Suppose {a1,...,am} is a complete set of representatives for Z/mZ. Show:

(i) If (b,m)=1, then{b*a1,...,b*am}is a complete set of
representatives.

(ii) If (b,m)> 1, then{b*a1,...,b*am}is not a
complete set of representatives.

A plane delivers two types of cargo between two destinations. Each crate of cargo I is 5 cubic feet in volume and 145 pounds in weight, and earns $35 in revenue. Each crate of cargo II is 5 cubic feet in volume and 290 pounds in weight, and earns $45 in revenue. The plane has available at most 425 cubic feet and 13,920 pounds for the crates. Finally, at least twice the number of crates of I as II must be shipped. Find the number of crates of each cargo to ship in order to maximize revenue. Find the maximum revenue.

2. (a) Prove that U45 is generated by the set {14,28}.

(b) Prove that the additive group Z×Z is generated by the set S={(3,1),(−2,−1),(4,3)}.

Please be thorough step by step with details, please.

For this assignment, you will use the provided database in the Unit 5 script file. You will add statements to this file to query the database tables. For your reference, below is a screenshot of the enhanced entity relationship diagram (ERD) as a reference when you write your queries. With the data types listed in the diagram, this will help you identify the types of operators that you can use for particular queries.

Use paiza.io for MySQL to execute and troubleshoot your Structured Query Language (SQL) statements. It is recommended that you use Notepad to write your SQL statements. Then, copy and paste your SQL statements to paiza.io to test your statements to ensure that they execute without errors. Save your work frequently.

The asterisk (*) indicates that a column is not null (i.e., required to have a value).

1. If you would like to see the test SQL statements, click on “Run” to see the statements execute. You should see “Hello” appear in the Output window (see the following screenshot).
2. Because you do not require these test SQL statements for your assignment, delete the sample SQL statements. To do this, select the text, and click on the Delete key on your keyboard. Your MySQL paiza.io screen should now be blank, as you see in the following screenshot. Note that if you ran the test statements, “Hello” will still appear in the Output window.
3. Copy and paste the code from the provided script file into the code editor, and click on “Run” (“Ctrl + Enter”). You should see no error messages displayed in the Output area at the bottom of your paiza.io screen. After you click on “Run,” you should see a green bar with “Success” at the top. You will see this circled in the following screenshot:
4. Next, you will write 1 query to respond to each of the following questions. Note that you can only use the information that is in the question or the enhanced ERD. Write a query to do the following:
   1. Display all of the rows in the publisher table.
   2. Display all of the books in the book table that were written by the author whose author ID is 1504192.
   3. Display all of the purchases in the shopbasket that were ordered on 2020-02-29.
   4. Display the largest quantity ordered in the shopbasket.
   5. Display the authors' first and last names sorted by their last name.
   6. Display a count of the number of orders placed via the shopbasket.
   7. Display the order date and quantity of orders in the shopbasket that have a quantity of more than 25.
   8. Display the first and last names of those authors who have a null Facebook.
   9. Display all of the customers' names, city, and state if they live in GA, FL, or CA.
   10. Display the book titles of those books that were not published by Scholastic Press.
   11. Display the first and last names of the authors and the book titles. Only display those authors who wrote a book with the word database in the title.
   12. Add a multiline comment before the first CREATE TABLE statement that includes your name, the course code (ITCO231), and the date when you are submitting your assignment.
5. Save your script file using your last name, ITCO231, U5, and the file extension .sql, as in “Smith_ITCO231_U5.sql.”
   1. Tip: When saving a Notepad file, you can change the file extension to .sql as required for the assignment by changing the “Save as type” to “All Files” and then typing the .sql extension, as shown in the example.

I didnt understand by what you mean by SQL TEST. If what you are asking me is that an SQL TEST? Yes! It is SQL QUERY TEST!!

Solve the initial value problem: 9y″+18y′+19y=0, y(π/2)=−2, y′(π/2)=−2. Give your answer as y=... . Use x as the independent variable.

