Mathematical Kangaroo

The sum of the first 100 positive integers can be calculated using the formula n(n+1)/2, where n is the last integer in the series. In this case, n = 100, so the sum is 100(101)/2 = 5050.

To find the total number of animals, we simply add the number of sheep, cows, and pigs. 12 + 6 + 8 = 26.

The area of a circle is calculated using the formula πr², where r is the radius of the circle. In this case, r = 5 cm, so the area is π(5²) = 25π cm².

To find the time at which the second train will overtake the first train, we need to find the difference in their speeds and then divide the distance between them by that difference. The distance between the trains is the speed of the first train multiplied by the time difference between the two trains. In this case, the speed difference is 75 mph - 60 mph = 15 mph. The time difference is 11:00 AM - 10:00 AM = 1 hour. The distance between the trains is 60 mph * 1 hour = 60 miles. Therefore, the time at which the second train will overtake the first train is 60 miles / 15 mph = 4 hours. Since the second train leaves at 11:00 AM, it will overtake the first train at 11:00 AM + 4 hours = 12:30 PM.

The area of a rectangle is calculated by multiplying its length by its width. In this case, the length is 10 meters and the width is 5 meters, so the area is 10 meters * 5 meters = 50 square meters.

To solve for x, we need to isolate x on one side of the equation. We can do this by subtracting 5 from both sides of the equation: 3x + 5 - 5 = 17 - 5. This simplifies to 3x = 12. Then, we divide both sides of the equation by 3: 3x / 3 = 12 / 3. This simplifies to x = 4.

To find the sale price of the shirt, we need to multiply the original price by the discount percentage and then subtract the result from the original price. In this case, the original price is $20 and the discount percentage is 20%. So, the sale price is $20 * 0.20 = $4. We then subtract $4 from $20 to get the sale price of $16.

The volume of a cube is calculated by cubing its side length. In this case, the side length is 4 cm, so the volume is 4 cm * 4 cm * 4 cm = 64 cm³.

To find the number of women who work for the company, we need to multiply the total number of employees by the percentage of women. In this case, the total number of employees is 100 and the percentage of women is 20%. So, the number of women who work for the company is 100 * 0.20 = 20.

When flipping a coin, there are two possible outcomes: heads or tails. Since both outcomes are equally likely, the probability of getting a head is 1/2.

To find the distance between the two trains at 12:00 PM, we need to find the distance traveled by each train and then subtract the distance traveled by the first train from the distance traveled by the second train. The distance traveled by the first train is 60 mph * 2 hours = 120 miles. The distance traveled by the second train is 75 mph * 2 hours = 150 miles. Therefore, the distance between the two trains at 12:00 PM is 150 miles - 120 miles = 30 miles.

The sum of the first 100 positive integers can be calculated using the formula n(n+1)/2, where n is the last integer in the series. In this case, n = 100, so the sum is 100(101)/2 = 5050.

To find the total number of animals, we simply add the number of sheep, cows, and pigs. 12 + 6 + 8 = 26.

The area of a circle is calculated using the formula πr², where r is the radius of the circle. In this case, r = 5 cm, so the area is π(5²) = 25π cm².

To find the time at which the second train will overtake the first train, we need to find the difference in their speeds and then divide the distance between them by that difference. The distance between the trains is the speed of the first train multiplied by the time difference between the two trains. In this case, the speed difference is 75 mph - 60 mph = 15 mph. The time difference is 11:00 AM - 10:00 AM = 1 hour. The distance between the trains is 60 mph * 1 hour = 60 miles. Therefore, the time at which the second train will overtake the first train is 60 miles / 15 mph = 4 hours. Since the second train leaves at 11:00 AM, it will overtake the first train at 11:00 AM + 4 hours = 12:30 PM.

The area of a rectangle is calculated by multiplying its length by its width. In this case, the length is 10 meters and the width is 5 meters, so the area is 10 meters * 5 meters = 50 square meters.