# Examples for 9th grade - page 55

1. Rope slack Between two streets 20 m away give the lamp, which is in the middle and hanging 60 cm bellow the taut rope. Can be done with 20.5 meters rope?
2. Alcohol mixing How much 55% alcohol we must pour into 1500 g 80% alcohol to form a 60% alcohol? How much 60% alcohol created?
3. Salary in enterprise The average salary in the company is 27 000 CZK, 30% of workers have the lowest average income of 19 thousand CZK. There were an increase in the salary in this group by 2%. How much % increased the average salary across the company?
4. Rhombus and diagonals The a rhombus area is 150 cm2 and the ratio of the diagonals is 3:4. Calculate the length of its height.
5. QuizQ2 The square of the first number is equal to three-fifths of the second number. Determine both numbers if you know that the second number is 5 times greater than the first, and neither of numbers is not equal to zero.
6. The fence I'm building a fence. Late is rounded up in semicircle. The tops of late in the field between the columns are to copy an imaginary circle. The tip of the first and last lath in the field is a circle whose radius is unknown. The length of the circle chord i
7. Chord 3 What is the radius of the circle where the chord is 2/3 of the radius from the center and has a length of 10 cm?
8. Compound interest Compound interest: Clara deposited CZK 100,000 in the bank with an annual interest rate of 1.5%. Both money and interest remain deposited in the bank. How many CZK will be in the bank after 3 years?
9. Park In the park is marked diamond shaped line connecting locations A, D, S, C, B, A. Calculate its length if |AB| = 108 m, |AC| = 172.8 m.
10. Draw a trapezoid Draw a trapezoid if given a = 7 cm, b = 4 cm, c = 3.5 cm, diagonal AC = 5cm. Solve as a construction task.
11. Bookshelve Bookshelve with an original price of € 200 twice become cheaper. After the second discounted by 15% the price was € 149.60. Determine how much % become cheaper for the first time.
12. Balls Michal said to Martin: give me one ball and I'll have twice as you. Martin said: give me 4 and we will have equally. How many balls each have?
13. Garden pond Concrete garden pond has bottom shape of a semicircle with a diameter 1.7 m and is 79 cm deep. Daddy wants make it surface. How many liters of water is in pond if watel level is 28 cm?
14. Reference angle Find the reference angle of each angle:
15. Cube wall The perimeter of one cube wall is 120 meters. Calculate the surface area and the body diagonal of this cube.
16. MO Z9–I–2 - 2017 In the VODY trapezoid, VO is a longer base and the diagonal intersection K divides the VD line in a 3:2 ratio. The area of the KOV triangle is 13.5 cm2. Find the area of the entire trapezoid.
17. Prices prices The meter of the textille was reduced by CZK 42, so 4 meters of the new price was 20 CZK cheaper than 3 meters of the original price. What was the original and new price of the textille?
18. Brunette Of the girls who attend primary school are 30% blondes and 70% brunette. 81% blondes and 19% brunette has blue eyes. How many girls attending school altogether if 470 girls has blue eyes?
19. Copiers Three copiers will do the same in an hour k copies. How many copies would be done in an hour by four such copiers? ?
20. Workers 2 Worker dug the trench for 7 hours, another worker for 10 hours. They recruited to work even one worker more. Digging should be done for 2 hours. For how long would dig third worker alone?

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