Eli Orchid has designed a new pharmaceutical product, Orchid Relief, which improves the night sleep. Before initiating mass production of the product, Eli Orchid has been market-testing Orchid Relief in Orange County over the past 8 weeks. The daily demand values are recorded in the Excel file provided. Eli Orchid plans on using the sales data to predict sales for the upcoming week. An accurate forecast would be helpful in making arrangements for the company’s production processes and designing promotions.
Before a forecasting model is built and a forecast for the next week is generated, the COO of the company has asked the data analyst for an exploratory analysis of the demand.
Specifically, the COO has asked the analyst[1]:
|
To provide a bar chart (with data labels rounded to two decimal points) showing the average demand for each week day (Sun., Mon., etc.) |
[add chart here] |
|
To fit a simple linear regression model to the data and to provide its equation (d = a*t + b), along with R2 |
d = R2= |
|
To fit a multiple regression model with a dummy variable representing the weekend, and to provide the regression equation (d = a*t + b*w + c), along with Adjusted R2. |
d = Adjusted R2= |
|
To provide a run-series plot of the actual demand with simple regression and multiple regression overlay. |
[add chart here] |
|
To write a short paragraph explaining the observations and providing general recommendations for the next seven days demand forecast. Note: this paragraph can be on page 2. The answers to previous questions must all fit on the first page. |
[write your paragraph here] |
[1] Round numbers to four decimal points (e.g. 0.1234), unless explicitly requested otherwise.
| Day | Date | Weekday | Daily Demand | Weekend |
| 1 | 4/25/2016 | Mon | 297 | 0 |
| 2 | 4/26/2016 | Tue | 293 | 0 |
| 3 | 4/27/2016 | Wed | 327 | 0 |
| 4 | 4/28/2016 | Thu | 315 | 0 |
| 5 | 4/29/2016 | Fri | 348 | 0 |
| 6 | 4/30/2016 | Sat | 447 | 1 |
| 7 | 5/1/2016 | Sun | 431 | 1 |
| 8 | 5/2/2016 | Mon | 283 | 0 |
| 9 | 5/3/2016 | Tue | 326 | 0 |
| 10 | 5/4/2016 | Wed | 317 | 0 |
| 11 | 5/5/2016 | Thu | 345 | 0 |
| 12 | 5/6/2016 | Fri | 355 | 0 |
| 13 | 5/7/2016 | Sat | 428 | 1 |
| 14 | 5/8/2016 | Sun | 454 | 1 |
| 15 | 5/9/2016 | Mon | 305 | 0 |
| 16 | 5/10/2016 | Tue | 310 | 0 |
| 17 | 5/11/2016 | Wed | 350 | 0 |
| 18 | 5/12/2016 | Thu | 308 | 0 |
| 19 | 5/13/2016 | Fri | 366 | 0 |
| 20 | 5/14/2016 | Sat | 460 | 1 |
| 21 | 5/15/2016 | Sun | 427 | 1 |
| 22 | 5/16/2016 | Mon | 291 | 0 |
| 23 | 5/17/2016 | Tue | 325 | 0 |
| 24 | 5/18/2016 | Wed | 354 | 0 |
| 25 | 5/19/2016 | Thu | 322 | 0 |
| 26 | 5/20/2016 | Fri | 405 | 0 |
| 27 | 5/21/2016 | Sat | 442 | 1 |
| 28 | 5/22/2016 | Sun | 454 | 1 |
| 29 | 5/23/2016 | Mon | 318 | 0 |
| 30 | 5/24/2016 | Tue | 298 | 0 |
| 31 | 5/25/2016 | Wed | 355 | 0 |
| 32 | 5/26/2016 | Thu | 355 | 0 |
| 33 | 5/27/2016 | Fri | 374 | 0 |
| 34 | 5/28/2016 | Sat | 447 | 1 |
| 35 | 5/29/2016 | Sun | 463 | 1 |
| 36 | 5/30/2016 | Mon | 291 | 0 |
| 37 | 5/31/2016 | Tue | 319 | 0 |
| 38 | 6/1/2016 | Wed | 333 | 0 |
| 39 | 6/2/2016 | Thu | 339 | 0 |
