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Home » A sphere has a volume of 288Ï cubic centimeters. What is its radius? - Abbey Badges

A sphere has a volume of 288Ï cubic centimeters. What is its radius? - Abbey Badges

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Among these, the divisors \( \leq 60 \) are all except 120. So there are \( 16 - 1 = 15 \) divisors of 120 that are \( \leq 60 \).

📌 There are 60 positive integers from 1 to 60.

📌 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:

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