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📰 Question: What is the smallest three-digit number divisible by 11 and 13? 📰 Solution: The LCM of 11 and 13 is $143$. The smallest three-digit multiple of 143 is $143 \times 1 = 143$ (since $143 \times 2 = 286$ is also three-digit, but 143 is smaller). Thus, the answer is $\boxed{143}$.Question: Two marine biologists, Dr. Coral and Dr. Tide, arrive at a research station at random times between 7:00 and 8:00. If Dr. Coral arrives after Dr. Tide, what is the probability that Dr. Tide arrived before 7:45? 📰 Solution: Let the arrival times of Dr. Tide and Dr. Coral be $ x $ and $ y $, respectively, where $ x, y \in [0, 60] $ minutes after 7:00. The condition $ y > x $ defines a triangular region in the $ xy $-plane with area $ \frac{60^2}{2} = 1800 $. The favorable region is where $ x < 45 $ and $ y > x $. Integrating over $ x \in [0, 45] $, the area is $ \int_{0}^{45} (60 - x) \, dx = 60 \cdot 45 - \frac{45^2}{2} = 2700 - 1012.5 = 1687.5 $. The conditional probability is $ \frac{1687.5}{1800} = \frac{3}{4} $. 📰 This Microsoft Mouse Bluetooth Revolution Will Change How You Work Forever 8744828 📰 Emoji Location 1461886 📰 You Wont Believe What Hidden Secrets Lurk In Yakuza Games 9528704 📰 Finally Found The Perfect Couple App That Makes You Fall For Each Other All Over Againclick To See 5414389 📰 Viserys Targaryen Exposed The Secret That Ruined His Dynastys Promise 2704585 📰 Finally The Ultimate Full Screen Keyboard Shortcut You Need For Fast Typing 4579509 📰 You Wont Believe What Hidden Gems Span Torontos Zip Codezip Toronto On Canada 9976590 📰 Moon Drawn By Trembling Clouds This Ethereal Twist Will Haunt Your Dreams 7757628 📰 Arcola Country Club 5368878 📰 David Tamil Film 2365781 📰 This Poetic Cat Just Wrote A Love Letter The Internet Is Obsessed 5766870 📰 Step Up Your Health Game This Simple Stepsapp Trick Is Life Changing 4512525 📰 But In The Initial Problems Even With Percentages Answers Were Exact 2030918 📰 Color Box 395855 📰 Film A December Bride 72461