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I have this equation (identity?): $$3^{3x}=3^{2y+1}$$ I understand that this simplifies to: $$3x=2y+1$$ So, the base (of the exponentials) cancel out. I w...
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So if we have a game with player A who roll 2 dice with 6-sides and player B with one 12-sided die what is the probability to win for the player A and the...
I have a clarification to make with my notes. This is about functions. It defines the function $$f(x) = \sqrt[5]{x+1} \space\text{from} \space x=(-1,\inft...
The regular expression for accepting odd a's and even b's I calculated is: (aa)*a(bb)* and the NFA: +-------+-----+---+ | State | a | b | +-----...
An experiment consists of throwing two dice. (a) Write down the sample space of this experiment (b) If E is the event "total score is at most 10", list th...
The above series can be simplified as: $$\sum_{n=1}^{\infty}\frac{n!}{(k)^n}$$ Does it mean that there is no such a positive integer k exits so that the s...
Given n non-negative values. Their sum is k. $x_1+x_2+⋯+x_n=k$ Given the constraints $x_i \leq \sqrt{k}$ (thus, $n \geq \sqrt{k}$) Is it possible to prove...
(I don't know how to make a matrix here, someone please correct it into a better format, thanks~) So I'm applying the Gaussian Elimination to fi...
In ordinary matrix multiplication $AB$ where we multiply each column $b_{i}$ by $A$, each resulting column of $AB$ can be viewed as a linear combination o...
