answer:**Analysis** This question mainly tests the calculation of the derivative of a function. The key to solving this question is the formula for the derivative of a composite function, which is quite basic. The calculation can be done directly using the formula for the derivative of a function. **Solution** Consider the function f(x)=(1-2x^{3})^{10} as being composed of the function y=u^{10}, where u=1-2x^{3}. Since y′=-60 x^{2}(1-2x^{3})^{9}, Therefore, f′(1)=60. Hence, the answer is boxed{60}.

answer:Let's denote the percentage of ryegrass in seed mixture X as R%. We know that seed mixture Y contains 25% ryegrass. We are given that when we mix X and Y, the resulting mixture contains 30% ryegrass. We are also given that 33.33333333333333% (which is equivalent to 1/3) of the weight of the mixture is X, and therefore, 66.66666666666667% (which is equivalent to 2/3) of the weight of the mixture is Y. Let's set up an equation to represent the mixture: (R% * 1/3) + (25% * 2/3) = 30% To solve for R%, we multiply out the terms: (R/3) + (50/3) = 30 Now, we multiply through by 3 to get rid of the denominators: R + 50 = 90 Subtract 50 from both sides to solve for R: R = 90 - 50 R = 40 Therefore, seed mixture X is boxed{40%} ryegrass.

answer:1. Let's denote the coordinates of points (A) and (B) as (Aleft(x_{1}, y_{1}right)) and (Bleft(x_{2}, y_{2}right)). 2. The midpoint (D) of the segment (AB) has coordinates given by [ Dleft(frac{x_{1} + x_{2}}{2}, frac{y_{1} + y_{2}}{2}right). ] 3. According to the problem, the slope of the line (OD) is 1. Hence, we have [ k_{OD} = 1 implies frac{y_{1} + y_{2}}{2} div frac{x_{1} + x_{2}}{2} = 1 implies x_{1} + x_{2} = y_{1} + y_{2}. ] 4. Given that points (A) and (B) lie on the ellipse (C), we have [ frac{x_{1}^{2}}{6} + frac{y_{1}^{2}}{3} = 1 quad text{and} quad frac{x_{2}^{2}}{6} + frac{y_{2}^{2}}{3} = 1. ] Subtracting these equations, we get [ frac{x_{1}^{2} - x_{2}^{2}}{6} + frac{y_{1}^{2} - y_{2}^{2}}{3} = 0. ] 5. This implies [ frac{(x_{1} - x_{2})(x_{1} + x_{2})}{6} + frac{(y_{1} - y_{2})(y_{1} + y_{2})}{3} = 0. ] Using (x_{1} + x_{2} = y_{1} + y_{2}), we substitute: [ frac{(x_{1} - x_{2})(y_{1} + y_{2})}{6} + frac{(y_{1} - y_{2})(y_{1} + y_{2})}{3} = 0. ] Let (u = y_{1} + y_{2}), then: [ frac{(x_{1} - x_{2})u}{6} + frac{(y_{1} - y_{2})u}{3} = 0 implies frac{(x_{1} - x_{2})}{6} = -frac{(y_{1} - y_{2})}{3} implies x_{1} - x_{2} = -2(y_{1} - y_{2}). ] 6. Solving the system of equations (x_{1} + x_{2} = y_{1} + y_{2}) and (x_{1} - x_{2} = -2(y_{1} - y_{2})), we get: [ x_{1} = frac{-y_{1} + 3 y_{2}}{2} quad text{and} quad x_{2} = frac{3 y_{1} - y_{2}}{2}. ] 7. Substituting (x_{1}) and (x_{2}) into the ellipse equation, we have: [ frac{left(-y_{1} + 3 y_{2}right)^{2}}{24} + frac{y_{1}^{2}}{3} = 1. ] Expanding and simplifying: [ 3x_{1}^{2} + y_{1}^{2} = 8 + 2 y_{1} y_{2}. ] 8. We need to determine (k_{1} times k_{2}): [ k_{1} k_{2} = frac{(y_{1} - 1)(y_{2} - 1)}{(x_{1} - 2)(x_{2} - 2)}. ] 9. Substituting values, we get: [ k_{1} k_{2} = frac{y_{1} y_{2} - (y_{1} + y_{2}) + 1}{x_{1} x_{2} - 2(x_{1} + x_{2}) + 4}. ] 10. Substitute (3(x_{1}^{2} + y_{2}^{2}) = 8 + 2y_2y_1) to solve: [ k_{1} k_{2} = frac{1}{2}. ] # Conclusion: [ boxed{frac{1}{2}} ]

answer:First, let's find out how many stickers Oliver used to decorate his notebook. He used 3/8 of his 180 stickers, so: (3/8) * 180 = 540/8 = 67.5 Since Oliver can't use half a sticker, we'll round down to the nearest whole number, which is 67 stickers. Now, let's subtract the stickers he used from the total to find out how many he had left: 180 - 67 = 113 stickers remaining Next, Oliver gave 5/11 of the remaining stickers to his friend: (5/11) * 113 = 565/11 = 51.363636... Again, since Oliver can't give a fraction of a sticker, we'll round down to the nearest whole number, which is 51 stickers. Now, let's subtract the stickers he gave away from the remaining stickers to find out how many he had left: 113 - 51 = 62 stickers remaining Finally, Oliver divided the rest of the stickers equally between his two siblings. Since he has two siblings, we divide the remaining stickers by 2: 62 / 2 = 31 stickers So, each sibling received boxed{31} stickers.