# Examples for secondary school students - page 67

1. Combinations 6 6 purses 9 flaps 12 straps Every combination must include 1 purse, 1 flap and 1 strap. How many possible combinations?
2. A book A book contains 524 pages. If it is known that a person will select any one page between the pages numbered 125 and 384, find the probability of choosing the page numbered 252 or 253.
3. Two cities The car goes from city A to city B at an average speed of 70 km/h, back at an average speed of 50 km/h. If it goes to B and back at an average speed of 60 km/h, the whole ride would take 8 minutes less. What is the distance between cities A and B?
4. AP RT triangle The length of the sides of a right triangle form an arithmetic progression, longer leg is 24 cm long. What are the perimeter and area?
5. Lunch Seven classmates go every day for lunch. If they always come to the front in a different order, will be enough school year to take of all the possibilities?
6. Two cyclists 2 At the same time, two cyclists left the towns A and B at constant speeds. The first one going from town A to town B, and the second one from town B to town A. At one point of the trip they met. After they met, the first cyclist arrived at town B in 36min,.
7. Tropical, mild and arctic How many percents of the Earth's surface lies in the tropical, mild and arctic range? The border between the ranges is the parallel 23°27 'and 66°33'.
8. US GDP Consider the following dataset , which contsins the domestic US gross in millions of the top grossing movie over the last 5 years. 300,452,513,550,780 I. Find the Mean of the Dataset II. Find the Squared deviation of the second observation from the mean I
9. On line On line p: x = 4 + t, y = 3 + 2t, t is R, find point C, which has the same distance from points A [1,2] and B [-1,0].
10. Find the 3 Find the distance and mid-point between A(1,2) and B(5,5).
11. Two resistors Two resistors when they give 25 ohms in series and 4 ohms in parallel what the values of
12. Circle described The radius of the circle described to the right triangle with 6 cm long leg is 5 cm. Calculate the circumference of this triangle.
13. Exponential warm Suppose that a body with temperature T1 is placed in surroundings with temperature T0 different from that of T1. The body will either cool or warm to temperature T(t) after time t, in minutes, where T(t)=T0 + (T1-T0)e^(-kt) . If jello salad with 30 degre
14. Triangular pyramid What is the volume of a regular triangular pyramid with a side 3 cm long?
15. Sum of inner angles Prove that the sum of all inner angles of any convex n-angle equals (n-2) . 180 degrees.
16. Three workplaces How many ways can we divide nine workers into three workplaces if they need four workers in the first workplace, 3 in the second workplace and 2 in the third?
17. Rectangular garden The sides of the rectangular garden are in ratio 1: 2. The diagonal has a length of 20 meters. Calculate the area and perimeter of the garden.
18. Water current speed. Two cities along the river are 100 km apart. The powerboat downstream runs for 4 hours, upstream for 10 hours. Determines the river's current speed.
19. Borrowing I borrow 25,000 to 6.9% p.a.. I pay 500 per month. How much will I pay and for how long?
20. Isosceles triangle 8 If the rate of the sides an isosceles triangle is 7:6:7, find the base angle correct to the nearest degree.

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