Math Answers

The formula for final velocity of an object starting from zero and undergoing constant acceleration is v=1/2at^2, what is the time it will take a car accelerating at 4 m/s^2 to reach 50m/s

If A B C are three vectors show that A*(B+C)=A*B+B*C

a) Your friend has some money to invest and is deciding between an investment in Dolly Ltd or Yaalu Ltd. In the most recent reporting period, Dolly Ltd made a profit after tax of
R1 250 000 after investing R8 500 000, compared to Yaalu’s after-tax profit of R1 000 000 after investing R6 000 000. The average return that investors are currently looking for in the market is 15% (cost of capital). On the basis of the higher profit achieved, your friend believes that Dolly Ltd is the superior investment. Discuss your friend’s investment choice. In doing so, suggest other financial data that should be considered. Discuss and analyse the benefits and limitations of each. What non-financial data may be of interest to inform your friend’s investment decision?

QUESTION 3
Three television channels (103, 104 and 119) have telemovies, reality shows and drama series. The number of each programmeis shown in Table 5,
Table 5
Type of Show 103 104 119
Telemovie 5 2 1
Reality show 3 2 8
Drama series 4 4 2

a) Calculate the probability that a programme is a telemovie or it is shown on channel 104. (4 Marks)

b) Calculate the probability that a programme is a drama series or a reality show. (4 Marks)
c) Calculate the probability that a programme is on channel 119 and a drama series. (2 Marks)
[Total: 10 marks]

QUESTION 2
The number of goals conceded in the first five games by the two bottom teams in a Football Championship League 2016 are as shown inTable 4,
Table 4
Team A 3 3 5 3 1
Team B 3 3 0 2 1

a) Calculate the standard deviation of the goals conceded for each team. (6 Marks)
b) Calculate and compare the coefficient of variation of both teams. (4 Marks)
[Total: 10 marks]

QUESTION 1
The cumulative grade-point average (CGPA) for the top 25 undergraduates in one particular university are listed in Table 3,
Table 3
3.80 3.77 3.70 3.74 3.70
3.86 3.76 3.68 3.67 3.57
3.83 3.70 3.80 3.74 3.67
3.78 3.74 3.73 3.65 3.66
3.75 3.64 3.78 3.73 3.64

a) Calculate the mean, the median and the mode of the CGPA. (8 Marks)
b) Comment on the shape of the distribution of the CGPA based on the values gathered in (a). (2 Marks)

sum <-- 2 * n + 404
for (int i==1; i < n + 1; i++ ) do
sum <-- sum + i + MyA[i] + 404
for (int j = 0; j <= i; j++) do
sum <-- sum * MyA[j] + i + 404 * n
end-for (j)
for (int k = 0; k <= n; k++) do
sum <-- sum * k + MyA[k]
end-for (k)
sum <-- sum + 303
end-for(i)
sum <-- sum + 303 * n

Find an explicit expression for T(n), the count function for the number of times that your operation is executed (is a function of n). It likely starts with one more summations, and ends with a polynomial in n in standardized form (i.e. simplest terms). Show work.

Your friend has some money to invest and is deciding between an investment in Dolly Ltd or Yaalu Ltd. In the most recent reporting period, Dolly Ltd made a profit after tax of R1 250 000 after investing R8 500 000, compared to Yaalu’s after-tax profit of R1 000 000 after investing R6 000 000. The average return that investors are currently looking for in the market is 15% (cost of capital). On the basis of the higher profit achieved, your friend believes that Dolly Ltd is the superior investment. Discuss your friend’s investment choice. In doing so, suggest other financial data that should be considered. Discuss and analyse the benefits and limitations of each. What non-financial data may be of interest to inform your friend’s investment decision?

Find the unit outward drawn normal to the surface
(
x
−
1
)
2
+
y
2
+
(
z
+
2
)
2
(x−1)2+y2+(z+2)2
= 9 at the point (3, 1, -4)