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+1.960.7459(1−0.7459)1050.7459 + 1.96 \sqrt{\frac{0.7459 \left(1 - 0.7459\right)}{105}}

MathBot Answer:

0.7459+1.960.7459(1−0.7459)105=539372951250000+745910000≈0.829172970673562499009663999782020.7459 + 1.96 \sqrt{\frac{0.7459 \left(1 - 0.7459\right)}{105}} = \frac{539 \sqrt{37295}}{1250000} + \frac{7459}{10000} \approx 0.82917297067356249900966399978202

0.7459+1.960.7459(1−0.7459)105=745910000+(1+96100)⋅745910000⋅(1−745910000)⋅1105=745910000+(1+2425)⋅745910000⋅(1−745910000)⋅1105=745910000+4925⋅745910000⋅(1−745910000)⋅1105=745910000+4925⋅745910000⋅254110000⋅1105=745910000+4925⋅745910000⋅12150000=745910000+4925⋅902539500000000=745910000+4925⋅1150000⋅37295=745910000+5391250000⋅37295\begin{aligned}0.7459 + 1.96 \sqrt{\frac{0.7459 \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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