Demand for walnut fudge ice cream at the Sweet Cream Dairy can be approximated by a normal distribution with a mean of 17 gallons per week and a standard deviation of 3.2 gallons per week. The new manager desires a service level of 90 percent. Lead time is two days, and the dairy is open seven days a week. (Hint: Work in terms of weeks.)

a-1. If an ROP model is used, what ROP would be consistent with the desired service level? (Do not round intermediate calculations. Round your final answer to 2 decimal places.)

ROP ______ gallons

a-2. How many days of supply are on hand at the ROP, assuming average demand? (Do not round intermediate calculations. Round your final answer to 2 decimal places.)

Days _______

b-1. If a fixed-interval model is used instead of an ROP model, what order size would be needed for the 90 percent service level with an order interval of 7 days and a supply of 8 gallons on hand at the order time? (Do not round intermediate calculations. Round your final answer to the nearest whole number.)

Order size _______ gallons

b-2. What is the probability of experiencing a stockout before this order arrives? (Do not round intermediate calculations. Round your final answer to the nearest whole percent. Omit the "%" sign in your response.)

Probability _________ %

c. Suppose the manager is using the ROP model described in part a. One day after placing an order with the supplier, the manager receives a call from the supplier that the order will be delayed because of problems at the supplier’s plant. The supplier promises to have the order there in two days. After hanging up, the manager checks the supply of walnut fudge ice cream and finds that 2 gallons have been sold since the order was placed. Assuming the supplier’s promise is valid, what is the probability that the dairy will run out of this flavor before the shipment arrives? (Do not round intermediate calculations. Round your final answer to the nearest whole percent. Omit the "%" sign in your response.)

Risk probability _________ %

U(C1, C2, C3, C4, C5) = C1∙C2∙C3∙C4∙C5

As a mathematical function, does U have a maximum or minimum value? What values of Ci correspond to the minimum value of U? What values of Ci correspond to the maximum value of U? Do these values of Ci make sense from an economic standpoint?

Now let us connect the idea of economic utility to actual dollar values. To keep the values more manageable, we will use household income rather than the entire state budget, and retail costs and measures rather than industrial ones. Find the Median Household Income for Mesa, AZ for the most recent year possible. Then find the dollar cost in Mesa, AZ for a Penny, a pound of Ground Beef, a pair of Jeans, fresh Orange Juice, and a Movie Ticket. (Entertainment is often used as a stand-in for Climate.) A Cost-of- Living Index is a good place to find much of this data. Record these prices as P1, P2, P3, P4, and P5 respectively.

Construct an equation using Median Income, the Ci and Pi values that illustrates how much of each resource the Median Household can afford to purchase. Given this restriction, do the maximum or minimum values of U change? Do the values of Ci that give the maximum or minimum values change? What are these new values? How should the Median Household budget its Income so as to maximize its Economic Utility?

Write up your findings in a paper that you could turn in to an employer. Be sure to show all your work. Include any appropriate references as well as any computational devices used.

* Solve the questions, make the table, and the graph.

Students will be asked to formulate, define, and interpret mathematical modeling (particularly ordinary differential equation) which involves real engineering applications and related to their majoring (E.g. Newton’s law cooling/warming, mixture problem, radioactive decay, spring-mass system, series circuit, deflection of the beam, etc.).. The selected model should be solved analytically using any methods that have been learnt in the mathematic lecture. just give me an example with related topic and how to solve it using math

Show that the quotient ring Q[x]/(x2 − 3) is isomorphic to a subfield of the real numbers R.

Consider the given matrix.

Find the eigenvalues. (Enter your answers as a comma-separated list.)

λ = 3i,−3i

(I got these right)
Find the eigenvectors of the matrix. (Enter your answers in order of the corresponding eigenvalues, from smallest to largest by real part, then by imaginary part.)

I can't seem to get the eigenvectors right.

Given the differential equation dy/dx =x. With intitial condition y(1)=0.5. Use eulers method with dx = 0.1 , to approximate the value of y when x=1.8

Find the general solution of the given system.

[x(t), y(t)]= _____________, _______________

(6c1​+8c2​)10​sin(6t)+(6c2​+8c1​)10​cos(6t), c1​cos(6t)+c2​sin(6t)

^above is the answer I got, which is incorrect.