# Examples for secondary school students - page 37

- Holidays

Of the 35 students of class were 7 on holiday in Germany and just as much in Italy. 5 students visited Austria. In none of these countries was 21 students, all three visited by one student . In Italy and Austria were 2 students and in Austria and Germany. - travel agency

Small travel agency offers 5 different tours at honeymoon. What is the probability that the bride and groom choose the same tour (they choose independently)? - 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? - 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? - Ring

The ring made from gold and copper alloy has a weight of 14.5 g and a volume of 1.03 cm^{3}. How much gold and how much copper it contains? The metal densities are Au 19.3 g/cm³ and Cu 8.94 kg·dm-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. - Count of triangles

Given a square ABCD and on each side 8 internal points. Determine the number of triangles with vertices at these points. - 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. - 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? - 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 - 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. - Sides of the triangle

Calculate triangle sides where its area is S = 84 cm^{2}and a = x, b = x + 1, xc = x + 2 - 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? - Cube from sphere

What largest surface area (in cm^{2}) can have a cube that was cut out of a sphere with radius 43 cm? - 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. - 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. - 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? - Quadrant

In what quadrant is a -1165° angle? - Product

The product of two consecutive odd numbers is 8463. What are this numbers? - 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?

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