Let G = Z x Z and H = {(a, b) in Z x Z | 8 divides a+b}

a. Prove directly that H is a normal subgroup in G (use the fact that closed under composition and inverses)

b. Prove that G/H is isomorphic to Z8.

c. What is the index of [G : H]?

1.  Describe in point form what happens in the assessment, diagnosis, planning, implementation and evaluation stages of the nursing process.

2.  Provide a brief explanation of what data clustering is?

3. Provide one open ended question and one closed ended question that could be used in a client assessment interview?

Calculate the Fourier Series of the function below. Results should be in full, closed-form series. Graph using Octave or Matlab to compare and check answer. Period is 2pi.

f(x)= 1 for -pi<x<-pi/2, -1 for -pi-2<x<0, 0 for 0<x<pi

JAVA

Please put detailed comments as well explaining your program.

I'm in a beginning programming class, and so please use more basic techniques such as if else statements, switch operators, and for loops if needed.

http://imgur.com/a/xx9Yc

Pseudocode for the main method:

Print the headings

            Print the directions

            Prompt for the month

            If the month is an integer       (Hint: Use the Scanner class hasNextInt method.)

                        Input the integer for the month

                        Get the string for the month (Use your method)

            Otherwise

                        Input the string for the month

                        Get the integer for the month (Use your method)

            Prompt for the day

            Input the day

            Prompt for the year

            Input the year

            Get the holiday

            Print the output

THE PROBLEM:

You must use switch statements for some part of the homework.

Write a program that inputs a month, day, and year from the user and outputs the corresponding date in the following two standard date formats:

6/12/2005      June 12, 2005

Also your program must print the name of any holiday associated with the date.

For example:

             3/17/2010        March 17, 2010           St. Patrick’s Day

Your program should ask the user how many times the user wants to run the code and then you need to use a for loop to repeat the run that many times.

REQUIREMENTS:

You must use good programming style.

The user can enter the month either as a numeric value or a String. i.e. the user could enter a 5 or May.

You may assume the data that the user enters is valid data.

Your program must print a report similar to that shown in the sample output on the last page of this handout.

You must solve this problem by implementing and using the following methods:

printDirections

void method that prints a message to the user that explains what the program will do and how the month data can be entered. (See the sample output above.)

getMonthString

method that has 1 parameter, the month as an integer (1..12).

This method returns the corresponding name of the month as a String.

getMonthNumber

method that has 1 parameter, the name of the month in a String.

This method returns the corresponding integer value for that month name.

HINT: Before you read the data for the month, use the Scanner class hasNextInt method to determine what kind of data the user entered for the month. Using hasNextInt you can determine if the user is entering an integer for the month or not.

            getHoliday

                        This method has 2 int type parameters for month and day.

                        The method returns a String that is the name of a holiday that is associated with the date represented by the parameters. If there is no holiday associated with that date, then the method returns an empty String (“”).

                        Use nested switch statements to implement this method. Use one switch statement for the months. Inside the case for each month, use a switch statement that has a case for each day in that month that is a holiday. Inside each of those day cases, set the holiday string to the name of the holiday.

NOTE: You can also include holidays for your birthday, anniversary, or whatever …

isEaster

                        This method has 3 int type parameters for month, day and year.

This method returns true if the date represented by the 3 parameters is Easter, otherwise it returns false.

To implement this method:   use the following formula to figure out the month and the day of easter for the given year.

goldenNumber = (year % 19) + 1;

a = (24 + 19*(goldenNumber - 1)) % 30;   b = a - a/28;

c = (year + year/4 + b - 13) % 7;   d = b - c;

easterMonth = 3 + (d + 40)/44;

easterDay = d + 28 - 31*(easterMonth/4);

To use this method, you will have to add a third parameter to the getHoliday method for the year, and then inside the getHoliday method, after the switch statements, call this method.

