# Grade - examples - page 180

1. Two workers The first worker would himself completed the work in 8 hours, the other in 6 hours. After two hours of joint work left the first worker to a doctor and other completed work himself. How many hours worked the other worker himself?
2. Ratio 11 Simplify this ratio 10 : 1/4
3. Bean bag A student tossed a bean bag. It landed 216 inches away. How many yards are equal to 216 inches?
4. Steps Walkway from the house to the school is 180 m long. How many more steps Michael makes than his father on the way to school, if the length of Michael's step is 60 cm and the length of his father's step is 90 cm.
5. The determinant The determinant of the unit matrix equals 7. Check how many rows the A matrix contains.
6. Five inlets The tank can be filled with five equally powerful inlets. If the tank is filled by four of these inlets, it takes a total of 30 minutes to fill one-third of the tank. How many minutes does it take to fill an empty tank if it is filled with all five inlets?
7. Annual rainfall The average annual rainfall is 686 mm. How many liters will fall on the 1-hectare field?
8. Cylindrical container An open-topped cylindrical container has a volume of V = 3140 cm3. Find the cylinder dimensions (radius of base r, height v) so that the least material is needed to form the container.
9. Area of garden If the width of the rectangular garden is decreased by 2 meters and its length is increased by 5 meters, the area of the rectangle will be 0.2 ares larger. If the width and the length of the garden will increase by 3 meters, its original size will increas
10. Viju viju has 40 chickens and rabbits. If in all there are 90 legs. How many rabbits are there with viju??
11. Inscribed circle Calculate the magnitude of the BAC angle in the triangle ABC if you know that it is 3 times less than the angle BOC, where O is the center of the circle inscribed in the triangle ABC.
12. Work The first worker would need less than 4 hours to complete the task than the other worker. In fact, both workers worked for two hours together, then the first worker did the remaining work himself. In what proportion should the remuneration of the workers b
13. School There are 150 pupils in grade 5 . 2/3 of it are female. By what fractions are the males?
14. The sides 2 The sides of a trapezoid are in the ratio 2:5:8:5. The trapezoid’s area is 245. Find the height and the perimeter of the trapezoid.
15. Cube surface and volume Find the surface of the cube with a volume of 27 dm3.
16. The tank The tank had 9 inflows to be filled in 21 days. After 9 days, 3 trips out. How many days did the remaining 6 tributaries fill the tank?
17. Brackets 2 Add parenthesis to make true: 5-2×6-4+2=5
18. Diamond diagonals Find the diamond diagonal's lengths if the area is 156 cm2 and side is 13 cm long.
19. How much How much money will we pay for 20 planks 4m long, 15cm wide and 26mm thick when 1m³ of wood costs 4500kč?
20. Nonagon Calculate the area and perimeter of a regular nonagon if its radius of inscribed circle is r = 10cm

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