| 40 | 6/3/2016 | Fri | 416 | 0 |
| 41 | 6/4/2016 | Sat | 475 | 1 |
| 42 | 6/5/2016 | Sun | 459 | 1 |
| 43 | 6/6/2016 | Mon | 319 | 0 |
| 44 | 6/7/2016 | Tue | 326 | 0 |
| 45 | 6/8/2016 | Wed | 356 | 0 |
| 46 | 6/9/2016 | Thu | 340 | 0 |
| 47 | 6/10/2016 | Fri | 395 | 0 |
| 48 | 6/11/2016 | Sat | 465 | 1 |
| 49 | 6/12/2016 | Sun | 453 | 1 |
| 50 | 6/13/2016 | Mon | 307 | 0 |
| 51 | 6/14/2016 | Tue | 324 | 0 |
| 52 | 6/15/2016 | Wed | 350 | 0 |
| 53 | 6/16/2016 | Thu | 348 | 0 |
| 54 | 6/17/2016 | Fri | 384 | 0 |
| 55 | 6/18/2016 | Sat | 474 | 1 |
| 56 | 6/19/2016 | Sun | 485 | 1 |
In: Statistics and Probability
| Day | Date | Weekday | Daily Demand | Weekend |
| 1 | 4/25/2016 | Mon | 297 | 0 |
| 2 | 4/26/2016 | Tue | 293 | 0 |
| 3 | 4/27/2016 | Wed | 327 | 0 |
| 4 | 4/28/2016 | Thu | 315 | 0 |
| 5 | 4/29/2016 | Fri | 348 | 0 |
| 6 | 4/30/2016 | Sat | 447 | 1 |
| 7 | 5/1/2016 | Sun | 431 | 1 |
| 8 | 5/2/2016 | Mon | 283 | 0 |
| 9 | 5/3/2016 | Tue | 326 | 0 |
| 10 | 5/4/2016 | Wed | 317 | 0 |
| 11 | 5/5/2016 | Thu | 345 | 0 |
| 12 | 5/6/2016 | Fri | 355 | 0 |
| 13 | 5/7/2016 | Sat | 428 | 1 |
| 14 | 5/8/2016 | Sun | 454 | 1 |
| 15 | 5/9/2016 | Mon | 305 | 0 |
| 16 | 5/10/2016 | Tue | 310 | 0 |
| 17 | 5/11/2016 | Wed | 350 | 0 |
| 18 | 5/12/2016 | Thu | 308 | 0 |
| 19 | 5/13/2016 | Fri | 366 | 0 |
| 20 | 5/14/2016 | Sat | 460 | 1 |
| 21 | 5/15/2016 | Sun | 427 | 1 |
| 22 | 5/16/2016 | Mon | 291 | 0 |
| 23 | 5/17/2016 | Tue | 325 | 0 |
| 24 | 5/18/2016 | Wed | 354 | 0 |
| 25 | 5/19/2016 | Thu | 322 | 0 |
| 26 | 5/20/2016 | Fri | 405 | 0 |
| 27 | 5/21/2016 | Sat | 442 | 1 |
| 28 | 5/22/2016 | Sun | 454 | 1 |
| 29 | 5/23/2016 | Mon | 318 | 0 |
| 30 | 5/24/2016 | Tue | 298 | 0 |
| 31 | 5/25/2016 | Wed | 355 | 0 |
| 32 | 5/26/2016 | Thu | 355 | 0 |
| 33 | 5/27/2016 | Fri | 374 | 0 |
| 34 | 5/28/2016 | Sat | 447 | 1 |
| 35 | 5/29/2016 | Sun | 463 | 1 |
| 36 | 5/30/2016 | Mon | 291 | 0 |
| 37 | 5/31/2016 | Tue | 319 | 0 |
| 38 | 6/1/2016 | Wed | 333 | 0 |
| 39 | 6/2/2016 | Thu | 339 | 0 |
| 40 | 6/3/2016 | Fri | 416 | 0 |
| 41 | 6/4/2016 | Sat | 475 | 1 |
| 42 | 6/5/2016 | Sun | 459 | 1 |
| 43 | 6/6/2016 | Mon | 319 | 0 |
| 44 | 6/7/2016 | Tue | 326 | 0 |
| 45 | 6/8/2016 | Wed | 356 | 0 |
| 46 | 6/9/2016 | Thu | 340 | 0 |
| 47 | 6/10/2016 | Fri | 395 | 0 |
| 48 | 6/11/2016 | Sat | 465 | 1 |
| 49 | 6/12/2016 | Sun | 453 | 1 |
| 50 | 6/13/2016 | Mon | 307 | 0 |
| 51 | 6/14/2016 | Tue | 324 | 0 |
| 52 | 6/15/2016 | Wed | 350 | 0 |
| 53 | 6/16/2016 | Thu | 348 | 0 |
| 54 | 6/17/2016 | Fri | 384 | 0 |
| 55 | 6/18/2016 | Sat | 474 | 1 |
| 56 | 6/19/2016 | Sun | 485 | 1 |
Eli Orchid has designed a new pharmaceutical product, Orchid Relief, which improves the night sleep. Before initiating mass production of the product, Eli Orchid has been market-testing Orchid Relief in Orange County over the past 8 weeks. The daily demand values are listed above. Eli Orchid plans on using the sales data to predict sales for the upcoming week. An accurate forecast would be helpful in making arrangements for the company’s production processes and designing promotions.
