1 votes
0 answers
41
Consider the following three functions defined for all positive integers $n \geq 0$.\[\begin{array}{l}f(n)=|\sin (n)+n|, \\g(n)=n, \\h(n)=|\sin (n)| .\end{array}\]Which o...
0 votes
1 answer
42
0 votes
1 answer
43
For any positive integer $\text{N}$, let $\text{p(N)}$ be the probability that a uniformly random number $a \in\{1, \ldots, N\}$ has an odd number of factors (including 1...
1 votes
1 answer
55
Consider the following automata:Let $N$ be the number of $0 / 1$-strings of length exactly $6$ accepted by this automata. Which of the following is true about $\text{N}$?...
0 votes
1 answer
56
If $\text{O}$ is the center of the circle, what is the area of the shaded portion in square cm?$4 \pi-4 \sqrt{2}$$\frac{7}{2} \pi-4 \sqrt{2}$$\frac{7}{2} \pi-4 \sqrt{3}$$...
0 votes
1 answer
57
Let $\sigma$ be a uniform random permutation of $\{1, \ldots, 100\}$. What is the probability that $\sigma(1)<\sigma(2)<\sigma(3)$ (i.e., what is the probability that the...