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A shipment of five computer contains two that are slightly defective. If a retailer receive three of computers at random,list the elements of the sample paces using the letters D and N for defective and non-defective computers, respectively.to each sample point assign a value of X of the random variable X representing the numbers computers purchased by the retailer which are slightly defective




In the Cartesian plane, two vertices of a square have coordinates (3 ; 4) and ( -2 ; - 1). One of the other two vertices, has coordibates


Price X Y

20 40 50

30 40 40

40 60 50

50 55 60

60 60 40

70 70 60




1. Find the cross elasticity of commodity X and Y when price changed from

i. 20 to 30

ii. 40 to 50 

iii. 60 to 70

2. Interpret your answers in I, ii and iii above 



A straight line passes through the points (2; -3) and (4 - 4). The coordinate of the x intercept of this line is ?


1.     The Hardrock Concrete Company has plants in three locations and is currently working on three major construction projects, each located at a different site. The shipping cost per truckload of concrete, daily plant capacities, and daily project requirements are provided in the table below.


A jewellery store sells beads necklaces.Each necklace cost R40 for the wire and R15 per bead.There exists a linear relation between the cost if the necklace and the number of beads the necklace has.The cost,C is dependent on the number of beads,n. The graph that represents this relation correctle is?


Phosphorus pentachloride is formed when 17.2 g of chlorine gas react with 23.2 g of solid phosphorus (P2). Determined the reactant that is in excess


Calculate the work done by 2.4N force pushing a 400.g sandwich across a table 0.75m wide

Suppose the price level in a particular economy equals 1.3 and that the quantity of real GDP demanded at that price level is $1,200. An increase of 0.1 point in the price level reduces the quantity of real GDP demanded by $220, and a reduction of 0.1 point would produce an increase in the quantity of real GDP demanded of $220. Draw the aggregate demand curve and show the price level and quantity of real GDP demanded at three points

a) i) Give an inductive formula for the sum of the first n odd numbers:

1 + 3 + 5 + ... + 2n -1

Show your induction process.

ii) Use the proof by mathematical induction to prove the correctness of your

inductive formula in i) above.


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