# Examples for secondary school students - page 51

- Sequence

Find the common ratio of the sequence -3, -1.5, -0.75, -0.375, -0.1875. Ratio write as decimal number rounded to tenth. - Cinema 4

In cinema are 1656 seats and in the last row are 105 seats , in each next row 3 seats less. How many are the total rows in cinema? - Gas consumption

The vessel consume 100 tons of gas in 250 miles. How many fuel will the vessel consume if it travels 400 miles? - Variations 4/2

Determine the number of items when the count of variations of fourth class without repeating is 600 times larger than the count of variations of second class without repetition. - Disco

On the disco goes 12 boys and 15 girls. In how many ways can we select four dancing couples? - Hexagonal prism 2

The regular hexagonal prism has a surface of 140 cm^{2}and height of 5 cm. Calculate its volume. - Saving per cents

The first day I save 1 cent and every next day cent more. How many I saved per year (365 days)? - Two planes

Two planes flying from airports A and B, 420 km distant against each other. Plane from A took off 15 minutes later and flies at an average speed of 40 km/h higher than the plane from B. Determine the average speed of this two aircraft if you know that it - Centre of mass

The vertices of triangle ABC are from the line p distances 3 cm, 4 cm and 8 cm. Calculate distance from the center of gravity of the triangle to line p. - Diameters of circles

How many percent of the area of a larger circle is a smaller circle if the smaller circle has a diameter 120 mm and a larger one has a diameter 300 mm? - Geometric sequence 4

It is given geometric sequence a_{3}= 7 and a_{12}= 3. Calculate s_{23}(= sum of the first 23 members of the sequence). - Contestants

In the competition it was possible to get 0-5 points. In fact, 5 contestants of the 15 best contestants has earned 5 points or 4 points (which have won 10 contestants). The number of contestants who earned 3 points was the same as the number of contestan - 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) - 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}. - 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 - 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? - 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?

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