Math1151 Algebra. S1 2013 Test 2. Version 2a.

I need some help with the document in this question. It is an algebra test that needs to be completed. There is not a whole lot that I can pay but should not take an expert to long.

1. Math1151 Algebra. S1 2013 Test 2. Version 2a.

(1) Is the vector u = (1,−5,−2)T parallel to the plane x = (2,4,−1)T +λv+µw where v = (1,2,2)T and w = (3,−1,7)T?

(2) Compute

(3) Find the shortest distance from the point with coordinate vector a = (3, −1, 4) T to the plane Π with equation x + 3y + 3z = 5.

(4) A fifth of the items handled by a courier company are parcels, and the rest are documents. The company delivers 80% of parcels on time and delivers 90% of documents on time. If an item is selected at random, find the probability that

(a) The item is a parcel and it was delivered on time

(b) an item was delivered on time

(c) The item is a parcel, given that it was delivered on time.

2. Math1151 Algebra. S1 2010 Test 2. Version 2b.

(1) A chemical plant produces two substances, eubutymate and barbidol. To produce one unit of eubutymate requires 0.1 units of barbidol, and to produce one unit of barbidol requires 0.2 units of eubutymate. If the plant receives an order for 1900 units of eubutymate and 300 units of barbidol, how much of each needs to be produced altogether?

(2) Compute

(3)For the vectors v = (7, 1, −1) T and w = (−3, 1, 2) T, find (a) a vector perpendicular to both v and w

(b) The area of the parallelogram spanned by v and w

Suppose that bag 1 contains three red balls and a black ball, and bag 2 contains one red ball and two black balls. If a bag is selected at random and a ball is drawn at random from it, find the probability that

(a) Bag 1 was selected and a black ball was drawn Solution. 1/2 × 1/4 = 1/8

(b) a black ball was drawn

Solution. 1/2 × 1/4 + 1/2 × 2/3 = 1/8 + 1/3 = 11/24

(c) bag 1 was selected, given that a black ball was drawn