186-1.96((6)/(\sqrt(40)))

asked by guest
on Nov 24, 2024 at 6:46 am



You asked:

Evaluate the expression: \(186 - 1.96 \cdot \frac{6}{\sqrt{40}}\)

MathBot Answer:

\[186 - 1.96 \cdot \frac{6}{\sqrt{40}} = 186 - \frac{147 \sqrt{10}}{250} \approx 184.14058073582099295278465059587356\]

\[\begin{aligned}186 - 1.96 \cdot \frac{6}{\sqrt{40}}& = 186 - \left(1 + \frac{96}{100}\right) \cdot 6 \cdot \frac{1}{\sqrt{40}}\\& = 186 - \left(1 + \frac{24}{25}\right) \cdot 6 \cdot \frac{1}{\sqrt{40}}\\& = 186 - \frac{49}{25} \cdot 6 \cdot \frac{1}{\sqrt{40}}\\& = 186 - \frac{49}{25} \cdot 6 \cdot \frac{1}{2 \cdot \sqrt{10}}\\& = 186 - \frac{49}{25} \cdot \frac{3}{10} \cdot \sqrt{10}\\& = 186 - \frac{147}{250} \cdot \sqrt{10}\end{aligned}\]

+ Submit Question