# Examples for 9th grade - page 31

1. Chess How many ways can select 4 fields on classic chess board with 64 fields, so that fields don't has the same color?
2. Cone container Rotary cone-shaped container has a volume 1000 cubic cm and a height 12 cm. Calculate how much metal we need for making this package.
3. Grandfather The grandfather is three years older than an grandmother. The average age of the grandmother, the grandfather and their seven grandchildren is 28 years. The grandchildren have a total of 105 years. Calculate how old is grandfather.
4. Bronze, tin and copper Bronze is an alloy of tin and copper. An alloy of 10% tin and 90% copper is Gunmetal. If it contains 20% tin and 80% copper, it is bell metal. How many tons of molten bell metal and how many tons of copper is needed to make 100 tons of Gunmetal?
5. Gasholder The gasholder has spherical shape with a diameter 20 m. How many m3 can hold in?
6. Elections In elections candidate 10 political parties. Calculate how many possible ways can the elections finish, if any two parties will not get the same number of votes.
7. Rectangle - parallelogram It is given a rectangle that is circumscribed by a circle with a radius of 5 cm. The short side of the rectangle measures 6 cm. Calculate the perimeter of a parallelogram ABCD whose vertices are the midpoints of the sides of the rectangle. The voltage station is every day changing the master password, which consists of three letters. Code generation process does not change and is based on the following procedure: The following letters (A) to (I) correspond to different numbers from 1 to 9. I
9. Work First paver pave pavement for 27 hours. Second for 27 hours. Started first paver and after 4 hours, join the second. How long will they finish pavement?
10. Bath In the bath is 30 liters of hot water. Then added 36 liters of cold water at temperature of 19 °C decreased temperature of water to 41 °C. What was the initial temperature of the hot water?
11. Diamond Side length of diamond is 35 cm and the length of the diagonal is 56 cm. Calculate the height and length of the second diagonal.
12. Triangle Calculate the area of ​​the triangle ABC if b = c = 17 cm, R = 19 cm (R is the circumradius).
13. Painters First painter painted fence himself for 4 hours, the second painter 1.2 hours sooner than first, and the third painters slowest up to 16 hours. How long took them paint fence if worked together?
14. Resistors Two resistors connected in series give the resulting resistance 216Ω and 48Ω in parallel. Determine the resistance of these resistors.
15. Isosceles triangle The perimeter of an isosceles triangle is 112 cm. The length of the arm to the length of the base is at ratio 5:6. Find the triangle area.
16. Paul and Honza Honza went to chat on a bike without a break 4.0 hours. Paul the same way without breaks 50 minutes longer. The difference between the speeds of the two boys was the one kilometer per hour. How fast was Paul, if you know that the speed of the boys did not.
17. Examination The class is 21 students. How many ways can choose two to examination?
18. Enterprise and wages The enterprise operates a total 162 workers and their average salary is M dollars. If the company has hire an additional 18 employees whose average wage would be the S dollars, would reduce the overall average salary in the company of 3.6%. Calculate the
19. Two workers Two workers carry will do certain work for 12 days. After 8 days of working was one removed, and then the other finished the job alone in 10 days. For how many days would do this work alone each worker?
20. ISO trapezoid v2 bases of Isosceles trapezoid measured 12 cm and 5 cm and its perimeter is 21 cm. What is the are of a trapezoid?

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