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Using the principle of induction, prove that 64 is a factor of 3^(2n+2)- 8n-9 ∀ n∈N

Sketch the graph of the function, f defined by


f(x)= |x-3| +[x], x∈ [2,4] where [x] denotes the greatest integer function

A cigarette labeled 100’s means that each stick is 100mm long. What will be the total length in inches of all the sticks in a pack if they are placed end to end in a column. Assume that one pack contains 20 sticks.

a laser emits light of frequency 4.7 x 10¹⁴ sec-1. What is the wavelenght of the light in nm? Inanometer (nm) = 1 x 10 -⁹ m

a global positioning system (GPS) receives a radio signal from a satrlite in 1.7 x 10-⁴ seconds. Assuming vacuum conditions for simplicity, how far is the the GPS receiver from the satellite?

The enzyme that is secreted from the small intestine and completes the action of another enzyme is secreted from stomach is?


How far from the y-axis is the center of the curve 2x²+2y²+10x-6y-55=0


Given two numbers X and Y, develop a program to determine the difference between X and Y



If X – Y is negative, Ans = X + Y;



If X – Y is zero, Ans = 2X + 2Y;



and if X – Y is positive, compute Ans = X * Y.



The lifetime of bulbs produced by Tariqs lightening company follows a normal distribution with a mean of 3462 hours and a standard deviation 1070 hours. What is the probability that randomly selected bulb will have a lifetime of at most 2800?


Given two numbers X and Y, develop a program to determine the difference between X and Y




If X – Y is negative, Ans = X + Y;




If X – Y is zero, Ans = 2X + 2Y;




and if X – Y is positive, compute Ans = X * Y.




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