The sum of the first 100 positive integers can be calculated using the formula: Sum = n(n+1)/2, where n is the last integer in the series. In this case, n = 100. Therefore, Sum = 100(100+1)/2 = 5050.

To solve this problem, we can use the formula: Distance = Speed * Time. Let x be the time at which the two trains meet. The distance traveled by the first train is 60 * x, and the distance traveled by the second train is 70 * (x - 1), since it leaves one hour later. Since the total distance between New York City and Chicago is 900 miles, we can set up the equation: 60 * x + 70 * (x - 1) = 900. Solving for x, we get x = 3. Therefore, the two trains will meet at 3:00 PM.

The area of the path can be calculated by subtracting the area of the garden from the area of the larger rectangle formed by the garden and the path. The area of the garden is 20 * 15 = 300 square meters. The length of the larger rectangle is 20 + 2x meters, and the width is 15 + 2x meters. Therefore, the area of the larger rectangle is (20 + 2x) * (15 + 2x) = 400 + 100x + 4x^2. Subtracting the area of the garden, we get the area of the path: 400 + 100x + 4x^2 - 300 = 400 + 100x square meters.

Let x be the total population of the town. Since 60% of the population are women, there are 0.6x women in the town. We know that there are 1200 women in the town, so we can set up the equation: 0.6x = 1200. Solving for x, we get x = 2000. Therefore, the total population of the town is 2000.

Since 60% of the employees are male, 40% of the employees are female. Therefore, the number of female employees is 0.4 * 100 = 40.

The farmer plants corn on 40% of the land, which is 0.4 * 120 = 48 acres. He plants soybeans on 30% of the land, which is 0.3 * 120 = 36 acres. Therefore, he plants wheat on 120 - 48 - 36 = 36 acres.

The discount is 20% of the original price, which is 0.2 * $20 = $4. Therefore, the sale price of the shirt is $20 - $4 = $16.

To solve this problem, we can use the formula: Distance = Speed * Time. Let x be the time at which the second train overtakes the first train. The distance traveled by the first train is 60 * x, and the distance traveled by the second train is 70 * (x - 1), since it leaves one hour later. Since the two trains are traveling in the same direction, we can set up the equation: 60 * x = 70 * (x - 1). Solving for x, we get x = 2.5. Therefore, the second train will overtake the first train at 12:30 PM.

The profit in the second year is 110% of the profit in the first year. Therefore, the profit in the second year is 1.1 * $100,000 = $110,000.

The area of the room is simply the length multiplied by the width. Therefore, the area of the room is 12 * 8 = 96 square meters.

The circumference of a circle is given by the formula: C = 2πr, where r is the radius of the circle. Therefore, the circumference of the circle is 2π * 10 = 20π centimeters.

To solve this problem, we can use the formula: Distance = Speed * Time. Let x be the time at which the two trains are 300 miles apart. The distance traveled by the first train is 60 * x, and the distance traveled by the second train is 70 * x, since they are traveling in opposite directions. The total distance between the two trains is 300 miles. Therefore, we can set up the equation: 60 * x + 70 * x = 300. Solving for x, we get x = 2. Therefore, the two trains will be 300 miles apart at 1:00 PM.

Since 60% of the employees are male, 60% of 100 employees are male. Therefore, the number of male employees is 0.6 * 100 = 60.

The farmer plants soybeans on 30% of the land, which is 0.3 * 120 = 36 acres.

The discount is 20% of the original price, which is 0.2 * $20 = $4.