Closed right circular cylinder 2 meter in diameter and 2-meter tall is partially filled with water. When lying in a horizontal position, the depth of water is 2/3 the diameter. When the cylinder is in the vertical position, what is the depth of water?

Closed right circular cylinder 2 meter in diameter and 2-meter tall is partially filled with water. When lying in a horizontal position, the depth of water is 2/3 the diameter. When the cylinder is in the vertical position, what is the depth of water?

If a certain soccer game ended 3:2, what is the probability that the side that lost scored first? Assume that all scoring scenarios are equiprobable.

If a certain soccer game ended 3:2, what is the probability that the side that lost scored first? Assume that all scoring scenarios are equiprobable.

The probability that a visitor at the mall buys a pack of candy is 30%. If three visitors come to the mall today, what is the probability that exactly two will buy a pack of candy?

The probability that a visitor at the mall buys a pack of candy is 30%. If three visitors come to the mall today, what is the probability that exactly two will buy a pack of candy?

A furniture manufacturer has two machines, but only one can be used at a time.

A furniture manufacturer has two machines, but only one can be used at a time. Machine A is utilized during the first shift and Machine B during the second shift, while both works half of the third shift. If Machine A can do the job in 12 days working two shifts and Machine B can do the job in 15 days working two shifts, how many days will it take to do the job with the current work schedule?

If the power of an engine grows by 10% when the number of its cylinders is increased by one, which of the following is closest to the ratio of the power of a 9-cylinder engine to that of a 12-cylinder engine?

If the power of an engine grows by 10% when the number of its cylinders is increased by one, which of the following is closest to the ratio of the power of a 9-cylinder engine to that of a 12-cylinder engine?

The box contains 10 tablets of medicine A and 15 tablets of medicine B. N tablets are taken from the box at random. What is the least possible N that ensures that at least two tablets of each kind are among the extracted?

The box contains 10 tablets of medicine A and 15 tablets of medicine B. N tablets are taken from the box at random. What is the least possible N that ensures that at least two tablets of each kind are among the extracted?

9. Two cities A and B are 30 km apart. From both of these cities, simultaneously, two hikers start their journeys towards each other.

Two cities A and B are 30 km apart. From both of these cities, simultaneously, two hikers start their journeys towards each other. They are walking at a constant speed of 5 km/hour each. Simultaneously, a fly leaves the city A. It flies at the speed of 10 km/hour and passes the hiker from its city. When it reaches the B hiker, it turns around and flies back to A hiker. It keeps doing so until the hikers meet.

Eight books are to be arranged on a bookshelf. Three of the books are by the same author. In how many ways can the book be arranged on the bookshelf if the books by the same author are to stay together?

Eight books are to be arranged on a bookshelf. Three of the books are by the same author. In how many ways can the book be arranged on the bookshelf if the books by the same author are to stay together?