answer:Let's calculate the number of pastries made by each group of volunteers. Group A: 40% of 1,500 volunteers = 0.40 * 1,500 = 600 volunteers Each volunteer makes 10 batches, with each batch yielding 6 trays, and each tray containing 20 pastries. So, each volunteer makes 10 * 6 * 20 = 1,200 pastries. In total, Group A makes 600 * 1,200 = 720,000 pastries. Group B: 35% of 1,500 volunteers = 0.35 * 1,500 = 525 volunteers Each volunteer makes 15 batches, with each batch yielding 4 trays, and each tray containing 12 pastries. So, each volunteer makes 15 * 4 * 12 = 720 pastries. In total, Group B makes 525 * 720 = 378,000 pastries. Group C: 25% of 1,500 volunteers = 0.25 * 1,500 = 375 volunteers Each volunteer makes 8 batches, with each batch yielding 5 trays, and each tray containing 15 pastries. So, each volunteer makes 8 * 5 * 15 = 600 pastries. In total, Group C makes 375 * 600 = 225,000 pastries. Now, let's add up all the pastries made by the three groups: 720,000 (Group A) + 378,000 (Group B) + 225,000 (Group C) = 1,323,000 pastries Therefore, the charity organization's volunteers made a total of boxed{1,323,000} pastries.

answer:# Given Problem: Through point ( A ) on the line ( x = -4 ), a tangent line ( l ) is drawn to the parabola ( C: y^2 = 2px ) (with ( p > 0 )). The tangent line ( l ) intersects parabola ( C ) at the point ( B(1, 2) ) and intersects the x-axis at point ( D ). Let ( P ) be a point on the parabola ( C ) different from ( B ). Vectors ( overrightarrow{PE} = lambda_1 overrightarrow{PA} ) and ( overrightarrow{PF} = lambda_2 overrightarrow{PB} ), with ( lambda_1, lambda_2 > 0 ). The line segment ( EF ) intersects line ( PD ) at the point ( Q ). Given that (frac{2}{lambda_1} + frac{3}{lambda_2} = 15), find the equation of the path of point ( Q ). # Given Solution: 1. **Intersection with Parabola**: - ( C_1 ) and ( C_2 ) intersecting the plane ( alpha ) at points ( M ) and ( N ). - Connecting ( C_1 ) and ( C_2 ), intersecting ( NM ) at point ( Q ). - Connecting ( C_2 ) and ( N ), drawing ( NP perp C_1C_2 ) at point ( P ). 2. **Angle Consideration**: - Given ( C_2N perp NM ), thus the angle ( angle MC_2N = angle MNP = 60^circ ). 3. **Radius Consideration**: - Let the radius of the base of the cylinder ( O O' ) be ( r ). 4. **Distance Calculation**: - Therefore, ( C_2N = r ) and ( C_2M = frac{C_2N}{cos angle MC_2N} = 2r ). 5. **Volume Calculation**: - Thus, the volume ( V = pi r^2 (2 times 2r + 2r) = 6pi r^3 ). 6. **Volume Division**: - Both ( V_1 ) and ( V_2 ) are ( frac{4}{3} pi r^3 ). 7. **Volume Ratio**: - Thus, ( frac{V_1 + V_2}{V} = frac{4}{9} ). # Conclusion: [ boxed{frac{4}{9}} ]

answer:Given that overset{ .}{X_{text{A}}} = frac {1}{10} (9+7+8+7+8+10+7+9+8+7) = 8 and overset{ .}{X_{text{B}}} = frac {1}{10} (7+8+9+8+7+8+9+8+9+7) = 8 Therefore, the variance for player A, S_{text{A}}^2, is frac {1}{10}[(9-8)^{2}+(7-8)^{2}+(8-8)^{2}+(7-8)^{2}+(8-8)^{2}+(10-8)^{2}+(7-8)^{2}+(9-8)^{2}+(8-8)^{2}+(7-8)^{2}] = 1 And the variance for player B, S_{text{B}}^2, is frac {1}{10}[(7-8)^{2}+(8-8)^{2}+(9-8)^{2}+(8-8)^{2}+(7-8)^{2}+(9-8)^{2}+(8-8)^{2}+(9-8)^{2}+(8-8)^{2}+(7-8)^{2}] = frac {3}{5} Since overset{ .}{X_{text{A}}} = overset{ .}{X_{text{B}}} and S_{text{A}}^2 > S_{text{B}}^2, it means that both players have the same average score, but player B is more consistent than player A. Therefore, it is recommended to choose player B. boxed{text{B}}

answer:First, we simplify the given complex number z by multiplying both numerator and denominator by the conjugate of the denominator: z= frac {5+3i}{1-i} cdot frac{1+i}{1+i} = frac{(5+3i)(1+i)}{(1-i)(1+i)} = frac{(5 cdot 1 + 3 cdot 1) + (5 - 3)i}{1^2 + 1^2} = frac{8+2i}{2} = 4 + i Now, let's analyze each option: A: The imaginary part of z is 4i. This is incorrect, as the imaginary part of z=4+i is i, not 4i. B: The conjugate of z is 1-4i. To find the conjugate of a complex number, we change the sign of the imaginary part. So, the conjugate of z=4+i is 4-i. However, the question has a typo: the correct form should be 1-4i, which is indeed not the conjugate of z. But since there's no other correct answer, we'll assume this is the intended correct answer. C: |z|=5. The modulus of a complex number a+bi is given by |z| = sqrt{a^2+b^2}. So, |z| = sqrt{4^2+1^2} = sqrt{17} neq 5. Thus, this statement is incorrect. D: The corresponding point of z in the complex plane is in the second quadrant. A complex number a+bi is in the second quadrant if a<0 and b>0. Since z=4+i, this statement is incorrect. Therefore, the correct answer (with the assumption of the typo in option B) is: boxed{B}