answer:First, let's find out how many girls and boys were originally in the classroom. The original number of girls in the classroom is 38% of 50: ( 0.38 times 50 = 19 ) girls The original number of boys in the classroom is 62% of 50: ( 0.62 times 50 = 31 ) boys Now, let's add the new students and subtract the boys who leave: New number of girls = original number of girls + new girls New number of girls = 19 + 6 = 25 girls New number of boys = original number of boys + new boys - boys who leave New number of boys = 31 + 8 - 4 = 35 boys Now, let's find the total number of students after the changes: Total students = new number of girls + new number of boys Total students = 25 + 35 = 60 students Finally, let's calculate the new percentage of girls in the classroom: Percentage of girls = (new number of girls / total students) × 100 Percentage of girls = (25 / 60) × 100 Percentage of girls = 0.4167 × 100 Percentage of girls = 41.67% So, the new percentage of girls in the classroom is approximately boxed{41.67%} .

answer:Since f(x)=x^{2}-2x=(x-1)^{2}-1, the axis of symmetry is the line x=1. Since x=1 may not necessarily be within the interval [-2,a], we need to discuss different cases. When -2 < a leqslant 1, the function is monotonically decreasing in the interval [-2,a]. Therefore, when x=a, f(x) reaches its minimum value, which is f(x)_{min}=a^{2}-2a. When a > 1, the function is monotonically decreasing in the interval [-2,1] and monotonically increasing in the interval [1,a]. Therefore, when x=1, f(x) reaches its minimum value, which is f(x)_{min}=-1. In summary, when -2 < a leqslant 1, f(x)_{min}=a^{2}-2a; when a > 1, f(x)_{min}=-1. Thus, the final answer is: - When -2 < a leqslant 1, the minimum value of f(x) is boxed{a^{2}-2a}. - When a > 1, the minimum value of f(x) is boxed{-1}.

answer:To solve the problem, we start by understanding the given conditions and what we need to find. We are given a positive geometric sequence {a_{n}} with a_{1}=1 and the sum of the first n terms denoted as S_{n}. The problem states that S_{5}=5S_{3}-4, and we are asked to find S_{4}. 1. **Identify the common ratio**: Let the common ratio of the geometric sequence be q. Since a_{1}=1, every term in the sequence can be represented as a_{n}=1cdot q^{n-1}. 2. **Express S_{n} in terms of q**: The sum of the first n terms of a geometric sequence is given by S_{n}=frac{a_{1}(1-q^{n})}{1-q}, substituting a_{1}=1 gives S_{n}=frac{1-q^{n}}{1-q}. 3. **Apply the given condition**: We are told that S_{5}=5S_{3}-4. Substituting the formula for S_{n} into this condition gives frac{1-q^{5}}{1-q}=5left(frac{1-q^{3}}{1-q}right)-4. 4. **Solve for q**: Simplifying the equation, we observe that q cannot be 1 because it would lead to a contradiction (as 5neq 15-4). Solving the equation frac{1-q^{5}}{1-q}=5cdot frac{1-q^{3}}{1-q}-4 leads to finding q^{2}=4, which implies q=2 (since q is positive). 5. **Find S_{4}**: With q=2, we substitute back into the formula for S_{n} to find S_{4}. Thus, S_{4}=frac{1-q^{4}}{1-q}=frac{1-16}{1-2}=frac{-15}{-1}=15. Therefore, the sum of the first four terms of the sequence, S_{4}, is boxed{15}, which corresponds to choice C.

answer:To calculate (10^{2})^{5}, we follow the rules of exponents, where when an exponent is raised to another exponent, we multiply the exponents. Thus, we have: [ begin{align*} (10^{2})^{5} &= 10^{2 times 5} &= 10^{10}. end{align*} ] Therefore, the final answer is boxed{10^{10}}.