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You flip 3 coins. Let X, the random variable, be the number of tails on all three coins. Construct a probability distribution for this experiment.



A firm manufactures two products; the net profit on product 1 is Birr 3 per unit and Birr 5 per unit on product 2. The manufacturing process is such that each product has to be processed in two departments D1 and D2. Each unit of product1 requires processing for 1 minute at D1 and 3 minutes at D2; each unit of product 2 requires processing for 2 minutes at D1 and 2 minutes at D2. Machine time available per day is 860 minutes at D1 and 1200 minutes at D2. How much of product 1 and 2 should be produced every day so that total profit is maximum. (solve with graphical method)


The simple interest rate which is equal to a discount rate of 12% per year for a period of 18 months is ?


1. 10.32%

2. 0.12%

3. 12.00%

4. 14.36%


How do I work it out?


solve the equation in exact differentials

(2-9xy2)xdx+(4y2-6x3)ydy=0


solve the equation in exact differentials

2xydx+(x2-y2)dy=0



Solve the first order linear inhomogeneous differential equation using the bernoulli method

xy,-2y=2x4

Solve the first order linear inhomogeneous differential equation using the constant variation method

(2x+1)y,=4x+2y


Solve the first order linear inhomogeneous differential equation using the constant variation method

xy,-2y=2x4

Reduce the homogeneous equation to the separated one

(x+2y)dx-xdy=0


separate the differential equation into variables

(x2-1)y,+2xy2=0


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