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Dresden Database Research Group 14

1 + \left(5 \times p + 1\right) \times 19 = x \times 5 \Rightarrow 19 \times p + 4 = x

(n + 1)^2 = n^2 + 2*n + 1 = (n + \left(-1\right))^2 + 2*n + (-1) + 2*n + 1 = (n + (-1))^2 + 4*n

190 = (20 + (-1))*20/2

|(t + \frac{1}{2}) * (t + \frac{1}{2}) + \dfrac74|/(\sqrt{2}) = \frac{1}{\sqrt{1^2 + 1^2}}*|t * t + 2 + t|

0 = \dfrac{0}{1 + 0^2}

\int\limits_{-1}^1 \left(a + h\right)^2\,dz = \int (a * a + \int (h^2 + 2\int ah\,dz)\,dz)\,dz = \int (a^2 + \int h^2\,dz)\,dz

10 = -6 + 5*a + 7*(-1) = 5*a + 13*(-1)

\dfrac{x}{z} = \frac{x}{z}

41625 = \frac{1}{5}125*(1 + 2 + 3 + 4 + 5)*111

z^2 - 10 z + 25 = (z + 5 (-1))^2

{8 \choose 5}\cdot 5 = 280

72-32=40

x = \tfrac{1}{2}(x + y - z + x + z - y) \geq \sqrt{(x + y - z) (z + x - y)}

1 - 1/36 - \frac{20}{36} = \frac{1}{36}\cdot 15

\left(b + g\right) \cdot (b + g) = b^2 + g^2 + b \cdot g + b \cdot g

\tfrac{30}{z*15 + 12} = \frac133*\dfrac{10}{z*5 + 4}

180 + 30 \cdot (-1) - 48.59 = 101.41

4*(-1) + a^3 - a^2*3 + 5*a = (a + (-1))^3 + 2*(a + (-1)) + (-1)

29 \cdot 29 + 29 \cdot 37 + 37^2 = 49 \cdot \left(2^2 + 2 \cdot 7 + 7^2\right) = 49 \cdot 67

(s*2)^2 = s^2*4

-15 = 35 + 2 \cdot t + 9 = 2 \cdot t + 44

\sin(\beta + \alpha) = \sin(\beta) \times \cos(\alpha) + \cos(\beta) \times \sin(\alpha)

(z + \frac{z^2}{2!} + \frac{1}{3!} \cdot z \cdot z \cdot z + \ldots)^{-1} = \frac{1}{e^z + \left(-1\right)}

\sqrt{a * a + b^2} = (b^2 + a^2)^{\frac12}

a^2\cdot \dfrac{\frac{1}{a}\cdot 1/b}{b^2}\cdot 1\cdot b^6 = \frac{1}{b\cdot \dfrac{1}{b^6\cdot a^2}\cdot b \cdot b\cdot a}

4/4 \cdot \frac{1}{-10} \cdot (z \cdot 2 + 2) = \left(z \cdot 8 + 8\right)/\left(-40\right)

h = h*d = d\Longrightarrow h = d

{5 \choose 2}*{9 \choose 2} = 360

(x^2)^3 + 64 = (x \cdot x)^3 + 4^3 = (x^2 + 4)\cdot \left(x^4 - 4\cdot x^2 + 16\right)

5 \cdot (-1) \cdot (-5) \cdot (-25) \cdot \left(-110\right) = 68750

\left(t + p\right) (a \frac{p}{p + t} + b \dfrac{t}{p + t}) = a p + b t

\lim_{x \to 1}(3*x^2 - 4*x + 1) = 0 = \lim_{x \to 1}(x + \left(-1\right))

\operatorname{asin}(\theta) = \frac{1}{\sin(\theta)} = \frac{1}{\sin(\theta)}

(x^3 + 0x^2 + 1x + 0) = (x^2 + 0x + 1) * (x + 0)

2 = (i + 1)^1 + (1 - i)^1

8/8*\frac{7*t}{t*6 + 4} = \tfrac{56*t}{32 + 48*t}

e^{1/x} = 1 + \frac1x + \tfrac{1}{2 \cdot x^2} + \ldots > \dfrac{1}{2 \cdot x^2}

q^2 - q \times 6 + 8 = (q + 2 \times \left(-1\right)) \times (4 \times (-1) + q)

-10 x + 3x + 12 x = 15 x - 10 x = 5x

\dfrac{4}{2\cdot (2\cdot x + 1)} = \dfrac{1}{2\cdot x + 1}\cdot 2 = \frac{1}{x + 1} + \dfrac{1}{(x + 1)\cdot (2\cdot x + 1)}

1 - \frac{1}{2^5}(\binom{5}{0} + \binom{5}{2}) = 1 - \frac{1}{32}(1 + 5) = 0.8125

a^2*M + I + M*a^2 = I + 2*M*a * a

\sin(\frac12 \cdot \pi + k) = \cos{1/k} \geq 1 - \dfrac{1}{k^2}

28 = 35 + 7*(-1)

