In a village, there are exactly $10$% more boys than girls; $15$% more women than men; $20$% more children than adults. The population is less than $6000$...

The question is: Prove that: $2tan^{-1}2=\pi-cos^{-1}\frac{3}{5}$ Hint: use the fact that $tan(\pi-x)=-tanx$ I did the question without using the Hint, bu...

Prove that if $ f\mathrm{(}z\mathrm{)} $ is analytic at the infinity ,then : $ {\lim}_{{z}\mathrm{\rightarrow}\mathrm{\infty}}{f}\prime{\mathrm{(}}{z}{\ma...

Given Random variables $X$ and $Y$ is it true always that; $$E(XY)^2 \le E(X^2)E(Y^2)$$ Is it easy to prove?

Can someone explain why taking an average of an average usually results in a wrong answer? Is there ever a case where the average of the average can be us...

Is there any way I can calculate derivatives using a Casio Graphing Calculator? Is there a program available for the calculator which can calculate them?

How do I solve First I thought the difference is $D - A = 9^{12} - 9^9$, but I didn't know the rules for subtracting exponents with different bases. ...

In my text book Lebesgue measure is shown to have countable additivity on disjoint sets, i.e. if $A_k$ is a countable sequence of disjoint measurable sets...

I'm currently studying compilers and am having some issues with understanding regular sets. For example, lets say I had a set of binary strings, (0, ...

Having read the classical proof of the existence of an Algebraic Closure (originally due to Artin), I wondered what is wrong with the following simplifica...