# Examples for 9th grade - page 50

1. Interest p.a. Calculate the value of interest in period of 1 year from the deposit 62000 CZK at 8 percent interest rate, after deducting 15 percent tax.
2. Eva When Eva buys 8 packages of cookies 4 CZK left her. If she wanted to buy 10 packages, she would have to borrow 20 CZK. How much money has Eva in her wallet?
3. Two months Mars has two months, Phobos and Deimos. Phobos orbits around Mars in 7 hours 39 minutes and Deimos in 30 h 14 min. How long will repeat the relative position of the three celestial bodies?
4. MATES In MATES (Small Television tipping) from 35 randomly numbers drawn 5 winning numbers. How many possible combinations there is?
5. Ratio of two unknown numbers Two numbers are given. Their sum is 30. We calculate one-sixth of a larger number and add to both numbers. So we get new numbers whose ratio is 5:7. Which two numbers were given?
6. Power Number ?. Find the value of x.
7. Unknown number Unknown number is divisible by exactly three different primes. When we compare these primes in ascending order, the following applies: • Difference first and second prime number is half the difference between the third and second prime numbers. • The produ
8. Arc-sector arc length = 17 cm area of sector = 55 cm2 arc angle = ? the radius of the sector = ?
9. The field The player crossed the field diagonally and walked the length of 250 m. Calculate the length of the field, circumference if one side of field 25 meters.
10. Hexagon rotation A regular hexagon of side 6 cm is rotated through 60° along a line passing through its longest diagonal. What is the volume of the figure thus generated?
11. Square circles Calculate the length of the described and inscribed circle to the square ABCD with a side of 5cm.
12. Rhombus One angle of a rhombus is 136° and the shorter diagonal is 8 cm long. Find the length of the longer diagonal and the side of the rhombus.
13. Obtuse angle The line OH is the height of the triangle DOM, line MN is the bisector of angle DMO. obtuse angle between the lines MN and OH is four times larger than the angle DMN. What size is the angle DMO? (see attached image)
14. Three men Alex is half younger than Jan, which is one-third younger than George. The sum of their ages is 48. How are these three men old?
15. Isosceles trapezoid What is the height of an isosceles trapezoid, the base of which has a length of 11 cm and 8 cm and whose legs measure 2.5 cm?
16. Laths There are two laths in the garage opposite one another: one 2 meters long and the other 3 meters long. They fall against each other and lean against the opposite walls of the garage both laths and touch at a height of 70 cm above the garage floor. How wide
17. Average height In a class are 34 students. The average height of students is 165 cm. What will be the average height of students in the classroom when two pupils tall 176 cm and 170 cm moved from this school/class?
18. Tray Wjat height reach water level in the tray shaped a cuboid, if it is 420 liters of water and bottom dimensions are 120 cm and 70 cm.
19. Annual income The annual incomes (in thousands of \$) of fifteen families is: 60, 80, 90, 96, 120, 150, 200, 360, 480, 520, 1060, 1200, 1450, 2500, 7200 Calculate harmonic and geometric mean.
20. The city In the city is 2/4 of women married to 3/4 men. What percentage of townspeople is single (not married)?

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