Consider a triangle ABC, where $A=(x_1,y_1), B=(x_2,y_2)$ and $C=(x_3,y_3).$ Then it is well known that the centroid is $(\frac{x_1+x_2+x_3}{3}, \frac{y_1...

If there are 10,000 people, how many people must have the same birthday (ignoring year)? This is the way I went about this problem: 10000 people / 365 day...

A driver averaged 50 km/h on the roundtrip between home and a city d kilometers away. The average speeds for going and returning were x and y km/h, respec...

The following definition is given in Dummit and Foote's Abstract Algebra on page 146. For any group $G$ define the dual group of $G$ (denoted $\hat{G...

I am talking about classical logic here. I admit this might be a naive question, but as far as I understand it: Syntactic entailment means there is a proo...

The question was: A radioactive element decays at a rate proportional to the mass remaining. Initially the mass is 10mg and after 20 days it is 5mg. Set u...

I tried using $\int_a^bf(x)dx=\int_a^bf(a+b-x)dx$ but it's giving back the same result. I tried using integration by parts but it's giving a ver...

I understand that two independent random variables are by definition uncorrelated as their covariance is equivalent to 0: $Cov(x,y) = E(xy)- E(x)E(y)$ $E(...

How many rays can made from $4$ collinear points? The answer is $6$ (as floating around the internet) but I am not sure how is it possible, as far I know ...

I want to find the basin of attraction of a fixed point. For example, I have $f(x)=\frac 1{x+1}$, whose fixed points are $\frac{-1\pm \sqrt{5}}{2}$. Now, ...