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4. The population of a certain village at one time was a perfect square. Later, with an increase of 100, the population was one more than a perfect square. Now, with an additional increase of 100, the population is again a perfect square. What was the original population? (Give all possible answers.)
The number of men needed to cement a barangay road vanes directly with the length of the road at a constant
width and inversely with the number of days required to do the job. If a 30m road can be cemented by 10 men in
12 days how wide is the road? How many days will it take 50 men to cement a road that is 1 km long?
A certain college has 52 students participating in games.30 play netball, 25 play football , 10 play handball and football ,13 play netball and handball,9 play netball and football while 2 play all the three games. How many students play handball and no other game?
Determine if the statement is TRUE or FALSE. Justify your answer. All numbers under discussion are
integers.
10. Given a positive integer N ≥ 10, form the number N' by removing the ones digit from N
and subtracting this digit from the remaining truncated integer. (For example, if N = 1309,
N' = 130 0 9 = 121.) If N' is divisible by 11, then N is divisible by 11.
Determine if the statement is TRUE or FALSE. Justify your answer. All numbers under discussion are
integers.
5. For each m ≥ 1 and n ≥ 1, if mn is a multiple of 4, then m or n is a multiple of 4.
6. For each m ≥ 1 and n ≥ 1, if mn is a multiple of 3, then m or n is a multiple of 3
The demand for a commodity is given by p = 400 q. The average total cost of producing the commodity is given by
where p is the price in shillings and q is the quantity in kilograms.
Required
What does in the ATC equation represent economically? (1 mark)
Determine the output that leads to maximum profit and the profit at the level of output. (9 marks)
Alpha industries sells two products, X and Y, in related markets, with demand functions given by:
Px 13 + 2X + Y = 0
Py 13 + X + 2Y = 0
The total cost, in shillings, is given by:
TC = X + Y
Required:
Determine the price and the output for each good which will maximize profits.
A manager claims that the company has given an average salary increment of RM 40
to all the employees per year. A researcher wants to check if this claim is true. A
random sample of 45 employees taken by the researcher showed that these employees
got an average increment of RM 38 per year with a standard deviation of RM 8.
a) Is there enough evidence to accept the manager’s claim at 0.1 level of significance?
b) Test at 2.5% significance level whether the average salary increment of all
employees is less than RM 40 per year.
Peter travels from his place to his uncle house a distance of 30km.He cycles for two thirds of the journey before walking for the rest of the journey. If his cycling speed is 10km/hr more than the walking speed and the whole journey took him 3hrs 20 minutes, calculate his cycling speed.
A certain college has 52 students participating in games.30 play netball, 25 play football , 10 play handball and football ,13 play netball and handball,9 play netball and football while 2 play all the three games. How many students play handball and no other game?
1. Identify the property that justifies each statement.
a. If AB ¯≅ PR ¯ and PR ¯≅ ST ¯, then AB ¯≅ ST ¯.
