1. How does the center of mass velocity of the two objects which collide change during an elastic collision? Inelastic collision? Explain.

2. In an inelastic collision, the forces between the two gliders are equal and opposite according to newtons 3rd law. What makes the energy gained by one object unequal (less) than the energy lost by the other in an inelastic collision?

For this final problem we will create two samples of dice rolls. First You need to roll two dice in the standard way 25 times and record the results. Then roll two dice in a “lucky” way 25 times and record the results. As you complete this problem use the known standard deviation for the sum of two dice : σ1 = 2.415 and σ2 = 2.415

(a) Write down the results of your rolls and find the average for the first sample, ¯x1, and the ”lucky” sample, ¯x2

(b) Create a 95% confidence interval for the difference in the averages of the two samples, µ1 − µ2.

(c) Create a hypothesis test to determine whether the average of the second sample is greater than the average of the first sample. Be sure to include:

i. The null and alternative hypotheses

ii. The test statistic (and how it was calculated)

iii. The p-value (and how it was calculated)

iv. Your conclusion with α = 0.05. Does this conclusion mean that the “lucky” rolls land on higher numbers than the regular rolls

Four bounds with 6, 12, 18, and 24 months of maturity and $10,000 face value are selling for $9,400, $8,900, $9,484, and $9,625 respectively. The first two are discount bonds, the third one pays 8% and the last one pays 9% /year coupon semi-annually. Using the bootstrapping method, calculate the 6, 12, 18, and 24 month zero rates.

Write a Java program (name it PasswordTest) that reads from the user a string input (representing a password) and determines whether the password is “Valid Password” or “Invalid Password”. A valid password has at least 7 characters and includes at least one lower-case letter, at least one upper-case letter, at least one digit, and at least one character that is neither a letter nor a digit. Your program will need to check each character in the string in order to render a verdict. For example, CS5000/01 is invalid password; however, Cs5000/01 is a valid password. The program should display the entered password and the judgment as shown in the following sample runs:

Entered Password: CS5000/01

Verdict: Invalid Password

Entered Password: Cs5000/011

Verdict: Valid Password

Entered Password: MyOldDogK9

Verdict: Invalid Password

Entered Password: MyOldDogK9#

Verdict: Valid Password

Entered Password: Ab1#

Verdict: Invalid Password

Document your code, and organize and space out your outputs as shown. Design your program such that it allows the user to re-run the program with different inputs in the same run (i.e., use a sentinel loop structure).

a) Demand for blue jeans in a competitive market is given by P=130-.003Qd. Supply for Blue jeans is given by P=5+.002Qs. Assuming the market is taken over by a monopolist, how much surplus is lost by the market?

A long cylindrical wire made of a magnetic metal with relative permeability has a uniform current density J flowing along its length. An insulated wire runs along the axis of the cylinder and carries a current I. Find the magnetic field, magnetic induction, magnetization, and bound currents in the magnetic material.

5c.

Milly (mass 60.9 kg) runs at 4.11 m/s along the positive x-axis and then jumps onto a stationary 112 kg box. Milly and the box slide across the floor for distance 0.244 m, and then they come to a stop. Find the coefficient of kinetic friction between the box and the floor.

1. The product offers life protection, savings and even has investment component. Even though it runs for a specified period, life assurance companies are flexible to extend cover so that they make sure that money became available to the policyholders dependents on their death.

Identify and describe the variations under this product.                            [25 marks]

2. In a closed economy, how would each of the following events affect bond price and market interest rate? Use the figures of both bond market and market of loanable funds to illustrate the changes to the interest rates.

A. The expected rate of inflation decreases.

B. The federal government runs a budget deficit.