You are a new financial analyst for Acme Bank and Funeral Directors. You are looking at the following for a company you are considering for a loan. Sales = $650,000, their operating profit was $400,000, their interest expense = $35,000, the par value of their common stock was $20,000, the paid-in-capital in excess of par was $210,000 and they have 10,000 shares of common stock outstanding. Assume a 21% tax rate.

Given this information: What was the price of a share of common stock when it was sold (assume no flotation costs and they only sold stock once) ?
AND
If they had no preferred stock, what must have been their earnings per share?

Consider the low-speed airflow over the NACA 0012 airfoil at low angles of attack. The Reynolds number based on the chord is roughly Rec = 2.88 × 10^6. This flow can reasonably be modeled as incompressible and inviscid. The initial input value for your simulations is provided on the bottom of this assignment. Your need to generate a report to give background introduction, and address the following issues: (inlet Velocity: 1.5 Attack angle: 5)

1. Incompressible, Inviscid Model: Explain why the incompressible, inviscid model for this flow should yield lift coefficient values that match well with experiment but will yield a drag coefficient that is always zero.
2. Boundary Value Problem: What is the boundary value problem (BVP) you need to solve to obtain the velocity and pressure distributions for this flow at any angle of attack? Indicate governing equations, domain and boundary conditions (u = 0 at a certain boundary etc.). For each of the boundary conditions, indicate also the corresponding boundary type that you need to select.
3. Coefficient of Pressure: Run a simulation for the NACA 0012 airfoil based on the initial conditions assigned to you with a mesh with 15000 elements and a mesh with 40000 elements. Plot the pressure coefficient obtained from FLUENT on the same plot as data obtained from experiment. The experimental data is from Gregory & O’Reilly, NASA R&M 3726, Jan 1970 and plot is provided in PDF format for you to digitize in Excel. Follow the aeronautical convention of flipping the vertical axis so that negative Cp values are above and positive Cp values are below.
4. Lift and Drag Coefficient: Obtain the lift and drag coefficients from the FLUENT results on the two meshes. Compare these with experimental or expected values (present this comparison as a table). For example, the experimental values for 10 degree angle of attack are: Cl = 1.2219; Cd = 0.0138.

Fifteen students from Poppy High School were accepted at Branch University. Of those students, six were offered academic scholarships and nine were not. Mrs. Bergen believes Branch University may be accepting students with lower ACT scores if they have an academic scholarship. The newly accepted student ACT scores are shown here.

Academic scholarship: 25, 24, 23, 21, 22, 20
No academic scholarship: 23, 25, 30, 32, 29, 26, 27, 29, 27

Part A: Do these data provide convincing evidence of a difference in ACT scores between students with and without an academic scholarship? Carry out an appropriate test at the α = 0.02 significance level. (5 points)

Part B: Create and interpret a 98% confidence interval for the difference in the ACT scores between students with and without an academic scholarship. (5 points)

WXY Inc. declared a dividend on July 27, 2004 to be payable on September 10, 2004. The list of shareholders who would be entitled to this dividend would be prepared on August 10, 2004.

a) Identify the key dates involved with dividend payment (4 points)

b) If Tom bought some shares on August 7, 2004, would he have received the dividend declared for this period? If not, who would receive it? (3 points)

c) You buy a share of stock before the ex‐dividend date for US$15. The dividend declared is US$1.50 per share. Ignoring the effect of taxes, does the value of your investment increase after the ex‐dividend date? Does it decrease? Why? Why not? (3 points)

Please prove American inequality boundary in the options market.

Please prove American inequality boundary in the options market.

Multivariable calculus

Evaluate: ∮ 3? 2 ?? + 2???? using two different methods. C is the boundary of the graphs C y = x2 from (3, 9) to (0, 0) followed by the line segment from (0, 0) to (3, 9).

2. Evaluate: ∮(8? − ? 2 ) ?? + [2? − 3? 2 + ?]?? using one method. C is the boundary of the graph of a circle of radius 4 oriented counterclockwise

(a) Find all positive values of λ for which the following boundary value problem has a nonzero solution. What are the corresponding eigenfunctions? X′′ + 4Xʹ + (λ + 4) X = 0, X′(0) = 0 and X′(1) = 0. Hint: the roots of its auxiliary equation are –2 ± σi, where λ = σ².

(b) Is λ = 0 an eigenvalue of this boundary value problem? Why or why not?

Let C₀=[0,1]. C_n is obtained by removing the middle open interval of length α/3ⁿ from each interval of C_n-1 where α∈(0,1).

Let C=⋂C_n. Prove that C contains only boundary points, i.e., x∈C is a boundary point of C if every neighborhood of x contains at least one point in C and at least one point not in C.