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Home » Countdown to Merry Christmas Eve Eve: Surprise Secrets Everyone’s Spotting! - Network4

Countdown to Merry Christmas Eve Eve: Surprise Secrets Everyone’s Spotting! - Network4

📅 May 20, 2026 👤 scraface

May 20, 2026

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📌 We are given that \( p \) is a positive multiple of 6 and \( p^3 < 8000 \). To find the largest possible value of \( p \), we first determine the cube root of 8000:

📌 \sqrt[3]{8000} = 20

📌 Since \( p \) must be a multiple of 6, we consider multiples of 6 that are less than 20. These multiples are 6, 12, and 18. We check which of these satisfy \( p^3 < 8000 \):

📌 For \( p = 18 \), \( 18^3 = 5832 \) which is less than 8000.

📌 For \( p = 24 \), \( 24^3 = 13824 \) which exceeds 8000, but 24 is not less than 20.

📌 Thus, the largest multiple of 6 less than 20 is 18, and it satisfies \( 18^3 = 5832 < 8000 \). Therefore, the largest possible value of \( p \) is \(\boxed{18}\).

📌 Question:** A virologist is studying viral loads and notes that a particular parameter \( v \) is a positive integer less than or equal to 30. If the probability that \( v \) is a factor of 360 is to be calculated, what is this probability?

📌 First, we determine the number of positive integers \( v \) that are factors of 360 and are less than or equal to 30. Begin by finding the prime factorization of 360:

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