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Home » $ 5a \cdot 7b = 35ab $, - Portal da AcÃºstica

$ 5a \cdot 7b = 35ab $, - Portal da AcÃºstica

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 $$Question: A researcher tracks 120 birds using GPS. What is the sum of the distinct prime factors of 120?

📌 Solution: Factor 120 into primes: $120 = 2^3 \times 3 \times 5$. The distinct primes are 2, 3, and 5. Their sum is $2 + 3 + 5 = 10$. \boxed{10}

📌 Question: In a study of 45 bird species, what is the probability that a randomly selected number from 1 to 45 is a factor of 45?

📌 Solution: The factors of 45 are 1, 3, 5, 9, 15, 45. There are 6 factors. The probability is $\frac{6}{45} = \frac{2}{15}$. \boxed{\dfrac{2}{15}}

📌 Question: A migratory bird travels a distance $v$ that is a multiple of 7. If $v^3$ is less than 3500, what is the maximum possible value of $v$?

📌 Solution: Find the largest multiple of 7 where $v^3 < 3500$. Test $v = 7$: $343 < 3500$. $v = 14$: $2744 < 3500$. $v = 21$: $9261 > 3500$. Maximum is 14. \boxed{14}

📌 Question: Two bird species migrate every 12 and 18 days. What is the least common multiple of their migration cycles?

📌 Solution: Prime factors of 12: $2^2 \times 3$, of 18: $2 \times 3^2$. LCM is $2^2 \times 3^2 = 36$. \boxed{36}

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