Math Answers

A meeting of envoys was attended by 4 Koreans and 2 Filipinos. If two envoys were

selected at random one after the other, determine the values of the random variable K

representing the number of Koreans. Construct the probability histogram.

A questionnaire asks shareholders of a company to state whether they consider the chairman’s salary to be too high, about right, or too low. Excluding shareholders who have no opinion, the probabilities of answers from randomly selected shareholders are as follows:</span><span lang="EN-US"><o:p></o:p></span>

Too High       0.80

About Right   0.25

Too Low         0.05

           What are the probabilities that if three shareholders are selected at random,

a.      They will all answer, ‘too high’?

b.     Exactly two will answer ‘too low’?

c.      Exactly two will give the same answer?

a machine starts production of matchboxes at the rate of 12000 per hour. The rate of production decreases by 40% every hour. Calculate the total nimber of matchboxes produced in first 2 hours

 Assume the total cost of a tertiary education will be R75 000 when your child enters university in 18 years. You presently have R7 000 to invest. What rate of interest must you earn on your investment to cover the cost of your child’s tertiary education?

In a certain Algebra 2 class of 27 students, 11 of them play basketball and 13 of them play baseball. There are 5 students who play neither sport. What is the probability that a student chosen randomly from the class plays basketball or baseball?

Find the equations of the tangents to the graph of y=x+1/x that are parallel to y+2x=0

Find the equation of the tangent to at the point where , in f(x)=x^2+4x-5

standard form.

. (a) How many different positive three-digit whole numbers can be formed from

the four digits 2, 6, 7, and 9 if any digit can be repeated?

(b) How many different positive whole numbers less than 1000 can be formed

from 2, 6, 7, 9 if any digit can be repeated?

(c) How many numbers in part (b) are less than 680 (i.e. up to 679)?

(d) What is the probability that a positive whole number less than 1000, chosen

at random from 2, 6, 7, 9 and allowing any digit to be repeated, will be less

than 680?

7. Answer question 7 again for the case where the digits 2, 6, 7, 9 can not be repeated

Academicians was surveyed of their loyalty to the university. They're asked “If given an offer by other university equivalent or slightly better than present position, would you remain or not?Table 4 represents the responses of the 200 academicians which were cross-classified with their length of service. 

Table 4: Loyalty of Academicians & Length of Service.

Length of Service Total

Loyalty Less than1 yr, 1-5 yr, 6-10 yr, More than 10 yr

Remain 10 30 5 75 120

Not remain 25 15 10 30 80  

a)represent the information in Table 4 as a tree diagram.             

b)What's the probability of randomly who is loyal and who has more than 10 yr service?

c)What's the probability of who would not remain and has less than 1-yr of service?

d)What's the probability of who would remain, given that he or she has 1-5 yr of service?

e)What's the probability of who would not remain, given that he or she 6-10 yr of service?

Solve y’=y-x2

, y(0)=1, by Picord’s method upto the third approximation . Hence find

the value of y(0,1), y(0,2)