answer:First, we compute 7! = 7 times 6 times 5 times 4 times 3 times 2 times 1 = 5040. We want to find the value of n such that 5 times 8 times 2 times n = 5040. Dividing both sides by 5 times 8 times 2, we get n = frac{5040}{5 times 8 times 2}. Simplifying, we have n = frac{5040}{80}. Further simplifying, we have n = 63. Therefore, the value of n is boxed{63}. The answer is: 63

answer:We can rewrite the inequality as frac{7}{9} > frac{x}{13}. Multiplying both sides by 13, we have 13left(frac{7}{9}right) > x. Simplifying, we get frac{91}{9} > x. The greatest integer x that satisfies this inequality is boxed{10}. The answer is: 10

answer:Meso can type 15 pages in 5 minutes, so he can type 15/5 = 3 pages per minute. Tyler can type the same 15 pages in 3 minutes, so he can type 15/3 = 5 pages per minute. Together, Meso and Tyler can type 3 + 5 = 8 pages per minute. If they want to type 40 pages, it would take them 40/8 = 5 minutes. 5 The answer is: 5

answer:The given matrix is a rotation matrix that rotates a vector counterclockwise by 170^circ. For the rotation matrix to be equal to the identity matrix, the angle of rotation must be a multiple of 360^circ. The smallest positive integer n for which 170^circ cdot n is a multiple of 360^circ is n = frac{360^circ}{10^circ} = boxed{36}. The answer is: 36