Before a forecasting model is built and a forecast for the next week is generated, the COO of the company has asked the data analyst for an exploratory analysis of the demand.
Specifically, the COO has asked the analyst1:
|
To provide a bar/column chart (with data labels rounded to two decimal points) showing the average demand for each day of the week (Sun., Mon., etc.) |
[ chart ] |
|
To fit a simple linear regression model to the data and to provide its equation (d = a*t + b), along with R2 |
d = R2= |
|
To fit a multiple regression model with a dummy variable representing the weekend, and to provide the regression equation (d = a*t + b*w + c), along with Adjusted R2. |
d = Adjusted R2= |
|
To provide a line graph of the actual demand with a simple regression and multiple a regression overlay. |
[ chart ] |
|
Specifically:
|
In: Statistics and Probability
Use the following information on Company Y and perform pro-forma financial modeling using a planned expansion method to answers question (1) and (2). To do this assume that the percentage values with respect to sales of the (i) costs except depreciation, (ii) cash and equivalents, (iii) accounts receivable, (iv) inventories, and (v) accounts payable will stay fixed at the values corresponding for 2016.
Assume also that income tax will remain at 35% of the Pretax Income.
Consider Company Y. This firm sells a product for which in 2016 the total market size was of 1999000 units, of which Company Y owned a share of 30%.
Both, the total market size and Company Y’s market share are expected to grow at a 4% yearly rate for the next five years.
The price of the product is $114 in 2016 and is expected to remain at that price for the next years.
|
Market Analysis |
2016 |
2017 |
2018 |
2019 |
|
Market Size |
1,999,000 |
2,078,960 |
2,162,118 |
2,248,603 |
|
Market Share |
30% |
31% |
32% |
34% |
|
Production Volume |
599,700 |
|||
|
Sales Price: |
$ 114.00 |
|||
|
Sales |
In 2016, the outstanding debt of Company Y is $900000, for which the company makes yearly interest payments of 11%. The executives of Company Y are considering making a significant capital investment in 2017 of $2900000 to purchase new machinery. The company plans to finance this investment with a 30-year loan that makes yearly interest payments equivalent to 8% of its principal. The principal is paid when the loan matures.
The following table summarizes the debt and interest payment of Company Y.
|
Debt and Interest Table |
2016 |
2017 |
2018 |
|
|
Outstanding Debt |
900,000 |
900,000 |
3,800,000 |
|
|
New Net Borrowing |
2,900,000 |
|||
|
Interest on Debt |
||||
Currently, Company Y makes yearly expenditures on replacement capital investment of $90000. If the company makes the planned expansion it is decided the company will perform yearly expenditures on replacement capital investment of $325000. The current and the planned expenditures on replacement of capital investment will be financed by the company’s cash flow.
The following table indicates for 2016 Company Y’s values of i. opening book value, ii. capital investment, iii. depreciation, and iv. closing book value. The Table also indicates the 2017-2018 forecast values of capital depreciation if the planned expansion were to occur in 2017.
|
Fixed Assets & Capital Investment |
2016 |
2017 |
2018 |
|
Opening Book Value |
1,500,000 |
||
|
Capital Investment |
90,000 |
||
|
Depreciation |
-127,200 |
-356,224 |
-353,726 |
|
Closing Book Value |
1,462,800 |
The following table contains Company Y’s income statement.
|
Income Statement: |
2016 |
2017 |
|
Sales |
68,365,800 |
|
|
Costs except Depr. |
-5,469,264 |
|
|
EBITDA |
62,896,536 |
|
|
Depreciation |
-127,200 |
|
|
EBIT |
62,769,336 |
|
|
Interest Expense (net) |
-99,000 |
|
|
Pretax Income |
62,670,336 |
|
|
Income Tax |
-21,934,618 |
|
|
Net Income |
40,735,718 |
The following table contains Company Y’s balance sheet.
