# Examples for 9th grade - page 34

1. Water tank 2
Water tank cuboid is 12 meters long and 6.5 meters wide and 1.2 meters high. How many hectoliters are in the tank when it is filled to 81%?
What size have angles in quadrilateral (4-gon) if they are in a ratio of 8: 9: 10: 13?
3. Logik game
Letter game Logik is a two player game, which has the following rules: 1. The first player thinks five-letter word in which no letter is not repeated. 2. The second player writes a five-letter word. 3. The first player answers two numbers - the first numbe
4. Digits
How many natural numbers greater than 4000 which are formed from the numbers 0,1,3,7,9 with the figures not repeated, B) How many will the number of natural numbers less than 4000 and the numbers can be repeated?
5. Surface area
The volume of a cone is 1000 cm3 and the content area of the axis cut is 100 cm2. Calculate the surface area of the cone.
6. Passenger car
Passenger car travels 1 km for 2.3 minutes, a truck during a 50 seconds long. How much is the speed of the truck less?
7. ICE train
German runways test a new ICE train between Munich and Berlin. The train runs to Berlin at a slow speed of 100 km/h. Back from Berlin goes faster. How quickly did the train have to go on a return trip so that the total average train speed for both journeys
8. Unknown integer
Find the smallest integer that: divided by 2, the remainder is 1 divided by 3 the remainder is 2, divided by 4 remainder is 3, ... divided by eight reminder is 7, by 9 reminder is 8.
9. Ascent and descent
Car goes 114 km track, which consists of ascent and descent at time of 1 hour 35 minutes. When climbing moves at the speed 48 km/h and downhill 25 m/s. What is the length of climb and descent?
10. The angle of lines
Calculate the angle of two lines y=x-21 and y=-2x+14
11. Brass tube
The outer perimeter of brass tube (ρ = 8.5 g/cm3) is 38 cm. Its mass is 5 kg, length 54 cm. What is the pipe wall thickness?
12. Automaker
The automaker now produces daily 4 new cars more than last year so the production of 360 cars will save just one full working day. How many working days to produce 360 vehicles needed last year?
13. Angles of the triangle
ABC is a triangle. The size of the angles alpha, beta are in a ratio 4: 7. The angle gamma is greater than the angle alpha by a quarter of a straight angle. Determine angles of the triangle ABC.
14. Tournament
Determine how many ways can be chosen two representatives from 34 students to school tournament.
15. Maple
Maple peak is visible from a distance 3 m from the trunk from a height of 1.8 m at angle 62°. Determine the height of the maple.
16. Disinfecting solution
How much distilled water is necessary to pour into 500 ml of 33% hydrogen peroxide solution to obtain 3% disinfecting solution?
17. Painters
The first team of painters would paint bridge in 15 days, the second in 10 days. After 3 days of working together second team goes out and continue only first team. How many days took second team to finish painting the bridge?
18. Reflector
Circular reflector throws light cone with a vertex angle 49° and is on 33 m height tower. The axis of the light beam has with the axis of the tower angle 30°. What is the maximum length of the illuminated horizontal plane?
19. Angle
A straight line p given by the equation ?. Calculate the size of angle in degrees between line p and y-axis.
20. Medals
In how many ways can be divided gold, silver and bronze medal among 21 contestant?

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