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Multiplying both sides by \(k(k+2)\): - Portal da AcÃºstica

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 5Question: What is the arithmetic mean of all positive integers less than 30 that are divisible by both 3 and 5?

📌 Solution: To find the arithmetic mean, we first identify the positive integers less than 30 that are divisible by both 3 and 5. These numbers are multiples of the least common multiple of 3 and 5, which is 15. The multiples of 15 less than 30 are:

📌 There is only one such number. Therefore, the arithmetic mean is simply:

📌 \frac{15}{1} = \boxed{15}

📌 Question: What is the probability that a randomly chosen positive integer less than or equal to 50 is a factor of 60?

📌 Solution: First, we find all positive integers less than or equal to 50 that are factors of 60. The positive divisors of 60 are:

📌 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

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