answer:Let's denote the number of boys as B and the number of girls as G. We are given that G = 151. The total number of students in the school is 604, so the number of boys B is: B = Total students - Number of girls B = 604 - 151 B = 453 The average age of the school is 11 years 9 months, which we can convert to years as 11 + 9/12 = 11.75 years. The total age of all the students in the school is the average age multiplied by the number of students: Total age = Average age * Total students Total age = 11.75 * 604 The total age of the boys is the average age of the boys multiplied by the number of boys: Total age of boys = Average age of boys * Number of boys Total age of boys = 12 * 453 The total age of the girls is the total age of all the students minus the total age of the boys: Total age of girls = Total age - Total age of boys Total age of girls = (11.75 * 604) - (12 * 453) Now we can calculate the average age of the girls by dividing the total age of the girls by the number of girls: Average age of girls = Total age of girls / Number of girls Let's calculate it step by step: Total age = 11.75 * 604 Total age = 7097 Total age of boys = 12 * 453 Total age of boys = 5436 Total age of girls = 7097 - 5436 Total age of girls = 1661 Average age of girls = 1661 / 151 Now we calculate the average age of the girls: Average age of girls ≈ 11 So, the average age of the girls is approximately boxed{11} years.

answer:Let's calculate the total number of practice days Mike has until the next game. Since Mike practices every weekday and Saturday, that's 6 days a week. Given that he has 3 weeks until the next game, the total number of practice days is: 6 days/week * 3 weeks = 18 days We know that on Saturdays, Mike practices for 5 hours. Since there are 3 Saturdays in 3 weeks, the total number of hours he practices on Saturdays is: 5 hours/Saturday * 3 Saturdays = 15 hours Now, let's subtract the hours Mike practices on Saturdays from the total number of hours he will practice until the next game: 60 hours (total) - 15 hours (Saturdays) = 45 hours The remaining 45 hours will be spread across the weekdays. Since there are 5 weekdays in a week and he has 3 weeks, the total number of weekday practice days is: 5 days/week * 3 weeks = 15 days Now, we can calculate the number of hours Mike practices every weekday by dividing the remaining hours by the number of weekday practice days: 45 hours / 15 days = 3 hours/day Therefore, Mike practices for boxed{3} hours every weekday.

answer:Given M={a, b}, N={a+1, 3}, and M cap N = {2}, Since 2 in N, we have a+1=2, thus a=1, Since 2 in M, we have b=2, Therefore, M={1, 2}, N={2, 3}, and M cup N={1, 2, 3}. Hence, the correct option is boxed{D}.

answer:1. **Initial Condition**: Define the given functional equation: [ x f(x) - y f(y) = (x - y) f(x + y) quad text{for all real} ; x, y ] 2. **Setting (y = -x)**: Substitute ( y = -x ) into the equation: [ x f(x) - (-x) f(-x) = (x - (-x)) f(x + (-x)) ] [ x f(x) + x f(-x) = 2x f(0) ] Since (x ne 0), [ f(x) + f(-x) = 2b quad text{where} ; b = f(0) ] 3. **Setting ( y = -x/2 ) and ( x to 2x )**: Replacing ( x ) by ( 2x ) and ( y ) by ( -x ) gives: [ 2x f(2x) - (-x) f(-x) = (2x + x) f(2x - x) ] [ 2x f(2x) + x f(x) = 3x f(x) ] Dividing both sides by ( x ne 0 ), [ 2 f(2x) + f(x) = 3 f(x) ] Simplifying, [ 2 f(2x) = 2 f(x) ] Thus, [ f(2x) = f(x) ] 4. **Generalization for Positive Integers**: Conjecture that: [ f(nx) = n f(x) ; text{for all positive integers} ; n ] We prove this by induction: - Base Case: If ( n = 1 ) [ f(x) = f(x) ] - Inductive Step: Assume ( f(kx) = k f(x) ) holds, then for ( n = k + 1 ), [ xf(kx) - f(x) = (n - 1) f((n+1)x) ] [ k f(kx) - f(x) = k f((k+1)x) ] Thus, [ f((k+1)x) = (k + 1) f(x) ] 5. **Negative Integers**: For negative integers ( n ), [ f(-nx) = 2b - f(nx) ] Using the induction hypothesis: [ f(nx) = nx f(x) ] Thus, [ f(-nx) = 2b - nx f(x) ] 6. **Rational Numbers**: For ( x = frac{1}{n} ), [ fleft(frac{1}{n}right) = a left(frac{1}{n}right) + b ] 7. **General Form for Rational ( m/n )**: [ fleft(frac{m}{n}right) = m left(a left(frac{1}{n}right) + bright) - (m - 1)b ] [ fleft(frac{m}{n}right) = m left(frac{a}{n} + bright) - (m - 1)b ] Simplifying: [ fleft(frac{m}{n}right) = frac{ma}{n} + b ] 8. **Extension to Real Numbers**: Define ( g(x) = f(x) - b ), [ x g(x) - y g(y) = (x - y) g(x + y) ] [ g(-x) = -g(x) ] Setting ( -y ): [ x g(x) - y g(-y) = (x + y) g(x - y) ] Thus, [ frac{g(x + y)}{x + y} = frac{g(x - y)}{x - y} ] General ( k !=! 1): [ frac{g(x + 1)}{k} = frac{g(1)}{k} ] 9. **Conclusion**: [ f(x) = ax + b ] So, the solution to the functional equation is: [ boxed{f(x) = ax + b} ]