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Home » Therefore, the probability is $ \boxed{\frac325} $ - ClickBalance

Therefore, the probability is $ \boxed{\frac325} $ - ClickBalance

📅 May 18, 2026 👤 scraface

May 18, 2026

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📌 A seismologist at Caltech is analyzing data from 120 seismic sensors placed along a fault line. If 25% of the sensors detect a tremor within the first 10 seconds, and three times that number detect it within the next 20 seconds, how many sensors have not detected the tremor after 30 seconds?

📌 Total sensors that detect the tremor: 30 + 90 = <<30 + 90 = 120>>120 sensors.

📌 Total accounted for: 12 + 24 = <<12 + 24 = 36>>36 layers.

📌 Thus, number not processed in any phase: 26.

📌 A home-schooled student designs an algorithm that reduces seismic noise by 60% in the first stage. In the second stage, it improves signal clarity by 50% of the remaining noise. If initial noise level is 200 units, what is the final noise level?

📌 Total so far: 18 + 36 = <<18 + 36 = 54>>54.

📌 Total accounted: 30 + 150 = <<30 + 150 = 180>>180.

📌 But to be consistent with integer expectations, lets revise the numbers in the question to make it work. But we must generate. So we keep and compute:

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Use Heron’s formula to find the area $ A $:
A = \sqrt{s(s-a)(s-b)(s-c)} = \sqrt{9x(9x - 5x)(9x - 6x)(9x - 7x)} = \...
The radius $ r $ of the inscribed circle is given by:
r = \frac{A}{s} = \frac{6x^2\sqrt{6}}{9x} = \frac{2x\sqrt{6}}{3}
\boxed{\frac{2x\sqrt{6}}{3}}
Question: A marine biologist is designing a conical fish shelter with...
The lateral surface area of a cone is given by:
where $ r = 2x $ and $ l = 5x $. Substituting:
A = \pi (2x)(5x) = 10\pi x^2
\boxed{10\pi x^2}

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