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Home » So, \( 2^x+1 = 2^5 \). - Sterling Industries

So, \( 2^x+1 = 2^5 \). - Sterling Industries

📅 April 16, 2026 👤 scraface

Apr 16, 2026

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📌 Let the AI startups be $ A_1 $ and $ A_2 $. The condition is: both are funded or both are not funded.

📌 Case 1: Both AI startups are funded.

📌 Then, we must choose $ 3 - 2 = 1 $ more startup from the remaining $ 8 - 2 = 6 $ non-AI startups:

📌 Then, we choose all 3 funded startups from the 6 non-AI startups:

📌 Question: A weather model uses binary sequences of length 8 to represent daily temperature anomalies (1 = above average, 0 = below). How many such sequences have at least one pair of consecutive 1s?

📌 This is a classic Fibonacci recurrence:

📌 If the sequence ends in 0, the first $ n-1 $ digits can be any valid sequence of length $ n-1 $.

📌 If it ends in 1, the previous digit must be 0, so the first $ n-2 $ digits form a valid sequence of length $ n-2 $.

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