1/

a/

 When the iron rusts, the reaction below takes place.
4 Fe (s) + 3 O2 (g) → 2 Fe2O3 (s)                     ΔH = -1 643 kJ

What is the heat of formation (ΔHof) of Fe2O3? Is a calculation
necessary?

b/

The equation for the decomposition of mercury (II) oxide is as follows.
2 HgO (s) + 182 kJ →  2 Hg (l) + O2 (g)

Determine  ΔHof for HgO (s)?

c/

Calculate  ΔH in the following reactions.
 CO (g) + 1/2 O2 (g) → CO2 (g). 
CH4 (g) + 2 O2 (g)  → CO2 (g) + 2 H2O (g)
 CS2 (g) + 2 H2O (l)  → CO2 (g) + 2 H2S (g)

Jarvene Corporation uses the FIFO method in its process costing system. The following data are for the most recent month of operations in one of the company’s processing departments:

The cost of beginning inventory according to the company’s costing system was $7,830 of which $4,824 was for materials and the remainder was for conversion cost. The costs added during the month amounted to $184,110. The costs per equivalent unit for the month were:

Required:

1. Compute the total cost per equivalent unit for the month.

2. Compute the equivalent units of material and conversion in the ending inventory.

3. Compute the equivalent units of material and conversion that were required to complete the beginning inventory.

4. Compute the number of units started and completed during the month.

5. Compute the cost of ending work in process inventory for materials, conversion, and in total for the month.

6. Compute the cost of the units transferred to the next department for materials, conversion, and in total for the month.

Complete this question by entering your answers in the tabs below.

• Required 1
• Required 2
• Required 3
• Required 4
• Required 5
• Required 6

Compute the total cost per equivalent unit for the month. (Round your answer to 2 decimal places.)

Complete this question by entering your answers in the tabs below.

• Required 1
• Required 2
• Required 3
• Required 4
• Required 5
• Required 6

Compute the equivalent units of material and conversion in the ending inventory.

Complete this question by entering your answers in the tabs below.

• Required 1
• Required 2
• Required 3
• Required 4
• Required 5
• Required 6

Compute the equivalent units of material and conversion that were required to complete the beginning inventory.

Complete this question by entering your answers in the tabs below.

• Required 1
• Required 2
• Required 3
• Required 4
• Required 5
• Required 6

Compute the number of units started and completed during the month.

• Required 1
• Required 2
• Required 3
• Required 4
• Required 5
• Required 6

Compute the cost of ending work in process inventory for materials, conversion, and in total for the month. (Round your intermediate calculations to 2 decimal places.)

Compute the cost of the units transferred to the next department for materials, conversion, and in total for the month. (Round your intermediate calculations to 2 decimal places.)

DATA SHEET

A social scientist would like to analyze the relationship between educational attainment (in years of higher education) and annual salary (in $1,000s). He collects data on 20 individuals. A portion of the data is as follows:

a. Find the sample regression equation for the model: Salary = β₀ + β₁Education + ε. (Round answers to 2 decimal places.)

Salaryˆ= _________ + __________ Education

b. Interpret the coefficient for Education.

• As Education increases by 1 unit, an individual’s annual salary is predicted to decrease by $8,590.

• As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $6,890.

• As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $8,590.

• As Education increases by 1 unit, an individual’s annual salary is predicted to decrease by $6,890.

c. What is the predicted salary for an individual who completed 6 years of higher education? (Round coefficient estimates to at least 4 decimal places and final answer to the nearest whole number.)

Salaryˆ + _____ $

Consider the IVPs: 
        (A)  y'+2y = 1,   0<t<1 ,  y(0)=2.
        (B)  y' = y(1-y), 0<t<1 ,  y(0)=1/2.

1. For each one, do the following:
  a. Find the exact solution y(t) and evaluate it at t=1.
  b. Apply Euler's method with  Δt=1/4  to find Y4 ≈ y(1).
     Make a table of tn, Yn for n=0,1,2,3,4.
  c. Find the error at t=1.

2. Euler's method is obtained by approximating y'(tn) by a forward finite difference.
   Use the backward difference approximation to y'(tn+1) to derive the 
   Backward Euler Method:   Yn+1 = Yn + Δt f(tn+1, Yn+1) , n=0,1,2,...  

