1. Klara Klara and Jitka went on a hiking trip at 13 o'clock at speed 5km/h. At 14 o'clock, Tomas ride on the bike at an average speed of 28 km/h. How many hours and at what distance from the beginning of the road Tomáš caught the two girls? The angle of a straight road is approximately 12 degrees. Determine the percentage of this road.
3. Inscribed sphere How many percents of the cube volume takes the sphere inscribed into it?
4. Enlarged rectangle The rectangle with dimensions of 8 cm and 12 cm is enlarged in a ratio of 5:4. What are the circumference and the area of the enlarged rectangle?
5. Cancel fractions Compress the expression of factorial: (n+6)!/(n+4)!-n!/(n-2)!
6. Apples Zuzana bought 3 kg Jonathan apples. Then she noticed that Golden apples were 3 CZK a kilogram cheaper. So they bought 2 kg. For apples, she paid a total of CZK 109. How much did 1 kg Jonathan and how much Golden?
7. Speed of car The car went to a city that was 240 km away. If his speed increased by 8 km/h, it would reach the finish one hour earlier. Determine its original speed.
8. Candy and boxes We have some number of candy and empty boxes. When we put candies in boxes of ten, there will be 2 candies and 8 empty boxes left, when of eight, there will be 6 candies and 3 boxes left. How many candy and empty boxes left when we put candies in boxes of
9. Rhombus The rhombus has diagonal lengths of 4.2cm and 3.4cm. Calculate the length of the sides of the rhombus and its height
10. The truck The empty truck left the warehouse for goods at 10:00 and arrived at 11:30. At 2:00 pm, they loaded back on the same route. But it was a quarter slower than going to the warehouse. We know that on the way to the warehouse, the car was traveling at a speed
11. Merchant The merchant lower cost by 10% in December when it was not sold. Again in January lower cost by 20% and now costs 576 €. A. How much the goods stood originally? B, how much cost the goods after the first lowering? C, How many percents totally merchant l
12. Paul earned Paul earned 300 Kč in one hour, Václav 1/3 more than Paul. Václav worked 60 hours, which is 1/3 fewer hours than Paul worked. How many percents less earned Paul an hour than Václav? How many hours did Paul more than Václav? How much did Paul earn more
13. Young mathematician One young mathematician was bored again. He found that the average age of people in the room where the seminar is equal to its count. Then his 29-year-old brother entered this room. Even then, the average age of all present was the same as the count of pe
14. Ratio of sides The triangle has a circumference of 21 cm and the length of its sides is in a ratio of 6: 5: 3. Find the length of the longest side of the triangle in cm.
15. Our house Our house would paint four painters in 14 days. How long could it paint five painters? How long will it take if two other painters will come to help after 5 days? What overload in g (g-force) has passed the pilot if he accelerated from 0 to 600 km/h in 3 seconds?
17. A triangle A triangle has an angle that is 63.1 other 2 are in ratio of 2:5 What are the measurements of the two angles? Find radius of circle using pythagorean theorem where a=9, b=r, c= 6+r In the 45 rooms, there were 169 guests, some rooms were three-bedrooms and some five-bedrooms. How many rooms were? If 5/18=425 what is the value 13/18?