the PivotTable from largest to smallest expense.

10.000

13

Change the name for the Expenses column to Totals and format the field with Accounting number format.

4.000

14

Insert a calculated field to subtract 2659.72 from the Expense field. Format the field with the custom name Above or Below Average and apply Accounting number format to the field.

10.000

15

Set 12.25 width for column B and column C, change the row height of row 3 to 30, and apply word wrap to cell C3.

4.000

16

Create a clustered column PivotChart from the PivotTable. Move the PivotChart to a new sheet named Chart. Hide all field buttons in the PivotChart, if necessary.

Note, Mac users, select the range A3:C8 in the PivotTable. On the Insert tab, click Recommended Charts, and then click Clustered Column to make the chart.

10.000

17

Add a chart title above the chart and type Expenses by Employee. Change the chart style to Style 14.

6.000

18

Apply 11 pt font size to the value axis and display vertical axis as Accounting with zero decimal places.

4.000

19

Create a footer on all worksheets with your name in the left section, the sheet name code in the center section, and the file name code in the right section.

3.000

20

Ensure that the worksheets are correctly named and placed in the following order in the workbook: Subtotals, Summary, Chart, Totals, Expenses. Save the workbook. Close the workbook and then exit Excel. Submit the workbook as directed.

0.000
 

Total Points

100.000

https://www.dropbox.com/s/m7falnl85tfazl9/Torres%20DaSilva_exploring_e05_grader_a1_Expenses.xlsx?dl=0

 
 

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