# The most difficult problems

1. Intelligence test Paľo, Jano, Karol, and Rišo were doing an intelligence test. Palo correctly answered half of the questions plus 7 questions, Jano to a third plus 18 questions, Karol to a quarter plus 21 questions and Risho to a fifth plus 25 questions. After the test, K
2. Hexagon Calculate the surface of a regular hexagonal prism whose base edge a = 12cm and side edge b = 3 dm. The heights of five starters on redwood high’s basketball team are 5’11”, 6’3”, 6’6”, 6’2” and 6’. The average of height of these players is?
4. A loan A loan in the amount of \$944 is charged simple interest at an annual rate of 8.1%. How much money is owed 14 months after the loan was made?
5. The parabolic segment The parabolic segment has a base a = 4 cm and a height v = 6 cm. Calculate the volume of the body that results from the rotation of this segment a) around its base b) around its axis.
6. Bdf tablet Detective Harry Thomson has come across a surprising mystery. As part of the weekend's action, the tablet he looked for dropped by 30%. He also recommended this bargain to his friend. However, it came to the shop on Monday, and the tablet was 30% more exp
7. The wellbore The wellbore has a tributary of 2 m3 per hour. When there is no tapping, there are a stable 28 liters of water in the well. The pump suction basket is at the bottom of the well. At 14.00, the water was pumped out at a rate of 0.5 liters of water every se
8. Picture frames Destiny has to make 24 picture frames. Each frame uses 16 3/8 wood trim. 2/3 were completed on the first day. How many inches of wood trim is needed to complete the remaining frames on the second day?
9. Two cylinders Two cylinders are there one with oil and one with an empty oil cylinder has no fixed value assume infinitely. We are pumping out the oil into an empty cylinder having radius =1 cm height=3 cm rate of pumping oil is 9 cubic centimeters per sec and we are p
10. Two integers Two integers, a and b, have a product of 36. What is the least possible sum of a and b?
11. A number 2 A number decreased by the difference between four and the number
12. The tax The tax per gallon of gasoline in California is \$0.477. If you fill your gasoline tank with 14.4 gallons of gasoline in California, how much will you pay in taxes? Round to the nearest cent.
13. An animal shelter An animal shelter spends \$5.50 per day to care for each bird and \$8.50 per day to care for each cat. Nicole noticed that the shelter spent \$283.00 caring for birds and cats on Wednesday. Nicole found a record showing that there were a total of 40 birds an
14. A rectangle 2 A rectangle has a diagonal length of 74cm. Its side lengths are in ratio 5:3. Find its side lengths.
15. Heptagonal pyramid A hardwood for a column is in the form of a frustum of a regular heptagonal pyramid. The lower base edge is 18 cm and the upper base of 14 cm. The altitude is 30 cm. Determine the weight in kg if the density of the wood is 10 grams/cm3.
16. Coordinates of square vertices I have coordinates of square vertices A / -3; 1/and B/1; 4 /. Find coordinates of vertices C and D, C 'and D'. Thanks Peter.
17. The hemisphere The hemisphere container is filled with water. What is the radius of the container when 10 liters of water pour from it when tilted 30 degrees?
18. A concrete pedestal A concrete pedestal has a shape of a right circular cone having a height of 2.5 feet. The diameter of the upper and lower bases are 3 feet and 5 feet, respectively. Determine the lateral surface area, total surface area, and the volume of the pedestal.
19. Floating of wood - Archimedes law What will be the volume of the floating part of a wooden (balsa) block with a density of 200 kg/m3 and a volume of 0.02 m3 that floats in alcohol? (alcohol density is 789 kg/m3)
20. Cylinder and its circumference If the height of a cylinder is 4 times its circumference c, what is the volume of the cylinder in terms of its circumference, c?

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