answer:# Problem: In a parliament of 30 deputies, each pair of deputies either are friends or enemies, and each deputy has exactly 6 friends. Every three deputies form a committee. Find the total number of committees in which all three members are either all friends or all enemies. 1. We start by noting that each deputy can form a triangle (committee) with any two other deputies. Represent the deputies as points in a graph. Connect the points with a red edge if the corresponding deputies are friends and with a blue edge if they are enemies. 2. We are looking to find the number of monochromatic triangles (committees) in which all three members are friends (red triangles) or all three members are enemies (blue triangles). 3. The total number of triangles that can be formed with 30 deputies is given by [ binom{30}{3} = frac{30 times 29 times 28}{3 times 2 times 1} = 4060. ] 4. Let us count the number of non-monochromatic triangles (triangles that are not all red or all blue). In each non-monochromatic triangle, exactly two of the angles are formed with edges of different colors (one red and one blue edge). We will refer to such angles as mixed-color angles. 5. Since each deputy has exactly (6) friends, it implies that they have (30 - 1 - 6 = 23) enemies. 6. For a fixed deputy, there are (6 times 23 = 138) mixed-color angles formed by pairing their 6 friends with 23 enemies. 7. Considering the symmetry and the fact that every vertex is part of such triangles, the total number of non-monochromatic triangles is [ frac{138 times 30}{3} = 2070. ] 8. Consequently, the number of monochromatic triangles is the total number of triangles minus the number of non-monochromatic triangles: [ 4060 - 2070 = 1990. ] # Conclusion: Thus, the total number of committees in which all three members are either all friends or all enemies is: [ boxed{1990} ]

answer:Given right trapezoid vertices and the known properties: - Right trapezoid sides are parallel or perpendicular where relevant. - The lower base coordinates of the trapezoid are (5, -2) to (16, -2). - Semicircle equation centered at (10.5, -2) with radius 5.5 is (x - 10.5)^2 + (y + 2)^2 = 5.5^2. First, calculate the area of the slim trapezoidal region above the semicircle, treating it as a rectangle (as the height is very small, equal to 0.5 units, forming a negligible area): [ text{Base length} = 16 - 5 = 11 ] [ text{Area of rectangle} approx 0 ] Calculate the area of the semicircle: [ text{Area of semicircle} = frac{1}{2} pi r^2 = frac{1}{2} pi (5.5)^2 = frac{1}{2} pi (30.25) = 15.125 pi ] Sum to find the total intersected area component, which is effectively the area of the semicircle given that the rectangle's contribution is negligible: [ text{Total area} approx 15.125 pi ] Boxed final answer: [ boxed{15.125pi} ]

answer:A: The mean of 1, 2, 4, 3, 5 is: (1+2+3+4+5)÷5=3, thus, this option is incorrect; B: Since the sample data 1, 2, 4, 3, 5, each appeared only once, therefore, stating the mode is 5 is incorrect, thus, this option is correct; C: The range of the sample data 1, 2, 4, 3, 5, is 4, thus, this option is incorrect; D: The variance of the sample data 1, 2, 4, 3, 5, is 2, thus, this option is incorrect. Therefore, the correct choice is boxed{text{B}}.

answer:To compare the sets of numbers and identify the ones that are equal in value, we evaluate each option step by step: **Option A:** We compare -3^{5} and left(-3right)^{5}. - For -3^{5}, the negative sign applies to the result of 3^{5}, so we have -3^{5} = -243. - For left(-3right)^{5}, the base is -3, and since the exponent is odd, the result remains negative: left(-3right)^{5} = -243. Since both expressions yield the same result, we conclude that boxed{text{Option A meets the requirements}}. **Option B:** We compare -2^{2} and left(-2right)^{2}. - For -2^{2}, the negative sign is outside the square, so it's -2^{2} = -4. - For left(-2right)^{2}, the square applies to -2, making it positive: left(-2right)^{2} = 4. Since the results are different, boxed{text{Option B does not meet the requirements}}. **Option C:** We compare -4times 2^{3} and -4^{2}times 3. - For -4times 2^{3}, we calculate 2^{3} = 8 first, then multiply by -4: -4times 8 = -32. - For -4^{2}times 3, we calculate -4^{2} = -16 (since the exponent applies only to 4, not the negative sign), then multiply by 3: -16times 3 = -48. Since the results are different, boxed{text{Option C does not meet the requirements}}. **Option D:** We compare -left(-3right)^{2} and -left(-2right)^{3}. - For -left(-3right)^{2}, we calculate left(-3right)^{2} = 9 first, then apply the negative sign: -left(-3right)^{2} = -9. - For -left(-2right)^{3}, we calculate left(-2right)^{3} = -8 (since the base is negative and the exponent is odd), then apply the negative sign: -left(-2right)^{3} = -8. Since the results are different, boxed{text{Option D does not meet the requirements}}. Therefore, after evaluating each option, we conclude that the correct choice is boxed{text{A}}.