0.7459+1.96√((0.7459(1-0.7459))/105)

asked by guest
on Nov 26, 2024 at 12:08 pm



You asked:

Evaluate the expression: \(0.7459 + 1.96 \cdot \sqrt{\frac{0.7459 \cdot \left(1 - 0.7459\right)}{105}}\)

MathBot Answer:

\[0.7459 + 1.96 \cdot \sqrt{\frac{0.7459 \cdot \left(1 - 0.7459\right)}{105}} = \frac{539 \sqrt{37295}}{1250000} + \frac{7459}{10000} \approx 0.82917297067356249900966399978202\]

\[\begin{aligned}0.7459 + 1.96 \cdot \sqrt{\frac{0.7459 \cdot \left(1 - 0.7459\right)}{105}}& = \frac{7459}{10000} + \left(1 + \frac{96}{100}\right) \cdot \sqrt{\frac{7459}{10000} \cdot \left(1 - \frac{7459}{10000}\right) \cdot \frac{1}{105}}\\& = \frac{7459}{10000} + \left(1 + \frac{24}{25}\right) \cdot \sqrt{\frac{7459}{10000} \cdot \left(1 - \frac{7459}{10000}\right) \cdot \frac{1}{105}}\\& = \frac{7459}{10000} + \frac{49}{25} \cdot \sqrt{\frac{7459}{10000} \cdot \left(1 - \frac{7459}{10000}\right) \cdot \frac{1}{105}}\\& = \frac{7459}{10000} + \frac{49}{25} \cdot \sqrt{\frac{7459}{10000} \cdot \frac{2541}{10000} \cdot \frac{1}{105}}\\& = \frac{7459}{10000} + \frac{49}{25} \cdot \sqrt{\frac{7459}{10000} \cdot \frac{121}{50000}}\\& = \frac{7459}{10000} + \frac{49}{25} \cdot \sqrt{\frac{902539}{500000000}}\\& = \frac{7459}{10000} + \frac{49}{25} \cdot \frac{11}{50000} \cdot \sqrt{37295}\\& = \frac{7459}{10000} + \frac{539}{1250000} \cdot \sqrt{37295}\end{aligned}\]

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