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Home » $a + d = 5$ - Esdistancia

$a + d = 5$ - Esdistancia

📅 March 17, 2026 👤 scraface

Mar 17, 2026

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📌 9! = 362880,\quad 3! = 6

📌 \frac{362880}{6} = 60480

📌 Thus, the total number of unique check-in codes is $\boxed{60480}$.

📌 Question: An industrial hygienist in Los Angeles is analyzing exposure levels in 6 different work zones, each with 3 safety zones. If 2 zones are randomly selected for an immediate inspection, what is the probability that both are in the same work area (i.e., same high-risk level), assuming each work area contains exactly 2 zones?

📌 Solution: There are 6 work areas, each with 2 zones, making a total of $6 \times 2 = 12$ zones. Since 2 zones are selected at random, the total number of ways to choose 2 zones is:

📌 \binom{12}{2} = \frac{12 \times 11}{2} = 66

📌 To find favorable outcomes (both zones in the same work area), note that each work area has $\binom{2}{2} = 1$ way to choose both zones. With 6 work areas, the number of favorable outcomes is:

📌 \times 1 = 6

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So, compute $ f(-1) $:
f(-1) = (-1)^3 + 2 = -1 + 2 = 1
Question: Let $ a $ and $ b $ be complex numbers such that
\frac{a}{b} + \frac{b}{a} = 3.
Find the value of $ \frac{a^3}{b^3} + \frac{b^3}{a^3} $.
Let $ x = \frac{a}{b} \Rightarrow \frac{b}{a} = \frac{1}{x} $, so:
x + \frac{1}{x} = 3
We are to find:
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