# Examples for secondary school students - page 19

1. Lottery The lottery is 60000 elk in which 6200 wins. What is the probability that the purchase of 12 elks won nothing? Grass grows in the meadow equally fast and evenly. It is known that 99 cows graze meadow for 14 days and 95 cows by 22 days. How many cows graze meadow for 77 days?
3. Average What is the average speed of the car, where half of the distance covered passed at speed 66 km/h and the other half at 86 km/h.
4. Monty Hall Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. W
5. Property The length of the rectangle-shaped property is 8 meters less than three times of the width. If we increase the width 5% of a length and lendth reduce by 14% of the width it will increase the property perimeter by 13 meters. How much will the property cost
6. Triangular pyramid It is given perpendicular regular triangular pyramid: base side a = 5 cm, height v = 8 cm, volume V = 28.8 cm3. What is it content (surface area)?
7. Geometric sequence 3 In geometric sequence is a8 = 312500; a11= 39062500; sn=1953124. Calculate the first item a1, quotient q and n - number of members by their sum s_n.
8. Volume from surface area What is the volume of the cube whose surface area is 96 cm2?
9. Numbers How many different 3 digit natural numbers in which no digit is repeated, can be composed from digits 0,1,2?
10. Hexagonal pyramid Base of the pyramid is a regular hexagon, which can be circumscribed in a circle with a radius of 1 meter. Calculate the volume of a pyramid 2.5 meters high.
11. Cubes Surfaces of cubes, one of which has an edge of 48 cm shorter than the other, differ by 36288 dm2. Determine the length of the edges of this cubes.
12. Area codes How many 6 digit area codes are possible if the first number can't be zero?
13. Carpet The room is 10 x 5 meters. You have the role of carpet width of 1 meter. Make rectangular cut of roll that piece of carpet will be longest possible and it fit into the room. How long is a piece of carpet? Note .: carpet will not be parallel with the diag
14. Center In the triangle ABC is point D[1,-2,6], which is the center of the |BC| and point G[8,1,-3], which is the center of gravity of the triangle. Find the coordinates of the vertex A[x,y,z].
15. Angles in a triangle The angles of the triangle ABC make an arithmetic sequence with the largest angle γ=83°. What sizes have other angles in a triangle?
16. School trip The class has 19 students. What different ways students can be accommodated in the hostel, where available 3× 2-bed, 3× 3-bed and 1× 4-bed rooms. (Each room has its unique number)
17. Park In the newly built park will be permanently placed a rotating sprayer irrigation of lawns. Determine the largest radius of the circle which can irrigate by sprayer P so not to spray park visitors on line AB. Distance AB = 55 m, AP = 36 m and BP = 28 m.
18. Cotangent If the angle α is acute, and cotg α = 1/3. Determine the value of sin α, cos α, tg α.
19. Center Calculate the coordinates of the circle center: ?
20. Statue On the pedestal high 4 m is statue 2.7 m high. At what distance from the statue must observer stand to see it in maximum viewing angle? Distance from the eye of the observer from the ground is 1.7 m.

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