answer:1. Let's establish the relationship between the areas of the given strips and their respective lengths. Since the widths of the two resulting strips are identical, the areas of the strips are directly proportional to their lengths. Hence, the ratio of the areas will be the same as the ratio of their lengths. 2. Denote ( S ) as the area covered by both strips. According to the problem, the area covered only by the left strip is 27, and the area covered only by the right strip is 18. 3. Therefore, the total area covered by the left strip should be the sum of the area only covered by the left strip and the area covered by both strips, i.e., [ text{Total area covered by the left strip} = 27 + S ] 4. Similarly, the total area covered by the right strip is the sum of the area only covered by the right strip and the area covered by both strips, i.e., [ text{Total area covered by the right strip} = 18 + S ] 5. Given that the lengths of the left and right strips are 9 and 7 respectively, and because the areas are proportional to the lengths, we have: [ frac{27 + S}{18 + S} = frac{9}{7} ] 6. To solve for ( S ), we cross-multiply to eliminate the fraction: [ 7 cdot (27 + S) = 9 cdot (18 + S) ] 7. Expanding both sides: [ 189 + 7S = 162 + 9S ] 8. Rearrange to solve for ( S ): [ 189 + 7S - 162 = 9S ] [ 27 = 2S ] 9. Dividing both sides by 2: [ S = frac{27}{2} = 13.5 ] # Conclusion: The area of the part of the table covered by both strips is [ boxed{13.5} ]

answer:The hands of a clock are at right angles when they are 15 minutes apart, as each hour is divided into 12 segments of 5 minutes each (making a total of 60 minutes). In one hour, the minute hand and the hour hand are at right angles twice - once when the minute hand is 15 minutes ahead of the hour hand, and once when it is 15 minutes behind the hour hand. In a 12-hour period, this happens 2 times for each of the 12 hours, so there are 24 occurrences of right angles in 12 hours. Therefore, in a 24-hour period (one day), there are 24 * 2 = 48 occurrences. Over the course of 5 days, the hands will be at right angles 48 * 5 = boxed{240} times.

answer:Solution: For option A, a_{n}=2^{n}, by taking n=1, 2, 3, we get 2, 4, 8, hence option A is correct; For option B, a_{n}=n^{2}-n+2, by taking n=1, 2, 3, we get 2, 4, 8, hence option B is correct; For option C, a_{n}=2n, by taking n=1, 2, 3, we get 2, 4, 6, hence option C is incorrect; For option D, a_{n}=- frac {2}{3}n^{3}+5n^{2}- frac {25}{3}n+6, by taking n=1, 2, 3, we get 2, 4, 8, hence option D is correct; Therefore, the answer is C. By evaluating the given general formulas for the sequence with n=1, 2, 3 to see if the values are 2, 4, 8, if not, then it cannot represent its general term. This question mainly tests the concept of sequences and simple representation methods, as well as the ability to analyze problems, and is considered a basic question. boxed{text{C}}

answer:**Answer**: There is 1 square of size 8 times 8; 4 squares of size 7 times 7; 9 squares of size 6 times 6; 16 squares of size 5 times 5; 25 squares of size 4 times 4; 36 squares of size 3 times 3; 49 squares of size 2 times 2; 64 squares of size 1 times 1. In total, there are 204 squares. Therefore, the answer is boxed{text{C}}.