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Home » Set them equal since \( f(3) = g(3) \): - 500apps

Set them equal since \( f(3) = g(3) \): - 500apps

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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📌 Question: A graphic designer creates a social media post with a width-to-height ratio of 5:3. If the diagonal is 34 inches, what is the height of the post in inches?

📌 Solution: Let the width be $ 5k $ and height $ 3k $. By the Pythagorean theorem:

📌 \Rightarrow 25k^2 + 9k^2 = 1156

📌 \Rightarrow 34k^2 = 1156

📌 \Rightarrow k^2 = 34

📌 \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?

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