# Grade - examples - page 13

1. Slope of track
Calculate the average slope (in promiles and even in degrees) of the rail tracks between Prievidza (309 m AMSL) and Topoľčany (174 m AMSL), if the track is 44 km long.
2. Cyclist
Cyclist goes uphill 10 km for 50 minutes and downhill minutes for 29 minutes, both applied to the pedals same force. How long he pass 10 km by plane?
3. Railways
Railways climb 7.4 ‰. Calculate the height difference between two points on the railway distant 3539 meters.
4. Water
Mix 21 l of water with temperature of 38 °C, 67 l warm of 34 °C and 14 l water of 32 °C. What is the temperature of the mixed water immediately after mixing?
5. Theater
The theater has in each row with 19 seats. Ticket to the first 10 rows is for 30 USD. In next rows is for 15 USD. The theater was completely sold out. Revenue was 12255 USD. How many rows are in the theater?
6. Spherical cap
From the sphere of radius 18 was truncated spherical cap. Its height is 12. What part of the volume is spherical cap from whole sphere?
7. Right triangle
Legs of right are in ratio a:b = 6:8. Hypotenuse has a length of 61 cm. Calculate the perimeter and area of the triangle.
8. Pentagon
Calculate the area of regular pentagon, which diagonal is u=17.
9. Mast
Mast has 17 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 5°. Determine the height of the mast, if the sun above the horizon is at angle 37°12'.
10. Rhombus
It is given a rhombus of side length a = 29 cm. Touch points of inscribed circle divided his sides into sections a1 = 14 cm and a2 = 15 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus.
11. Sea water
Seawater contains about 4.3% salt. How many dm3 of distilled water we must pour into 5 dm3 of sea water to get water with 1.8% salt?
12. Present
Gift box has rectangular shape with dimensions of 8×8×3 cm. Miloslav wants to cover with square paper with sides of 18 cm. How much paper left him?
13. Camp
In the camp are children. 1/2 went on a trip, 1/4 went to bathe and 38 children remained in the room. How many children are in camp?
14. Piggy
A man bought a pig for € 60 then sold it for € 75. Then again bought for € 90 and sold it for € 100. How many € earned?
15. Wage
Increasing the minimum wage while maintaining the other parameters of the system, unemployment will be:
Road repair took 10 days for 36 workers if they worked 9 hours a day. How many days take repair same road 37 workers if they work 8 per day?
17. Rectangle
Calculate the length of the side GN and diagonal QN of rectangle QGNH when given: |HN| = 25 cm and angle ∠ QGH = 28 degrees.
18. Engineer Kažimír
The difference between politicians-demagogues and reasonable person with at least primary education beautifully illustrated by the TV show example. "Engineer" Kažimír says that during their tenure there was a large decline in the price of natural gas, pri
19. Pediatrician
Pediatrician this month of 21 working days takes 3 days holidays. What is the probability that on Monday will be at work?
20. Barrel of oil
Barrel of oil weighs 283 kg. When it mold 26% oil, weighed 216 kg. What is the mass of the empty barrel?

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