# Examples for 9th grade - page 23

1. Commitee A class consists of 6 males and 7 females. How many committees of 7 are possible if the committee must consist of 2 males and 5 females?
2. Hockey players After we cycle five hockey players sit down. What is the probability that the two best scorers of this crew will sit next to each other?
3. Salary Calculate equivalent annual salary to hourly salary \$ 19. Assume a 42-hour work week.
4. Horizontal Cylindrical Segment How much fuel is in the tank of horizontal cylindrical segment with a length 10m, width of level 1 meter and level is 0.2 meters below the upper side of the tank?
5. Line Straight line passing through points A [-3; 22] and B [33; -2]. Determine the total number of points of the line which both coordinates are positive integers.
6. Circle Circle is given by centre on S[-7; 10] and maximum chord 13 long. How many intersect points have circle with the coordinate axes?
7. Cable car 2 Cable car rises at an angle 41° and connects the upper and lower station with an altitude difference of 1175 m. How long is the track of cable car?
8. Angle of deviation The surface of the rotating cone is 30 cm2 (with circle base), its surface area is 20 cm2. Calculate the deviation of the side of this cone from the plane of the base.
9. Railway Railway line had on 5.8 km segment climb 9 permille. How many meters track ascent?
10. The car The car has traveled the distance between A and B for four hour. If we increased the average by 17 km/h the car travel this distance an hour earlier. Determine the initial speed of the car and the distance between A and B.
11. Column Perpendicular pole high 8 m tall broke and its toe fell 2.7 m from the bottom of the pole. At what height above the ground pole broke?
12. Vintner How high can vintner fill keg with crushed red grapes if these grapes occupy a volume of 20 percent? Keg is cylindrical with a diameter of the base 1 m and a volume 9.42 hl. Start from the premise that says that fermentation will fill the keg (the number. 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?
14. 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.
15. 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
16. 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
17. Truck In 7 hours started from town Krnov truck at speed 40 km/h. Passenger car started against it in 8 hours 30 minutes from the city of Jihlava at speed 70 km/h. Distance between this two cities is 225 km. At what time and at what distance from Krnov this two.
18. 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)?
19. Pharmacy At the pharmacy are in one container 20% solution in the second 50% solution of disinfectant. They need to prepare 4 L of 48-percent solution. What amount of solution from each container is needed to mix?
20. Circle On the circle k with diameter |MN| = 61 J lies point J. Line |MJ|=22. Calculate the length of a segment JN.

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