find the general solution of the given differential equation.

1. y''+2y'−3y=0

2.  6y''−y'−y=0

3.  y''+5y' =0

4.  y''−9y'+9y=0

The following independent events for Repertory Theatre Ltd. during the year ended December 31 2018, require a transaction journal entry or an adjusting journal entry, or both. The company adjusts its accounts annually.

1. Supplies on hand amounted to $1,500 at the beginning of the year. On March 1, additional supplies were purchased for $4,250 cash. At the end of the year, a physical count showed that supplies on hand amounted to $1,000.

2. The theatre owns a vehicle that was purchased on January 2 2018, for $120,000. The vehicle's estimated useful life is 4 years.

3. The theatre has nine plays each season, which starts in September 2018 and ends in May 2019 (one play per month). Season tickets sell for $360. On August 2, 600 season tickets were sold for the upcoming 2018-2019 season. The theatre credited Unearned Revenue for the full amount received on August 2 and uses a Ticket Revenue account to record revenue earned from season tickets.

4. On June 1, the theatre borrowed $30,000 from La Caisse Populaire Desjardins at an interest rate of 6%, to be repaid in one year. The interest is payable on the first day of each following month, and was last paid on December 1.

5. The total weekly payroll is $9,000, paid every Friday for employee salaries earned during the prior six-day workweek (Saturday - Thursday). This year, December 31 falls on Monday. Salaries were last paid (and recorded) on Friday, December 28 and will be paid next Friday, January 4.

6. Repertory Theatre rents a portion of its facilities for $600 a month to a local seniors' choir that uses the space for rehearsals. The choir's treasurer was ill during December, and on January.

7. the theatre receives a $1,200 cheque for both the amount owing for the month of December and the rent for the month of January. 7. Upon reviewing its books on December 31, the theatre noted that a telephone bill for the next month of December had not yet been received. A call to Bell Aliant determined that the telephone bill was for $1,125. The bill was paid on January 11. (Hint: use the Utilities Expense account for telephone services)

a) Prepare the journal entries to record the original transactions for items 1,2,3 and 4.

b) Prepare the year-end adjusting entries required for items 1 through 7 on December 31.

c) Record the subsequent cash transactions in January for (1) the interest paid on January 1 (item 4), (2) payment payroll on January 4 (item 5), (3) receipt of the rent on January 7 (item 6), and (4) payment of the telephone bill on January 11 (item 7)

Assume that you have a sample of n 1 equals 8​, with the sample mean Upper X overbar 1 equals 42​, and a sample standard deviation of Upper S 1 equals 4​, and you have an independent sample of n 2 equals 15 from another population with a sample mean of Upper X overbar 2 equals 34 and a sample standard deviation of Upper S 2 equals 5. What assumptions about the two populations are necessary in order to perform the​ pooled-variance t test for the hypothesis Upper H 0 : mu 1 equals mu 2 against the alternative Upper H 1 : mu 1 greater than mu 2 and make a statistical​ decision?

4. Construct a frequency distribution, find the summary statistics (including the quartiles) for customer age, and graph by each type of customer (regular or promotion). Comment on the shape of the distribution for each type and discuss similarities or differences if any. (Think whether you should create an ungrouped or grouped frequency distribution.) Label the graphs completely.

5. Construct a box-and-whisker plot and find the summary statistics (including the quartiles) for net sales by each type of customer (regular or promotion). Make sure that you format the x-axes on each plot and compare the plots using the same scale. Comment on the shape of the distribution for each type and compare.

Complete the following chi square test:Show all work.

Example Chi Sq.

40% of Americans say that their favorite pastime is sports, 40% say that it’s time with their family, and 20% name something else. A survey of your neighborhood finds that 10 people report a preference for sports, 15 for being with their families, and 5 something else. Do your neighbors differ from Americans overall?

Activity Observed Expected EF O-E (O-E)2 (O-E)2/E

Sport 10 .4 12 -2 4 .33

Fam 15 .4 12 3 9 .75

Other 5 .2 6 -1 1 .17

30 2 = ∑ (O-E)2/E = 1.25

Is Paris, Chicago, or NY the most romantic city?

City Observed Expected EF O-E (O-E)2 (O-E)2/E

Chicago 2 .33

NY 40 .33

Paris 58 .33

100 2 = ∑ (O-E)2/E =

Is there a significant correlation between these two sets of numbers?

Weight Time

46 44

55 27

61 24

75 24

64 36

75 36

71 44

59 44

64 120

67 29

A financial services company has a long list of potential projects to consider this year. Managers at this company must decide which projects to pursue and how to define the scope of the projects selected for approval. The company has decided to use a weighted scoring model to help in project selection, using criteria that map to corporate objectives. All projects selected must develop a WBS using corporate guidelines.

You are part of a team that will analyze proposals and recommends which projects to pursue. Your team has decided to create a weighted scoring model using the following criteria and weights:

• Criteria Weight 1
• Enhances new product development 20% 2
• Streamlines operations 20% 3
• Increases cross-selling 25% 4
• Has good NPV 35%

To determine the score for the last criterion, your team has developed the following scoring system:

• NPV is less than 0, the score is 0
• NPV is between 0 and $100,000, the score is 25
• NPV is between $100,000 and $200,000, the score is 50
• NPV is between $200,000 and $400,000, the score is 75
• NPV is above $400,000, the score is 100

The following is information for three potential projects:

• Project 1:
  • Scores for criteria 1, 2, and 3 are 10, 20, and 80, respectively
  • Estimated costs the first year are $500,000, and costs for years 2 and 3 are $100,000 each
  • Estimated benefits for years 1, 2, and 3 are $200,000, $400,000, and $600,000, respectively
• Project 2:
  • Scores for criteria 1, 2, and 3 are all 50
  • Estimated costs the first year are $700,000, and costs for the second year are $200,000
  • Estimated benefits for years 1 and 2 are $300,000 and $700,000, respectively
• Project 3:
  • Scores for criteria 1, 2, and 3 are 0, 50, and 80, respectively
  • Estimated costs the first year are $300,000, and costs for years 2, 3, and 4 are $100,000 each
  • Estimated benefits for years 1, 2, 3, and 4 are $0, $600,000, $500,000, and $400,000, respectively

• Develop a spreadsheet to calculate the NPVs and weighted scores for the three projects
• Use a 10 percent discount rate for the NPV calculations

Headland Clothiers Ltd.’s current dividend is $3.20. Dividends are expected to grow by 8 percent for years 1 to 3, 6 percent for years 4 to 7, and 2 percent thereafter. The required rate of return on the stock is 11 percent. What is the current stock price for Sunland? (Round intermediate calculations to 4 decimal places, e.g. 45.1771 and final answer to 2 decimal places, e.g. 45.17.)