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📰 #### 420Question: How many integers between 1 and 500 are congruent to 2 mod 7? 📰 Solution: To find the count of integers $ n $ such that $ 1 \leq n \leq 500 $ and $ n \equiv 2 \pmod{7} $, we note the sequence starts at 2 and increases by 7 each time: $ 2, 9, 16, \dots $. The general term is $ 7k + 2 $. Solving $ 7k + 2 \leq 500 $ gives $ k \leq rac{498}{7} pprox 71.14 $, so $ k = 0, 1, \dots, 71 $. This yields $ 72 $ integers. oxed{72} 📰 Question: What is the greatest common divisor of 210 and 294, representing shared efficiency metrics in clean energy systems? 📰 Unlock The Truth Windows 10 Release Date Confirmed Its Longer Than You Think 6941429 📰 The Ultimate Guide To Readysubno Click Just Value Youve Been Waiting For 9745335 📰 Purdue Mackey Arena 6129446 📰 Nees Today 391496 📰 Measles Rash 8613681 📰 You Wont Believe What Happens When You Roll A D20This 5 Minute Ritual Changes Everything 5898859 📰 Season 4 Finally Returns The Unthinkable Prison Break Revelation That Shocked Fans 8649779 📰 Mind Blowing Value Hidden In Plain Sight The Penny Thats Worth More Than You Think 9220892 📰 Death By Lightning Reviews 1238504 📰 Jasper Indiana Time 7248561 📰 Groundbreaking The Stunning Unifi App Icon That Transforms How You Manage Smart Devices 3303356 📰 Unlock Miamis Zip Code Secrets Where Every Street Has Surprising Historic Value 1564012 📰 Verizon Wireless Pontiac Illinois 3083597 📰 No Weights Neededpistol Squat Shocked Us All By Breaking Athletic Limits 6814546 📰 Colors That Go Together 1714612