Given two graphs G = [V ; E] and G0 = [V 0 ; E0 ], and an isomorphism, f : V → V 0 , and making direct use of the formal definition for isomorphism:

(a) Explain why G and G0 must have the same number of vertices.

(b) Explain why G and G0 must have the same number of edges.

(c) Explain why G and G0 must have the same degree sequences.

(d) Given two vertices, u, v ∈ V explain why: u is connected to v → f(u) is connected to f(v)

Note: Problems that ask you to “explain” are asking for responses that can be less formal than problems that ask you to “prove”. Nonetheless, responses need to be sufficiently precise and based on definitions and theorems as given in the text. Explanations should be concise, but care must be taken to ensure that explanations are at an appropriate level of detail and will be clear to the intended reader.

A graph is G is semi-Eulerian if there are distinct vertices u, v ∈ V (G), u =v such
that there is a trail from u to v which goes over every edge of G. The following
sequence of questions is towards a proof of the following:
Theorem 1. A connected graph G is semi-Eulerian (but not Eulerian) if and only
if it has exactly two vertices of odd degree.
Let G be semi-Eulerian with a trail t starting at a vertex u₀ and ending at a vertex
v₀ Let G ⁰ be a graph obtained by adding an edge e₀ joining u₀ and v₀ , so that
G ⁰ − e = G.
(a) Prove that given a semi-Eulerian trail t in G from v₀ to u₀ , it is possible to
construct a Eulerian trail in G₀.
(b) Prove that given an Eulerian trail in G 0 it is possible to construct a semi-Eulerian
trail in G.
(c) Prove Theorem 1.

Write a program to calculate fees that must be paid by a student at a State university using the following

values:

Each semester unit

$90.00

Regular room charge per semester

$200.00

Air conditioned room

$250.00

Food charge for the semester

$400.00

Matriculation fee (all students)

$30.00

Diploma fee (if graduating student)

$35.00

Input student ID number (one integer containing four digits), the type of room (regular or air conditioned), units, and whether or not the student is graduating. Output an itemized list of student

fees and a total of the student fee owed. Check for students taking more than 21 units and students

taking fewer than 12 units. Output a message to students enrolled in more than 21 units (this is not

allowed, do not process this data) or fewer than 12 units (warn them that they are not full time students

but do process this data).

Input

Three initials of the individual, student identification number, type of room (R, A), number of units, and

whether or not student is graduating (Y/N).

Sample

Output

Student ID

12345

Units

15

Charge for units

1350.00

Room charge

200.00

Food charge

400.00

Matriculation Fee

30.00

Total semester charges

1980.00

Adequately check all entered data for validity. Use adequate test data to process all valid data and use

representative data to show how your program handles invalid data. .

Label all output clearly.

Be sure your output contains user prompts and what was entered by the user in addition to the results

of your program processing.

BE SURE TO INCLUDE ADEQUATE ERROR CHECKING IN YOUR PROGRAM A

ND ERROR DATA WHEN YOU

RUN THE

PROGRAM TO DEMONSTRATE ERROR CHECKING.

BUSI 1110

Summer 2020 Weekly Assignment

Assignment number

9
General Information

Description

Chapter

Motivating Satisfying and Leading Employees

Due date

Prior to start of following week’s session

Students will answer a list of assigned questions. In order to receive full credit for each question, students need to sufficiently support answers with relevant application of course concepts and theories. All sources should be correctly cited using APA guidelines.

Report guidelines

Students will require to submit their weekly assignments online (Moodle) on or before the due date to location created under each week. All files should be submitted using pdf extension labelling the file name using the format <last name>_<first name>_<assignment number>.pdf. Students could also create other modes of submission such as power point, graphics, video clips etc..., in such events please speak to the instructor for uploading instructions. All submissions should be properly formatted, checked for spelling, grammar and use professional language. Students will use Font style Times New Roman and size 11 with a spacing of 1.5

Assignment – Week 9

1. Reflecting the motivation theories discussed, which theory do you think is most suitable to motivate?

a. Fast food chain employee b. Accountant

Explain your reasoning by applying to the motivational theory for positions a) and b)? (8 points)

2. Identify the hygiene and motivational factors for following positions

   1. Accountant (3)

   2. University student following BUSI 1110 (3)

   3. Cashier at a super market (3)

3. Following assignment guidelines, reliable and sufficient research performed to support the argument. Sources cited to support statements. Clear and concise writing (5 points)

Total Points 22 – (Percentage 5%)

Revision May 2020

Page 1

Let the function c(v) model the gas consumption (in liters/km) of a car going at velocity v (in kilometers/hour). In other words, c(v) tells you how many liters of gas the car uses to go 1 km, if it is going at velocity v.

