# Examples for secondary school students - page 48

1. Three friends Three friends divided the profit 104,650 CZK, so that for every 4 CZK, which got the first friend equals 5 crowns for second and for every 9 CZK, which got the second equals 16 CZK for third. Question: Who got the most and how much.
2. Fish tank A fish tank at a pet store has 8 zebra fish. In how many different ways can George choose 2 zebra fish to buy?
3. Water tank The water tank has a cylindrical shape with a base diameter of 4.2 m and is 80 cm deep. How many minutes will take fill it 10 cm below the edge of the tank if water flowing 2 liters per second?
4. Costume Denisa is preparing for a goldsmith's costume carnival. During the preparations, she thought she would let her hair wipe instead - she would apply a 5 μm thick layer of gold to each hair. How much gold would Denisa need? Assume that all hundred thousand De
5. Store Peter paid in store 3 euros more than half the amount that was on arrival to the store. When he leave shop he left 10 euros. How many euros he had upon arrival to the store?
6. Rectangle The rectangle has a perimeter 75 cm. Diagonal length is 32.5 cm. Determine the length of the sides.
7. Right triangle eq2 Hypotenuse of a right triangle is 9 cm longer than one leg and 8 cm longer than the second leg. Determine the circumference and area of a triangle.
8. Im>0? Is -10i a positive number?
9. Sweets We want to prepare 5 kg of sweets for 150 CZK. We will mix cheaper candy: 1 kg for 120 CZK and more expensive candy: 1 kg per 240 CZK. How much of this two types of candy is necessary to prepare this mixture?
10. Rectangle - sides 4 Perimeter of the rectangle is 72 cm. Calculate the length of the sides that are in the ratio 3:5.
11. AS sequence In an arithmetic sequence is given the difference d = -3 and a71 = 455. a) Determine the value of a62 b) Determine the sum of 71 members.
12. Rotary bodies The rotating cone and the rotary cylinder have the same volume 180 cm3 and the same height v = 15 cm. Which of these two bodies has a larger surface area?
13. Hydrochloric acid Determine the concentration of which must have a solution of hydrochloric acid that mixing 10 l of the solution with 8 liters of 26% solution to get the solution with a concentration of 50%?
14. Three ints The sum of three consecutive integers is 2016. What numbers are they?
15. Eight palm There grows 8 palms by the sea. At the first sitting one parrot, on second two, on third sits four parrots on each other twice the previous parrots sitting on a previous palm. How many parrots sitting on eighth palm?
16. Lottery Fernando has two lottery tickets each from other lottery. In the first is 973 000 lottery tickets from them wins 687 000, the second has 1425 000 lottery tickets from them wins 1425 000 tickets. What is the probability that at least one Fernando's ticket w
17. Octahedron All walls of regular octahedron are identical equilateral triangles. ABCDEF octahedron edges have a length d = 6 cm. Calculate the surface area and volume of this octahedron.
18. PIN - codes How many five-digit PIN - code can we create using the even numbers?
19. Cylinder diameter The surface of the cylinder is 149 cm2. The cylinder height is 6 cm. What is the diameter of this cylinder?
20. Seamstress 2 Seamstress bought two kinds of textile in whole meters. One at 50 SKK and the second 70 SKK per meter. How many meter bought from this two textiles when paid totally 1540 SKK?

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