|
Balance Sheet |
2016 |
2017 |
|
Assets |
||
|
Cash and Equivalents |
23,928,030 |
|
|
Accounts Receivable |
23,928,030 |
|
|
Inventories |
10,254,870 |
|
|
Total Current Assets |
58,110,930 |
|
|
Property Plant and Equipment |
1,462,800 |
|
|
Total Assets |
59,573,730 |
|
|
Liabilities and Equity |
||
|
Accounts Payable |
23,928,030 |
|
|
Total Current Liabilities |
23,928,030 |
|
|
Debt |
900,000 |
|
|
Total Liabilities |
24,828,030 |
|
|
Stockholders' Equity |
||
|
Starting Stockholders' Equity |
8,000,000 |
|
|
Net Income |
40,735,718 |
|
|
Dividends |
-13,990,018 |
|
|
Stockholders' Equity |
34,745,700 |
|
|
Total Liabilities & Equity |
59,573,730 |
1. Before making any adjustments to balance Total Assets with Total Liabilities and Equity, what is Company Y s forecast value of Total Liabilities and Equity for 2017?"
2. How much are the net new financing for Company Y s on 2017?
For question one i know the answer is 108,349,142 and question 2 answer is -41,399,784. but how do i get those answers? Can someone please show the steps.
In: Finance
Use the following information on Company Y and perform pro-forma financial modeling using a planned expansion method to answers question (1) and (2). To do this assume that the percentage values with respect to sales of the (i) costs except depreciation, (ii) cash and equivalents, (iii) accounts receivable, (iv) inventories, and (v) accounts payable will stay fixed at the values corresponding for 2016.
Assume also that income tax will remain at 35% of the Pretax Income.
Consider Company Y. This firm sells a product for which in 2016 the total market size was of 1999000 units, of which Company Y owned a share of 30%.
Both, the total market size and Company Y’s market share are expected to grow at a 4% yearly rate for the next five years.
The price of the product is $114 in 2016 and is expected to remain at that price for the next years.
|
Market Analysis |
2016 |
2017 |
2018 |
2019 |
|
Market Size |
1,999,000 |
2,078,960 |
2,162,118 |
2,248,603 |
|
Market Share |
30% |
31% |
32% |
34% |
|
Production Volume |
599,700 |
|||
|
Sales Price: |
$ 114.00 |
|||
|
Sales |
In 2016, the outstanding debt of Company Y is $900000, for which the company makes yearly interest payments of 11%. The executives of Company Y are considering making a significant capital investment in 2017 of $2900000 to purchase new machinery. The company plans to finance this investment with a 30-year loan that makes yearly interest payments equivalent to 8% of its principal. The principal is paid when the loan matures.
The following table summarizes the debt and interest payment of Company Y.
|
Debt and Interest Table |
2016 |
2017 |
2018 |
|
|
Outstanding Debt |
900,000 |
900,000 |
3,800,000 |
|
|
New Net Borrowing |
2,900,000 |
|||
|
Interest on Debt |
||||
Currently, Company Y makes yearly expenditures on replacement capital investment of $90000. If the company makes the planned expansion it is decided the company will perform yearly expenditures on replacement capital investment of $325000. The current and the planned expenditures on replacement of capital investment will be financed by the company’s cash flow.
The following table indicates for 2016 Company Y’s values of i. opening book value, ii. capital investment, iii. depreciation, and iv. closing book value. The Table also indicates the 2017-2018 forecast values of capital depreciation if the planned expansion were to occur in 2017.
|
Fixed Assets & Capital Investment |
2016 |
2017 |
2018 |
|
Opening Book Value |
1,500,000 |
||
|
Capital Investment |
90,000 |
||
|
Depreciation |
-127,200 |
-356,224 |
-353,726 |
|
Closing Book Value |
1,462,800 |
The following table contains Company Y’s income statement.
|
Income Statement: |
2016 |
2017 |
|
Sales |
68,365,800 |
|
|
Costs except Depr. |
-5,469,264 |
|
|
EBITDA |
62,896,536 |
|
|
Depreciation |
-127,200 |
|
|
EBIT |
62,769,336 |
|
|
Interest Expense (net) |
-99,000 |
|
|
Pretax Income |
62,670,336 |
|
|
Income Tax |
-21,934,618 |
|
|
Net Income |
40,735,718 |
The following table contains Company Y’s balance sheet.
|
Balance Sheet |
2016 |
2017 |
|
Assets |
||
|
Cash and Equivalents |
23,928,030 |
|
|
Accounts Receivable |
23,928,030 |
|
|
Inventories |
10,254,870 |
|
|
Total Current Assets |
58,110,930 |
|
|
Property Plant and Equipment |
1,462,800 |
|
|
Total Assets |
59,573,730 |
|
|
Liabilities and Equity |
||
|
Accounts Payable |
23,928,030 |
|
|
Total Current Liabilities |
23,928,030 |
|
|
Debt |
900,000 |
|
|
Total Liabilities |
24,828,030 |
|
|
Stockholders' Equity |
||
|
Starting Stockholders' Equity |
8,000,000 |
|
|
Net Income |
40,735,718 |
|
|
Dividends |
-13,990,018 |
|
|
Stockholders' Equity |
34,745,700 |
|
|
Total Liabilities & Equity |
59,573,730 |
1. Before making any adjustments to balance Total Assets with Total Liabilities and Equity, what is Company Y s forecast value of Total Liabilities and Equity for 2017?"
