Math Problem Solver

\[\frac{1}{\sqrt{2 \cdot \pi} \cdot 2.67} \cdot {e}^{\frac{-{\left( 10.59 - 4.11 \right)}^{2}}{2 \cdot 7.15}} = \frac{50 \sqrt{2}}{267 \sqrt{\pi} e^{\frac{52488}{17875}}} \approx 0.00792757085269139177627395012868\]

\[\begin{aligned}\frac{1}{\sqrt{2 \cdot \pi} \cdot 2.67} \cdot {e}^{\frac{-{\left( 10.59 - 4.11 \right)}^{2}}{2 \cdot 7.15}}& = \frac{1}{\sqrt{2 \cdot \pi} \cdot \left(2 + \frac{67}{100}\right)} \cdot e^{- \cdot \left(10 + \frac{59}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} \cdot \frac{1}{2 \cdot \left(7 + \frac{15}{100}\right)}}\\& = \frac{1}{\sqrt{2} \cdot \sqrt{\pi} \cdot \left(2 + \frac{67}{100}\right)} \cdot e^{- \cdot \left(10 + \frac{59}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} \cdot \frac{1}{2 \cdot \left(7 + \frac{15}{100}\right)}}\\& = \frac{1}{\sqrt{2} \cdot \sqrt{\pi} \cdot \frac{267}{100}} \cdot e^{- \cdot \left(10 + \frac{59}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} \cdot \frac{1}{2 \cdot \left(7 + \frac{15}{100}\right)}}\\& = \frac{1}{\frac{267}{100} \cdot \sqrt{2} \cdot \sqrt{\pi}} \cdot e^{- \cdot \left(10 + \frac{59}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} \cdot \frac{1}{2 \cdot \left(7 + \frac{15}{100}\right)}}\\& = \frac{50}{267} \cdot \sqrt{2} \cdot \frac{1}{\sqrt{\pi}} \cdot e^{- \cdot \left(10 + \frac{59}{100} - \left(4 + \frac{11}{100}\right)\right)^{2} \cdot \frac{1}{2 \cdot \left(7 + \frac{15}{100}\right)}}\\& = \frac{50}{267} \cdot \sqrt{2} \cdot \frac{1}{\sqrt{\pi}} \cdot e^{- \cdot \left(10 + \frac{59}{100} - \frac{411}{100}\right)^{2} \cdot \frac{1}{2 \cdot \left(7 + \frac{15}{100}\right)}}\\& = \frac{50}{267} \cdot \sqrt{2} \cdot \frac{1}{\sqrt{\pi}} \cdot e^{- \cdot \left(\frac{1059}{100} - \frac{411}{100}\right)^{2} \cdot \frac{1}{2 \cdot \left(7 + \frac{15}{100}\right)}}\\& = \frac{50}{267} \cdot \sqrt{2} \cdot \frac{1}{\sqrt{\pi}} \cdot e^{- \cdot \left(\frac{162}{25}\right)^{2} \cdot \frac{1}{2 \cdot \left(7 + \frac{15}{100}\right)}}\\& = \frac{50}{267} \cdot \sqrt{2} \cdot \frac{1}{\sqrt{\pi}} \cdot e^{- \cdot \frac{26244}{625} \cdot \frac{1}{2 \cdot \left(7 + \frac{15}{100}\right)}}\\& = \frac{50}{267} \cdot \sqrt{2} \cdot \frac{1}{\sqrt{\pi}} \cdot e^{- \cdot \frac{26244}{625} \cdot \frac{1}{2 \cdot \left(7 + \frac{3}{20}\right)}}\\& = \frac{50}{267} \cdot \sqrt{2} \cdot \frac{1}{\sqrt{\pi}} \cdot e^{- \cdot \frac{26244}{625} \cdot \frac{1}{2 \cdot \frac{143}{20}}}\\& = \frac{50}{267} \cdot \sqrt{2} \cdot \frac{1}{\sqrt{\pi}} \cdot e^{- \cdot \frac{26244}{625} \cdot \frac{1}{\frac{143}{10}}}\\& = \frac{50}{267} \cdot \sqrt{2} \cdot \frac{1}{\sqrt{\pi}} \cdot e^{- \frac{52488}{17875}}\\& = \frac{50}{267} \cdot \sqrt{2} \cdot \frac{1}{\sqrt{\pi}} \cdot \frac{1}{e^{\frac{52488}{17875}}}\\& = \frac{50}{267} \cdot \sqrt{2} \cdot \frac{1}{\sqrt{\pi}} \cdot e^{- \frac{52488}{17875}}\end{aligned}\]

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