NOTE: If the holiday string is already longer than 0, this day is already associated with another holiday,

(For example, maybe “Grandma’s Birthday”, then getHoliday should return “Easter and Grandma’s Birthday”.

To test the isEaster method, make April 4 “Grandma’s Birthday” and test this method using 4/4/2010. Also test it for Easter in a year where Easter is not on April 4.

Here is a list of holidays that your need needs to generate the appropriate output:

1/1 "New Year's Day";                            

1/18 "Martin Luther King Jr. Day";                            

2/2 "Ground Hog Day";

2/12 "Abraham Lincoln's Birthday";

2/14 "St. Valeninte's Day";

2/22 "George Washington's Birthday";

3/17 "St. Patrick's Day";   4/1 "April Fool's Day";

4/4 "Grandma's Birthday";

4/22 "Earth Day";

4/30 "Arbor Day";

5/1 "May Day";

5/5 "Cinco de Mayo";

7/4 "Independence Day";

8/1 "International Friendship Day";

10/1 "Columbus Day";

10/31 "Halloween";                         

11/11 "Vereran's Day";

12/25 "Christmas";

12/31 "New Year's Eve";                              

?? "Easter";

Sample outputs  

Pseudocode for the main method:

            Print the headings

            Print the directions

            Prompt for the month

            If the month is an integer       (Hint: Use the Scanner class hasNextInt method.)

                        Input the integer for the month

                        Get the string for the month (Use your method)

            Otherwise

                        Input the string for the month

                        Get the integer for the month (Use your method)

            Prompt for the day

            Input the day

            Prompt for the year

            Input the year

            Get the holiday

            Print the output

The Young family is purchasing a $130,000 house with a VA mortgage. The bank is offering them a 25- year mortgage with an interest rate of 9.5%. They have $20,000 invested that they could use for a down payment. Since they don’t need a down payment, Mr. Young wants to keep the money invested. Mrs. Young believes that they should make a down payment of $20,000.

Option 1 DO NOT MAKE down payment If they Young’s do not make the down payment they will finance $130,000 with monthly payments of $1135.81. The total cost of the house would be $340,473 and $210,743 of this would be interest. If they invest the $20,000 in an account with an APR of 10% compounded quarterly, in 25 years the accumulated amount of the investment would be $236,274.33.

1) If the Young’s choose option 1 and do not make the down payment, what is the difference between the amount they have in their investment after 25 years and the total cost that they spend on the house?

Option 2 MAKE a $20,000 down payment

2) Determine the amount of the mortgage if they make the $20,000 down payment.

3) Determine the monthly payment for principal and interest if they make a $20,000 down payment.

4) Determine the total cost of the house if they make a down payment of $20,000.

5) How much of the total cost is interest?

6) If the Youngs use the $20,000 as a down payment, their monthly payment will decrease. Determine the difference of the monthly payments from option 1 to option 2.

7) Assume that the difference in monthly payments is invested in an ordinary annuity each month at a rate of 6% compounded monthly for 25 years. Determine the value of the investment in 25 years.

8) If the Young’s choose option 2 and make the down payment, what is the difference between the amount they have in their ordinary annuity after 25 years and the total cost that they spend on the house?

9) Use the information from options 1 and 2 to analyze the problem. Would you recommend that the Youngs not make the down payment and keep the $20,000 invested (as in option 1) or make the down payment of $20,000 and invest the difference in their monthly payments (as in option 2)? Explain.

The Young family is purchasing a $130,000 house with a VA mortgage. The bank is offering them a 25- year mortgage with an interest rate of 9.5%. They have $20,000 invested that they could use for a down payment. Since they don’t need a down payment, Mr. Young wants to keep the money invested. Mrs. Young believes that they should make a down payment of $20,000.

Option 1 DO NOT MAKE down payment If they Young’s do not make the down payment they will finance $130,000 with monthly payments of $1135.81. The total cost of the house would be $340,473 and $210,743 of this would be interest. If they invest the $20,000 in an account with an APR of 10% compounded quarterly, in 25 years the accumulated amount of the investment would be $236,274.33.

