Question

what is the variance of this? (random variables)

score 42 · Answer 1 · 2026-04-14 18:35:56

42

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what is the variance of this? (random variables)

Published on 14 Apr 2026 - 18:35

score 95 · Answer 2 · 2026-04-15 18:54:47

95

Views

Assuming that $P(x)$ is a polynomial and it is true that $P(3x)=26 \cdot P(x+1)$, then of what degree is the polynomial?

Published on 15 Apr 2026 - 18:54

score 35 · Answer 3 · 2026-04-15 14:48:08

35

Views

If $\frac{y}{x}=\frac{3x+y-w}{6x-y-z}=\frac{y+w}{7y-x+z}$ with $x,y,z,w>0$, $6x\ne y+z$, $7y\ne x-z$, then what is the value of $\frac{x}{y}$?

Published on 15 Apr 2026 - 14:48

score 92 · Answer 4 · 2026-04-16 00:25:21

92

Views

If for the real numbers $a,b(a\ne b)$ it is true that $a^2=2b+15$ and $b^2=2a+15$, then what is the value of the product $ab$?

Published on 16 Apr 2026 - 0:25

score 128 · Answer 5 · 2026-04-24 10:14:28

128

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Find the value of the expression: $\frac{1}{\sqrt{4}+\sqrt{7}}+\frac{1}{\sqrt{7}+\sqrt{10}}+\cdots+\frac{1}{\sqrt{13}+\sqrt{16}}$

Published on 24 Apr 2026 - 10:14

score 200 · Answer 6 · 2026-04-16 02:55:10

200

Views

German Math Olympiad Qualifier 2020

Published on 16 Apr 2026 - 2:55

score 114 · Answer 7 · 2026-04-14 14:16:14

114

Views

Solve two multiplication equations with one multiplication operator

Published on 14 Apr 2026 - 14:16

score 61 · Answer 8 · 2026-04-16 10:37:47

61

Views

If $\cos{x}*\cos{2x}=\frac{1}{4}$, $x\in[0,90^o)$, then what is the solution of the equation?

Published on 16 Apr 2026 - 10:37

score 47 · Answer 9 · 2026-04-15 06:14:31

47

Views

If $\frac{a}{b}=\frac{c}{d}=\frac{e}{z}=\frac{2}{3}$, then what is the value of the expression $\frac{2a-6c-3e}{2b-6d-3z}$, while $bdz(2b-6c-3z)\ne0$

Published on 15 Apr 2026 - 6:14

score 108 · Answer 10 · 2026-04-15 02:14:18

108

Views

Which is the smallest parameter of the polynomial of the smallest degree such that it has $\frac{\sqrt{3}}{2},\frac{\sqrt{2}}{3}$ as roots?

Published on 15 Apr 2026 - 2:14

score 83 · Answer 11 · 2026-04-13 21:48:06

83

Views

Trouble applying theory to practice

Published on 13 Apr 2026 - 21:48

score 203 · Answer 12 · 2026-04-16 08:53:37

203

Views

Given the number $N=3^{12}-1$. Find how many even and odd divisors of $N$ exist, which divide $N$ but don't divide $3^k-1$, for $1\le k\le 11$

Published on 16 Apr 2026 - 8:53

score 140 · Answer 13 · 2026-04-13 17:34:10

140

Views

Combinatorics Problem: Building numbers from the difference of the first 2021 numbers

Published on 13 Apr 2026 - 17:34

score 136 · Answer 14 · 2026-04-13 23:53:24

136

Views

Simplify $2\log 4 + 3\log 8 - \log 2$ using logarithmic laws, then evaluate.

Published on 13 Apr 2026 - 23:53

score 57 · Answer 15 · 2026-04-16 07:30:57

57

Views

If the operation $\&$ has the following properties: $x\&0=0\forall x\in \mathbb{R}$ and $x\&(y+1)=x\&y+(x-y)\forall x,y\in \mathbb{R}$

Published on 16 Apr 2026 - 7:30

List Question

what is the variance of this? (random variables)

Assuming that $P(x)$ is a polynomial and it is true that $P(3x)=26 \cdot P(x+1)$, then of what degree is the polynomial?

If $\frac{y}{x}=\frac{3x+y-w}{6x-y-z}=\frac{y+w}{7y-x+z}$ with $x,y,z,w>0$, $6x\ne y+z$, $7y\ne x-z$, then what is the value of $\frac{x}{y}$?

If for the real numbers $a,b(a\ne b)$ it is true that $a^2=2b+15$ and $b^2=2a+15$, then what is the value of the product $ab$?

Find the value of the expression: $\frac{1}{\sqrt{4}+\sqrt{7}}+\frac{1}{\sqrt{7}+\sqrt{10}}+\cdots+\frac{1}{\sqrt{13}+\sqrt{16}}$

German Math Olympiad Qualifier 2020

Solve two multiplication equations with one multiplication operator

If $\cos{x}*\cos{2x}=\frac{1}{4}$, $x\in[0,90^o)$, then what is the solution of the equation?

If $\frac{a}{b}=\frac{c}{d}=\frac{e}{z}=\frac{2}{3}$, then what is the value of the expression $\frac{2a-6c-3e}{2b-6d-3z}$, while $bdz(2b-6c-3z)\ne0$

Which is the smallest parameter of the polynomial of the smallest degree such that it has $\frac{\sqrt{3}}{2},\frac{\sqrt{2}}{3}$ as roots?

Trouble applying theory to practice

Given the number $N=3^{12}-1$. Find how many even and odd divisors of $N$ exist, which divide $N$ but don't divide $3^k-1$, for $1\le k\le 11$

Combinatorics Problem: Building numbers from the difference of the first 2021 numbers

Simplify $2\log 4 + 3\log 8 - \log 2$ using logarithmic laws, then evaluate.

If the operation $\&$ has the following properties: $x\&0=0\forall x\in \mathbb{R}$ and $x\&(y+1)=x\&y+(x-y)\forall x,y\in \mathbb{R}$

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