Other Math Answers

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?  

A computer program in Shannon’s computer carries out a single mathematical operation in 1.5 × 10^-6 seconds. How much time would the program take to complete 2.5 × 10³ mathematical operations?

Which pre-mathematical concept is best described by this illustration, where learners must draw a line to those shapes that look the same? 1) Matching 2) Patterning 3) Classifying 4) Abstraction

A manufacturer produces a product which it sells for $60 per unit. The variable cost per unit is $20 and the fixed cost per month is $10,000. 

1.  How many units must be sold per month to break even?

a. 167      b. 500      c. 400      d. 250      e. None of these

2.  Determine the monthly profit (loss) if it sells 325 units per month.

a. $1500      b. ($1500)      c. $3000      d. $0      e. None of these

3.      How many units must be sold per month to earn a profit of $7000?

a. 342         b. 425      c. 675          d. 575           e. None of these

4.  Find the percent discount for an article listed at $40 whose net price is $25.

a. 15%        b. 25%     c. 37.5%      d.  62.5%       e. None of these

5.   The net price of an article is $125.46. What is the list price if a discount of 38% was allowed?

a. $200.90     b. $204.13       c. $90.91       d. $202.35      e. None of these

Solve using Polya’s four-step problem solving strategies. 

1. A big department store is having a clearance sale, discounting all items by 40%. If the appliance you’re eyeing on is Php 1,500 after the markdown, how much did it cost before? How much will you save if you took advantage of this sale?

Disprove the following statements using counterexample. 

1) (𝑥 + 4)2 = 𝑥2 + 16  

2) 𝑥2 > x  

3) √𝑥2 = 𝑥