\frac{2^k*6}{\left(2^k*6\right)^2} = \frac{1}{2^k*6}

1 - \frac{1}{K + 1} = \frac{1}{K + 1}*K = \frac{1}{1 + 1/K}

\left|{D^t\times D}\right| = \left|{D\times D^t}\right|

2/7 = 6/21

\frac{1}{\frac12 \cdot 6} = 1/3

\sqrt{7} + \sqrt{112} - \sqrt{63} = -\sqrt{9 \cdot 7} + \sqrt{7} + \sqrt{16 \cdot 7}

\tan(y + 2\times \pi) = \tan(y)

1 + 2 + 3 + \cdots + 21 = 21\times 22/2 = 231

\pi^{-1}[\pi[U]] = U

(4 \cdot x + z) \cdot (z + x) = x \cdot x \cdot 4 + 5 \cdot x \cdot z + z \cdot z

1 = \cos^2{\dfrac{\pi}{2}} + \sin^2{\pi/2}

\frac{1000}{2 + (-1)} + \frac{1}{1 + 0(-1)}0 = 1000

x \cdot 3 + 3 \cdot y = (x + y) \cdot 3

10 + \frac1210 = 10 + 5 = 15

\sin(\tan^{-1}(y)) = \frac{y}{(y^2 + 1)^{1 / 2}}

y + ly^2 + l^2 y^3 + \dotsm = (ly + (ly)^2 + (ly)^3 + \dotsm)/l = \frac{1}{1 - ly}

11 - k\cdot 4 = 3\Longrightarrow k = 2

\frac{1}{-3 l + l^2} (15 (-1) + l^2 + 2 l) = \frac{(3 (-1) + l) (l + 5)}{(l + 3 (-1)) l}

(1 + n + 1)\cdot (n + 1)! = (1 + n + 1)\cdot (n + 1)!

F + B = -(-B + 180 - F) + 180

12 \times 16^0 + 5 \times 16^1 + 16^2 = 348

9/8 = 3/2*\dfrac{1}{4}*3

1/256 = \left((1/2)^2\right)^4

(x^2 + z^2) \cdot (x + z) \cdot (-z + x) = x^4 - z^4

(T + 1)^2 = T^2 + 2*T + 1 > T^2 + 1

\sqrt{5/3} = \sqrt{\frac{1}{12}20}

1 \leq 4 \cdot x < 2 \implies 4 \cdot x = 4 \cdot x + 1

(s * s)^2 = s^4

2*\sqrt{7} = \sqrt{7}*(3*(-1) + 1 + 4)

(c + a)*\left(a - c\right) = a * a - c^2

\sqrt{1 + s} = 1 + s/2 + \ldots

2^{d + f} = 2^d\cdot 2^f

xv vx = (vx) * (vx) xv\Longrightarrow 1 = vx

4 + z^4 - z^2\cdot 5 = ((-1) + z)\cdot (z + 2\cdot (-1))\cdot (z + 1)\cdot (z + 2)

z_0^4 - z_0^2*2 + 1 = 0 \implies (z_0^2 + (-1))^2 = 0

(z + (-1) + 1)^{\dfrac12} = \sqrt{z}

29/3 = -\dfrac{2}{3}*2 + 35 - 8*3

\frac{8 + y}{8 - y} = 1 + \frac{2 \cdot y}{8 - y} = 1 + \frac{1}{8/y + \left(-1\right)} \cdot 2

\frac{65}{8 + 5} = \frac{1}{13}65 = 65/13 = 5

A*z = z/(1/A)

-(l + 1)! + (2 + l)! = (l + 1)!\cdot (l + 1)

\cos(-G) = \cos\left(G\right)

b^2 + \frac{1}{b * b} + 1 = (b + \tfrac1b)^2 + (-1) = (b + \frac{1}{b} + 1)*(b + \tfrac{1}{b} + (-1))

\frac{l_2}{l_1} = \frac{1}{l_1}l_2

\sqrt{3} \cdot (4 + 2 + 3(-1)) = \sqrt{3} \cdot 3

120/36*\dfrac{1}{r^4}*r^5 = \frac{r^5*120}{36*r^4}*1

\left(3\times (-1) + x\right)\times y = C + e^x\times 6 \Rightarrow y = \frac{C + e^x\times 6}{3\times (-1) + x}

4^{\frac23} = 2^{1/3}*2

a \cdot h = -a \cdot (-h)

d_1^2 - d_2^2 = (d_1 + d_2) (-d_2 + d_1)

f^{-x}*b = \tfrac{1}{f^x}*b

5^{20} \cdot \binom{19}{9} = 5 \cdot 5^{19} \cdot \binom{19}{9}

2/31 = 1/31 + \frac{1}{30} \cdot 30 \cdot 1/31

\left(k + \left(-1\right)\right) (k + 1) k \ldots = (1 + k)!

ak = ai \Rightarrow a^k = a^i

\mathbb{Var}[S_m] = \mathbb{E}[(S_m - \mathbb{E}[S_m]) * (S_m - \mathbb{E}[S_m])] = \mathbb{E}[(S_m + 5*\left(-1\right))^2]