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Home » study for geometry eoc in 1 hour - AssociationVoting

study for geometry eoc in 1 hour - AssociationVoting

📅 May 16, 2026 👤 scraface

May 16, 2026

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📌 \Rightarrow k = \sqrt{34}

📌 The height is $ 3k = 3\sqrt{34} $. Numerically, $ \sqrt{34} pprox 5.83 $, so height $ pprox 17.49 $, but exact form is required: $oxed{3\sqrt{34}}$ inches.

📌 Question: An AI programmer models two diagnostic tests. The probability of a positive result for Test A is $ rac{2}{3} $, and for Test B is $ rac{3}{4} $. If both tests are independent, what is the probability that at least one test is positive?

📌 Solution: The probability of neither test being positive is $ \left(1 - rac{2}{3}

📌 ight)\left(1 - rac{3}{4}

📌 ight) = rac{1}{3} imes rac{1}{4} = rac{1}{12} $. Thus, the probability of at least one positive is $ 1 - rac{1}{12} = rac{11}{12} $. Final answer: $oxed{\dfrac{11}{12}}$.Question: Define $M(u) = u - rac{u^2}{2}$ for all real numbers $u$. If $a_1 = 1$ and $a_{n+1} = M(a_n)$ for $n \geq 1$, find $a_3$.

📌 Solution: Start with $a_1 = 1$. Compute $a_2 = M(a_1) = 1 - rac{1^2}{2} = rac{1}{2}$. Next, compute $a_3 = M(a_2) = rac{1}{2} - rac{(rac{1}{2})^2}{2} = rac{1}{2} - rac{1}{8} = rac{3}{8}$. Thus, the value of $a_3$ is $oxed{\dfrac{3}{8}}$.

📌 Question: Let $x, y, z$ be positive real numbers such that $2x + 3y + 4z = 12$. Find the minimum value of $x^2 + y^2 + z^2$.

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