1) If the Young’s choose option 1 and do not make the down payment, what is the difference between the amount they have in their investment after 25 years and the total cost that they spend on the house?

Option 2 MAKE a $20,000 down payment

2) Determine the amount of the mortgage if they make the $20,000 down payment.

3) Determine the monthly payment for principal and interest if they make a $20,000 down payment.

4) Determine the total cost of the house if they make a down payment of $20,000.

5) How much of the total cost is interest?

6) If the Youngs use the $20,000 as a down payment, their monthly payment will decrease. Determine the difference of the monthly payments from option 1 to option 2.

7) Assume that the difference in monthly payments is invested in an ordinary annuity each month at a rate of 6% compounded monthly for 25 years. Determine the value of the investment in 25 years.

8) If the Young’s choose option 2 and make the down payment, what is the difference between the amount they have in their ordinary annuity after 25 years and the total cost that they spend on the house?

9) Use the information from options 1 and 2 to analyze the problem. Would you recommend that the Youngs not make the down payment and keep the $20,000 invested (as in option 1) or make the down payment of $20,000 and invest the difference in their monthly payments (as in option 2)? Explain.

The eardrum, which transmits vibrations to the sensory organs of your ear, lies at the end of the ear canal. In adults, that ear canal is about

2.5 cm in length. We can treat the ear canal as a tube, closed by the eardrum at one end, and open to the atmosphere at the external end. Consider a fluctuating air column in the canal: similar to a vibrating†string with one fixed end. Its fundamental frequency becomes half that of a string of the same length with both ends fixed. (You can convince yourself of this by imagining a tube with one end closed and the other end open. Sketch the node and antinode of the possible fundamental mode in the tube!)

f_n = nv/4L

Use the above equation to find what frequency standing waves can occur within the ear canal that are within the range of human hearing. The speed of sound in the warm air of the ear canal is 350 m/s. The audible range is 20 Hz to 20 KHz.

a. all Hypothesis Tests must include all four steps, clearly labeled;

b. all Confidence Intervals must include all output as well as the CI itself

c. include which calculator function you used for each problem.

2. An experiment was done to see whether open-book tests make a difference. A calculus class of 48 students agreed to be randomly assigned by the draw of cards to take a quiz either by open-notes or closed-notes. The quiz consisted of 30 integration problems of varying difficulty. Students were to do as many as possible in 30 minutes. The 24 students taking the exam closed-notes got an average of 15 problems correct with a standard deviation of 2.5. The open-notes crowd got an average of 12.5 correct with a standard deviation of 3.5. Assume that the populations are approximately normal. At the 5% significance level, does this data suggest that differences exist in the mean scores between the two methods?

A portfolio manager controls $10 million in common stock. In anticipation of a stock market decline, the decision is made to hedge the portfolio using the S&P 500 futures contract. The portfolio's beta is 1.1 and the dividend yield on this portfolio is 3% annually. One S&P 500 futures contract with 90 days to settlement date is traded at 1164.50. The S&P 500 index itself is at 1150.  (Use 365 days a year)

1. Calculate the number of futures contracts that should be bought or sold. Indicate whether you should buy or sell.
2. Suppose that when the contracts are closed out, the S&P 500 index has increased to 1380. Calculate the gain or loss on the combined positions (stock portfolio and futures contracts).
3. Suppose that when the contracts are closed out, the S&P 500 index has decreased to 1035. Calculate the gain or loss on the combined positions (stock portfolio and futures contracts).

2a)Which of the following is not a type of financial inflow?

b)

If imports exceed exports, then there is a balance of trade _________, resulting in a financial _________.

c)If net taxes exceed government purchases, then the government may __________, causing interest rates to __________.

d)In the closed nation of Zeeland, government spending exceeds net taxes. We would expect interest rates to __________ and economic growth to _________.

e)