# Examples for secondary school students - page 64

1. Classroom Of the 26 pupils in the classroom, 12 boys and 14 girls, four representatives are picked to the odds of being: a) all the girls b) three girls and one boy c) there will be at least two boys
2. The coil How many ropes (the diameter 8 mm) fit on the coil (threads are wrapped close together) The coil has dimension: the inner diameter 400mm, the outside diameter 800mm and the length of the coil is 470mm
3. Left handed It is known that 25% of the population is left-handed. What is the probability that there is a maximum of three left-handers at a seminar where there are 30 participants?
4. The determinant The determinant of the unit matrix equals 7. Check how many rows the A matrix contains.
5. Area of garden If the width of the rectangular garden is decreased by 2 meters and its length is increased by 5 meters, the area of the rectangle will be 0.2 ares larger. If the width and the length of the garden will increase by 3 meters, its original size will increas
6. The pond We can see the pond at an angle 65°37'. Its end points are 155 m and 177 m away from the observer. What is the width of the pond?
7. Inscribed circle Calculate the magnitude of the BAC angle in the triangle ABC if you know that it is 3 times less than the angle BOC, where O is the center of the circle inscribed in the triangle ABC.
8. Cylindrical container An open-topped cylindrical container has a volume of V = 3140 cm3. Find the cylinder dimensions (radius of base r, height v) so that the least material is needed to form the container.
9. Diamond diagonals Find the diamond diagonal's lengths if the area is 156 cm2 and side is 13 cm long.
10. Nonagon Calculate the area and perimeter of a regular nonagon if its radius of inscribed circle is r = 10cm
11. Cuboid walls If the areas of three adjacent faces of a cuboid are 8 cm², 18 cm² and 25 cm². Find the volume of the cuboid.
12. Rectangles The perimeter of a rectangle is 90 m. Divide it into three rectangles, the shorter side has all three rectangles the same, their longer sides are three consecutive natural numbers. What is the dimensions of each rectangle?
13. Linsys2 Solve two equations with two unknowns: 400x+120y=147.2 350x+200y=144
14. Pyramid cut We cut the regular square pyramid with a parallel plane to the two parts (see figure). The volume of the smaller pyramid is 20% of the volume of the original one. The bottom of the base of the smaller pyramid has a content of 10 cm2. Find the area of the o
15. Repay, interest, loan Ramchacha takes a loan amount of 240000 from a bank for constructing a house at the rate of simple interest of 12% per annum. After 1 yr. of taking the loan he rents the house at the rate of 5200 per month. Determine the number of years he would take to re
16. Inverse matrix Find how many times is the larger determinant is the matrix A, which equals 9 as the determinant of its inverse matrix.
17. Three points 2 The three points A(3, 8), B(6, 2) and C(10, 2). The point D is such that the line DA is perpendicular to AB and DC is parallel to AB. Calculate the coordinates of D.
18. Three students Three students independently try to solve the problem. The first student will solve a similar problem with a probability of 0.6, the second student will solve at a probability of 0.55, and the third will solve at a probability 0.04. The problem is resolved
19. Two pipes How long will the pool be filled with a double supply pipe if it takes the pool to fill the first pipe by 4 hours longer and the second pipe 9 hours longer than both pipes open at the same time?
20. Peroxide How many ml 30% of peroxide (H2O2) should be poured into 100ml H2O to give a 20% solution?

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