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what is a mariner - Coaching Toolbox

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 P(X=8) = C(10,8) (0.8)^8 (0.2)^2 = 45 × 0.16777216 × 0.04 ≈ 0.30199

📌 P(X=9) = C(10,9) (0.8)^9 (0.2)^1 = 10 × 0.134217728 × 0.2 ≈ 0.268435

📌 P(X=10) = C(10,10) (0.8)^10 = 1 × 0.1073741824 ≈ 0.10737

📌 Sum ≈ 0.30199 + 0.268435 + 0.10737 = <<0.30199+0.268435+0.10737=0.677795>>0.6778 (rounded to 4 decimal places)

📌 #### 0.6778

📌 An ornithologist observes that a flock of birds increases its daily migration distance by 12% each day during a 5-day journey. If they fly 40 km on the first day, what is the total distance flown over the 5 days?

📌 This is a geometric sequence with first term a = 40, ratio r = 1.12, n = 5 terms.

📌 Sum = a(r^n - 1)/(r - 1) = 40(1.12^5 - 1)/(0.12)

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