If u(t) = < sin(8t), cos(4t), t > and v(t) = < t, cos(4t), sin(8t) >, use the formula below to find the given derivative.

d/(dt)[u(t)* v(t)] = u'(t)* v(t) + u(t)*  v'(t)

d/(dt)[u(t) x v(t)] = <.______ , _________ , _______>

If u(t) = < sin(5t), cos(5t), t > and v(t) = < t, cos(5t), sin(5t) >, use the formula below to find the given derivative.

d/dt[ u(t) * v(t)] = u'(t) * v(t) + u(t)* v'(t)

d/dt [ u(t) x v(t)] = ?

Draw a probability tree diagram for the following experiment: Suppose there are five balls in an urn. Three are red and two are blue. We will select a ball, note the color, and, without replacing the first ball, select a second ball. What is the sample space of this

experiment? What is the associated probability distribution in this

experiment?

You collected some ecological samples in a field experiment in west Texas. Collected were soil samples to determine the amount of nutrients that would need to be applied to sustain a desired level of crop growth. The observation was the amount of nutrient the soil contained. Samples were taken from 100 different locations. It was found that the nutrient data are normally distributed. The mean value of the samples was 16 units (the exact name for the units do not really matter in this problem, so just call them “units”). The sample standard deviation of the samples is 3.5 units.

a. estimate the probability range for the Confidence Interval of the Mean (95% confidence) for the parameters given above.

b. What is the interpretation of the Confidence Interval of the Mean?

c. Consider the experiment was performed again in a second year, however, this time only 15 sites were sampled. The mean value in year two was found to be 14.5 units and the sample standard deviation was found to be 2.2 units. Using equation 3.16, estimate the probability ranges for the 90%, 95%, and 99% confidence intervals of the mean.. You will need to estimate THREE probability ranges to answer this question. One range for 90%; one range for 95%, and one range for 99%.

d. Describe how the probability range changes as the confidence interval increases. e. What is the probability range for the 50% confidence?

f. If you were to repeat the experiment described initially (100 samples per year) for twenty years, what percentage of the years would you expect the true mean value to be bracketed by the 50% confidence interval? Additionally, what percentage of the years would you expect the true mean value to be bracketed by the 95% confidence interval

Edit: Please show work on how to calculate Confidence intervals.

Loblaw Companies Limited (Loblaw) is a Canadian food retailer that owns 1,000 corporate and

franchise supermarkets that operate under 22 regional and market segment banners. Loblaw

brands include President’s Choice, No Name, Joe Fresh, T&T, Everyday Living, Exact,

Seaquest, Azami, and Teddy’s Choice. Loblaw is a public company, and its shares are listed on

the Toronto stock exchange.

Below you will find the 2016 and 2015 consolidated balance sheets (statement of financial

position). You will also find some excerpts from its notes section. All amounts are in millions of

Canadian dollars.

The fiscal year of the Company ends on the Saturday closest to December 31. Any references

below to 2015 relate to the fiscal year ended January 2, 2016, and any references below to 2016

relate to the fiscal year ended December 31, 2016.

REQUIRED:

a) Calculate the following ratios for both 2016 and 2015:

a. Current ratio

b. Quick ratio

b) (3marks) Based on your calculation in a), comment on the liquidity of Loblaw and how/if

it has changed between fiscal year 2015 and 2016.

c) Cost of goods sold is $33,213 million for 2016 and $32,846 million for 2015.

Inventory balance was $4,309 million for 2014. Calculate the followings for both 2016

and 2015:

a. Inventory turnover

b. Days to sell inventory

d) Based on the brief description of Loblaw and your understanding of retail

business operations, do you think your calculations in c) are reasonable and why?

e) Use the information below from Note 12 “Inventories” and answer the

following:

a. Prepare a journal entry to record the write-down of inventories.

b. Give two examples and explain why a write-down of inventories is necessary for

Loblaw.