2. How much are the net new financing for Company Y s on 2017?
In: Accounting
Use the following information on Company Y and perform pro-forma financial modeling using a planned expansion method to answers question (1) and (2). To do this assume that the percentage values with respect to sales of the (i) costs except depreciation, (ii) cash and equivalents, (iii) accounts receivable, (iv) inventories, and (v) accounts payable will stay fixed at the values corresponding for 2016.
Assume also that income tax will remain at 35% of the Pretax Income.
Consider Company Y. This firm sells a product for which in 2016 the total market size was of 1999000 units, of which Company Y owned a share of 30%.
Both, the total market size and Company Y’s market share are expected to grow at a 4% yearly rate for the next five years.
The price of the product is $114 in 2016 and is expected to remain at that price for the next years.
|
Market Analysis |
2016 |
2017 |
2018 |
2019 |
|
Market Size |
1,999,000 |
2,078,960 |
2,162,118 |
2,248,603 |
|
Market Share |
30% |
31% |
32% |
34% |
|
Production Volume |
599,700 |
|||
|
Sales Price: |
$ 114.00 |
|||
|
Sales |
In 2016, the outstanding debt of Company Y is $900000, for which the company makes yearly interest payments of 11%. The executives of Company Y are considering making a significant capital investment in 2017 of $2900000 to purchase new machinery. The company plans to finance this investment with a 30-year loan that makes yearly interest payments equivalent to 8% of its principal. The principal is paid when the loan matures.
The following table summarizes the debt and interest payment of Company Y.
|
Debt and Interest Table |
2016 |
2017 |
2018 |
|
|
Outstanding Debt |
900,000 |
900,000 |
3,800,000 |
|
|
New Net Borrowing |
2,900,000 |
|||
|
Interest on Debt |
||||
Currently, Company Y makes yearly expenditures on replacement capital investment of $90000. If the company makes the planned expansion it is decided the company will perform yearly expenditures on replacement capital investment of $325000. The current and the planned expenditures on replacement of capital investment will be financed by the company’s cash flow.
The following table indicates for 2016 Company Y’s values of i. opening book value, ii. capital investment, iii. depreciation, and iv. closing book value. The Table also indicates the 2017-2018 forecast values of capital depreciation if the planned expansion were to occur in 2017.
|
Fixed Assets & Capital Investment |
2016 |
2017 |
2018 |
|
Opening Book Value |
1,500,000 |
||
|
Capital Investment |
90,000 |
||
|
Depreciation |
-127,200 |
-356,224 |
-353,726 |
|
Closing Book Value |
1,462,800 |
The following table contains Company Y’s income statement.
|
Income Statement: |
2016 |
2017 |
|
Sales |
68,365,800 |
|
|
Costs except Depr. |
-5,469,264 |
|
|
EBITDA |
62,896,536 |
|
|
Depreciation |
-127,200 |
|
|
EBIT |
62,769,336 |
|
|
Interest Expense (net) |
-99,000 |
|
|
Pretax Income |
62,670,336 |
|
|
Income Tax |
-21,934,618 |
|
|
Net Income |
40,735,718 |
The following table contains Company Y’s balance sheet.
|
Balance Sheet |
2016 |
2017 |
|
Assets |
||
|
Cash and Equivalents |
23,928,030 |
|
|
Accounts Receivable |
23,928,030 |
|
|
Inventories |
10,254,870 |
|
|
Total Current Assets |
58,110,930 |
|
|
Property Plant and Equipment |
1,462,800 |
|
|
Total Assets |
59,573,730 |
|
|
Liabilities and Equity |
||
|
Accounts Payable |
23,928,030 |
|
|
Total Current Liabilities |
23,928,030 |
|
|
Debt |
900,000 |
|
|
Total Liabilities |
24,828,030 |
|
|
Stockholders' Equity |
||
|
Starting Stockholders' Equity |
8,000,000 |
|
|
Net Income |
40,735,718 |
|
|
Dividends |
-13,990,018 |
|
|
Stockholders' Equity |
34,745,700 |
|
|
Total Liabilities & Equity |
59,573,730 |
1. Before making any adjustments to balance Total Assets with Total Liabilities and Equity, what is Company Y s forecast value of Total Liabilities and Equity for 2017?"
