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Home » Alternative: maybe first term is 1? But says 5. - inBeat

Alternative: maybe first term is 1? But says 5. - inBeat

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 Question:** A retired scientist is reflecting on their research on prime numbers and wants to know the probability that a randomly selected positive integer less than or equal to 30 is a prime number. What is this probability?

📌 Solution:** First, list the prime numbers less than or equal to 30. These are: 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. Count the number of prime numbers:

📌 \text{Number of primes} = 10

📌 The total number of positive integers less than or equal to 30 is 30. Therefore, the probability that a randomly selected integer is prime is:

📌 \text{Probability} = \frac{\text{Number of primes}}{\text{Total numbers}} = \frac{10}{30} = \frac{1}{3}

📌 Thus, the probability is \(\boxed{\frac{1}{3}}\).

📌 Question:** A scientist mentoring young researchers discusses measurements, noting a piece of copper wire is 3.4 meters long and another is 7.2 meters long. What is the average length, in meters, of these two pieces of wire?

📌 Solution:** Calculate the average length of the two pieces of wire. The length of the first piece is 3.4 meters, and the length of the second piece is 7.2 meters. The average length is calculated as follows:

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