The neighborhood of a vertex in a graph consists of the vertex itself, together with all vertices that are connected to it by an edge. Each graph has a variable xi associated with the i-th vertex, and the vertex has a known value that is equal to the sum of the variables for all neighborhood vertices. Start with a graph with 5 vertices forming a pentagon, with edges joining vertices 1 and 2, 2 and 3, 3 and 4, 4 and 5, and 5 and 1. Then draw an edge joining vertices 2 and 4, and an edge joining vertices 2 and 5. The known values at vertices 1 through 5 are, respectively, 2, 1, −1, 3, and 5.

(a) Find the augmented matrix for the system of equations satisfied by x₁, x₂, x₃, x₄, x_5.

This is a python question.

Write a function mult_table(n) that consumes a natural number n and returns the n+1 by n+1 multiplication table (where each entry in the inner list is equal to the product of which list it is and the inner list position number, or in other words, the product of the row and column numbers). Use accumulative recursion.

def mult_table(n)
'''
Returns the n+1 by n+1 multiplication table
  
mult_table: Nat => (listof (listof Nat))
  
Examples:
mult_table(0) => [[0]]
mult_table(1) => [[0, 0],
[0, 1]]
mult_table(2) => [[0, 0, 0],
[0, 1, 2],
[0, 2, 4]]
mult_table(5) => [[0, 0, 0, 0, 0, 0],
[0, 1, 2, 3, 4, 5],
[0, 2, 4, 6, 8, 10],
[0, 3, 6, 9, 12, 15],
[0, 4, 8, 12, 16, 20],
[0, 5, 10, 15, 20, 25]]
'''

No loops! Only accumulative recursion can be used!

Using the Motor Trend Cars Data Set, you would like to determine if there is a relationship between MPG (miles per gallon) and specific variables included in the data set.

1. Develop a correlation matrix using MPG (miles per gallon), HP (horsepower), WT (weight). Is the correlation between the variables MPG v HP significant? Perform the appropriate test and use a level of significance of 0.05
2. Fit a multiple regression model using MPG (miles per gallon) as the dependent variable and HP (horsepower), and WT (weight) as the independent variables. State your regression model.
3. Is the overall regression model significant? Conduct the appropriate hypothesis test for the significance of the overall regression model. Use a 0.05 level of significance.
4. Are the individual independent variables significant? Conduct the hypothesis tests for the significance of each independent variable at the= 0.05 level of significance.
5. What proportion of the variation in MPG is explained by the independent variables HP and WT?
6. Graph the residuals from the regression you developed in part (a). Do the regression assumptions appear to be appropriate given the residual plots? Explain your answer.

Using the Motor Trend Cars Data Set, you would like to determine if there is a relationship between MPG (miles per gallon) and specific variables included in the data set.

1. Fit a multiple regression model using MPG as the dependent variable and DISP, HP, and WT as the independent variables.  
2. Is the overall regression model significant?  Test at the α = 0.05 level of significance. State the null hypothesis, the alternative hypothesis =, the test statistic calculated and critical values and your test conclusion.  
3. Are all of the individual independent variables significant?  (Use a level of significance of 0.05 to conduct your tests).  State the null and alternative hypotheses, the test statistic critical and calculated values and the conclusion for each independent variable.  
4. Based on the results from parts b and c would you suspect that multicollinearity might be a problem in this case?  Support your answer by computing the variance inflation factors for each of the explanatory (independent) variables in your model.

Make a Console application

Language should be Visual Basic

You will be simulating an ATM machine as much as possible

Pretend you have an initial deposit of 1000.00. You will

Prompt the user with a Main menu:

Enter 1 to deposit

Enter 2 to Withdraw

Enter 3 to Print Balance

Enter 4 to quit

When the user enters 1 in the main menu, your program will prompt the user to enter the deposit amount.

If the user enter more than 2000, Print "Deposit of more than $2000 is not allowed" and

Prompt the user with a SubMenu:

Enter 1 for the Main Menu. If user enters 1, display the main menu

Enter 0 to quit. If user enter 0, exit the application

if the user enters less than 2000,

Print "Deposit Transaction Successful" and

Add the amount to the Balance

Prompt the user with a SubMenu:

Enter 1 for the Main Menu. If user enters 1, display the main menu

Enter 0 to quit. If user enter 0, exit the application

When the user enters 2 in the main menu, your program will prompt the user to enter a withdraw amount.

If the user enter more than 200, Print "Withdrawing more than $200 is not allowed

Prompt the user with a SubMenu:

Enter 1 for the Main Menu. If user enters 1, display the main menu

Enter 0 to quit. If user enter 0, exit the application

If the user enter less than 200, Print "Withdraw Transaction Successful."

deduct the amount from the Balance

Prompt the user with a SubMenu:

Enter 1 for the Main Menu. If user enters 1, display the main menu

Enter 0 to quit. If user enter 0, exit the application

When the user enters 3 in the main menu, print the balance as "Your Current Balance = "

Prompt the user with a SubMenu:

Enter 1 for the Main Menu. If user enters 1, display the main menu

Enter 0 to quit. If user enter 0, exit the application

When the user enters 4 in the main menu, exit the application

When the user enters other than 1-4, print "Invalid Transaction Requested"

Here is the output of my program, with user entered numbers highlighted in yellow

Enter 1 for Deposit
Enter 2 for Withdraw
Enter 3 for Print Balance
Enter 4 for Quit
1
Enter the amount to Deposit
3000
Deposit More than $2000 is not allowed
Enter 1 to Main Menu
Enter 2 to Quit
1
Enter 1 for Deposit
Enter 2 for Withdraw
Enter 3 for Print Balance
Enter 4 for Quit
1
Enter the amount to Deposit
1999
Deposit Transaction successful
Enter 1 to Main Menu
Enter 2 to Quit
1
Enter 1 for Deposit
Enter 2 for Withdraw
Enter 3 for Print Balance
Enter 4 for Quit

