# Grade - examples - page 140

1. Cards
Suppose that are three cards in the hats. One is red on both sides, one of which is black on both sides, and a third one side red and the second black. We are pulled out of a hat randomly one card and we see that one side of it is red. What is the probabi
2. Cube in sphere
The sphere is inscribed cube with edge 8 cm. Find the radius of the sphere.
3. Lawns
Before a sports hall are two equally large rectangular lawns, each measuring 40 m and 12 m. Maintenance of 10m² lawn cost 45 CZK yearly. On each lawn is circular flowerbed with a diameter 8 meters. How much money is needed each year to take on lawn care?.
4. Infirmary
Two thirds of children from the infirmary went on a trip seventh went to bathe and 40 children remained in the gym. How many children were treated in the infirmary?
5. Three-digit
How many three-digit natural numbers do not have the number 7?
6. Earth and Sun
Earth is 150 million km away from the Sun, 300,000 km of sunlight travels in 1 second. How long will the light come from the Sun to the Earth?
7. Florist's
The florist got 72 white and 90 red roses. How many bouquets can bind from all these roses when each bouquets should have the same number of white and red roses?
8. Tailor
From the rest of the cloth tailor could cut off either 3 m in men's suits without vest or 3.6 m with vest. What shortest possible length could the rest of the cloth have? How many suits a) without a vest b) with vest could make the tailor from the re
9. Hypotenuse
Calculate the length of the hypotenuse of a right triangle with a catheti 71 cm and 49 cm long.
10. Bags
The first bag has a weight of 18 kg, the second bag is a one-third lighter than the first and the third bag has three times less the weight of all three bags together. Determine their weights.
11. Two-digit number
I am a two-digit number less than 20. When I divided by three, then you get the rest 1 and when you divide me by four you get also rest 1. What number am I?
12. Cuboid enlargement
By how many percent increases the volume of cuboid if its every dimension increases by 30%?
13. Cars 6
At 9:00 am two cars started from the same town and traveled at a rate of 35 miles per hour and the other car traveled at a rate of 40 miles per hour. After how many hours will the cars be 30 miles apart?
14. Working together
One painter paint the nursery in 10 days, the second in 8 days. How many days will the nursery be painted if they work together?
15. Cuboid surface
Determine surface area of cuboid if its volume is 52.8 cm cubic and length of the two edges are 2 cm and 6 cm.
16. Televisions
Television is the fifth most expensive and tenth cheapest TV. How many different TVs are in stores?
17. Circle - simple
The circumference of a circle is 930 mm. How long in mm is its diameter?
18. Water reservoir
The reservoir shape of a cylinder having a diameter 8 m and a height 2.8 m. The device indicates that the reservoir contains 800 hectoliters of water. Calculate how much % of volume is used.
19. De Moivre's formula
There are two distinct complex numbers z such that z3 is equal to 1 and z is not equal 1. Calculate the sum of these two numbers.
20. Calculation
How much is sum of square root of six and the square root of 225?

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