# Examples for 8th grade - page 106

1. KLMN trapezoid
The KLMN trapezoid has bases KL 40cm and MN 16cm. On the KL base is point P. The segment NP divides the trapezoid into units with the same area. What is the distance of point P from point K?
2. Prime number
Jan wrote any number from 1 to 20. What is the probability that he wrote the prime number?
3. Meat loses
Meat loses 18% of its weight by smoking. How much raw meat butcher used to manufacture 35 kilos of smoked?
4. Desks
A class has 20 students. The classroom consists of 20 desks, with 4 desks in each of 5 different rows. Amy, Bob, Chloe, and David are all friends, and would like to sit in the same row. How many possible seating arrangements are there such that Amy, Bob, C
5. Rectangle diagonal
The rectangle, one side of which is 5 cm long, is divided by a 13 cm diagonal into two triangles. Calculate the area of one of these triangles in cm2.
6. New ratio
The ratio of ducks and chicken in our yard is 2 : 3. The total number of ducks and chickens together is 30. Mother gave 3 of the chickens to our neighbor. What is the new ratio now?
7. Dining questionnaire
In the class of 32 pupils, the class teacher delivered a satisfaction questionnaire to the school canteen. Eleven people have questioned whether they are satisfied with the dining room. The completed questionnaire also included the vote of the class teache
8. 3d printer
3D printing ABS filament with diameter 1.75 mm has density 1.04 g/cm3. Find the length of m = 5 kg spool filament. (how to calculate length)
9. Sugars
In what ratio must two sorts of sugar, costing #390 and #315 per kg respectively, be mixed in order to produce a mixture worth #369 per kg?
10. Cylinder height
Calculate the height of the cylinder and its surface is 2500 dm2 and the bases have a diameter 5dm.
11. RT - inscribed circle
In a rectangular triangle has sides lengths> a = 30cm, b = 12.5cm. The right angle is at the vertex C. Calculate the radius of the inscribed circle.
12. Wiring 2
Willie cut a piece of wire that was 3/8 of the total length of the wire. He cut another piece that was 9m long. The two pieces together were one half of the total length of the wire. How long was the wire before he cut it?
13. Motorcyclist
From Trutnov, the motorcyclist started at an average speed of 60km/hour. At 12.30hrs the passenger car was started at a speed of 80km/hour. How many hours and at what distance from Trutnov will car catch a motorcycle?
14. Progression
12, 60, -300,1500 need next 2 numbers of pattern
15. The swimmer
The swimmer swims at a constant speed of 0.85 m/s relative to water flow. The current speed in the river is 0.40 m/s, the river width is 90 m. a) What is the resulting speed of the swimmer with respect to the tree on the riverbank when the swimmer motion
16. Soup from canteen
For how many people is 90 liters of soup enough if we assume 3/8 liter of soup per person in the canteen?
17. Equation - inverse
Solve for x: 7: x = 14: 1000
18. Two trains
From station A, the freight train traveled at a speed of 40 km/h in 9h. When he drove 15km, the fast train started from station A in the same direction at a speed of 70km/h. When will it the freight train catch up?
19. Square
Calculate the area of the square shape of the isosceles triangle with the arms 50m and the base 60m. How many tiles are used to pave the square if the area of one tile is 25 dm2?
20. Discount price
Coat cost 150 euros after sales discount. What is the original price when the discount is 25% of the original price?

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