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Home » Sponsored Lonely? These SpongeBob Lyrics Broke the Internet—Watch Now! - Abbey Badges

Sponsored Lonely? These SpongeBob Lyrics Broke the Internet—Watch Now! - Abbey Badges

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 \(y = 2(2)^2 - 8(2) + 10 = 8 - 16 + 10 = 2\)

📌 Minimum altitude is 2 meters

📌 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}

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