# Examples for secondary school students - page 50

1. Reward Three workers have shared a common reward 13110 CZK follows: first worker got 35% less than the second and third worker got 20% more than the second worker. How much got each worker?
2. Ballistic curve The ballistic grenade was fired at a 45° angle. The first half ascended, the second fall. How far and how far it reached if his average speed was 1200km/h, and 12s took from the shot to impact.
3. 30-gon At a regular 30-gon the radius of the inscribed circle is 15cm. Find the "a" side size, circle radius "R", circumference, and content area.
4. CuZn Brass is an alloy of copper and zinc. The 10 centimeter brass cube has a weight of 8.6 kg. Copper density is 8930 kg/m3, the zinc density is 7130 kg/m3. Calculate how many kg of copper and zinc a cube contains.
5. Combinations of sweaters I have 4 sweaters two are white, 1 red and 1 green. How many ways can this done?
6. Diagonal of the rectangle Calculate the diagonal of the rectangle which area is 54 centimeters square and the circuit is equal to 30 cm.
7. Password dalibor Kamila wants to change the password daliborZ by a) two consonants exchanged between themselves, b) changes one little vowel to such same great vowel c) makes this two changes. How many opportunities have a choice?
8. Infinite decimal Imagine the infinite decimal number 0.99999999 .. ... ... ... That is a decimal and her endless serie of nines. Determine how much this number is less than the number 1. Thank you in advance.
9. Coins Denis and Zdeno together have 97 coins. If Denis had 4 coins less than he has now, the number of the coins would be in the ratio 14: 17. Determine the number of coins owned by Denis and Zdeno.
10. Pharmacy The pharmacy add to 3 liters of 95-percent alcohol 5 liters of 38.04 percent alcohol. How many percent pharmacy got?
11. The confectionery The confectionery sold 5 kinds of ice cream. In how many ways can I buy 3 kinds if order of ice creams does not matter?
12. Unknown number 7 Calculate unknown number whose 12th power when divided by the 9th power get a number 27 times greater than the unknown number. Determine the unknown number.
13. Flowerbed Family cultivated tulips on a square flower bed of 6 meters. Later they added the square terrace with a side of 7 meters to their house. One vertex of the terrace lay exactly in the middle of a tulip bed, and one side of the terrace divided the side of the
14. Blueberries 2 Lenka and Martin collected eight liters of blueberries in two hours. How long will take to collect blueberries by Lenka itself, if we know that she collect all 2.5 hours less than Martin?
15. Square roots What is equal to the product of the square roots of 295936?
16. Add vector Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of vector PQ.
17. Cycling trip At 8 am started a group of children from the camp to day cycling trip. After 9:00 weather deteriorated sharply and the leader decided to send for the children bus on the same route, which started at 10 hours. For how long and at what distance from the camp
18. Men, women and children On the trip went men, women and children in the ratio 2:3:5 by bus. Children pay 60 crowns and adults 150. How many women were on the bus when a bus was paid 4,200 crowns?
19. Digits How many five-digit numbers can be written from numbers 0.3,4, 5, 7 that is divided by 10 and if digits can be repeated.
20. Two planes Two planes flying from airports A and B, 420 km distant against each other. Plane from A took off 15 minutes later and flies at an average speed of 40 km/h higher than the plane from B. Determine the average speed of this two aircraft if you know that it

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