3
Your Current Balance =2999
Enter 1 to Main Menu
Enter 2 to Quit
1
Enter 1 for Deposit
Enter 2 for Withdraw
Enter 3 for Print Balance
Enter 4 for Quit
2
Enter the amount to Withdraw
250
Withdrawing More than $200 is not allowed
Enter 1 to Main Menu
Enter 2 to Quit
1
Enter 1 for Deposit
Enter 2 for Withdraw
Enter 3 for Print Balance
Enter 4 for Quit
2
Enter the amount to Withdraw
150
Withdraw Transaction successful
Enter 1 to Main Menu
Enter 2 to Quit

1
Enter 1 for Deposit
Enter 2 for Withdraw
Enter 3 for Print Balance
Enter 4 for Quit
3
Your Current Balance =2849
Enter 1 to Main Menu
Enter 2 to Quit
1
Enter 1 for Deposit
Enter 2 for Withdraw
Enter 3 for Print Balance
Enter 4 for Quit

5
Invalid Transaction requested
Enter 1 to Main Menu
Enter 2 to Quit
1
Enter 1 for Deposit
Enter 2 for Withdraw
Enter 3 for Print Balance
Enter 4 for Quit

4

You should test for the same output as mine. Upload the VB script and screenshot of your application.

1.Includes a summary of the conditions with definition, signs and symptoms and treatment

2. Place the conditions by a system in alphabetical order

Liquids and electrolytes
1 hypervolemia
2. Hypovolemia
3. Hypernatremia
4. Hyponatremia
5. Hyperkalemia
6. Hypokalemia
7. Hypercalcemia
8. Hypocalcemia

Immunology
1. AIDS

Cancer
1 leukemia
2. Hodgkin
3. Myeloma
4. Lymphoma

Use Newton's method to find a solution for the equation in the given interval. Round your answer to the nearest thousandths. ? 3 ? −? = −? + 4; [2, 3] [5 marks] Answer 2.680

Q6. Use the Taylor Polynomial of degree 4 for ln(1 − 4?)to approximate the value of ln(2). Answer: −4? − 8?2 − 64 3 ? 3 − [6 marks]

Q7. Consider the curve defined by the equation 2(x2 + y2 ) 2 = 25(x2 − y2 ). Find the equation of the line tangent to the curve at the point(3, 1). [5 marks]

The molecular weight of methylene blue is 320 g/mol. The concentration of the original sample was 0.005 mg/ml in 10 ml. Determine the molarity (M) of your original sample and each dilution.

Original:
Dilution 1 (1:2 add 3mL of methylene blue + 3mL of water) :
Dilution 2 (1:4 use 3mL of of 1:2 solution + 3mL of water) :
Dilution 3 (1:8 use 3mL of 1:4 solution + 3 mL of water) :
Dilution 4 (1:10 use 0.5 ml of the original methylene blue + 4.5 mL of water) :

Please show all work!!

Consider the following game between Bobbi and Gary:

1. T/F Gary has a dominant strategy.

2. T/F  Bobbi has a dominant strategy.

3. Does Gary have a dominated strategy? If so, what is it?

4. Does Bobbi have a dominated strategy? If so, what is it?

5. What is Gary's choice in the Nash Equilibrium?

6. What is Bobbi's choice in the Nash Equilibrium?

Trump De Drum Ltd (TDT) is a company in aquacultural industry specialised in farming of aquatic organisms. DT is considering opening a new farm in Sandy Bay. This project would involve the purchase of 13 hectares land at a price of $1,000,000 (Note that: The land is not subject to depreciation for accounting and tax purposes). In addition to that, the company will need to purchase eight special equiments which cost $125,000 each. The equipments are expected to be in use for 5 years and after that, they will be scrapped without any residual value. Each year, each of these equipments will incur $5,000 maintenance cost. It is assumed that the farm will first be used at the beginning of the next financial year: 1 July 2021.

Before starting this new operation, TDT will need to redevelop and renovate the warehouse at the farm. This is expected to cost $200,000. Assume that TDT is not able to claim any annual tax deduction for the capital expenditure to the renovation of the building until the business is sold.

Revenue projections from the farm for the next five years are as follows:

Operating variable costs associated with the new business including material costs and labour costs. Estimated material costs per tons in year 1 is $2,000 and this cost will increase by 3.5% every year. The farm will require about 6 workers working for 8 hours a day, 200 days per year. The pay rate is flat at $20/ hour including superannuation. Annual operating fixed costs associated with production (excluding depreciation) are $100,000. Existing administrative costs are $550,000 per annum. As a result of the new operation, these administrative costs will increase by 30%. The company is subject to a tax rate of 30% on its profits.

Meanwhile, TDT Ltd is currently financed by 60% of equity and 40% of debt. Company’s bond is traded at a price of $980. The bond has 10 year term, 8% coupon rate paid semi-annually and face value of $1,000. In addition, company’s equity has a beta of 1.2 while the risk-free rate in the market is 3% and market portfolio return is estimated to be 12%.

P. De Potato, the company CFO would like you to help him examine the viability of the project for the next five years, taking into account the projections of sales and operations costs prepared by company’s accountants.

Your tasks:

Based on the information in the case study, P. De Potato has asked you to write a report to TDT’s management advising them as to the best course of action regarding this project. Your report should address the following specific questions asked by management:

1. Discuss which costs are relevant for the evaluation of this project and which costs are not. Your discussion should be justified by a valid argument and supported by references to appropriate sources