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Home » أوجد قيمة \(x\) في المعادلة \(3x^2 - 12x + 9 = 0\). - Red Crowns

أوجد قيمة \(x\) في المعادلة \(3x^2 - 12x + 9 = 0\). - Red Crowns

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 $ k = 2 $: $ \binom{3}{2} \cdot 1^7 = 3 \cdot 1 = 3 $

📌 $ k = 3 $: $ -\binom{3}{3} \cdot 0^7 = -1 \cdot 0 = 0 $

📌 Sum: $ 2187 - 384 = 1803 $, $ 1803 + 3 = 1806 $, $ 1806 + 0 = 1806 $

📌 Thus, the number of valid frequency assignments is $ \boxed{1806} $.

📌 \boxed{1806}

📌 Question: A researcher studying microfossil assemblages collects samples from 5 stratigraphic layers, each containing fossils from 4 different geological epochs. If one fossil is selected from each layer, and no two adjacent layers can contribute a fossil from the same epoch, how many valid selections are possible?

📌 Solution: We are to count the number of sequences of length 5 (one per layer), where each element is an epoch from 1 to 4, and no two consecutive layers have the same epoch.

📌 This is a classic recurrence problem.

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