2. How much are the net new financing for Company Y s on 2017?
For question one i know the answer is 108,349,142 and question 2 answer is -41,399,784. but how do i get those answers? Can someone please show the steps.
In: Accounting
Wage and Tax Statement Data on Employer FICA Tax
Ehrlich Co. began business on January 2, 20Y8. Salaries were paid to employees on the last day of each month, and social security tax, Medicare tax, and federal income tax were withheld in the required amounts. An employee who is hired in the middle of the month receives half the monthly salary for that month. All required payroll tax reports were filed, and the correct amount of payroll taxes was remitted by the company for the calendar year. Early in 20Y9, before the Wage and Tax Statements (Form W-2) could be prepared for distribution to employees and for filing with the Social Security Administration, the employees' earnings records were inadvertently destroyed.
None of the employees resigned or were discharged during the year, and there were no changes in salary rates. The social security tax was withheld at the rate of 6.0% and Medicare tax at the rate of 1.5%. Data on dates of employment, salary rates, and employees’ income taxes withheld, which are summarized as follows, were obtained from personnel records and payroll records:
Employee |
Date First Employed |
Monthly Salary |
Monthly Income Tax Withheld |
||
| Arnett | Jan. 2 | $3,500 | $490 | ||
| Cruz | Oct. 1 | 5,500 | 990 | ||
| Edwards | Apr. 16 | 2,600 | 325 | ||
| Harvin | Nov. 1 | 2,200 | 275 | ||
| Nicks | Jan. 16 | 5,650 | 1,271 | ||
| Shiancoe | Dec. 1 | 3,800 | 589 | ||
| Ward | Feb. 1 | 6,300 | 1,355 | ||
Required:
1. Calculate the amounts to be reported on each employee's Wage and Tax Statement (Form W-2) for 20Y8.
Note: Round amounts to the nearest whole dollar and enter all amounts as positive values.
Employee |
Gross Earnings |
Federal Income Tax Withheld |
Social Security Tax Withheld |
Medicare Tax Withheld |
||||
| Arnett | $ | $ | $ | $ | ||||
| Cruz | ||||||||
| Edwards | ||||||||
| Harvin | ||||||||
| Nicks | ||||||||
| Shiancoe | ||||||||
| Ward | ||||||||
| $ | $ | |||||||
2. Calculate the following employer payroll taxes for the year: (a) social security; (b) Medicare; (c) state unemployment compensation at 5.4% on the first $10,000 of each employee’s earnings; (d) federal unemployment compensation at 0.6% on the first $10,000 of each employee’s earnings; (e) total.
Note: Round amounts to the nearest whole dollar and enter all amounts as positive values.
| (a) | $ |
| (b) | |
| (c) | |
| (d) | |
| (e) | $ |
Feedback
Consider each employee's date of hire. Remember there is a limit on how much the employer pays for state and feder
In: Accounting
tow conducting cones (θ = π/10 and θ = π/6) of infinite extent are separated by an infinitesimal gap at r = 0. If V(θ = π/10) = 0 and V(θ = π/6) = 50 V, find V and E between the cones. Solution:
In: Electrical Engineering
Hands-on Lab: Air Resistance and Free Fall Name(s): Date: Please use a font color other than black, red or green for your answers. Theory: for several centuries, it was believed that heavy objects fall to the earth at a faster rate than lighter ones. Galileo (1564-1642) performed experiments to show that this was not true. He showed that it was possible for light objects to fall at the same rate as their heavy counterparts. Please watch the following videos for a review. https://www.youtube.com/watch?v=_Kv-U5tjNCY https://www.youtube.com/watch?v=feFw8Ygn3fk https://www.youtube.com/watch?v=aRhkQTQxm4w https://www.youtube.com/watch?v=_mCC-68LyZM We now know that in the absence of air resistance, all objects regardless of mass, size or shape, fall at the same rate when dropped from the same height. This was demonstrated on the Moon (where there is no atmosphere, and therefore no air resistance) by the Apollo 15 mission in 1971, as shown in this video: https://www.youtube.com/watch?v=ZVfhztmK9zI The air resistance an object encounters depends on the object’s surface area and its speed. The air resistance is directly proportional to the object’s surface area. As the object’s surface area increases, so does the air resistance it encounters. A light object with a large surface area such as a flat piece of paper will encounter significant air resistance as it falls. This air resistance is relatively large compared to the weight of the paper and will oppose the paper’s motion causing it to fall at a slower rate or with a smaller acceleration. If we were to somehow remove the air resistance the paper encounters (for example, by dropping it in a vacuum), then the paper would fall at the same rate as a heavier compact object such as a book. A heavier object with the same surface area as the paper, such as a book, on the other hand, will encounter a relatively small air resistance compared to its weight, and will fall at a faster rate or with a larger acceleration compared to the paper. In this lab, we will explore the above concepts. Materials needed: one sheet of letter-sized paper (8.5 x 11 inches), a heavy book of the same size, or a book and paper of matching size - that is having similar lengths and widths. Experiment 1: drop a sheet of paper and a book side by side from the same height at the same time. Important: ensure there are no strong air currents such as those produced by a fan or air conditioner while doing these experiments. Observe what you see and answer the following questions. Please select (highlight in a different color), the best answer from the choices provided. 