# Examples for secondary school students - page 65

1. 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.
2. Boys and girls There are 11 boys and 18 girls in the classroom. Three pupils will answer. What is the probability that two boys will be among them?
3. Diagonals of a rhombus 2 One diagonal of a rhombus is greater than other by 4 cm . If the area of the rhombus is 96 cm2, find the side of the rhombus.
4. 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
5. First man What is the likelihood of a random event where are five men and seven women first will leave the man?
6. 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?
7. Peroxide How many ml 30% of peroxide (H2O2) should be poured into 100ml H2O to give a 20% solution?
8. Children playground The playground has the shape of a trapezoid, the parallel sides have a length of 36 m and 21 m, the remaining two sides are 14 m long and 16 m long. Determine the size of the inner trapezoid angles.
9. Diagonals What x-gon has 54 diagonals?
10. Tetrahedron What is the angle of the sides from the base of a three-sided pyramid where the sides are identical?
11. Rate or interest At what rate percent will Rs.2000 amount to Rs.2315.25 in 3 years at compound interest?
12. Utopia Island A probability of disease A on the island of Utopia is 40%. A probability of occurrence among the men of this island, which make up 60% of all the population (the rest are women), is 50%. What is the probability of occurrence of A disease among women on Uto
13. Average age The company of five people has an average age of 46 years. The average age of the first four is 43 years. How many years has the fifth member of this company?
14. Hyperbola Find the equation of hyperbola that passes through the point M [30; 24] and has focal points at F1 [0; 4 sqrt 6], F2 [0; -4 sqrt 6].
15. Cube edges If the edge length of the cube increases by 50%, how does the volume of this cube increase?
16. Electric input power Solve problems related to electric power: a) U = 120 V, I = 0.5 A, P =? b) P = 200 W, U = 230 V, I =? c) I = 5 A, P = 2200W, U =?
17. Exponential equation Determine the value of having y in the expression (3^y): (4^-1)=36.Y is a natural number greater than zero.
18. Two diggers Two diggers should dig a ditch. If each of them worked just one-third of the time that the other digger needs, they'd dig up a 13/18 ditch together. Find the ratio of the performance of this two diggers.
19. PIN code PIN on Michael credit card is a four-digit number. Michael told this to his friend: • It is a prime number - that is, a number greater than 1, which is only divisible by number one and by itself. • The first digit is larger than the second. • The second.
20. Six terms Find the first six terms of the sequence a1 = -3, an = 2 * an-1

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