# Examples for secondary school students - page 50

1. Combinations of sweaters I have 4 sweaters two are white, 1 red and 1 green. How many ways can this done?
2. Motel Three different dinners A, B, C are served in the motel. Three 20 members went to motel. Group 1 ordered dinners: A 20 members and their average dinner price in the group was CZK 200. From Group 2, they ordered a A: 10 persons, B 10 dinners, and their aver
3. Numbers Write smallest three-digit number, which in division 5 and 7 gives the rest 2.
4. 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.
5. 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?
6. Mass The thickness of a metallic tube is 1cm and its outer radius is 11cm. Find the mass of such 1m long tube, if the density of the metal is 7.5g per cubic cm.
7. 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.
8. 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.
9. Diagonal of the rectangle Calculate the diagonal of the rectangle which area is 54 centimeters square and the circuit is equal to 30 cm. 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?
11. 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.
12. 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.
13. 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?
14. Pharmacy The pharmacy add to 3 liters of 95-percent alcohol 5 liters of 38.04 percent alcohol. How many percent pharmacy got?
15. 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
16. 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.
17. 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?
18. Square roots What is equal to the product of the square roots of 295936? Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of vector PQ. 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