# Examples for secondary school students - page 52

- Population

What is the population of the city with 3% annual growth, if in 10 years the city will have 60,000 residents? - Geometric sequence 5

About members of geometric sequence we know: ? ? Calculate a_{1}(first member) and q (common ratio or q-coefficient) - Cards

From a set of 32 cards we randomly pull out three cards. What is the probability that it will be seven king and ace? - Virus

We have a virus that lives one hour. Every half hour produce two child viruses. What will be the living population of the virus after 3.5 hours? - Cuboid edges in ratio

Cuboid edges lengths are in ratio 2:4:6. Calculate their lengths if you know that the cuboid volume is 24576 cm^{3}. - Balls

We have n identical balls (numbered 1-n) is selected without replacement. Determine 1) The probability that at least one tensile strength number coincides with the number of balls? 2) Determine the mean and variance of the number of balls, which coincides. - Tree

Between points A and B is 50m. From A we see a tree at an angle 18°. From point B we see the tree in three times bigger angle. How tall is a tree? - Glass

Trader ordered from the manufacturer 200 cut glass. The manufacturer confirmed the order that the glass in boxes sent a kit containing either four or six glasses. Total sent 41 boxes. a) How many boxes will contain only 4 glasses? b) How many boxes will co - Roof 8

How many liters of air are under the roof of tower which has the shape of a regular six-sided pyramid with a 3,6-meter-long bottom edge and a 2,5-meter height? Calculate the supporting columns occupy about 7% of the volume under the roof. - Three numbers

What is three numbers which have the property: the sum of the reciprocals of the first and second numbers is 12/7, the first and third 11/24 and the second and the third 3/8. - VCP equation

Solve the following equation with variations, combinations and permutations: 4 V(2,x)-3 C(2,x+ 1) - x P(2) = 0 - Cards

Suppose that are three cards in the hats. One is red on both sides, one of which is black on both sides, and a third one side red and the second black. We are pulled out of a hat randomly one card and we see that one side of it is red. What is the probabi - Bags

The first bag has a weight of 18 kg, the second bag is a one-third lighter than the first and the third bag has three times less the weight of all three bags together. Determine their weights. - Water reservoir

The reservoir shape of a cylinder having a diameter 8 m and a height 2.8 m. The device indicates that the reservoir contains 800 hectoliters of water. Calculate how much % of volume is used. - AP 6

Calculate the first five items of an arithmetic sequence if it is given: a_{2}– a_{3}+ a_{5}= 20 a_{1}+ a_{6}= 38 - De Moivre's formula

There are two distinct complex numbers z such that z^{3}is equal to 1 and z is not equal 1. Calculate the sum of these two numbers. - Angles in ratio

The size of the angles of the triangle are in ratio x: y = 7: 5 and the angle z is 42° lower than the angle y. Find size of the angles x, y, z. - Balls

The urn is 8 white and 6 black balls. We pull 4 randomly balls. What is the probability that among them will be two white? - Calculation

How much is sum of square root of six and the square root of 225? - Stadium

A domed stadium is in the shape of spherical segment with a base radius of 150 m. The dome must contain a volume of 3500000 m³. Determine the height of the dome at its centre to the nearest tenth of a meter.

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