1. In Experiment 1 we see that a) the sheet of paper falls at the same rate as the book and lands at exactly the same time the book does. b) the sheet of paper falls at a faster rate and hits the floor before the book does. c) the sheet of paper falls at a slower rate and hits the floor after the book does. d) the sheet of paper moves upwards towards the roof, while the heavier book falls straight down to the floor. 2. The observations in Experiment 1 can be best explained as follows: a) The air resistance felt by the paper is small compared to its weight, it therefore does not slow down as much. The air resistance felt by the book is large compared to its weight, it therefore slows down more than the paper and falls at a slower rate than the paper. b) Both the paper and the book feel the same amount of air resistance compared to their weights. Their motion is not affected by air resistance at all. That is why they both hit the floor at the same time. c) The paper is much lighter than the book. This causes the air to push upwards on the paper, and downwards on the book. Therefore, the paper and the book move in opposite directions d) The air resistance felt by the paper is large compared to its weight, this slows it down. The air resistance felt by the book is small compared to its weight, it therefore does not slow down as much. Therefore, the book hits the floor before the paper. Experiment 2: place the paper beneath the book (against the book’s lower surface) and drop the book and paper at the same time. Observe carefully, and answer the following questions. Please select (highlight in a different color), the best answer from the choices provided. 3. In Experiment 2 we see that a) the book pushes the paper out of the way and falls to the floor several seconds before the paper does. b) the paper and the book fall at the same rate and hit the floor at the same time. c) the paper accelerates to the floor at a much faster rate than the book, and falls several seconds earlier than the book. d) the paper accelerates to the floor at a much slower rate than the book, and falls several seconds after the book. 4. The observations in Experiment 2 can be best explained as follows: a) since the paper is below the book, it has a distance advantage over the book, it needs to travel a shorter distance to the floor than the book does. Therefore, the paper speeds up faster than the book, and hits the floor several seconds before the book does. b) the greater weight of the book pushes the paper out of the way, and the book falls straight down due to gravity due to its greater weight, while the much lighter paper remains floating in the air. c) the greater weight of the book pushes down on the paper, overcoming the air resistance in the path of the paper, and therefore allowing it to fall at the same rate. d) although the paper and book are released at the same time, the paper is lighter and therefore experiences a smaller gravitational acceleration. That is why the paper hits the floor several seconds after the book does. Experiment 3: drop the book and paper, but this time place the paper on top of the book. Observe carefully, and answer the following questions. Please select (highlight in a different color), the best answer from the choices provided. 5. In Experiment 3 we see that a) the paper being much lighter is left floating at the same place, the book accelerates downwards and hits the floor, while the paper remains floating hardly moving at all. b) the book accelerates to the floor at a much faster rate than the paper, and hits the floor several seconds earlier than the paper. d) the paper accelerates to the floor at a much faster rate than the book, and hits the floor several seconds earlier the book. d) the paper and the book fall at the same rate and hit the floor at the same time. 6. The observations in Experiment 3 can be best explained as follows: a) the paper is several times lighter than the book, therefore the acceleration due to gravity the paper experiences is several times greater than what the book experiences. Therefore, the paper hits the floor several seconds earlier than the book. b) the lightness of the paper enables it to float in the air, the book being much heavier is pulled down by the force of gravity immediately, thus the book falls while the paper floats. c) the book falls through the air before the paper and as it falls it clears the air resistance in the path of the paper, allowing the paper to fall at the same rate. d) the book is several times heavier than the paper, therefore the acceleration due to gravity the book experiences is several times greater than that what the paper experiences. Therefore, the books hits the floor several seconds earlier than the paper. Experiment 4: crumple the paper to make a compact ball or wad. Now hold the paper and the book side by side, and drop them both from the same height at the same time. Observe carefully, and answer the following questions. Please select (highlight in a different color), the best answer from the choices provided. 