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Home » \( 119 + 8.33 = 127.33 \). - Blask

\( 119 + 8.33 = 127.33 \). - Blask

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Use the Law of Total Probability to find \( P(F) \):

📌 P(F) = P(F|T)P(T) + P(F|M)P(M) = (0.25)(0.60) + (0.10)(0.40) = 0.15 + 0.04 = 0.19

📌 Apply Bayes’ Theorem:

📌 P(T|F) = \frac{P(F|T)P(T)}{P(F)} = \frac{0.15}{0.19} \approx 0.7895

📌 A spherical balloon is being inflated such that its radius increases at a constant rate of 0.5 cm/s. At what rate is the volume increasing when the radius is 10 cm?

📌 Volume of a sphere:

📌 Differentiate with respect to time \( t \):

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