answer:- Calculate the number of players excluding the captain shooting free throws: 15 - 1 = 14 players. - Each captain takes turns being the target captain, while the other players, including the other captain, make free throws. - Multiply the number of players making free throws by the number of captains: 14 times 2 = boxed{28} free throws.

answer:To find the value of 120 ab, we need to first determine the value of ab from the given equation 10 a = 6 b = 20. Since 10 a = 20, we can solve for a: a = 20 / 10 a = 2 Similarly, since 6 b = 20, we can solve for b: b = 20 / 6 b = 10 / 3 Now we can find the value of ab: ab = a * b ab = 2 * (10 / 3) ab = 20 / 3 Now we can find the value of 120 ab: 120 ab = 120 * (20 / 3) 120 ab = (120 * 20) / 3 120 ab = 2400 / 3 120 ab = 800 Therefore, 120 ab = boxed{800} .

answer:The center of the circle (x-1)^2+(y-3)^2=10 is at (1,3), and its radius r= sqrt {10}. The distance d from the center of the circle to the line x-3y+3=0 is d= frac {|1-9+3|}{ sqrt {10}}= frac {5}{ sqrt {10}}. Therefore, the length of chord AB is 2 sqrt {10- frac {25}{10}}= sqrt {30}. Hence, the correct answer is boxed{A}. This problem tests the knowledge of the relationship between a line and a circle. Mastering the formula for the length of a chord in a circle is key to solving it.

answer:To analyze the given propositions, we need to consider the geometric relationships between lines and planes: **Option A:** If m perp n and n parallel alpha, then m could be contained in alpha, m could be parallel to alpha, or m could intersect alpha at some angle. Since being perpendicular (perp) is a specific case of intersection and not guaranteed by the given conditions, we conclude that option A might not always be true. **Option B:** Given m parallel n and n perp alpha, we can deduce that line m, being parallel to line n, must also be perpendicular to plane alpha because all lines parallel to a line that is perpendicular to a plane are themselves perpendicular to the plane. This makes option B correct. **Option C:** If m perp alpha and m perp n, this implies that line n could either be contained within plane alpha or be parallel to plane alpha. It does not necessarily imply that n is parallel to alpha since n could also intersect alpha at some angle other than being parallel. Therefore, option C is not necessarily correct. **Option D:** When m perp alpha and alpha perp beta, line m could either be contained within plane beta or be parallel to beta. This does not ensure that m is perpendicular to beta, as the relationship between a line perpendicular to one plane and another plane perpendicular to the first plane does not automatically imply perpendicularity between the line and the second plane. Thus, option D is incorrect. Based on the analysis, the correct proposition is: boxed{text{B}} If m parallel n and n perp alpha, then m perp alpha.