Math Problem Solver

\[\frac{1}{\sqrt{2 \cdot \pi} \cdot 5.86} \cdot {e}^{\frac{-{\left( 10.5 - 10.19 \right)}^{2}}{2 \cdot 34.35}} = \frac{25 \sqrt{2}}{293 \sqrt{\pi} e^{\frac{961}{687000}}} \approx 0.06798372285014779400804731420691\]

\[\begin{aligned}\frac{1}{\sqrt{2 \cdot \pi} \cdot 5.86} \cdot {e}^{\frac{-{\left( 10.5 - 10.19 \right)}^{2}}{2 \cdot 34.35}}& = \frac{1}{\sqrt{2 \cdot \pi} \cdot \left(5 + \frac{86}{100}\right)} \cdot e^{- \cdot \left(10 + \frac{5}{10} - \left(10 + \frac{19}{100}\right)\right)^{2} \cdot \frac{1}{2 \cdot \left(34 + \frac{35}{100}\right)}}\\& = \frac{1}{\sqrt{2} \cdot \sqrt{\pi} \cdot \left(5 + \frac{86}{100}\right)} \cdot e^{- \cdot \left(10 + \frac{5}{10} - \left(10 + \frac{19}{100}\right)\right)^{2} \cdot \frac{1}{2 \cdot \left(34 + \frac{35}{100}\right)}}\\& = \frac{1}{\sqrt{2} \cdot \sqrt{\pi} \cdot \left(5 + \frac{43}{50}\right)} \cdot e^{- \cdot \left(10 + \frac{5}{10} - \left(10 + \frac{19}{100}\right)\right)^{2} \cdot \frac{1}{2 \cdot \left(34 + \frac{35}{100}\right)}}\\& = \frac{1}{\sqrt{2} \cdot \sqrt{\pi} \cdot \frac{293}{50}} \cdot e^{- \cdot \left(10 + \frac{5}{10} - \left(10 + \frac{19}{100}\right)\right)^{2} \cdot \frac{1}{2 \cdot \left(34 + \frac{35}{100}\right)}}\\& = \frac{1}{\frac{293}{50} \cdot \sqrt{2} \cdot \sqrt{\pi}} \cdot e^{- \cdot \left(10 + \frac{5}{10} - \left(10 + \frac{19}{100}\right)\right)^{2} \cdot \frac{1}{2 \cdot \left(34 + \frac{35}{100}\right)}}\\& = \frac{25}{293} \cdot \sqrt{2} \cdot \frac{1}{\sqrt{\pi}} \cdot e^{- \cdot \left(10 + \frac{5}{10} - \left(10 + \frac{19}{100}\right)\right)^{2} \cdot \frac{1}{2 \cdot \left(34 + \frac{35}{100}\right)}}\\& = \frac{25}{293} \cdot \sqrt{2} \cdot \frac{1}{\sqrt{\pi}} \cdot e^{- \cdot \left(10 + \frac{1}{2} - \left(10 + \frac{19}{100}\right)\right)^{2} \cdot \frac{1}{2 \cdot \left(34 + \frac{35}{100}\right)}}\\& = \frac{25}{293} \cdot \sqrt{2} \cdot \frac{1}{\sqrt{\pi}} \cdot e^{- \cdot \left(10 + \frac{1}{2} - \frac{1019}{100}\right)^{2} \cdot \frac{1}{2 \cdot \left(34 + \frac{35}{100}\right)}}\\& = \frac{25}{293} \cdot \sqrt{2} \cdot \frac{1}{\sqrt{\pi}} \cdot e^{- \cdot \left(\frac{21}{2} - \frac{1019}{100}\right)^{2} \cdot \frac{1}{2 \cdot \left(34 + \frac{35}{100}\right)}}\\& = \frac{25}{293} \cdot \sqrt{2} \cdot \frac{1}{\sqrt{\pi}} \cdot e^{- \cdot \left(\frac{31}{100}\right)^{2} \cdot \frac{1}{2 \cdot \left(34 + \frac{35}{100}\right)}}\\& = \frac{25}{293} \cdot \sqrt{2} \cdot \frac{1}{\sqrt{\pi}} \cdot e^{- \cdot \frac{961}{10000} \cdot \frac{1}{2 \cdot \left(34 + \frac{35}{100}\right)}}\\& = \frac{25}{293} \cdot \sqrt{2} \cdot \frac{1}{\sqrt{\pi}} \cdot e^{- \cdot \frac{961}{10000} \cdot \frac{1}{2 \cdot \left(34 + \frac{7}{20}\right)}}\\& = \frac{25}{293} \cdot \sqrt{2} \cdot \frac{1}{\sqrt{\pi}} \cdot e^{- \cdot \frac{961}{10000} \cdot \frac{1}{2 \cdot \frac{687}{20}}}\\& = \frac{25}{293} \cdot \sqrt{2} \cdot \frac{1}{\sqrt{\pi}} \cdot e^{- \cdot \frac{961}{10000} \cdot \frac{1}{\frac{687}{10}}}\\& = \frac{25}{293} \cdot \sqrt{2} \cdot \frac{1}{\sqrt{\pi}} \cdot e^{- \frac{961}{687000}}\\& = \frac{25}{293} \cdot \sqrt{2} \cdot \frac{1}{\sqrt{\pi}} \cdot \frac{1}{e^{\frac{961}{687000}}}\\& = \frac{25}{293} \cdot \sqrt{2} \cdot \frac{1}{\sqrt{\pi}} \cdot e^{- \frac{961}{687000}}\end{aligned}\]

\(e\) is Euler's number, a mathematical constant that is approximately \(2.71828\).