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Home » Winterize Sprinklers Like a Pro — Save Money & Avoid Leaks This Winter! - Groen Casting

Winterize Sprinklers Like a Pro — Save Money & Avoid Leaks This Winter! - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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= \int_0^{0.8} \int_0^{0.2} 30 s^4 ds \, du + \int_{0.8}^1 \int_0^{1 -...
First integral:
\int_0^{0.2} 30 \cdot \frac{s^5}{5} ds = 6 \int_0^{0.2} s^5 ds = 6 \cd...
Multiply by 1 (no outer u): $ \frac{1}{15625} $
Second integral:
\int_{0.8}^1 30 \cdot \frac{(1 - u)^5}{5} du = 6 \int_{0.8}^1 (1 - u)^...
Let $ w = 1 - u $, $ dw = -du $, limits $ w = 0.2 $ to $ 0 $:
\int_0^{0.2} w^5 dw = 6 \cdot \frac{w^6}{6} \Big|_0^{0.2} = (0.2)^6 =...
Total: $ \frac{1}{15625} + \frac{1}{15625} = \frac{2}{15625} $
Thus, the probability that all 6 vehicles arrive within some 2-minute...

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