   Note that now the unknown Yn+1 appears inside f(.,.), so this equation needs to be 
   solved for Yn+1 at each time-step!!! whence it is also called Implicit Euler Method.
   For the simple ODEs (A), (B) above, the updating equation can be solved by hand, 
   but in general a root-finder (like Newton-Raphson) is needed.
   This scheme is also 1st order, but it has better stability properties than Explicit Euler.

   For each IVP problem (A), (B), do the following:
  a. Apply the Backward Euler Method with  Δt=1/4  to find Y4 ≈ y(1).
  b. Find the error at t=1 and compare with Explicit Euler.


3. Use the centered difference approximation to y'(tn) to derive the so called 
   Midpoint Method:   Yn+1 = Yn-1 + 2 Δt f(tn, Yn) , n=1,2,... 
 
   Note that this requires both Yn-1 and Yn to produce Yn+1.  It is a 2-step method, 
   hence not self-starting (need Y0 and Y1 before it can be applied), 
   so some single-step method (like Euler) must be used to start it off.
   However, it has the advantage of being a 2nd order method, and explicit.
 
   For each IVP problem (A), (B), do the following:
  a. Apply the Midpoint Method with  Δt=1/4  to find Y4 ≈ y(1).
  b. Find the error at t=1 and compare with Explicit Euler and with Implicit Euler.
     Which method seems to be doing better in this case ?

Solve y^(4) + y′′/4 = 2x + 4. (Hint: The method of undetermined coefficients may be useful in this case.)

Suppose an object is 4 sided marked as {1,2,3,.., 4. Now you toss this object 4 times. Let nS be the number of outcomes in this sample space. Let A be the event consisting of all outcomes in which 2 occurs at least once. How many outcomes are there in A? It is whole number. Computer follows comma rule when entering large numbers. For example, 1123 is entered as 1,123

24. Show that (x ^p) − x has p distinct zeros in Zp, for any prime p. Conclude that (x ^p) − x = x(x − 1)(x − 2)· · ·(x − (p − 1)).

(this is not as simple as showing that each element in Z_p is a root -- after all, we've

seen that in Z₆[x], the polynomial x^2-5x has 4 roots, 0, 5, 2, and 3, but x^2-5 is not equal to (x-0)(x-5)(x-2)(x-3))

Carla Vista Co. has had 4 years of record earnings. Due to this success, the market price of its 470,000 shares of $4 par value common stock has increased from $15 per share to $54. During this period, paid-in capital remained the same at $5,640,000. Retained earnings increased from $4,230,000 to $28,200,000. CEO Don Ames is considering either (1) a 15% stock dividend or (2) a 2-for-1 stock split. He asks you to show the before-and-after effects of each option on (a) retained earnings, (b) total stockholders’ equity, and (c) par value per share.

(A)

1.      Stock dividend - retained earnings $______

2.      2-for-1 stock split - retained earnings $______

(B)

PAID-IN CAPITAL: Original Balance: ______ After dividend: _____ After Split: _____
RETAINED EARNINGS: Original Balance: _____ After dividend: _____ After Split: _____
TOTAL STOCKHOLDERS EQUITY: Originical Balance: _____ After dividend: _____ After Split: _____
SHARES OUTSTANDING: Original Balance: _____ After dividend: _____ After Split: ______

(C)

Stock dividend - par value per share $______

2-for-1 stock split - par value per share $______

Investor W has the opportunity to invest $615,000 in a new venture. The projected cash flows from the venture are as follows. Use Appendix A and Appendix B.

Investor W uses a 7 percent discount rate.

a-1. Complete the table below to calculate NPV. Assume her marginal tax rate over the life of the investment is 15 percent.

a-2. Should Investor W make the investment?

b-1. Complete the table below to calculate NPV. Assume her marginal tax rate over the life of the investment is 20 percent.

b-2. Should Investor W make the investment?

c-1. Complete the table below to calculate NPV. Assume her marginal tax rate in years 1 and 2 is 10 percent and in years 3 and 4 is 25 percent.

c-2. Should Investor W make the investment?