You find that (80) 0.04 and '(80) 0.0004

1. Let the function d(v) model the distance the same car goes on 1 L of gas at velocity v.

a. Express the relationship between c(v) and d(v) in an equation. [4 pts]

b. Find d(80) and d’(80). (Hint: Find the general d’(v) first.) [4 pts]

c. Interpret your result for d’(80) in a sentence. (That is, “When the car is travelling at 80 kph ….” ) [4 pts] (Even if you couldn’t get part b, you can still tell me what d’(80) means about the car.) [5 pts]

Using the data on 4137 college students, the following equation was estimated

Using the data on 4137 college students, the following equation was estimated

by OLS

colgpai =β0 +β1hsperci +ui, i=1,2,...,4137

where colgpa is measured on a four-point scale and hsperc is the percentile in the high school graduating class (defined so that, for example, hsperc = 5 means the top 5 percent of the class).

  Coefficients:

Estimate Std. Error t value Pr(>|t|) (Intercept) 2.9803872 0.0141800 210.2 <2e-16 *** hsperc -0.0170349 0.0005585 -30.5 <2e-16 ***

---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.5952 on 4135 degrees of freedom Multiple R-squared: 0.1836, Adjusted R-squared: 0.1834 F-statistic: 930.2 on 1 and 4135 DF, p-value: < 2.2e-16

1. (i) Why does it make sense for the coefficient on hsperc to be negative?

2. (ii) Interpret the coefficient of hsperc.

3. (iii) Is it statistically different than zero at the 5% level?

4. (iv) What other factors do you think might be relevant for explaining colgpa?

5. (v) Are these other factors likely to be correlated with hsperc? If so, what can you say about the interpretation of the coefficients on hsperc?

Please show your work, thank you!

Which of the following are consequences of the Central Limit Theorem? I'm not sure why II and III are correct and the others are not.

I) A SRS of resale house prices for 100 randomly selected transactions from all sale

transactions in 2001 (in Toronto) will be obtained. Since the sample is large, we

should expect the histogram for the sample to be nearly normal.

II) We will draw a SRS (simple random sample) of 100 students from all University

of Toronto students, and measure each person’s cholesterol level. The average

cholesterol level for the sample should be approximately normally distributed.

III) We want to estimate the proportion of Ontario voters who intend to vote for the

Liberal party in the next election, and decide to draw a SRS of 400 voters. The

percentage of the people in the sample who will say that they intend to vote

Liberal is approximately normally distributed.

IV) We will draw a SRS of 100 adults from the Canadian military, and count the

number who have the AIDS virus. The number of individuals in the sample who

will be found to have the AIDS virus should be approximately normally

distributed.

V) We are interested in the average income for all Canadian families for 2001. The

mean income for all Canadian families should be approximately normal, due to

the large number of families in the population.

Calculate a geometric series

1.For v greater than 0 and less than 1, what is the Sum(v^i) for i = 1 to 100?

2.For v greater than 0 and less than 1, what is the Sum(v^i) for i = 1 to infinity?

3.Let v = 1/(1+r). State the answer to question 2 in terms of r.

You have the following information on return on the stocks of Target (T), Macy's (M),and Best Buy (B)

Target (T) Macy's (M) Best Buy (B)

$6 $3 $11

$7 $8 $5

$3 $5 $8

$4 $8 $4

What are the variances and standard deviations of the returns on the three stocks?

What is the covariance of the returns on T and M?

What is the covariance of M and B?

1. There are multiple sections of 3 classes that have to be offered. Class A has an average enrollment of 120 per term. Class B has an average of 100 students per term and Class C has an average enrollment of 85 students per term. The rules for opening and cancelling sections are as follows:

1. Any section of this class must have at least 15 students to run. Any less than this and the section is cancelled.
2. Each section has a maximum enrollment of 45 students.
3. A new section will open up when the previous section (s) have an average enrollment of 40.
4. A new section will open up to accommodate department regulations on staffing.

For each class run a simulation using your chosen distribution and determine the following:

1. Given that anytime enrollment in a class reaches over 175 students, there will be 5 sections of class, what is the probability of this happening with each class?

Class A =

Class B =

Class C =

ii)    Given that anytime enrollment in a class reaches 135 students to 180 students, there will be 4 sections of class, what is the probability of this happening with each class?

Class A =

Class B =

Class C =

3. Given that anytime enrollment in a class reaches 95 students to 120 students, there will be 3 sections of class, what is the probability of this happening with each class?

Class A =

Class B =

Class C =

4. If a third section of Class C opens when enrollment goes above 80, and it gets cancelled when enrollment is below 95, How often does the third section get cancelled? (Enrollment is between 80 and 95)

5. Based upon the probabilities you found above, how many sections of each class do you offer? 2, 3, 4 or 5?

Class A =

Class B =

Class C =

Using the number of sections, you found above create a schedule that maximizes the quality of teaching these classes. Full Time profs must teach 3-4 sections. Part time profs must teach 1-2 sections.

6. What is the minimum number of sections (total) that need to be offered?

7. What is the maximum number of sections (total) you can offer?

Professor Data is below:

Given your answers in part v, and possibly modified by your answers in part vi, what is the quality score of your department’s teaching?

How many sections of each class do the professors teach?