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Home » Discover "New Horizons New": The Breakthrough Journey That Will Change Everything! - Get link 4share

Discover "New Horizons New": The Breakthrough Journey That Will Change Everything! - Get link 4share

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Solution: Let $x$ be the integer. Then $x \equiv -1 \pmod{5}$ and $x \equiv -1 \pmod{7}$. This implies $x + 1$ is divisible by both 5 and 7, so $x + 1 = \text{LCM}(5, 7) = 35$. Thus, $x = 34$. $\boxed{34}$Question: A retired engineer designing a robotic arm observes that the sum of two gear rotation speeds $ a $ and $ b $ is 10, and the sum of their squares is 58. What is $ a^3 + b^3 $?

📌 Solution: We are given $ a + b = 10 $ and $ a^2 + b^2 = 58 $. We want to find $ a^3 + b^3 $.

📌 We already know $ a + b = 10 $, so compute $ (a + b)^3 = 10^3 = 1000 $.

📌 To find $ ab $, use the identity:

📌 a^3 + b^3 = 1000 - 3(21)(10) = 1000 - 630 = 370

📌 Thus, the value is $ \boxed{370} $.

📌 Question: A retired scientist mentoring students notes that a scientist previously conducted 40 experiments, with 75% successful. After 10 more experiments, the success rate rose to 78%. How many of the last 10 experiments were successful?

📌 Solution: Initially, the scientist conducted 40 experiments with a 75% success rate:

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