Video Discussion: MSTE-00 Problem Set 7

Set 7 Part 1

1. A strip of 640 m² is sold from a triangular field whose sides are 96 m, 72 m, and 80 m. The strip is of uniform width h and has one of its sides parallel to the longest side of the field. Find the width of the strip.
2. Water evaporates at the rate of two liters per hour per one square meter of surface. How long will it take to evaporate 30 liters of water from a cylindrical swimming pool full of water with 6 m in diameter and 2 m depth?
3. A disease is known to affect 1 in 10,000 people. It can be fatal, but it is treatable if it is detected early. A screening test for the disease shows a positive result for 99% of the people with the disease. The test also shows positive for 2% of people who do not have the disease. For a population of one million people how many would you expect to test positive but do not have the disease?
4. There are four red, three green and five blue discs in a bag. Find the probability that two discs of the same color are drawn.
5. Five men and three women are arranged randomly in a row. What is the probability that there are not two women standing together anywhere in the row?

Set 7 Part 2

1. The DOH encourages elderly people to have a flu vaccination each year. The vaccination reduces the likelihood of getting a flu from 40% to 10%. If 45% of the elderly people visiting the doctor have the vaccination, find the probability that an elderly person chosen at random had the vaccination, given that they get flu.
2. 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?
3. Pass a plane through a cube so that the section formed will be a regular hexagon. If the edge of the cube is 2 units, find the area of this section.
4. 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. At the moment they do meet, the fly lands on the shoulder of the A hiker as he continues his journey to B. How many kilometers has the fly flown?
5. 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?

Set 7 Part 3

1. 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?
2. At what angle do the lines $y = 2x + 2$ and $y = x - 4$ intersect?
3. 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?
4. 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?
5. 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.