answer:To find the distance the boat travels downstream, we need to calculate the effective speed of the boat when it is moving downstream. The effective speed of the boat downstream is the sum of the speed of the boat in still water and the speed of the stream. Speed of boat in still water = 13 km/hr Speed of the stream = 4 km/hr Effective speed downstream = Speed of boat in still water + Speed of the stream Effective speed downstream = 13 km/hr + 4 km/hr Effective speed downstream = 17 km/hr The boat takes 4 hours to go a certain distance downstream. To find the distance, we use the formula: Distance = Speed × Time Distance downstream = Effective speed downstream × Time taken Distance downstream = 17 km/hr × 4 hours Distance downstream = 68 km Therefore, the distance the boat travels downstream is boxed{68} km.

answer:1. **Identify the property of red numbers:** - By the problem's rule, if x is red, then x+1 and frac{x}{x+1} must also be red. - We start with 1 being red. - Thus, we need to determine which additional numbers will also turn red. 2. **Positivity and Rationality of Red Numbers:** - Given that 1 is the initial red number (which is a positive rational number), and applying the functions x mapsto x + 1 and x mapsto frac{x}{x+1} to a rational number results in another rational number, we infer that all subsequent red numbers must be positive rational numbers. 3. **Show that all positive rational numbers are red:** - We'll show that any positive rational number x > 0 can be traced back to 1 using the inverse of the given functions. - Consider a positive rational number x = frac{p}{q} where p and q are positive integers with gcd(p, q) = 1. 4. **Inverses of the given mappings:** - The function f_1: x mapsto x + 1 has an inverse f_1^{-1}: x mapsto x - 1: [ x = frac{p}{q} mapsto frac{p}{q} - 1 = frac{p - q}{q} ] This can be applied if and only if frac{p}{q} > 1 (i.e., p > q). - The function f_2: x mapsto frac{x}{x + 1} has an inverse f_2^{-1}: x mapsto frac{x}{1 - x}: [ x = frac{p}{q} mapsto frac{frac{p}{q}}{1 - frac{p}{q}} = frac{frac{p}{q}}{frac{q - p}{q}} = frac{p}{q - p} ] This can be applied if and only if frac{p}{q} < 1 (i.e., p < q). 5. **Application of inverse mappings:** - By repeatedly applying these inverse mappings: - If x > 1, use f_1^{-1}. Each time, subtract q from p. - If x < 1, use f_2^{-1}. Each time, subtract p from q. - Since p and q are both positive integers, every application of the corresponding inverse function adjusts their values while ensuring the rationality and positivity of the resulting number. - Eventually, this process will lead to p = q, resulting in frac{p}{q} = 1. 6. **Conclusion:** - Since any positive rational x can be reduced to 1 via a finite number of steps using the inverses of the given functions, starting from 1 and applying x mapsto x+1 and x mapsto frac{x}{x+1} will generate all positive rational numbers – turning them all red. [ boxed{text{All positive rational numbers will be red.}} ]

answer:Given that the absolute value of any real number is not less than 0, it is known that the event where the absolute value of a real number is less than 0 is an impossible event. Therefore, the probability is 0. Hence, the answer is boxed{0}.

answer:Given that line l passes through point P(-2, 0) and has a slope of 3, we can use the point-slope form of the equation of a line: Starting with the point-slope formula: y - y_1 = m(x - x_1) Where m is the slope of the line and (x_1, y_1) is a point on the line. Substituting in the given point P(-2, 0) and the slope m = 3, we have: [ y - 0 = 3(x - (-2)) ] Simplify the equation: [ y = 3(x + 2) ] Further simplification gives: [ y = 3x + 6 ] Hence, the correct equation is: [ boxed{y = 3x + 6} ]