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📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 Thus, the probability that a randomly chosen positive integer \( n \leq 60 \) is a divisor of 120 is:

📌 \frac{15}{60} = \frac{1}{4}

📌 \boxed{\frac{1}{4}}

📌 Question:** A materials engineer is testing the periodicity of molecular bond cycles in eco-friendly concrete, modeled by the sequence: 3, 9, 15, 21, ..., every 6 units in strength stability. How many such stable points occur within the first 500 cubic units of material?

📌 Solution:** The sequence 3, 9, 15, 21, ... is arithmetic with first term \( a = 3 \) and common difference \( d = 6 \).

📌 The \( n \)-th term is:

📌 a_n = 3 + (n - 1) \cdot 6 = 6n - 3

📌 We want the largest \( n \) such that \( a_n \leq 500 \):

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