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Home » Why All Medium-Haired Guys Are Now Turning to This Simple Styling Hack! - AMAZONAWS

Why All Medium-Haired Guys Are Now Turning to This Simple Styling Hack! - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 A community nutrition educator is organizing a cooking workshop. If the number of participants on two consecutive days are \( p \) and \( q \), and it is known that \( p + q = 150 \), what is the greatest possible value of \(\gcd(p, q)\)?

📌 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:

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2A patent attorney files 12 provisional patents and 5 non-provisional...
The provisional patents cost 12 × $150 = $<<12*150=1800>>1800
The non-provisional patents cost 5 × $800 = $<<5*800=4000>>4000
Total before discount: $1800 + $4000 = $<<1800+4000=5800>>5800
Since $5800 < $10,000, no discount applies.
The client pays $5800.
#### 5800
An epidemiologist estimates that a disease spreads such that each infe...
Week 0: 1 infected
Week 1: 1 × 2.5 = 2.5 → total = 1 + 2.5 = 3.5

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