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Find the direction cosine (l, m, n) of vector r = 3i -2j + 6k b. Given that p = -12 and q = 1. Find a unit vector u such that │u│= 35 and u is the direction of p-3q 5 -1

a. Where in the world do we find some early evidence that people counted?


b. Approximately what year does this evidence date back?


c. Where in the Caps is this type of counting covered as a topic?



Find the probanility of getting.

a.fewer than 4 head.

b.exactly 4 head.

C.not more than 4 head.

d.two or more heads.


5 Test the following numbers for divisibility by 6, 9 and 11. (Do not divide or factorise.)


a) 6 798 340


b) 54 786 978

How many different committees of 5people can be chosen from 10 people

In its first year, “ABC Co” had the following experience





Sales = 50,000 units Selling price = br. 50





TVC = br. 1,000,000 TFC = br. 250,000





Required:





Develop Revenue, cost & profit functions for the co. in terms of quantity.





Find the Breakeven point in terms of quantity





Convert the cost equation in terms of quantity in to a cost equation in terms of revenue





Find the Breakeven revenue





If profit had been br. 500,000 what would have been the sales volume (revenue) & the quantity of sales





What would have been the profit if sales are br. 2,000,000.

one of the characteristics of binominal experiment is that each trial can result in two or more outcomes?


QUESTION 1. [34 MARKS] 1.1 Determine whether each of the following mappings T is linear, or not. Justify your answer.

(a) T: R2 - R3, where T(z, y) = (3y, 2x, —y).

(b) T: P1 - R2, where T[p(x)] = [p(0), p(1)].

(c) T: R3 - R2, where T(z, y,z) = (x+1,y+2).


Let the probability that a successful rocket launching will be equal to 0.4. Find,


Average number of trials required for the successful rocket launching.

The probability that the successful launching will be made on the third attempt.

The probability that successful rocket launching requires less than 5 attempts.


if X~B(n₁ = 5, p = 1/4) and Y~B(n = 8, p = 1/4).Then what is the distribution of X+Y?


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