# Grade - examples - page 82

1. RWY Calculate the opposite direction of the runway 13. Runways are named by a number between 01 and 36, which is generally one tenth of the azimuth of the runway's heading in degrees: a runway numbered 09 points east (90°), runway 18 is south (180°), runway.
2. Pumps First pump flows 16 liters per second into the basin by the second pump 75% of the first and by third pump half more than the second. How long will take fill basin by all three pumps simultaneously volume 15 m3 (cubic meters)?
3. Probabilities If probabilities of A, B and A ∩ B are P (A) = 0.62 P (B) = 0.78 and P (A ∩ B) = 0.26 calculate the following probability (of union. intersect and opposite and its combinations):
4. Rings groups 27 pupils attend some group; dance group attends 14 pupils, 21 pupils sporty group and dramatic group 16 pupils. Dance and sporting attend 9 pupils, dance and drama 6 pupil, sporty and dramatic 11 pupils. How many pupils attend all three groups?
5. Divisibility 2 How many divisors has integer number 13?
6. Theorem prove We want to prove the sentense: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
7. Water In the garden with an area of 8 ares rain 40hl of water. To what heights leveled water?
8. Direct route From two different places A and B connected by a direct route, Adam (from city A) and Bohus (from city B) started at a constant speed. As Adam continued to go from A to B, Bohus turned around at the time of their meeting and at the same speed he returned t
9. Right triangle - leg Calculate to the nearest tenth cm length of leg in right-angled triangle with hypotenuse length 9 cm and 7 cm long leg.
10. Jumps At least how many jumps must do frog to overcome the distance of 7 meters? Jump of frog is 18 cm long.
11. Harvesters The first harvester reaps the grain from land for 24 hours, the second harvester for 16 hours. For how many hours will take harvest by two harvesters, but the second harvester started working four hours later than the first?
12. Shot Shot with a mass 43 g flying at 256 m/s penetrates into the wood to a depth 25 cm. What is the average force of resistance of wood?
13. Center of gravity In the isosceles triangle ABC is the ratio of the lengths of AB and the height to AB 10:12. The arm has a length of 26 cm. If the center of gravity T of triangle ABC find area of triangle ABT.
14. Painters One painter could paint a school for 7 days. The second one for 6 days. It was necessary to paint the school in two days. Next painter was invited and all worked together. How long would this painter painted the school itself?
15. Znojmo From Znojmo to Brno started truck with a trailer at an average speed 53 km per hour. Against him 14 minutes later from Brno started car with an average speed of 1.2-times greater than the truck. How long and how far from Znojmo, they meet if the distanc
16. Weekly service In the class are 20 pupils. How many opportunities have the teacher if he wants choose two pupils randomly who will weeklies?
17. Product V2 The price of product was increased by 12%. Price increased by 273. How much money it would cost this product, if it was on the contrary by 19% discounted.
18. Coffee Coffee merchant has coffee robusta and arabica species. 1 kg Robusta worth 450 CZK, Arabica 1 kg is 300 CZK more expensive. Calculate how many kilograms of Robusta and Arabica will need to produce 30 kg of the mixture so that the mixture cost is 490 CZK p
19. Glass How many glass are needed to produce glass with base regular 5-gon if one base triangle in the base is 4.2 square cm and the height is 10 cm?
20. Tangents construct Circle is given k (S; 2.5 cm) and an outer line p. Construct a tangent t of the circle that has with a line p angle 60°. How many solutions has the task?

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