# Examples for secondary school students - page 51

1. Potatoes Daniela and Michael would jointly dug potatoes for 7.5 hours. But if Daniela was working alone she would take 2.5 hours more as if he were working with Michael. Determine how much for the work done by Michael himself and how much Daniela herself.
2. 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?
3. 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.
4. 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?
5. Hexagonal prism 2 The regular hexagonal prism has a surface of 140 cm2 and height of 5 cm. Calculate its volume.
6. 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
7. Disco On the disco goes 12 boys and 15 girls. In how many ways can we select four dancing couples?
8. Gas consumption The vessel consume 100 tons of gas in 250 miles. How many fuel will the vessel consume if it travels 400 miles?
9. Saving per cents The first day I save 1 cent and every next day cent more. How many I saved per year (365 days)?
10. 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.
11. 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.
12. 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?
13. Geometric sequence 4 It is given geometric sequence a3 = 7 and a12 = 3. Calculate s23 (= sum of the first 23 members of the sequence).
14. Population What is the population of the city with 3% annual growth, if in 10 years the city will have 60,000 residents?
15. Geometric sequence 5 About members of geometric sequence we know: ? ? Calculate a1 (first member) and q (common ratio or q-coefficient)
16. 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?
17. 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 cm3.
18. Resistance Determine the resistance of the bulb with current 200 mA and is in regular lamp (230V).
19. 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.
20. 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?

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