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Abongile, the manager of a construction company is renovating a home and has expenses of R200 000,00
now and another R41 812,00 in six months’ time. As he finds it difficult to find the cash now, he proposes
to settle all the debt after six months with a single payment. The debt is subject to an interest rate of 9,5%
per annum, compounded quarterly. What is the value of the payment that will settle his debt at the end of
month six?
Suppose, you want to get admitted into an English Language Course run by British Council. Now, write an e-mail to the manager for the details of the course.
Suppose you placed an order of some items of Computers and Accessories for your Software Farm from “TECH Mart Computer and Accessories” Company. The quality promised and the quality of the items received is not the same. Write a complaint letter to the manager of the company.
What is the agenda of a meeting? Give a sample of an agenda of meeting.
Bongeka purchased a new refrigerator and were expected to pay R1 684,00 five months ago and another
R1 323,00 in eight months’ time. She could not make the payment five months ago, but after receiving a
bonus at work, she rescheduled to repay the loan in two equal payments, the first due in two months and the
second due in five months’ time. The payment at month five will settle the debt, therefore, the settlement
date is month five. The debts and payments are subject to the same interest rate of 11,4% per annum,
compounded monthly.
@ 11,4% per year, compounded monthly
The value of each of the payments, rounded to the nearest rand, is equal to
Draw the chemical structure of cholesterol and state its functions
25. For each of the linear operators below, determine whether it is normal, self adjoint, or neither (a) T : R2 → R2 defined by T(x, y) = (2x − 2y, −2x + 5y). (b) T : C 2 → C 2 defined by T(x, y) = (2x + iy, x + 2y).
Consider a two-player game where the player A chooses “up” or “down” and player B chooses
“left” or “right” Their payoffs are as follows: When player A chooses “up” and player B
chooses “left” they both get $3. When player A chooses “up” and player B chooses “right”
they get $2(for A) and $4(for B). When player A chooses “down” and player B chooses
“left” they get $1(for A) and $6(for B). Finally, when player A chooses “down” and player
B chooses “right” they both get $5. The two players decide simultaneously.
(a) Draw the strategic form game. Is there any dominant strategy? Justify your answer.
(b) Is there a Nash equilibrium in pure strategies? Justify your answer.
(c) Find the best response functions and the mixed strategies Nash Equilibrium if each
player randomizes over his actions.
(d) Show graphically the best response functions and the Nash Equilibria (in pure and in
mixed strategies).
Briefly explain why Sodium ions have a charge of 1+
(2 marks)
Define professional communication. Explain the importance of effective communication in the workplace.
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