A bubble-point feed mixture of 5 mol% A and 95 mol% B is to be distilled to obtain a distillate containing 35 mol% A and a bottoms containing 0.2 mol% A. The column has a partial reboiler and a partial condenser. If the constant relative volatility is given to be ?A,B = 6. Using graphical method, find out:

a) The minimum number of equilibrium stages.

b) The minimum boilup ratio: ??? /??

c) The actual number of stages if the boilup ratio is 1.2 times the minimum.

Suppose for a random sample of 49 CMU students, the mean amount of time spent eating or drinking per day is 1.58 hours with a S.D. of 0.62 hours!

a. What is the Standard Error of the estimate of the population mean?

b. What is the Margin of Error at a C.L. of 90%?

c. What is the right boundary of the C.I. at a C.L. of 90%?

d. At a 98% C.L., if the researcher wants to limit the error within 0.2 hours range, what size of the sample is needed?

With the aid of fourth order Runge-Kutta method, solve the competing species model defined by

dx/dt =x(2 − 0.4x − 0.3y), x(0) = 2

dy/dt =y(1 − 0.1y − 0.3x), y(0) = 4

where the populations x(t) and y(t) are measured in thousands and t in years. Use a step size of 0.2 for 0 ≤ t ≤ 2 and plot the trajectories of the populations with Matlab or GNU Octave.

two subway cars as shown in Figure 1 have mass m = 2000 kg and are connected by a coupler that can be modeled as a spring of stiffness k = 280,000 N/m. Use Newton’s method to derive the equations of motion, calculate the natural frequencies and determine the associated mode shapes. also, find the time response x1(t) and x2(t) of the subway initial conditions: x(0)= [ 0, 0.2] with zero initial velocity vector.  

A stream containing toluene (T), heptane (H) and benzene (Z) is fed into a distillation column at a rate of 200kmol/hr. The composition of the feed has molar fractions for T of 0.4, H of 0.2, Z of 0.4. The amount of toluene in the bottoms is 60% the amount of toluene in the distillate. The molar fraction of hexane in the bottom stream is 1/21 and the molar fraction of benzene in the distillate is 2/19. Solve for the distillate and bottoms and the molar composition of both outlet streams.

You consider investing in an emerging market. Its stock market volatility (standard deviation of returns measured in U.S. dollars) is 25%. The volatility of the World index of developed markets is 15%. The correlation between the emerging market and the World index is 0.2.

a. What would be the volatility of a portfolio invested 95% in the World index and 5% in this emerging market?

b. Compare the result found in the previous question with the volatility of the World index and give an intuitive explanation.

Consider the following returns. The Correlation between Stock X's and Stock Z's returns is closest to: Year End Stock X Realized Return Stock Y Realized Return Stock Z Realized Return 2004 20.1% -14.6% 0.2% 2005 72.7% 4.3% -3.2% 2006 -25.7% -58.1% -27.0% 2007 56.9% 71.1% 27.9% 2008 6.7% 17.3% -5.1% 2009 17.9% 0.9% -11.3% 0.71 0.60 0.62 0.05

consider the following returns. The Correlation between Stock X's and Stock Z's returns is closest to: Year End Stock X Realized Return Stock Y Realized Return Stock Z Realized Return 2004 20.1% -14.6% 0.2% 2005 72.7% 4.3% -3.2% 2006 -25.7% -58.1% -27.0% 2007 56.9% 71.1% 27.9% 2008 6.7% 17.3% -5.1% 2009 17.9% 0.9% -11.3% 0.71 0.60 0.62 0.05

In the figure, block 1 of mass m1 slides from rest along a frictionless ramp from height h = 3.3 m and then collides with stationary block 2, which has mass m2 = 5m1. After the collision, block 2 slides into a region where the coefficient of kinetic friction μk is 0.2 and comes to a stop in distance d within that region. What is the value of distance d if the collision is (a) elastic and (b) completely inelastic?

1. A five-year bond with a yield of 11% (compounded annually) pays an 8%

   coupon at the end of each year.

   1. (a) What is the bond’s price?

   2. (b) What is the bond’s duration?

   3. (c) Use the duration to calculate the effect on the bond’s price of a 0.2% de-

      crease in its yield.

   4. (d) Recalculate the bond’s price on the basis of a 10.8% per annum yield and

      verify that the result is in agreement with your answer to (c).