7. In Experiment 4 we see that a) the paper starts to spin while falling, this slows it down and it hits the floor several seconds after the book does. b) the paper and the book fall at the same rate and hit the floor at the same time. c) the book accelerates to the floor at a much faster rate than the paper, and hits the floor several seconds earlier than the paper. d) the paper accelerates to the floor at a much faster rate than the book, and hits the floor several seconds earlier the book. 8. The observations in Experiment 4 can be best explained as follows: a) the circular shape of the wad of paper creates an axis of rotation through its center. As it falls, the air pushes up on the paper causing it to rotate about this axis. This drains energy from the paper causing it to fall at a slower rate. Therefore, the paper hits the floor several seconds after the book. b) crumpling up the sheet of paper into a wad reduces its surface area. Due to its smaller surface area, the wad of paper experiences a much smaller air resistance. Since it has the same acceleration due to gravity as the book, it falls at the same rate as the book and hits the floor at the same time. c) the book is several times heavier than the paper, therefore the acceleration due to gravity the book experiences is several times greater than what the paper experiences. The shape of the paper has no effect at all, and thus the book hits the floor several seconds earlier than the paper. d) the paper is several times lighter than the book, and it is also now smaller in size than the book, therefore the acceleration due to gravity the paper experiences is several times greater than that which the book experiences. Therefore, the paper hits the floor several seconds earlier than the book. Multiple choice questions continued: Please select (highlight in a different color), the best answer from the choices provided. 9. From these experiments we can see that since the paper and book have different masses, a) the acceleration due to gravity that falling objects experience increases proportionally with mass. b) the acceleration due to gravity that falling objects experience decreases proportionally with mass. c) the acceleration due to gravity that falling objects experience increases with mass, but the increase is not proportional to the object’s mass, it is described by another more complicated equation. d) the acceleration due to gravity that falling objects experience does not depend on mass. 10. From these experiments we can see that a) lighter objects fall faster than heavier objects, regardless of how the objects are shaped. b) heavier objects fall faster than lighter objects, regardless of how the objects are shaped. c) in the absence of air resistance, all objects regardless of mass, shape and size, fall at the same rate. d) air resistance is so small in everyday life that it does not affect the motion of light objects such as sheets of paper or feathers and leaves when they fall down to the earth. Problem 1: a) An eagle with a mass of m = 7 kg while high up in the air, falls straight down vertically against an air resistance of R = 70 N. Find the acceleration of the eagle if the force of gravity pulling it down is equal to the air resistance R, in other words if mg = 70 N. (Note: please use g = 10 m/s2 in this problem). Hint: use the equation for Newton’s second law to find the acceleration: (for more information please see section 4.6 of your textbook) Net force = (mass)(acceleration) or in symbols: Fnet = ma We rearrange this equation to solve for the acceleration a: a = Fnet/m In this case if we take the downward direction as positive, then the force of gravity will have a positive sign and the air resistance which is acting upwards in the opposite direction to the force of gravity, will have a negative sign. In the above equation, Fnet is the sum of all forces acting on the object. In this problem, Fnet is the force of gravity (mg) minus the air resistance (R). We can write this in equation form as: Fnet = mg – R We substitute this term for Fnet in the above equation for the acceleration a, to get: a = (mg – R)/m Substitute the given values for all terms on the right hand side to find the acceleration a. Please show the values you substituted, your answer and the units for the answer. Answer: b) Based on your calculated value of the acceleration, what can you say about the speed of the eagle’s descent? Is the eagle moving at all? Justify your answer. Answer: Please enter the names of all group members at the top of this document. Each member of the group must submit a copy of the lab report through their individual eCampus account.
In: Physics
Suppose that X1,X2,X3,X4 are independent random variables with common mean E(Xi) =μ and variance Var(Xi) =σ2. LetV=X2−X3+X4 and W=X1−2X2+X3+ 4X4.
(a) Find E(V) and E(W).
(b) Find Var(V) and Var(W).
(c) Find Cov(V,W).(
d) Find the correlation coefficientρ(V,W). Are V and W independent?
In: Statistics and Probability
Suppose that X1,X2,X3,X4 are independent random variables with common mean E(Xi) =μ and variance Var(Xi) =σ2. LetV=X2−X3+X4 and W=X1−2X2+X3+ 4X4.
(a) Find E(V) and E(W).
(b) Find Var(V) and Var(W).
(c) Find Cov(V,W).(
d) Find the correlation coefficientρ(V,W). Are V and W independent?
In: Statistics and Probability