Homework Answers

Estimate the mean weight of 6 students randomly chosen in a university if students 1 weight 53 kg students weight student 2 weight 64 kg student 3 weight 49 kg student 4 weight 59 kg student 5 weight 62 kg and student 6 weight 55 kg

For what values of α are vectors (1,1,2,1), (2,1,2,3), (1,4,2,1) (-1,3,5,α) are linearly inde-

pendent

Let S = {u1,u2,u3} be a basis for the vector space V. Show that T = {w1,w2,w3} is also

a basis for V, where w1 = u1 +u2 +u3, w2 = u2 +u3,w3 = u3.

Prove that a real number 𝑥 is irrational if and only if 5𝑥 is irrational

Find out if the following functions are one-to-one and/or onto. a. 𝑓: 𝑍 → 𝑅, 𝑓(𝑥) = 𝑥 3 + 1 b. 𝑓: 𝑅 + → 𝑅 +, 𝑓(𝑥) = |𝑥| + 5

Letv1 = (0,3,6,0),v2 = (0,2,4,6), and v3 = (1,−1,−2,1). Express (4,−1,−2,−11) as a

linear combination of v1,v2, and v3

Find the general solutions of the following differential equations using D-operator methods:

2.1 (D² - 2D + 5)y = x+5

2.2 (D+4)² x = sinh4t

Just before a referendum on a school​ budget, a local newspaper polls 405 voters to predict whether the budget will pass. Suppose the budget has the support of 55​% of the voters. What is the probability that the​ newspaper's sample will lead it to predict​ defeat?