Math Answers

The table below shows the weight of 21 students (on the left) and the corresponding number of students with that weight (on the right). Compute the Mean of the data below.

Weight No. of Students

34 5

39 8

43 2

45 6

250 members of a certain society have voted to elect a new chairman. Each member may vote for either one or two candidates. The candidate elected is the one who polls most votes. Three candidates x, y z stood for election and when the votes were counted, it was found that: - 59 voted for y only, 37 voted for z only - 12 voted for x and y, 14 voted for x and z - 147 voted for either x or y or both x and y but not for z - 102 voted for y or z or both but not for x Required i. Present the information in a Venn diagram. (6 Marks) ii. How many voters did not vote? (4 Marks) iii. How many voters voted for x only? (2 Marks) iv. Who won the elections?

Show that T(x1, x2, x3, x4) = 3x1 −7x2 + 5x4 is a linear transformation by finding the

matrix for the transformation. Then find a basis for the null space of the transforma￾tion.

The probability distribution of X, the number

of imperfections per 10 meters of a synthetic fabric in

continuous rolls of uniform width, is given by

x 01234

f(x) 0.41 0.37 0.16 0.05 0.01

Construct the cumulative distribution function of X.

determine whether the homogeneous system has nontrivial solutions by inspection (without pencil and paper).

 2x1 − 3x2 + 4x3 − x4 = 0,

7x1 + x2 − 8x3 + 9x4 = 0,

2x1 + 8x2 + x3 − x4 = 0

solve the linear system by gauss-jordan elimination

 − 2b + 3c = 1 ,

3a + 6b − 3c = −2,

6a + 6b + 3c = 5

solve the linear system by gaussian elimination

 x − y + 2z − w = −1,

2x + y − 2z − 2w = −2 ,

−x + 2y − 4z + w = 1 ,

3x − 3w = −3

In a certain town, 40% of the eligible voters prefer candidate

A, 10% prefer candidate B, and the remaining 50% have no

preference. You randomly sample 10 eligible voters. What is

the probability that 4 will prefer candidate A, 1 will prefer

candidate B, and the remaining 5 will have no preference?

A firm faces the demand function

P = 190 - 0.6Q and the total cost function

C = 40 + 30Q + 0.4Q2

The number of patients seen in the emergency room in any hour is a random variable represented by x. Find the probability that in a given hour at least 14 patients will arrive. The probability distribution of x is: *