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Home » Establecer n(n + 1)/2 = 210. - Aurero

Establecer n(n + 1)/2 = 210. - Aurero

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 + 9e^{-0.5t} = 2

📌 9e^{-0.5t} = 1

📌 e^{-0.5t} = \frac{1}{9}

📌 -0.5t = \ln\left(\frac{1}{9}\right) = -\ln 9

📌 Solve for \(t\):

📌 t = \frac{-\ln 9}{-0.5} = \frac{\ln 9}{0.5} = 2 \ln 9 = \ln(9^2) = \ln 81

📌 Alternatively, express the final result clearly:

📌 t = \frac{\ln 9}{0.5} = 2 \ln 9 = 2 \ln(3^2) = 4 \ln 3

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\frac{70 \cdot 66}{38760} = \frac{4620}{38760} = \frac{77}{646}
\boxed{\frac{77}{646}}
Question: A philosopher of science is analyzing 12 key scientific theo...
We use combinations to find the probability.
Total number of ways to choose 4 theories from 12:
\binom{12}{4} = 495
Number of favorable outcomes (choosing 2 from the 5 20th-century theor...
\binom{5}{2} \cdot \binom{7}{2} = 10 \cdot 21 = 210
\frac{210}{495} = \frac{14}{33}
\boxed{\frac{14}{33}}

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