# Examples for secondary school students - page 37

1. 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?
2. 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?
3. 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.
4. RTriangle 17
The hypotenuse of a right triangle is 17 cm. If you decrease both two legs by 3 cm you will reduce the hypotenuse by 4 cm. Determine the length of this legs.
5. Count of triangles
Given a square ABCD and on each side 8 internal points. Determine the number of triangles with vertices at these points.
6. Crowns
1180 crowns is divided into three people that A got 20% less than B and C by 15% more than B. How many got A,B and C?
7. Chocholate pyramid
How many chocolates are in the third shelf when at the 8th shelf are 41 chocolates in any other shelf is 7 chocolates more the previous shelf.
8. Sides of the triangle
Calculate triangle sides where its area is S = 84 cm2 and a = x, b = x + 1, xc = x + 2
9. Jane and Miro
Jane brother Miro is 42 years. And he is three times old as it was Jane when Miro was for so many years as there are now Jane. How old is Jane?
10. Hot air balloon
Hot air balloon ascends 25 meters up for a minute after launch. Every minute ascends 75 percent of the height which climbed in the previous minute. a) how many meters ascends six minutes after takeoff? b) what is the overall height 10 minutes after launch
11. Cube from sphere
What largest surface area (in cm2) can have a cube that was cut out of a sphere with radius 43 cm?
12. Rotating cone
Calculate the volume and the surface area of a rotating cone of base radius r = 2.3 dm and a height h = 46 mm.
In what quadrant is a -1165° angle?
14. Product
The product of two consecutive odd numbers is 8463. What are this numbers?
15. Big factorial
How many zeros end number 116! ?
16. Mean
if the mean of the set of data 5, 17, 19, 14, 15, 17, 7, 11, 16, 19, 5, 5, 10, 8, 13, 14, 4, 2, 17, 11, x is -91.74, what is the value of x?
17. Pine
How much of a mixed forest rangers want to cut down, if their head said: "We only cut down pine trees, which in our mixed forest 98%. After cut pine trees constitute 94% of all trees left."
18. Three vectors
The three forces whose amplitudes are in ratio 9:10:17 act in the plane at one point so that they are in balance. Determine the angles of the each two forces.
19. Two pipes
One pipe fill one-fifth volume 20 minutes before by second one. The two pipes together will fill the tank in two hours. How long is will fill tank each pipe separately?
20. Tower model
Tower height is 300 meters, weight 8000 tons. How high is the model of the tower weight 1 kg? (State the result in the centimeters). The model is made from exactly the same material as the original no numbers need to be rounded. The result is a three-digi

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