# Grade - examples - page 85

1. Silver medal
To circular silver medal with a diameter of 10 cm is inscribed gold cross, which consists of five equal squares. What is the content area of silver part?
2. Is right triangle
One angle of the triangle is 36° and the remaining two are in the ratio 3:5. Determine whether triangle is a rectangular triangle.
3. travel agency
Small travel agency offers 5 different tours at honeymoon. What is the probability that the bride and groom choose the same tour (they choose independently)?
4. Children
Margaret and Zdena weighs the same and Petra 3 kg more. Together weigh 156 kg. How much does they weigh?
5. Comsumption
On route 150 km long car consumed 13 liters of gasoline. How much gasoline consumed for driving 300 km?
6. Green - Red
We have 5 bags. Each consist one green and 2 red balls. From each we pull just one ball. What is the probability that we doesn't pull any green ball?
7. Solution
What amount of 80% solution and what amount of water is needed to mix in order to obtain two liters of 60% solution of this mixture?
8. Ring
The ring made from gold and copper alloy has a weight of 14.5 g and a volume of 1.03 cm3. How much gold and how much copper it contains? The metal densities are Au 19.3 g/cm³ and Cu 8.94 kg·dm-3
9. Alfa, beta, gama
In the triangle ABC is the size of the internal angle BETA 8 degrees larger than the size of the internal angle ALFA and size of the internal angle GAMA is twice the size of the angle BETA. Determine the size of the interior angles of the triangle ABC.
10. Cube 3
How many times will increase the volume of a cube if we double the length of its edge?
11. Wheel diameter
A 1m diameter wheel rolled along a 100m long track. How many times did it turn?
12. Prism
Calculate the surface area and volume of a prism with a body height h = 10 cm and its base has shape of a rhomboid with sides a = 5.8 cm, b = 3 cm and the distance of its two longer sides is w = 2.4 cm.
13. 12 Moons
Good Marry came to ask twelve moons for help with collecting strawberries. All twelve moons 1200 strawberries picked in 20 minutes. But lazy months July and August cease tear after 5 minutes. How many minutes in total will take collect strawberries?
14. Seamstress
Seamstress bought two kinds of textile together 25 meters. One at 50 SKK and the second 70 SKK per meter. How many meter bought from this two textiles when paid totally 1540 SKK?
15. Line segment
For the line segment whose endpoints are L[-1, 13] and M[18, 2], find the x and y value for the point located 4 over 7 the distance from L to M.
16. Smallest internal angle
Calculate what size has the smallest internal angle of the triangle if values of angles α:β:γ = 3:4:8
17. The balls
You have 108 red and 180 green balls. You have to be grouped into the bags so that the ratio of red to green in each bag was the same. What smallest number of balls may be in one bag?
18. Janitor
Janitor tosses 26 cm layer of snow on the school grounds for 90 minutes. How many friends would have to call for help if snow needs to have bowled for 15 minutes. We assume that at the same time bow all the same amount of snow.
19. Feed for horses
In the kennel have feed for two horses for 21 days. The station brought an additional 5 horses. How many days will last the feed for all the horses if they have the same daily ration?
20. Count of triangles
Given a square ABCD and on each side 8 internal points. Determine the number of triangles with vertices at these points.

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