What was the purpose of the Northwest Ordinance?

Responses

It united the colonies together under a weak government.

It said that runaway slaves had to be returned.

It organized new territories in the West.

It forced the Cherokee Nation to move to Indian Territory.

Assume a proposed project under consideration by the James River Co. requires $28,900 in fixed assets. The firm plans to ignore bonus depreciation and instead apply straight-line depreciation to zero over the asset's 6-year life. An aftertax salvage value of $5,400 is expected. The project will produce an annual operating cash flow of $7,300 and will require net working capital of $500 initially plus an additional $500 in Year 3. Net working capital will be restored to its original level when the project ends at the end of Year 6. The tax rate is 21 percent and the required rate of return is 14 percent. What is the net present value of this project? Properties of Production Functions. (21 pts total)(a) Consider the "realistic" production function for motorcyclesf(z1,z2,z3) = 10(1 + z41 z42 z43 )1where z1 is the amount of labor, z2 is the amount of steel, and z3 is the amount of plastic.All inputs are in separate subsets from one another (z1 Nt, z2 Ns, and z3 Nr).Test whether or not the production function is strongly separable. (5 pts)(b) Consider the short-run version of this function when the amount of plastic is fixed(z3 = 1),f(z1,z2,z3) = 10(1 + z41 z42 )1Solve for and interpret the elasticity of substitution for inputs 1 and 2 (1,2). (6 pts)(c) How does 1,2 compare to a Cobb-Douglas function? What does this mean? (2 pts)(d) Solve for an interpret the local returns to scale for the short-run production function. The n x n Hilbert Matrix is a matrix with the entries: Hij = 1/1 + i + j(Here i = 0, ...n-1, j = 0, ..., n 1) Find the 4x4 Hilbert Matrix. H = 1 1/2 1/3 1/4 1/2 1/3 1/4 1/5 1/3 1/4 1/5 1/6 1/4 1/5 1/6 1/7 Find the smallest integer n so that the condition number of the n x n Hilbert Matrix is greater than 10^7. n = Fix a non-singular matrix B E Mmxn. Then we can define a function : Mnxn+R by det(AB) (A) = det(B) Show that f satisfies the four conditions used to define the determinant in Def. 2.1 on pp. 324. Use this to prove that for any non-singular matrix B, det(AB) = det(A) det(B). (b) (1 pt) Using the result from (a), for a non-singular matrix C, what is det(C-1) in terms of det (C)? (c) (6 pts) Does the result from (a) still hold if B is singular? Give a counterexample, or prove that it's still true. 2 a 2.1 Definition Anxn determinant is a function det: Mnxn R such that (1) det(21,..., k.i + Pj,...,n) = det(1, ... ,,..., Pn) for i ti (2) det(1, ..., , ..., Pi..., Pn) = -det(1, ..., P,..., , ..., Pn) for i #j (3) det(1, ..., kp,..., Pn) = k det(1, ...,,...,n) for any scalar k (4) det(I) = 1 where I is an identity matrix (the p's are the rows of the matrix). We often write |T| for det(T). Find the domain of the function. (Enter your answer using interval notation.) 2x + 1 f(x) = x2 + x - 20 ((-00,00) x Accelerated Return Notes provide payoffs at maturity that depend on the value of an under- lying stock and the notional N. Assume the stock pays no dividends. If the ending value of the underlying is below or at the starting value the note will pay Nx ending value starting value If the ending value is greater than the starting value then the payoff is given by ending value starting value min [x 1.2,N+N2 starting value (a) Draw the payoff diagram for the Accelerated Return Note and explain the payoff profile in your own words. Use a notional of N = 100 and an initial value of the underlying of $50. The maturity of the note is in one year. [8 marks] (b) If the only options traded on the underlying are European calls, how would you replicate the payoff? [6 marks] (c) How would you replicate the note if only European puts were available? [4 marks] (d) Now assume that the underlying stock has a volatility of 35% and the (continuously compounded) risk-free rate is given by r= 1%. What is the price of the note in the Black-Scholes-Merton model? Suppose we have a sample of five values of hemoglobin A1c (HgbA1c) obtained from a single diabetic patient. HgbA1c is a serum measure often used to monitor compliance among diabetic patients. The values are 8.5%, 9.3%, 7.9%, 9.2%, and 10.3%.(a) What is the standard deviation for this sample?(b) What is the standard error for this sample? The curve y = 2/3 ^x/ has starting point A whose x-coordinate is 3. Find the x-coordinate of 2 3 the end point B such that the curve from A to B has length 78.Expert Answer What is the depreciation charge of an equipment purchased four years ago for $120,000, a salvage value of $20,000, and a expected life of 4 years if it is depreciated using a straight line method?a. $25,000b. $11,428.60c. $20,000d. $14,285.71 Box 2. AB x 100 For James, Box 2 = 64 x 100 = $6,400Bob the Builder sold one of his used trucks for [Box 2]: At the time of the sale, its book value was $8,000. As a result of this sale, what would be an impact on total assets? You will have to indicate increase or decrease and by how much. If you cannot determine the impact based on the information given, please write down "the impact cannot be determined". A firm's treasury office is primarily responsible for all thefollowing, EXCEPT:A). Financial accounting reportingB). Identifying investment opportunitiesC). Raising long-term capitalD). Managing Discuss how individuals' attitudes toward work have changed as aresult of government programs and society's expectations. Lecture Notes onCONTROL SYSTEM THEORYAND DESIGNTamer Basar, Sean P. Meyn, and William R. Perkins5.5 Exercises 5.5.1 Investigate the controllability properties of the LTI model = Ax + Bu, for the three pairs of (A, B) matrices given below. (a) A=-5 1 B=1 0 4 1(b) A=3 3 6 B=0 1 1 2 0 2 2 4 1(c) A=0 1 0 B=0 0 0 1 0 0 0 0 1 c) Consider a bond with three years to maturity with a face value of $F. At the end of each year it pays a cash coupon of $C. Denote its yield to maturity by y. i. You buy the bond today for a price of $P, and sell it in one year (just after the payment of the coupon) for $P. If the yield to maturity does not change over time, write down expressions for P, and for P, in terms of C, F and y. [2 marks] ii. Define the return from holding the bond for that year in the normal fashion (i.e. the return is equal to the sum of its change in price over the period and any end of period cash payments, all divided by the initial price). Show how this return is related to the bond's yield to maturity. [4 marks] iii. Based on your preceding answer, discuss when yield to maturities are likely to be decent indicators of the returns from holding bond positions. [3 marks] Solve the following PDE (Partial Differential Equation) for when t > 0. Express the final answer in terms of the error function when it applies.{ ut - 9Uxx = 0 x E R u(x,0) = e^5x the nurse is caring for a postterm, small for gestational age (sga) newborn infant immediately after admission to the nursery. what would the nurse monitor as the priority? describe the three data fragmentation strategies. give some examples of each that are different from the book. Evaluate each of the following given f(x) = 6x-7, g(x) = -2x + 1 and h(x) = -2x. (1 point each) a) (f + g)(x) b) (g-f)(x) c) (h+g)(-3) d) (fh)(x) e) (fo h)(x) f) (foh)(4) Even with the power to change interest rates, the Fed is unable to directly impact inflation, output or unemployment. This is because: a. Interest rates do not affect inflation, output and unemployment b. Interest rates have no influence on the economy C. Interest rates determine the opportunity cost of spending money today d. Inflation, output and unemployment are fixed e. None of these Convert the angle pi/3 radians to degrees.