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Home » \( 2a = 13.85 \) → \( a = 6.925 \) - AIKO, infinite ways to autonomy.

\( 2a = 13.85 \) → \( a = 6.925 \) - AIKO, infinite ways to autonomy.

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 Dr. Kim is managing a portfolio of 12 research projects. If 3 projects are in biotech, 4 in renewable energy, and 5 in AI, and she selects 2 projects at random for a progress review, what is the probability both are AI-related?

📌 Total ways to choose 2 projects: \( \binom{12}{2} = \frac{12 \cdot 11}{2} = 66 \)

📌 Ways to choose 2 AI projects: \( \binom{5}{2} = \frac{5 \cdot 4}{2} = 10 \)

📌 Probability = \( \frac{10}{66} = \frac{5}{33} \)

📌 A high school student studying optics finds that the focal length \(f\) of a lens is related to object and image distances by \( \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \). If \(d_o = 30 \, \text{cm}\) and \(d_i = 60 \, \text{cm}\), what is \(f\) in cm?

📌 \frac{1}{f} = \frac{1}{30} + \frac{1}{60} = \frac{2}{60} + \frac{1}{60} = \frac{3}{60} = \frac{1}{20}

📌 So \(f = 20 \, \text{cm}\)

📌 Liam is analyzing solar panel efficiency. His panel produces 1.8 kW of power under ideal conditions. If cloud cover reduces output by 25% and temperature loss reduces it by an additional 10% of the remaining power, what is the final output in kW?

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