answer:3206_7 = 3(7^3) + 2(7^2) + 0(7^1) + 6(7^0) = 3(343) + 2(49) + 0(7) + 6(1) = 1029 + 98 + 0 + 6 = boxed{1133}. The answer is: 1133

answer:To solve this problem, we need to determine the value of x, which represents the radius of the base of the cylinder. We know that the sphere has a radius of 5 units and the cylinder is inscribed in the sphere. This means that the diameter of the sphere is equal to the height of the cylinder. The volume of the space inside the sphere and outside the cylinder is equal to the volume of the sphere minus the volume of the cylinder. The volume of the sphere is given by the formula (4/3)πr^3, where r is the radius of the sphere. The volume of the cylinder is given by the formula πr^2h, where r is the radius of the base of the cylinder and h is the height of the cylinder. We can set up the equation as follows: (4/3)π(5^3) - π(x^2)(2x) = Wπ Let's simplify and solve for x: (4/3)(125π) - 2x^3π = Wπ 500π/3 - 2x^3π = Wπ To isolate x, we divide both sides of the equation by 2π: 500π/3π - 2x^3π/2π = Wπ/2π 250/3 - x^3 = W/2 To solve for x, we take the cube root of both sides of the equation: ∛(250/3 - x^3) = ∛(W/2) 250/3 - x = ∛(W/2) To solve for x, we subtract 250/3 from both sides of the equation: 250/3 - 250/3 - x = ∛(W/2) - 250/3 -x = ∛(W/2) - 250/3 To solve for x, we multiply both sides of the equation by -1: x = 250/3 - ∛(W/2) We are given that the answer is 3. Therefore, we can set up the equation as follows: 250/3 - ∛(W/2) = 3 To solve for W, we isolate ∛(W/2) and then square both sides of the equation: 250/3 - 3 = ∛(W/2) 241/3 = ∛(W/2) To solve for W, we cube both sides of the equation: (241/3)^3 = (∛(W/2))^3 (241/3)^3 = W/2 To solve for W, we multiply both sides of the equation by 2: 2(241/3)^3 = W The value of W is 2(241/3)^3. The answer is: 3

answer:Half of the students play basketball, so there are 20 * 1/2 = 10 students who play basketball. Two-fifths of the students play volleyball, so there are 20 * 2/5 = 8 students who play volleyball. One-tenth of the students play both basketball and volleyball, so there are 20 * 1/10 = 2 students who play both. To find the number of students who do not participate in either game, we need to subtract the total number of students who play basketball and volleyball, including those who play both, from the total number of students. So, the number of students who do not participate in either game is 20 - 10 - 8 + 2 = 4. 4 The answer is: 4

answer:By definition, an obtuse triangle has one angle that is greater than 90 degrees. Therefore, in an obtuse triangle, there is only boxed{1} interior angle that is obtuse.The answer is: 1