Note 12 Inventories

For inventories recorded as at December 31, 2016, the Company recorded $22 million as

an expense for the write-down of inventories below cost to net realizable value. The

write-down was included in cost of merchandise inventories sold.

f) Calculate the debt-to-equity ratio for 2016. Explain what this ratio measures

and why creditors want to see this ratio.

g) Answer the following questions:

a. Loblaw has unlimited number of authorized shares on each class of shares. Why

do many companies today prefer to have an unlimited authorized number of

shares?

b. List and explain three differences between common shares and preferred shares.

c. Based on the information available, are you able to determine the net income for

the year ended December 31, 2016? Show your detailed calculations or explain

why not.

d. The unit price for Loblaw’s common shares was $70.33 on December 31, 2016

and $63.92 on December 31, 2015. Note 24 “Share Capital” (not provided)

indicated the following:

2016 2015

Dividends declared per share ($):

Common Share $1.03(2016)   $0.0995 (2015)

What is the dividend yield for common shareholders in each of 2016 and 2015? If

you are a common shareholder, are you happy to see the change and why? (3

marks)

Loblaw Companies Limited

Consolidated Balance Sheet

As of December 31

(in millions of Canadian Dollars)

2016 2015

Assets

Current Assets

Cash and cash equivalents $ 1,314 $ 1,018

Short term investments 241 64

Accounts receivable 4,048 4,115

Inventories 4,371 4,322

Prepaid expenses and other assets 230 336

Total Current Assets $ 10,204 $ 9,855

Non-current Assets

Fixed assets 11,592 11,558

Intangible assets 8,745 9,164

Goodwill 3,895 3,780

Total Non-current Assets $ 24,232 $ 24,502

Total Assets $ 34,436 $ 34,357

Liabilities

Current Liabilities

Bankindebtedness $ 115 $ 143

Trade payables 5,091 5,106

Provisionsand other liabilities 1,736 1,973

Total Current Liabilities $ 6,942 $ 7,222

Non-Current liabilities

Long term debt and other liabilities $ 14,466 $ 14,011

Total liabilities $ 21,408 $ 21,233

Equity

Share capital $ 7,913 $ 8,072

Retained Earnings 4,944 4,914

Contributed surplus 112 102

Accumulated other comprehensive

income 33 23

Non-controlling interest 26 13

Total Equity $ 13,028 $ 13,124

Total Liabilities and Equity $ 34,436 $ 34,357

A +7.50 μC point charge is sitting at the origin.

What is the radial distance between the 500 V equipotential surface and the 1000 V surface?

What is the distance between the 1000 V surface and the 1500 V surface?

1) True or False?

1. In multinomial logistic regression analysis, the model fit is given by the value of R-squared.

2. In linear regression analysis, the overall significance test is an F test.

3. In logistic regression analysis, the overall significance test is an F test.

4. When building a model for regression analysis, the type of data for the outcome variable

   guides you to choose linear, logistic, or multinomial logistic.

5. Two variables that covary might not have a causal relationship.

6. Causation implies correlation.

2) Which one should be analyzed by multinomial logistic regression analysis? Select all correct cases.

• 1) Dependent V: Attitude toward immigration policy (strongly agree/agree/disagree/strongly

  disagree). Independent V: Gender (female/male).

• 2) Dependent V: College major (Business/Biology/Economics/Psychology). Independent V:

  High school GPA (points)

• 3) Dependent V: Individual preference about automobile brand (Ford/Kia). Independent V: Age

• 4) Dependent V: A country’s trade policy (low tariff/moderate tariff/high tariff). Independent V: GDP ($)

• 5) None of them is correct.

3) Which one should be analyzed by logistic regression analysis? Select all correct cases. No partial credit is given.

• 1) Dependent V: Attitude toward gun policy (Agree/Disagree). Independent V: Gender (female/male).

• 2) Dependent V: College major (Business/Economics/Psychology). Independent V: Father’s major (Business/Economics/Psychology)

• 3) Dependent V: Individual preference about automobile brand (Ford/Kia). Independent V: Age

• 4) Dependent V: Starting salary (QAR). Independent V: College major (Business/Biology)

• 5) None of them is correct.

Robert Millikan was awarded the Nobel Prize for his experiment (The Millikan oil-drop experiment), which demonstrated that:

a) Describe an experiment that points to the particle property of light.

b) Describe an experiment that describes the wave property of light.