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Home » solving exponential equations using logarithms common core algebra 2 homework - IQnection

solving exponential equations using logarithms common core algebra 2 homework - IQnection

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 \text{Phases} = 11, 12, 13, 14, 15, 16, 17

📌 There are 7 such phases. Therefore, the number of phases that satisfy the condition is \(\boxed{7}\).

📌 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 \(\boxed{\frac{1}{3}}\).

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