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📰 Solution: The number of ways to choose 3 18th-century manuscripts is $inom{5}{3}$. Total ways to choose 3 manuscripts from 15 is $inom{15}{3}$. The probability is $rac{inom{5}{3}}{inom{15}{3}} = rac{10}{455} = rac{2}{91}$. $oxed{\dfrac{2}{91}}$Question: If the combined population of two marine mammal species in a region is 10 and the sum of their squared populations is 50, find the sum of their cubes. 📰 Solution: Let the populations be $ a $ and $ b $. Given $ a + b = 10 $ and $ a^2 + b^2 = 50 $. First, compute $ ab $ using $ (a + b)^2 = a^2 + 2ab + b^2 $. Substituting, $ 100 = 50 + 2ab $, so $ ab = 25 $. The sum of cubes is $ a^3 + b^3 = (a + b)^3 - 3ab(a + b) = 1000 - 3 \cdot 25 \cdot 10 = 1000 - 750 = oxed{250} $. 📰 Question: A financial model predicts revenue from two products with $ x + y = 4.5 $ and $ x^2 + y^2 = 10.25 $. What is $ 5x + 5y $? 📰 Sutures Of The Skull 9553518 📰 Watchmen Film Cast 4324096 📰 Why Gas Prices Went Up 1570652 📰 American Dragon Jake Long Show 8439650 📰 The Shocking Radius Of A Nuclear Explosionevery Dimension You Need To Know 2539268 📰 Flights To Virginia Beach 8835764 📰 Apple Tv Price 973792 📰 Credit Card Interest Calculator Monthly Payment 1871164 📰 Fire Emblem Sacred Stones This Hidden Treasure Changes Battle Dynamics Forever 8126002 📰 Portable Computer Monitor 2382515 📰 Excel If Then Statements 5053767 📰 Cast Of Captain Marvel 2985174 📰 Hhs Fy26 Budget Exposed You Wont Believe How Much Cuts Are Coming 9063258 📰 Roblox Peroxide 5468291 📰 Secureuxthemepatcher 5498970