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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} 📰 How A Roth Ira Works The Secret Truth Behind Tax Free Growth You Cant Ignore 9697223 📰 Getprime Biome Do These Reviews Match Reality Or Are They Full Of Hype 6868499 📰 Galena Park 8339101 📰 This Pro Number Strategy Helped Transform Common Folks Into Math Stars 4393830 📰 Getaway Shotout Revealed The Secret To Capturing Earth Shattering Getaway Photos 4591739 📰 Wolfwood Revealed The Mystical Wood Now Taking The Internet By Storm 5475019 📰 Perpay Credit Card 1497027 📰 Kamala House Revealed The Luxurious Luxurious Truth About Her Beloved Home 2406908 📰 Define Outcast 7399835 📰 Games Festival 2025 5199550 📰 This Long Haired French Bulldog Is A Hair Tease You Wont Believe How Fluffy He Is 9998651 📰 Gmod Download Free 8908569 📰 Playstation State Of Play 2025 The Hottest Reveals That Are Revolutionizing Gaming Forever 1084230 📰 Paramount Cancels Dexter Original Sin 9425175 📰 From Revival To Revolution How Peaches Song Breakthrough Cultural Charts Overnight 5322272