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Learners have to demonstrate knowledge and skills in calculating quantities such as mass, length, perimeter, temperature and the volume of objects. When teaching conversions, emphasis must be placed on multiplication by a thousand (since "kilo" means thousand) and one thousandth (since "milli" means one thousandth). Design an instructional activity to explain how you would teach grade 4 learners the conversion of units when measuring length. Refer to page 25 of the CAPS document, the second bullet under ‘Calculations and problem-solving involving length’. Your focus should be on whole numbers (
A loan is granted at 21,6 % p.a. compounded daily. It is repaid by means of regular, equal payments of R1500 made every four months, where the first payment is made one year after the loan is granted. If the last payment is made exactly five years after the loan is granted, then the value of the loan, to the nearest cent, is R
Solve the problem with 3 different Voting Method.
The Plurality Method\
The Plurality Method with Elimination
The Borda Count Method
The owner of a restaurant decides to poll regular customers to choose which dish she’ll submit to an annual citywide competition. The choices are lemon-crusted salmon (L), crab-stuffed chicken (C), garlic prime rib (G), and wasabi rolls (W). The results are shown in the preference table.
# of votes 8 8 5 5 4
C 1 4 3 2 2
G 3 3 2 1 4
L 4 1 4 4 3
W 2 2 1 3 1
Find the orthogonal trajectories of the following curves (where a is a parameter). r = a(1 + sin θ)
In a given normal distribution, the population mean is 80 and the population standard deviation is 2.5. Find the corresponding standard z – score of the following values.
The population of each classroom for face-to-face classes consists of the numbers 10, 11, 15, and 9. List all the sample size of 3 from this population and compute the mean of each sample.
The treasurer of Company ABC expects to receive a cash inflow of $18,000,000 in 90 days. The treasurer expects short-term interest rates to fall during the next 90 days. To hedge against this risk, the treasurer decides to use an FRA that expires in 90 days and is based on 90-day LIBOR. The FRA is quoted at 6%. At expiration, LIBOR is 4.8%. Assume that the notional principal on the contract is $18,000,000.
Calculate the gain or loss to Company ABC as a consequence of entering the FRA
An electrical firm manufactures light bulb that has a length of life that is approximately normally distributed with a mean of 800 hours and a standard deviation of 40 hours. The supervising electrical Engineer took a random sample of 30 bulbs with an average life of 788 hours, test the hypothesis that µ=800 hours against the alternative hypothesis µ is greater than 800.
Use confidence level of 96%.
Is it a two tailed or one tailed test?
Null hypothesis?
Alternative hypothesis?
Size of the test?
Test statistics?
Critical region?
Decision ( accept or reject null hypothesis)?
The population of each room in a classroom consist of the numbers 10, 11, 15, and 9. List all the sample size of 3 from this population and compute the mean of each sample
The prevalence of a certain type of cancer among men aged 55−𝟔𝟎 is 1 in 100. A blood test will
be positive 95% of the time if the cancer is present but it is also positive 4% of the time if the
cancer is not present.
2.1. In a routine checkup, 56-year-old men receive a positive blood test. What is the probability that
he has the type of cancer?
2.2. What is the probability that a randomly selected 56-year-old men tests negative?
#331389 on Nov 2022