A nonprofit company concerned with the school dropout rates has designed a tutoring program aimed at students between 16 to 18 years old. A national center for educational statistics reported that the high school dropout rate for the year 2000 was 10.9​%. One school​ district, who adopted the use of the​ nonprofit's tutoring program and whose dropout rate has always been very close to the national​ average, reported in 2004 that 183 of their 1772 students dropped out. Is their experience evidence that the tutoring program has been​ effective?

Question Three (3) [20 Marks]

a) The Memorandum of Incorporation (MOI) as well as the Articles of Associations (AOA) serve as
founding documents for a company; describe the purpose as well as differences between each of
these two documents.

b) Describe the process as set out in terms of the Companies Act 28 of 2004 from whence a
company is founded, the founding documents, the parties involved up until the entity is clothed
with legal personality and opens for business.

c) Which parties would actively be involved in the day to day running of a company?

(a) Employers at a firm are worried about the effect of March Madness, a basketball championship held each spring in the US, on employee productivity. They estimate that on a regular business day employees spend on average 15 minutes of company time checking personal email, making personal phone calls, etc. They also collect data on how much company time employees spend on such non-business activities during March Madness. They want to determine if these data provide convincing evidence that employee productivity decreases during March Madness.

(b) Since 2008, chain restaurants in California have been required to display calorie counts of each menu item. Prior to menus displaying calorie counts, the average calorie intake of diners at a restaurant was 1100 calories. After calorie counts started to be displayed on menus, a nutritionist collected data on the number of calories consumed at this restaurant from a random sample of diners. Do these data provide convincing evidence of a difference in the average calorie intake of diners at this restaurant?

(c) Based on the performance of those who took the GRE exam between July 1, 2004, and June 30, 2007, the average Verbal Reasoning score was calculated to be 462. In 2011 the average verbal score was slightly higher. Do these data provide convincing evidence that the average GRE Verbal Reasoning score has changed since 2004?

• Design employee compensation programs taking into account organizational circumstances
• Propose amendments benefit programs to meet changing employee and employer needs
• Assess employer costs of benefit programs

Part of a human resource managers job is to analyze the benefits programs to ensure that an organization is compliant and that the costs are within budget. There are a number of required programs such as social security, worker's compensation insurance, unemployment insurance, health care, and FMLA leave. In addition to these mandated programs, many employers offer additional benefits such as dental, vision, disability, life insurance, tuition reimbursement, holidays, vacation, other paid time off (jury duty, bereavement, etc), 401(k) or other retirement, student debt support and more.

Managed by Q Case Benefits Analysis: In the case study we learn that Managed by Q offers free health insurance, 40 hours of paid vacation and a 401(k) plan. In addition, they would have to offer the legally required benefits such as worker's compensation and unemployment. The financial spreadsheet indicates there is a 20% markup for benefits and taxes. In year 5, therefore, we could surmise that of the $2,729,927 in wages and taxes, 20% or approximately $545,000, went to benefits and taxes.

1. Create an analysis of the provided benefits and taxes (both mandatory and discretionary) and create an academic, data-guided, proposal of any changes you might suggest to Managed by Q.
2. For this analysis, assume a 4% 401(k) match, FUTA rate of .06 (of first $7000), SUTA rate of .019 (of first $9000).
3. Be sure to incorporate items such as cost sharing or creative benefits such as student loan repayment options in your recommendations if appropriate. Must be 5 to 6 pages plus cover and references.

Note: In this exercise you need to weigh out how many benefits you would like to offer verse the cost of those benefits. In your paper be sure to (1) explore the current benefit offering and (2) talk about what benefits you might offer and/or what changes you would recommend to Managed by Q.

An environmentally toxic radioactive chemical is continually released at a constant rate of 1 (mg per vol per time) at the midpoint of a canal of length L with still water. As it diffuses through the canal with diffusion constant D = 1, it decays at rate λ (per unit time) The ends of the canal are connected to large bodies of toxic-free water. Set up the model equations and the boundary conditions. Find the steady-state concentration and sketch its spatial profile for different values of L and λ.

[Hint: Break the problem up into two parts, on each side of the source. At the source the concentration must be continuous, and in a small interval about the source, the ‘flux in’ minus the ‘flux out’ equals one.]

Consider the following means and sample sizes for two independent samples (with the samples being denoted by the subscripts "_X" and "_Y"): M_X = 6.286, M_Y= 1.973, n_X= 16, n_Y= 16. If the standard error (s_Difference) is 2.256, what is the the upper boundary of the corresponding 95% confidence interval? Please use a typical null hypothesis that predicts no differences between the two populations when computing your answer. When calculating your answer, please ensure that you subtract the mean for group Y from the mean for group X (i.e., M_X - M_Y).  Please also retain three decimal places for all steps (if relevant) and provide three decimal places when reporting your answer.

Consider the 1D wave equation d^2u/dt^2 = c^2( d^2u/dx^2) with the following boundary conditions: u(0, t) = ux (L, t) = 0 . (a) Use separation of variables technique to calculate the eigenvalues, eigenfunctions and general solution. (b) Now, assume L = π and c = 1. With initial conditions u(x, 0) = 0 and ut(x, 0) = 1, calculate the solution for u(x, t). (c) With initial conditions u(x, 0) = sin(x/2) and ut(x, 0) = 2 sin(x/2) − 3 sin(5x/2) calculate the solution for u(x, t).

Using MATLAB:

Consider the following Boundary Value Differential Equation:

y''+4y=0

y(0)=-2

y(π/4)=10

Which has the exact solution: y(x)= -2cos(2x)+10sin(2x)

Create a program that will allow the user to input the step size (in x), and two guesses for y'(0). The program will then use the Euler method along with the shooting method to solve this problem. The program should give the true error at y(π/8). Run your code with step sizes of π/400 and π/4000 and compare the errors. Chose any guesses for y'(0) that are reasonable. Also list the two errors you calculated.

QUESTION 4 You are the owner-manager of a chain of coffee shops in Singapore, brewing and selling the latest types of expresso drink inhouse but buying all necessary factors from the market. Your 50 or so shops located around the city can seat around 20 patrons each and currently only sell caffeinated drinks. At this stage of growing your business you are considering vertical and horizontal integration. Using the theory of the optimal boundary of the firm, discuss the make-or-buy decision as well as the scope for horizontal integration and diversification of your business. What stages of the vertical chain should you consider conducting inhouse? What other horizontal markets may you integrate into?

Consider, in the xy-plane, the upper half disk of radius R, with temperature u governed by Laplace's equation, and with zero-Dirichlet B.C. on the (bottom) flat part of the disk, and Neumann B.C. ur=f(theta), on its (top) curved boundary.

(a)Use the Method of Separation of Variables to completely derive the solution of the BVP. Show all details of the procedure, and of your work. Do not start with with the eigenfunctions, the are to be derived. The final solution must be summarized and circled at the end of your work, showing the final complete expression for u(r,theta) and any coefficents and necessary conditions for f(theta).

(b) Obtain the complete simplified solution of the BVP above, with R=2 and f(theta) = 100.