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Six years ago olwethu lent happy R150 000 on condition that he would pay her back in nine years time. The applicable interest rate is 15,5% per year,compounded monthly. Happy also owes olwethu another amount of R250 000 that he has to pay back six years from now for a loan that earned interest at 16,4% per year , compounded semi annually. Happy asks olwethu if he can settle his debts three years from now. The total amount that Happy will have to pay in three years is
Estimate kurtosis.
XFrequency
1 – 512
5 – 1011
10 – 1510
15 – 204
20 – 253
Present complete solutions for each item. Illustrate the normal curve if possible.
2. The scores of individual students on a national test have a normal distribution with mean of
18.6 and a standard deviation of 5.9. At Federico Ramos Rural High School, 76 students
took the test. If the scores at this school have the same distribution as national scores, solve
for the following:
a. determine the mean and standard deviation of the sampling distribution of the sample
mean.
b. find the probability that the sample mean falls between 17 and 20 (P(17 < x̅< 20).
c. the number of sample means that is above 19.3 kilograms.
Present complete solutions for each item. Illustrate the normal curve if possible.
1. A population consists of six values (6, 9, 12, 15, 18, and 21).
a. Select a random sample of size 3. Explain the random sampling that you used.
b. How many possible samples can be drawn?
c. List all possible samples and compute the mean of each sample.
d. Construct a frequency distribution of the sample means obtained in step 2 including
x̅; f; P(x̅); ̅x ⋅ P(x̅); ̅x2⋅ P(x̅); ΣP(x̅); Σx̅⋅ P(x̅) and Σx̅2⋅ P(x̅).
e. Determine the mean, variance and standard deviation of the sample mean.
Project costs Rs 180,000 and is expected to generate cash inflows as:
Year Cash Inflow ( Rs )
1 20000
2 24000
3 30000
4 36000
5 40000
a. Discuss the characteristics of long term capital budgeting decisions
b. calculate the Net Present Value of the project if the cost of capital is 12% and conclude.
For a business firm leverage is about the fixed operating cost and the fixed finance costs in the cost structure of the firm. For the given details, identify for which firm the degree of operating leverage and degree of financial leverage are higher and why so:
Firms Amrit Baayu
Sales (Rs.) 360000 750000
Variable cost p.u 20 150
Fixed cost (Rs.) 72000 140000
Output (units) 6000 1500
Interest 40000 80000
Prove that if p, q are positive integers such that p|q and q|p, then p = q
Prove the 3√7 is irrational
.Rotate the region bounded by 𝑥 = 𝑦2 − 4 and x=6-3y about the line x=24.
I found the volume using circular ring: horizontal strip method as 2011.45
ACTIVITY IN BASIC CALCULUS
QUOTIENT RULE
I. Find the derivative of the following functions below using the quotient rule. Show your complete solution.
- "\\frac{x^2-7x}{2x^3+5x^2}"
- "\\frac{3x^2+7x-14}{x^3-4x^2}"
- "\\frac{2x^3+8x^2}{x^2+6x^2-10}"
II. Create your own given problem involving quotient rule and solve. Show your complete solution. Do not copy the given example below.
1. Example must have two different terms in numerator, and three different terms in denominator
eg. (do not copy)
y= "\\frac{8x^2-3x}{x^2+6x^2-10}"
2. Example must have three different terms in numerator, and three different terms in denominator
eg. (do not copy)
y= "\\frac{x^2+8x^2-3x}{2x^3+6x^2-10}"
