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📰 Question: What is the remainder when $1^2 + 2^2 + \cdots + 15^2$ is divided by 13? 📰 Solution: The sum of squares formula gives $S = rac{15 imes 16 imes 31}{6} = 1240$. Compute $1240 \mod 13$: $13 imes 95 = 1235$, so $1240 - 1235 = 5$. The remainder is $oxed{5}$.Question: A science educator is designing a lesson on probability using a digital simulation that generates random 6-digit numbers using only the digits 1, 2, and 3. What is the probability that a randomly generated number has exactly two consecutive digits that are the same? 📰 Solution: To solve this, we must count the number of 6-digit numbers using only the digits 1, 2, and 3 such that exactly one pair of consecutive digits are equal, and all other adjacent digits are different. 📰 Chicken Crust Pizza 7312452 📰 Self Employment Tax Explainedwhy It Could Cost You Thousands More 678547 📰 You Wont Believe What Mastemon Reveals About Your Skincare Routine 6571900 📰 Will You Be The Leader In Lord Of The Rings Conquest Game Changing Strategy Revealed 3507663 📰 Pistons Trade Rumors 101958 📰 Trackside Pizza 6132667 📰 3 This Lightning Mcqueen Bed Is Headlined As The Most Epic Nightstand Ever 9057902 📰 Are Green Potatoes Safe To Eat 2126219 📰 Performativity Meaning 3631942 📰 Futurecast Radar 1580824 📰 Final Fantasy 7 Final 7017160 📰 Upstart Stock 3037548 📰 Paul Dune 4591696 📰 La Ceiba Restaurant 7569387 📰 How Your Outlook Signature Could Be Boosting Your Credibility Without You Knowing 4908521