1. Consider historical data showing that the average annual rate of return on the S&P 500 portfolio over the past 85 years has averaged roughly 8% more than the Treasury bill return and that the S&P 500 standard deviation has been about 20% per year. Assume these values are representative of investors’ expectations for future performance and that the current T-bill rate is 5%.

1. Calculate the expected return and variance of portfolios invested in T-bills and the S&P 500 index with the following weights.                         [5]

2. Calculate the utility levels of each portfolio of Problem in a) for an investor with A =2. What do you conclude? [5]

3. Repeat Problem b) for an investor with A = 3. What do you conclude? [5]

Mass mA =2 .1 kg traveling with velocity~ vA = (1 .2m /s)ˆ x(2.3m /s)ˆ y collides with mass mB =4 .2 kg at rest. After collision, mass mA leaves with velocity |~ v0A| =0 .50 m/s at an angle = 35 .

(a) Calculate the total initial momentum of the system before the collision.

(b) What is the momentum ~ p 0 A of mass mA after the collision. Give your answer in ˆ x and ˆ y component form.

(c) What is the momentum ~ p 0 B of mass mB after the collision. Give your answer in ˆ x and ˆ y component form.

(d) Assuming the collision happened over a small time period of 1.0 millisecond, what average force ~ FA acted on mass mA during the collision.

(e) Is this an elastic or inelastic collision? Justify.

A CI is desired for the true average stray-load loss μ (watts) for a certain type of induction motor when the line current is held at 10 amps for a speed of 1500 rpm. Assume that stray-load loss is normally distributed with σ = 2.8. (Round your answers to two decimal places.)

(a) Compute a 95% CI for μ when n = 25 and x = 52.5.

...........................Watts?

(b) Compute a 95% CI for μ when n = 100 and x = 52.5.

.............................Watts?

(c) Compute a 99% CI for μ when n = 100 and x = 52.5.

.............................Watts?

(d) Compute an 82% CI for μ when n = 100 and x = 52.5.

..............................Watts?

(e) How large must n be if the width of the 99% interval for μ is to be 1.0? (Round your answer up to the nearest whole number.)

n =

You may need to use the appropriate table in the Appendix of Tables to answer this question.

A solution prepared by mixing 55.0 mL of 0.260 M AgNO3 and 55.0 mL of 0.260 M TlNO3 was titrated with 0.520 M NaBr in a cell containing a silver indicator electrode and a reference electrode of constant potential 0.175 V. The reference electrode is attached to the positive terminal of the potentiometer, and the silver electrode is attached to the negative terminal. The solubility constant of TlBr is Ksp = 3.6 × 10–6 and the solubility constant of AgBr is Ksp = 5.0 × 10–13. (a) Which precipitate forms first?(b) Which of the following expressions shows how the cell potential, E, depends on [Ag ]?(c) Calculate the first and second equivalence points of the titration.What is the cell potential when the following volumes of 0.520 M NaBr have been added? d) 1.0 mL e) 17.7 mL f) 26.5 mL g) 27.4 mL h) 27.8 mL i) 45.2 mL j) 55.0 mL k) 62.8 mL

5.) Two concentric current loops lie in the same plane. The smaller loop has a radius of 3.5 cm and a current of 12 A. The bigger loop has a current of 20 A . The magnetic field at the center of the loops is found to be zero. What is the radius of the bigger loop?

9.) An 1100-turn coil of wire that is 2.3 cm in diameter is in a magnetic field that drops from 0.15 T to 0 T in 11 ms . The axis of the coil is parallel to the field. What is the emf of the coil?

The magnetic field 10 cm from a wire carrying a 1 A current is 2 μT. What is the field 2 cmcm from the wire?

The earth's magnetic field strength is 5.0×10−5T . How fast would you have to drive your car to create a 3.0 V motional emf along your 1.0 m -long radio antenna? Assume that the motion of the antenna is perpendicular to B⃗ B→.

A mixture of 6.92e-02 mol of Cl2, 2.15e-02 mol of H2O, 6.78e-02 mol of HCl, and 5.04e-02 mol of O2 is placed in a 1.0-L steel pressure vessel at 1447 K.

The following equilibrium is established: 2 Cl2(g) + 2 H2O(g) 4 HCl(g) + O2(g)

At equilibrium 1.43e-02 mol of H2O is found in the reaction mixture.

Calculate the equilibrium pressures of all gases in the reaction vessel and the value of KP for the reaction.

Pick the correct statement from the multiple choices.

Use the value R = 0.0821 L-atm/mol-K for the gas constant.

a) The equilibrium constant is KP = 2.7e-03 .

b) The equilibrium pressure of O2 is PO2 = 6.42 atm.

c) The equilibrium pressure of HCl is PHCl = 6.34 atm.

d) The equilibrium pressure of Cl2 is PCl2 = 9.07 atm.

e) The equilibrium constant is KP = 7.4e+01 .

Suppose you have a concentrated solution (S1) with a concentration equal to 1 M. You use their solution to make more dilute solutions S2-S6. Complete the following table, which describes the solution process. NOTE: Not all of the solutions are diluted S1; some are made from solutions that are derived from S1. The equation C₁V₁ = C₂V₂ should be used as a starting point for calculation. You can assume all volumes are additive. S2 is shown as an example.

1).An aluminium oxalate complex was prepared by dissolving aluminium metal in potassium hydroxide, followed by reaction with oxalic acid.The resulting complex was analysed for oxalate content by titration against potassium permanganate:

A 0.1105 g sample of the aluminium oxalate complex was dissolved in deionized water (30 cm³) and bench dilute (2 M) sulphuric acid (10cm³)added. The resulting solution was heated to about 60 ºC and titrated against standardized potassium manganate (VII) solution.14.35 cm³ of a 0.02 mol dm^-3 KMn0₄ solution was required.

(i) Write out a balanced equation for the overall redox process.( 3 marks

(ii) Use the analytical data to deduce if the prepared complex was K₃Al(C₂O₄)₃.3H₂O or KAl(C₂O₄)₂(H₂O)₂.2H₂O. .

                        Molar masses /g mol^-1

                        K, 39.00; Al, 26.98; C, 12.01; O, 16.00; H, 1.0

Penelope’s ratio of marginal utility for a books to crayons (MU_B / MU_C) is 3/1, while the price ratio of books to crayons (P_B / P_C) is 1.5/1.0. Which of the following is/are true?  Hint: you can approach this question by considering the marginal rate of substitution relative to the price ratio (as presented), or you can cross-multiple to put it into the MU_B / P_B and MU_C / P_C format.

A. Penelope can increase utility by decreasing her consumption of books by 4 units and increasing her consumption of crayons by 6 units.

B. One more book provides Penelope with 3 times the utility of one more box of crayons.

C. Penelope can increase utility by decreasing her consumption of crayons by 1 unit and increasing her consumption of books by 1.5 units.

D. Penelope can increase utility by decreasing her consumption of crayons by 3 units and increasing her consumption of books by 2 units.