What is a rigorous mathematical/logical definition of 'randomness'? Under what conditions can we truthfully apply the predicate 'is random&...

Here are my full instructions: Find the transition matrix $P_{B'\leftarrow B}$ from $B=\left\{\left(1,1,\right),\left(2,3\right)\right\}$ to $B'...

Suppose a polygon with $n$ vertices is given $(V_1,V_2,... V_n)$. If the $(x,y)$ coordinates of the each vertex of the polygon are given, then how can we ...

Given $$\lim_{x\to 0} (e^x-2x)^\frac{1}{x} $$ I know that you take the natural log $$\lim_{x\to 0} \frac{1}{x}\ln(e^x-2x) $$ which is $$\lim_{x\to 0} \fra...

Find all solutions of the pair of equations $$x^2+x^2y^2+x^2y^4 = 525 \quad\text{and}\quad x+xy+xy^2=35$$ I got $(x,y)=(5,2)$, and $(x,y) = (20,1/2)$. Is ...

I am trying to solve for a variable, k, in terms of all the other variables. Here is the set up: solve({b*(e-f)*k = a-b(c-d-(e-f)/k-f-e)}, {k}) However, t...

No nodes have self referencing arrows. I tried solving on paper and got 14 graphs. 2 with 2 arrows, 4 with 3 arrows, 5 with 4 arrows, and 2 with 5 arrows,...

Assume $b$ is going to replace member $a$ in set $S$. That is, the set S is initially like this $S=\{a\}$, but now the new member $b$ is going to replace ...

Show that $$ \sum_{n=1}^\infty \left( \frac{1}{n(n+1)} \right) = \frac{1}{2}+\frac{1}{6}+\frac{1}{12}+ \;... $$ converges and find its sum. My solution so...

I have a question where I am trying to find the general solution of a linearised system, which I have linearised. I am just having difficulty obtaining th...