answer:Solution: ((1)) Using the coefficient of determination (R^{2}) to judge the fitting effect of the model, the larger the (R^{2}), the better the fitting effect of the model, so ((1)) is correct; ((2)) If two random variables have stronger linear correlation, then the absolute value of the correlation coefficient (r) is closer to (1), so ((2)) is incorrect; ((3)) If the variance of statistical data (x_{1}), (x_{2}), (x_{3}), (ldots), (x_{n}) is (1), then the variance of (2x_{1}), (2x_{2}), (2x_{3}), (ldots), (2x_{n}) is (4), so ((3)) is incorrect; ((4)) For the observed value (k_{0}) of the random variable (k^{2}) for categorical variables (x) and (y), the larger (k_{0}), the greater the certainty of judging "there is a relationship between (x) and (y)". Therefore, ((4)) is incorrect; Thus, the correct choice is: boxed{A} ((1)) Judged based on the properties of the coefficient of determination (R^{2}), ((2)) Judged based on the relationship between linear correlation and (r), ((3)) Judged based on the relationship of variance, ((4)) Judged based on the relationship of the observed value (k_{0}) of the random variable (k^{2}) for categorical variables (x) and (y). This question mainly examines the judgment of the truth or falsehood of propositions, involving the relationship of random variables and the study of correlation in probability and statistics, and the concept of regression line equation, testing reasoning ability, and is considered a basic question.

answer:Let's denote the length of the platform as ( L ). When the train crosses a signal pole, it only needs to cover its own length. The time it takes to pass the signal pole is 18 seconds, so we can calculate the speed of the train as follows: Speed of the train ( = frac{text{Distance covered}}{text{Time taken}} ) ( = frac{text{Length of the train}}{text{Time taken to pass the signal pole}} ) ( = frac{300 text{ metres}}{18 text{ seconds}} ) ( = frac{300}{18} text{ metres/second} ) ( = frac{50}{3} text{ metres/second} ) Now, when the train crosses the platform, it has to cover the length of itself plus the length of the platform. The time it takes to pass the platform is 39 seconds. We can use the speed we just calculated to find the length of the platform: Distance covered when crossing the platform ( = text{Length of the train} + text{Length of the platform} ) ( = 300 text{ metres} + L ) Using the speed of the train, we can write: ( frac{50}{3} text{ metres/second} times 39 text{ seconds} = 300 text{ metres} + L ) Now we solve for ( L ): ( frac{50}{3} times 39 = 300 + L ) ( 650 = 300 + L ) ( L = 650 - 300 ) ( L = 350 text{ metres} ) So, the length of the platform is boxed{350} metres.

answer:1. **Understanding the Problem**: We are given a grid composed of (1 times 1) squares. Within this grid, there are 2015 shaded regions. These shaded regions can consist of line segments that are either horizontal, vertical, or diagonal (connecting either midpoints or corners of the squares). We are tasked with determining the area of these shaded regions. 2. **Interpretation and Analysis**: Each shaded region forms part of a (1 times 1) square. The given problem suggests that by manipulating (moving and re-positioning) the small triangular shaded regions, we can reconfigure them into complete squares. This is necessary to find out the total area of these shaded regions. 3. **Procedure**: - We start with identifying that 2015 shaded regions need to be analyzed to form full squares. - Consider the reconfiguration of these triangular shaded parts to form complete (1 times 1) squares. This process will involve counting how many complete squares (sum of smaller triangular parts) can be formed. - According to the given analysis, these smaller triangular portions can be rearranged within the free spaces of the grid, giving us a total of 47 complete squares and an additional half square formed by the remaining triangular pieces. 4. **Calculation**: - As analyzed: - The number of complete (1 times 1) squares formed by rearranging the shaded triangular parts is 47 - The remaining shaded region forms an additional half square Thus, the total area of the shaded regions can be written as: [ 47 + frac{1}{2} = 47 frac{1}{2} ] # Conclusion: The area of the shaded regions within the grid is (47 frac{1}{2}). Thus, the correct answer is: [ boxed{B} ]

answer:**Analysis** This question examines the application of the Sine Rule and the Cosine Rule. According to the Sine Rule, we can set the three sides as 3k, 5k, and 7k, respectively. Then, we use the Cosine Rule to find the value of cos C. **Solution** In triangle ABC, sin A:sin B:sin C=3:5:7. According to the Sine Rule, we can set the three sides as 3k, 5k, and 7k, respectively. By the Cosine Rule, we get 49k^2=25k^2+9k^2-30k^2cos C. Solving the equation, we get cos C= -frac{1}{2}. Therefore, the answer is boxed{-frac{1}{2}}.