answer:To solve this problem, we need to calculate the rate at which each pipe fills the tank and then determine how long it takes to fill the tank when the pipes are used in the given sequence. First, let's find the rate at which each pipe fills the tank per minute: - Pipe a fills the tank in 60 minutes, so its rate is 1/60 of the tank per minute. - Pipe b fills the tank in 40 minutes, so its rate is 1/40 of the tank per minute. - Pipe c fills the tank in 30 minutes, so its rate is 1/30 of the tank per minute. - Pipe d fills the tank in 24 minutes, so its rate is 1/24 of the tank per minute. Now, let's calculate the combined rate of the pipes when they are used together: - Pipes a and b together: (1/60 + 1/40) = (2/120 + 3/120) = 5/120 = 1/24 of the tank per minute. - Pipes b, c, and d together: (1/40 + 1/30 + 1/24) = (3/120 + 4/120 + 5/120) = 12/120 = 1/10 of the tank per minute. - Pipes a, c, and d together: (1/60 + 1/30 + 1/24) = (2/120 + 4/120 + 5/120) = 11/120 of the tank per minute. Let's assume the total time to fill the tank is T minutes. Since the tank is filled in three equal time intervals, each interval is T/3 minutes. Now, we can calculate the fraction of the tank filled during each interval: - First interval (pipes a and b): (1/24) * (T/3) = T/72 of the tank. - Second interval (pipes b, c, and d): (1/10) * (T/3) = T/30 of the tank. - Third interval (pipes a, c, and d): (11/120) * (T/3) = 11T/360 of the tank. The sum of these fractions must equal 1 (the whole tank): T/72 + T/30 + 11T/360 = 1 To combine these fractions, we need a common denominator, which is 360: (5T/360) + (12T/360) + (11T/360) = 1 (5T + 12T + 11T) / 360 = 1 28T / 360 = 1 28T = 360 T = 360 / 28 T = 12.8571... Since we can't have a fraction of a minute, we round up to the nearest whole minute: T ≈ 13 minutes Therefore, it will take approximately boxed{13} minutes to fill the tank from an empty state under these conditions.

answer:First, let's calculate how many miles the car can travel on a full tank of fuel before the modification: 27 miles/gallon * 14 gallons = 378 miles After the modification, the car will use only 75% as much fuel, which means it will be 25% more fuel-efficient. To find the new fuel efficiency, we can calculate: 27 miles/gallon * (1 + 0.25) = 27 miles/gallon * 1.25 = 33.75 miles/gallon Now, let's calculate how many miles the car can travel on a full tank of fuel after the modification: 33.75 miles/gallon * 14 gallons = 472.5 miles To find out how many more miles the car will be able to travel per full tank of fuel after the modification, we subtract the original number of miles from the new number of miles: 472.5 miles - 378 miles = 94.5 miles So, the car will be able to travel an additional boxed{94.5} miles per full tank of fuel after it has been modified.

answer:The calculation of intersection points between five lines follows these steps: 1. **Maximum Intersections**: With five lines in a plane, each pair of lines can intersect once. The number of distinct intersection points is determined by binom{5}{2} = 10. 2. **Minimum Intersections**: The minimum number of intersection points is 0, which occurs when no two lines intersect, such as when all lines are parallel. 3. **Possible Configurations and Impossibilities**: Similar to the four-line case, configurations for five lines can yield different numbers of intersection points. However, configurations leading to some specific counts (like 7, 9) could be impossible due to geometric constraints: - For each intersection point, it involves exactly two lines. Hence, odd totals like 7 or 9 require an odd number of lines intersecting, which isn't possible because each intersection involves two lines. 4. **Valid Counts**: Possible numbers of intersection points are those even numbers and some odd numbers excluding those derived impossible from geometric constraints. These include 0, 1, 2, 3, 4, 5, 6, 8, 10. **Sum Calculation**: To find the sum of all possible values of N, we calculate: [ 0 + 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 = 39 ] Thus, the sum of all possible values of N is 39. The final answer is boxed{39}.

answer:First, let's find out how much the temperature dropped in total. The temperature dropped from 80 to 78.2, which is a drop of: 80 - 78.2 = 1.8 degrees Now, we know that it cost Sasha 108 to plant the trees that caused this temperature drop. Since each tree costs 6 to plant, we can find out how many trees she planted by dividing the total cost by the cost per tree: 108 / 6 per tree = 18 trees Now that we know Sasha planted 18 trees to achieve a temperature drop of 1.8 degrees, we can find out how much the temperature drops for each tree planted by dividing the total temperature drop by the number of trees: 1.8 degrees / 18 trees = 0.1 degrees per tree So, for each tree planted, the temperature drops by boxed{0.1} degrees.