0.7054-2.58√(0.7054(1-0.7054)/104)

asked by guest
on Nov 26, 2024 at 12:28 pm



You asked:

Evaluate the expression: 0.7054−2.580.7054(1−0.7054)1040.7054 - 2.58 \sqrt{\frac{0.7054 \left(1 - 0.7054\right)}{104}}

MathBot Answer:

0.7054−2.580.7054(1−0.7054)104=35275000−12913507704613000000≈0.590071369415649704153802948656710.7054 - 2.58 \sqrt{\frac{0.7054 \left(1 - 0.7054\right)}{104}} = \frac{3527}{5000} - \frac{129 \sqrt{135077046}}{13000000} \approx 0.59007136941564970415380294865671

0.7054−2.580.7054(1−0.7054)104=705410000−(2+58100)⋅705410000⋅(1−705410000)⋅1104=35275000−(2+58100)⋅705410000⋅(1−705410000)⋅1104=35275000−(2+2950)⋅705410000⋅(1−705410000)⋅1104=35275000−12950⋅705410000⋅(1−705410000)⋅1104=35275000−12950⋅705410000⋅(1−35275000)⋅1104=35275000−12950⋅705410000⋅14735000⋅1104=35275000−12950⋅705410000⋅1473520000=35275000−12950⋅35275000⋅1473520000=35275000−12950⋅51952712600000000=35275000−12950⋅1260000⋅135077046=35275000−12913000000⋅135077046\begin{aligned}0.7054 - 2.58 \sqrt{\frac{0.7054 \left(1 - 0.7054\right)}{104}}&=\frac{7054}{10000} - \left(2 + \frac{58}{100}\right) \cdot \sqrt{\frac{7054}{10000} \cdot \left(1 - \frac{7054}{10000}\right) \cdot \frac{1}{104}}\\&=\frac{3527}{5000} - \left(2 + \frac{58}{100}\right) \cdot \sqrt{\frac{7054}{10000} \cdot \left(1 - \frac{7054}{10000}\right) \cdot \frac{1}{104}}\\&=\frac{3527}{5000} - \left(2 + \frac{29}{50}\right) \cdot \sqrt{\frac{7054}{10000} \cdot \left(1 - \frac{7054}{10000}\right) \cdot \frac{1}{104}}\\&=\frac{3527}{5000} - \frac{129}{50} \cdot \sqrt{\frac{7054}{10000} \cdot \left(1 - \frac{7054}{10000}\right) \cdot \frac{1}{104}}\\&=\frac{3527}{5000} - \frac{129}{50} \cdot \sqrt{\frac{7054}{10000} \cdot \left(1 - \frac{3527}{5000}\right) \cdot \frac{1}{104}}\\&=\frac{3527}{5000} - \frac{129}{50} \cdot \sqrt{\frac{7054}{10000} \cdot \frac{1473}{5000} \cdot \frac{1}{104}}\\&=\frac{3527}{5000} - \frac{129}{50} \cdot \sqrt{\frac{7054}{10000} \cdot \frac{1473}{520000}}\\&=\frac{3527}{5000} - \frac{129}{50} \cdot \sqrt{\frac{3527}{5000} \cdot \frac{1473}{520000}}\\&=\frac{3527}{5000} - \frac{129}{50} \cdot \sqrt{\frac{5195271}{2600000000}}\\&=\frac{3527}{5000} - \frac{129}{50} \cdot \frac{1}{260000} \cdot \sqrt{135077046}\\&=\frac{3527}{5000} - \frac{129}{13000000} \cdot \sqrt{135077046}\end{aligned}

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