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📅 May 16, 2026 👤 scraface

May 16, 2026

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📌 We already know $ a + b = 10 $, so compute $ (a + b)^3 = 10^3 = 1000 $.

📌 To find $ ab $, use the identity:

📌 a^3 + b^3 = 1000 - 3(21)(10) = 1000 - 630 = 370

📌 Thus, the value is $ \boxed{370} $.

📌 Question: A retired scientist mentoring students notes that a scientist previously conducted 40 experiments, with 75% successful. After 10 more experiments, the success rate rose to 78%. How many of the last 10 experiments were successful?

📌 Solution: Initially, the scientist conducted 40 experiments with a 75% success rate:

📌 \times 40 = 30 \text{ successful experiments}

📌 After 10 more experiments, the total becomes $ 40 + 10 = 50 $ experiments. The new success rate is 78%, so total successful experiments now are:

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