# Examples for secondary school students - page 35

1. A three-digit numbers
Determine the total number of positive three-digit numbers that contain a digit 6.
2. Colors
Willie got birthday 6 colour pens in different colors. How many ways he can give them side by side in pencil?
3. Water reservoir
The water reservoir is filled through one inlet 4 hours later than both together, then another inlet 9 hours later than both together. For how long is filled by each separately?
4. Rings groups
27 pupils attend some group; dance group attends 14 pupils, 21 pupils sporty group and dramatic group 16 pupils. Dance and sporting attend 9 pupils, dance and drama 6 pupil, sporty and dramatic 11 pupils. How many pupils attend all three groups?
5. Probabilities
If probabilities of A, B and A ∩ B are P (A) = 0.62 P (B) = 0.78 and P (A ∩ B) = 0.26 calculate the following probability (of union. intersect and opposite and its combinations):
6. Water
In the garden with an area of 8 ares rain 40hl of water. To what heights leveled water?
7. Direct route
From two different places A and B connected by a direct route, Adam (from city A) and Bohus (from city B) started at a constant speed. As Adam continued to go from A to B, Bohus turned around at the time of their meeting and at the same speed he returned t
8. Theorem prove
We want to prove the sentense: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
9. Harvesters
The first harvester reaps the grain from land for 24 hours, the second harvester for 16 hours. For how many hours will take harvest by two harvesters, but the second harvester started working four hours later than the first?
10. Shot
Shot with a mass 43 g flying at 256 m/s penetrates into the wood to a depth 25 cm. What is the average force of resistance of wood?
11. Center of gravity
In the isosceles triangle ABC is the ratio of the lengths of AB and the height to AB 10:12. The arm has a length of 26 cm. If the center of gravity T of triangle ABC find area of triangle ABT.
12. Znojmo
From Znojmo to Brno started truck with a trailer at an average speed 53 km per hour. Against him 14 minutes later from Brno started car with an average speed of 1.2-times greater than the truck. How long and how far from Znojmo, they meet if the distanc
13. Weekly service
In the class are 20 pupils. How many opportunities have the teacher if he wants choose two pupils randomly who will weeklies?
14. Glass
How many glass are needed to produce glass with base regular 5-gon if one base triangle in the base is 4.2 square cm and the height is 10 cm?
15. Coffee
Coffee merchant has coffee robusta and arabica species. 1 kg Robusta worth 450 CZK, Arabica 1 kg is 300 CZK more expensive. Calculate how many kilograms of Robusta and Arabica will need to produce 30 kg of the mixture so that the mixture cost is 490 CZK p
16. Equation
Eequation f(x) = 0 has roots x1 = 64, x2 = 100, x3 = 25, x4 = 49. How many roots have equation f(x2) = 0 ?
17. Dices throws
What is the probability that the two throws of the dice: a) Six falls even once b) Six will fall at least once
18. Rhomboid
The dimensions of the rhomboid sides are a= 5cm, b = 6 cm and the size of the angle at the vertex A is 60°. What is the length of side AC?
19. G forces
Calculate deceleration of car (as multiple of gravitational acceleration g = 9.81 m/s2) which occurs when a car in a frontal collision slows down uniformly from a speed 111 km/h to 0 km/h in 1.2 meters trajectory.
20. Cuboid walls
Calculate the volume of the cuboid if its different walls have area of 195cm², 135cm² and 117cm².

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