1. The expected return on stock W is 10% and its standard deviation is 15%. Expected return on stock V is 16% and its standard deviation is 24%. The correlation between returns of W and V is 20%.
   1. calculate expected return and standard deviation of a portfolio that invests 40% in W and 60% in V.
   2. determine the minimum variance combination of W and V and determine its expected return and standard deviation.
   3. If the risk-free rate is 4%, determine the tangency portfolio and derive the capital market line equation.

VII. Deduce the line or lines necessary to show the validity of the following arguments. Be sure to cite the lines from which each conclusion follows and give its justification . Please copy these arguments into your exam booklet.

1.

1. (~F v X) ↄ (P v T)

2. F ↄ P

3. ~P

––––––––––––––––

T

2.

1. (H v ~B) ↄ R

2. (H v ~M) ↄ P

3. H

–––––––––––––––

R ∙ P

VII. Deduce the line or lines necessary to show the validity of the following arguments. Be sure to cite the lines from which each conclusion follows and give its justification . Please copy these arguments into your exam booklet.

1.

1. (~F v X) ↄ (P v T)

2. F ↄ P

3. ~P

––––––––––––––––

T

2.

1. (H v ~B) ↄ R

2. (H v ~M) ↄ P

3. H

–––––––––––––––

R ∙ P

The velocity of sound, v (m/s), increases as the square rootof the absolute temperature, T (K):

   v = v_o ?(T/T_o)

where v_o is the velocity of sound at temperatureT_o.

a) Make a rough sketch of how the graph of v versus T wouldlook.

b) If one measures v for several temperatures, T, how couldyou plot the data so as to get a straight line?

c) What would be the slope of this straight line, in terms ofv_o and T_o?

d) What would be the SI units of this slope?

The surface area of a right-circular cone of radius r and height h is S=πrr2+h2−−−−−−√, and its volume is V=1/3πr2h.

(a) Determine h and r for the cone with given surface area S=4 and maximal volume V.
h=  , r=

(b) What is the ratio h/r for a cone with given volume V=4 and minimal surface area S?
hr=

(c) Does a cone with given volume V and maximal surface area exist?
A. yes
B. no

Be sure to answer all parts.

Calculate E o , E, and ΔG for the following cell reactions:

(a) Mg(s) + Sn2+(aq) ⇌ Mg2+(aq) + Sn(s) where [Mg2+] = 0.045 M and [Sn2+] = 0.065 M

E ^o = _________ V

E = ____________ V

ΔG = __________kJ

(b) 3Zn(s) + 2Cr3+(aq) ⇌ 3Zn2+(aq)+ 2Cr(s) where [Cr3+] = 0.080 M and [Zn2+] = 0.0055 M

E ^o = __________ V

E = ____________ V

ΔG = ___________kJ

For any n ≥ 1 let Kn,n be the complete bipartite graph (V, E) where V = {xi : 1 ≤ i ≤ n} ∪ {yi : 1 ≤ i ≤ n} E = {{xi , yj} : 1 ≤ i ≤ n, 1 ≤ j ≤ n} (a) Prove that Kn,n is connected for all n ≤ 1. (b) For any n ≥ 3 find two subsets of edges E 0 ⊆ E and E 00 ⊆ E such that (V, E0 ) and (V, E00) are spanning trees which are not isomorphic.

Assume you are carrying out the titration of 50 mL of a 0.025 M solution of acetic acid with 0.1023 MNaOH. Acetic acid has aKaof 1.8×10−5.

(a) Calculate the pH of the solution at V= 0, V= 0.3Veq, V=Veq, and V= 1.2Veq. (Veq is the equivalence point volume)

(b) If a phenolphthalein indicator was used in this titration, where would the apparent endpoint occur? Assume the apparent endpoint would occur at the end of the color range of the indicator (pH’s of 8.0-9.6).

Amortizing Loan Assignment Excels: