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📰 Solution: First, calculate the total number of arrangements of the letters in "THEORETICAL". The word has 10 letters with repetitions: T (2), E (3), H (1), O (1), R (1), I (1), C (1), A (1). Total arrangements: $ \frac{10!}{2! \cdot 3!} = 302400 $. Next, subtract the arrangements where 'E' and 'A' are adjacent. Treat 'EA' or 'AE' as a single entity, reducing the problem to arranging 9 items (with T repeated twice and E reduced to 2). Number of such arrangements: $ 2 \cdot \frac{9!}{2! \cdot 2!} = 2 \cdot 362880 / 4 = 181440 $. The valid arrangements are $ 302400 - 181440 = 120960 $. Thus, the answer is $ \boxed{120960} $.Question: A 5 cm by 8 cm rectangle is inscribed in a circle. What is the number of centimeters in the circumference of the circle? Express your answer in terms of $\pi$. 📰 Solution: To find the circumference of the circle in which a rectangle is inscribed, we first recognize that the diagonal of the rectangle is the diameter of the circle. Using the Pythagorean theorem, the diagonal $d$ of a 5 cm by 8 cm rectangle is: 📰 d = \sqrt{5^2 + 8^2} = \sqrt{25 + 64} = \sqrt{89} 📰 Youll Never Remember Roman Numerals Again Test Your Knowledge Now 5941787 📰 Where Can I Watch The Long Walk 6054129 📰 Ipad Pro 2024 📰 James Frey 6345669 📰 Michelle Lavigne 📰 Bullish Vs Bearish Which Trend Is Moving Markets This Hidden Factor Surprised Even Experts 2454234 📰 New Statement Automobile Refinance Rates And The Impact Surprises 📰 Credit Card Application Bank Of America 📰 Discover The Best Of Anna Faris Movies And Tv Shows Every Fan Voice Demands You See These Now 4793568 📰 Fairfax Financial Holdings Stock Just Hit A Recordwhat Trails Are Missing 501854 📰 Mark Mulder 1893237 📰 Commodity Giants In Action Mullen Stock Hits All Time Highwhat It Means 7861346 📰 Download Charles 📰 Blockbreaker Exposes What No One Wants To Seewatch The Chain Reaction Begin 5433759 📰 Download Online Games Free