Math Answers

For the relation R = {(p,p) ,(q,p),(q,q),(r,r),(r,s),(s,s) ,(s,m) ,(m,m)}

1.Using warshall algorithm find the transitive closure R* of R

2.write matrix representation of R*

3.Check whether the relation of R* is an equivalence relation or a partial order.

Give what are asked for in the following problems:

1. The data given below are the weights (lbs) of 15 students.

35 38 39 38 39

45 40 47 38 43

40 42 45 50 48

a) Calculate the mean, median and mode.

b) Interpret the result.

Graph and discuss the continuity of the following functions:

1.f(x)= 3x-1, x≠1

2.f(x)=1/x+1

a right circular cylinder has a fixed height of 6 units. Find the rate of change of its volume V with respect to the radius r of its base. Find the rate of change of the total surface area A with respect to r.

(D^2 + 4) y = 4 sec 2x csc 2x

Eleven secretaries at a university in Kuala Lumpur were asked to take a special three-day intensive course to improve their keyboarding skills. At the beginning and again at the end of the course, they were given a particular two-page letter and asked to type it flawlessly. The data from the typing tests are shown in the following Table 3.

Table 3

Secretary

Number of years of experience x

Improvement

(words per minute)

5

140

3

120

c

2

80

4

100

5

130

4

90

4

110

5

120

6

130

5

130

4

100

a) Compute the correlation coefficient between the number of years of experience and the improvement.        (5 Marks)

b) Develop the regression equation for the improvement based on number of years of experience. (5 Marks)

the sale price of smart Tv is 40% lesser tha the sale price of smartphone . If the regular price of smartphone is Php 12,550.00 is on sale at 20% off . What is the sale price of the smart TV?

the sale price of smart Tv is 40% lesser tha the sale price of smartphone . If the regular price of smartphone is Php 12,550.00 is on sale at 20% off . What is the sale price of the smart TV?

A machine that produces ball bearings reports that the average diameter is not 0.5 cm. A sample of 10 ball bearings was measured and it was found that the average diameter is 0.48 cm, and the population standard deviation is 0.05 cm. (a = 0.05)

a) State the null hypothesis and the alternate hypothesis.   (2 Marks)

b) Find the critical values.     (1 Mark )

c) Calculate the test statistic (2 Marks)

d) State your decision regarding the null hypothesis (1 Mark )

e) Summarize the results.      (1 Mark )

f)  If the average diameter is less than 0.5 cm and a = 0 01,. what is the hypothesis and the critical values       (3 Marks)

range of the function f(x) = 5x − 3 defined by the domain {0,1,2}