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Home » The solutions in $ [0^\circ, 360^\circ] $ are: - Richter Guitar

The solutions in $ [0^\circ, 360^\circ] $ are: - Richter Guitar

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 Question: A student measures two strands of synthetic fiber, one 3.75 cm long and the other 8.25 cm long. What is the average length, in centimeters?

📌 Solution: Compute the average:

📌 So, the average length is $ \boxed{6} $ centimeters.Question: An archaeologist is analyzing 7 distinct artifacts found at an Inca settlement, and wishes to divide them into 3 identical storage containers such that each container holds at least one artifact. How many distinct ways can this be done?

📌 Solution: We are to partition 7 distinguishable artifacts into 3 indistinguishable non-empty containers. This is equivalent to finding the Stirling numbers of the second kind, denoted $ S(n, k) $, which count the number of ways to partition $ n $ distinguishable objects into $ k $ non-empty indistinguishable subsets.

📌 We need $ S(7, 3) $. The value of $ S(7, 3) $ can be computed using the recurrence:

📌 S(n, k) = k \cdot S(n-1, k) + S(n-1, k-1),

📌 with base cases $ S(n, 0) = 0 $ for $ n > 0 $, $ S(0, 0) = 1 $, and $ S(n, k) = 0 $ if $ k > n $.

📌 Using known values or computing step-by-step:

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