0.7054+2.58√((0.7054(1-0.7054))/104)

asked by guest
on Nov 26, 2024 at 12:29 pm



You asked:

Evaluate the expression: \(0.7054 + 2.58 \cdot \sqrt{\frac{0.7054 \cdot \left(1 - 0.7054\right)}{104}}\)

MathBot Answer:

\[0.7054 + 2.58 \cdot \sqrt{\frac{0.7054 \cdot \left(1 - 0.7054\right)}{104}} = \frac{129 \sqrt{135077046}}{13000000} + \frac{3527}{5000} \approx 0.82072863058435029584619705134329\]

\[\begin{aligned}0.7054 + 2.58 \cdot \sqrt{\frac{0.7054 \cdot \left(1 - 0.7054\right)}{104}}& = \frac{7054}{10000} + \left(2 + \frac{58}{100}\right) \cdot \sqrt{\frac{7054}{10000} \cdot \left(1 - \frac{7054}{10000}\right) \cdot \frac{1}{104}}\\& = \frac{3527}{5000} + \left(2 + \frac{58}{100}\right) \cdot \sqrt{\frac{7054}{10000} \cdot \left(1 - \frac{7054}{10000}\right) \cdot \frac{1}{104}}\\& = \frac{3527}{5000} + \left(2 + \frac{29}{50}\right) \cdot \sqrt{\frac{7054}{10000} \cdot \left(1 - \frac{7054}{10000}\right) \cdot \frac{1}{104}}\\& = \frac{3527}{5000} + \frac{129}{50} \cdot \sqrt{\frac{7054}{10000} \cdot \left(1 - \frac{7054}{10000}\right) \cdot \frac{1}{104}}\\& = \frac{3527}{5000} + \frac{129}{50} \cdot \sqrt{\frac{7054}{10000} \cdot \left(1 - \frac{3527}{5000}\right) \cdot \frac{1}{104}}\\& = \frac{3527}{5000} + \frac{129}{50} \cdot \sqrt{\frac{7054}{10000} \cdot \frac{1473}{5000} \cdot \frac{1}{104}}\\& = \frac{3527}{5000} + \frac{129}{50} \cdot \sqrt{\frac{7054}{10000} \cdot \frac{1473}{520000}}\\& = \frac{3527}{5000} + \frac{129}{50} \cdot \sqrt{\frac{3527}{5000} \cdot \frac{1473}{520000}}\\& = \frac{3527}{5000} + \frac{129}{50} \cdot \sqrt{\frac{5195271}{2600000000}}\\& = \frac{3527}{5000} + \frac{129}{50} \cdot \frac{1}{260000} \cdot \sqrt{135077046}\\& = \frac{3527}{5000} + \frac{129}{13000000} \cdot \sqrt{135077046}\end{aligned}\]

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