# Examples for 9th grade - page 11

1. Team The football team has 11 players. Their average age is 20 years. During the match due to injury, one player withdraws and the average age of the team is 18. How old was injured player? Between cities A and B is route 13 km long of stúpanie average 7‰. Calculate the height difference of cities A and B.
3. Diofant 2 Is equation ? solvable on the set of integers Z?
4. Speed of Slovakian trains Rudolf decided to take the train from the station 'Trnava' to 'Zemianske Kostoľany'. In the train timetables found train R 725 Remata : km0Bratislava hl.st.12:574Bratislava-Vinohrady13:0113:0219Pezinok13:1213:1346Trnava13:3013:3263Leopoldov13:4514:0168H
5. Right isosceles Calculate area of the isosceles right triangle which perimeter is 41 cm.
6. Parquet floor Three workers laid parquet floor for 2.301 hour. The first one would do this work alone 7 hours, the second in 6 hours. For how many hours would fulfill this work the third worker, if he worked alone?
7. Hole In the center of the cube with edge 14 cm we will drill cylinder shape hole. Volume of the hole must be 27% of the cube. What drill diameter should be chosen?
8. Tinsmith Tinsmith construct chimney pipe 145 cm long and 15 cm wide. What are the dimensions of the sheet will have to prepare for the construction of a pipe when the plate overlap at the joint add \$x cm width of the plate?
9. Cu wire Copper wire has a length l = 980 m and diameter d = 8 mm. Calculate the weight if density of copper is ρ = 8500 kg/m3. Result round to one decimal place. Determine the radius of the circle, if its perimeter and area is the same number.
11. Discount Product has been discounted twice by 19%. What is the total discount given?
12. Seedcake Seedcake costs 44 cents. How many minimum seedcakes we must buy that we can pay in cash only whole euros?
13. Parallelogram Calculate area of the parallelogram ABCD as shown if |AB| = 19 cm, |BC| = 18 cm and angle BAD = 90°
14. Euclid1 Right triangle has hypotenuse c = 27 cm. How large sections cuts height hc=3 cm on the hypotenuse c?
15. Phone numbers How many 7-digit telephone numbers can be compiled from the digits 0,1,2,..,8,9 that no digit is repeated? During the spring cleaning ladies going to wash windows. Mother takes wash all the windows 5 hours, the grandmother 3 times longer and Paula wash all windows in 2 hours. How many hours will spend washing the windows this "women's team" if working togethe
17. Diofant equation In the set of integers (Z) solve the equation: ? Write result with integer parameter ? (parameter t = ...-2,-1,0,1,2,3... if equation has infinitely many solutions)
18. Octahedron - sum On each wall of a regular octahedron is written one of the numbers 1, 2, 3, 4, 5, 6, 7 and 8, wherein on different sides are different numbers. For each wall John make the sum of the numbers written of three adjacent walls. Thus got eight sums, which also.
19. Cubes Cube, which consists of 27 small cubes with edge 4 dm has volume:
20. Two doctors Doctor A will determine the correct diagnosis with a probability 93% and doctor B with a probability 79%. Calculate probability of correct diagnosis if patient is diagnosed by both doctors.

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