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what are the differences between weight and mass - Coaching Toolbox

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 \boxed{\dfrac{28}{125}}

📌 Question: A robotics engineer programs a robot to navigate 3 sensors, each with a $ \frac{1}{4} $ chance of triggering independently. What is the probability that at least one sensor triggers?

📌 Solution: Use complementary probability. The probability no sensor triggers is $ \left(\frac{3}{4}\right)^3 = \frac{27}{64} $. Subtract from 1:

📌 - \frac{27}{64} = \frac{37}{64}.

📌 \boxed{\dfrac{37}{64}}

📌 What is the largest integer that must divide the product of any five consecutive integers?

📌 To solve this problem, consider five consecutive integers \( n, n+1, n+2, n+3, n+4 \). Among any set of five consecutive integers, at least one is divisible by 5, at least one is divisible by 2, and at least one is divisible by 3. This guarantees that the product is divisible by \( 5 \times 2 \times 3 = 30 \).

📌 To see if 30 is the largest such integer, observe:

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