answer:First, let's find out how many Spanish-speaking guides there are. We know there are 22 guides in total and that there are 10 English-speaking guides and 6 French-speaking guides. So, the number of Spanish-speaking guides is: 22 total guides - 10 English-speaking guides - 6 French-speaking guides = 6 Spanish-speaking guides Now let's calculate the number of children spoken to by each group of guides on each day. On Friday: - English-speaking guides: 10 guides * 20 children each = 200 children - French-speaking guides: 6 guides * 25 children each = 150 children - Spanish-speaking guides: 6 guides * 30 children each = 180 children On Saturday: - English-speaking guides: 10 guides * 22 children each = 220 children - French-speaking guides: 6 guides * 24 children each = 144 children - Spanish-speaking guides: 6 guides * 32 children each = 192 children On Sunday: - English-speaking guides: 10 guides * 24 children each = 240 children - French-speaking guides: 6 guides * 23 children each = 138 children - Spanish-speaking guides: 6 guides * 35 children each = 210 children Now, let's add up all the children spoken to over the three days: Friday total: 200 (English) + 150 (French) + 180 (Spanish) = 530 children Saturday total: 220 (English) + 144 (French) + 192 (Spanish) = 556 children Sunday total: 240 (English) + 138 (French) + 210 (Spanish) = 588 children Total over the three-day weekend: 530 (Friday) + 556 (Saturday) + 588 (Sunday) = 1674 children The zoo guides spoke to a total of boxed{1674} children over the three-day weekend.

answer:To evaluate each statement: **For option A:** In regression analysis, the width of the band area of residual points in the residual plot is a visual indicator of the regression model's accuracy. A narrower band suggests that the residuals are closer to the regression line, which in turn indicates a better fit of the model to the data. Therefore, a narrower width of the band area of residual points indicates a better, not worse, regression effect. Thus, option A is incorrect. **For option B:** The probability of precipitation being 90% means there is a high likelihood of rain, but it does not guarantee it. The occurrence or non-occurrence of rain on a single day does not invalidate the scientific basis of weather forecasting, which relies on probabilistic models. Weather forecasts are predictions based on the best available data and models, and they inherently involve uncertainty. Therefore, the fact that it did not rain on a day with a 90% forecasted chance of precipitation does not indicate that the weather forecast is unscientific. Hence, option B is incorrect. **For option C:** To calculate the variance of both sets of data, we first find their means. For the first set (2, 3, 4, 5), the mean is frac{2+3+4+5}{4} = frac{14}{4} = 3.5. For the second set (4, 6, 8, 10), the mean is frac{4+6+8+10}{4} = frac{28}{4} = 7. The variance of a set of data is calculated by averaging the squared differences from the mean. The second set of data is obtained by multiplying each element of the first set by 2. This scaling affects the variance by a factor of the square of the scale factor (2^2 = 4), making the variance of the second set four times the variance of the first set, not twice. Therefore, the statement in option C is incorrect. **For option D:** The regression line equation hat{y}=0.1x+10 describes how the predicted variable hat{y} changes with the explanatory variable x. The coefficient of x (which is 0.1 in this case) represents the change in the predicted variable for each one-unit increase in the explanatory variable. Therefore, when x increases by one unit, hat{y} indeed increases by 0.1 units, making option D correct. **Conclusion:** After evaluating each option, we find that option D is the only correct statement. Therefore, the correct option is boxed{text{D}}.

answer:**Analysis:** Given that m > n, we have n - m < 0. Since the coefficient of x is less than 0, and (n-m)x > 0, we can deduce the range of x. Therefore, the solution set is boxed{x < 0}.

answer:From the given information, we have V=ae^{-50k}=frac{4}{9}a, (1) Let the volume become frac{8}{27}a after t days, so we have V=ae^{-kt}=frac{8}{27}a, (2) From (1), we can derive e^{-50k}=frac{4}{9}, (3) Dividing (2) by (1), we get e^{-(t-50)k}=frac{2}{3}, Squaring both sides, e^{-(2t-100)k}=frac{4}{9}, Comparing with (3), we get 2t-100=50, solving which gives t=75 days, Thus, it takes 75 days for the volume to become frac{8}{27}a. Therefore, the answer is: boxed{D}. From the given information, we have V=ae^{-50k}=frac{4}{9}a. By letting the volume become frac{8}{27}a after t days, we can establish another equation and solve for t. This problem illustrates the application of functions in everyday life and is of moderate difficulty. To solve it, carefully read the problem, identify implicit conditions, and set up appropriate equations.