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ight)^3 \cdot \left(rac13 - IX Labs

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Question: A museum curator notes that the ratio of 19th-century telescopes to 20th-century microscopes in the collection is $5:4$. If there are 15 telescopes, how many microscopes are there?

📌 Solution: Let the number of microscopes be $x$. The ratio $5:4 = 15:x$ implies:

📌 \frac{5}{4} = \frac{15}{x} \implies 5x = 60 \implies x = 12

📌 Question: An AI ethics investigator evaluates algorithmic fairness by calculating the average of three fairness scores: $3x - 1$, $5x + 4$, and $2x - 7$. What is the average?

📌 Solution: Sum the expressions:

📌 \frac{10x - 4}{3}

📌 $\boxed{\dfrac{10x - 4}{3}}$

📌 Solution: The sequence is arithmetic with first term $a_1 = 2$ and common difference $d = 3$. The $n$-th term is:

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