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Home » \( r^2 = \frac50010\pi = \frac50\pi \) - AMAZONAWS

\( r^2 = \frac50010\pi = \frac50\pi \) - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 First term \( a = 300 \), ratio \( r = 1.18 \), n = 5

📌 \( S_5 = 300 \times \frac{1.18^5 - 1}{0.18} \)

📌 Calculate \( 1.18^5 \approx 2.2877 \)

📌 \( S_5 = 300 \times \frac{2.2877 - 1}{0.18} = 300 \times \frac{1.2877}{0.18} \approx 300 \times 7.1539 \approx 2146.17 \)

📌 Total distance ≈ 2146 meters

📌 An AI seismic network monitors 8 fault zones. Each zone has a 12% probability of generating a detectable tremor in a week. If tremors are independent, calculate the probability (to 3 decimal places) that at least 2 zones detect tremors in a given week.

📌 Use binomial: \( n = 8 \), \( p = 0.12 \), find \( P(X \geq 2) = 1 - P(X=0) - P(X=1) \)

📌 \( P(X=0) = (1 - 0.12)^8 = 0.88^8 \approx 0.3596 \)

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