17. Use the IS/LM model to predict the effects of each of the following shocks on income, the interest rate, consumption, and investment. Explain and illustrate your answers. Assume price level is constant and the economy is closed.

a. The Fed reducing the money supply

b. The government raising government expenditures and taxes by the same amount.

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

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)