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Home » How the Metro Exodus is Reshaping America—Entire Cities Are Emptying! - Databee Business Systems

How the Metro Exodus is Reshaping America—Entire Cities Are Emptying! - Databee Business Systems

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Let \( d = \gcd(p, q) \). Then \( p = dk \), \( q = dl \) with \(\gcd(k, l) = 1\), and:

📌 dk + dl = 150 \implies d(k + l) = 150

📌 To maximize \( d \), minimize \( k + l \). Since \(\gcd(k, l) = 1\), the smallest sum is 2 (when \( k = 1 \), \( l = 1 \)). Then:

📌 d imes 2 = 150 \implies d = 75

📌 Since 75 divides 150 and \( k + l = 2 \) satisfies coprimality, the largest possible \(\gcd(p, q)\) is \(oxed{75}\).

📌 An entomologist is examining the cycles of a rare insect species, where the cycle length is represented by a three-digit integer \( z \) such that \( z \) is divisible by 7, 11, and 13. What is the smallest such \( z \)?

📌 Since \( z \) is divisible by 7, 11, and 13, compute the least common multiple:

📌 ext{lcm}(7, 11, 13) = 7 imes 11 imes 13 = 1001

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Temps pour la deuxiÃ¨me partie : \( rac{200}{100} = 2 \) heures.
Distance totale : \( 150 + 200 = 350 \) km.
Temps total : \( 3 + 2 = 5 \) heures.
\[ rac{350}{5} = 70 ext{ km/h} \]
La vitesse moyenne est de 70 km/h.
#### 70
Le produit de deux nombres pairs consÃ©cutifs est 288. Trouvez les nom...
Soient les nombres \( x \) et \( x+2 \).
\[ x(x+2) = 288 \]
\[ x^2 + 2x - 288 = 0 \]

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