# Examples for 9th grade - page 18

- Class pairs

In a class of 34 students, including 14 boys and 20 girls. How many couples (heterosexual, boy-girl) we can create? By what formula? - Hockey game

In the hockey game was made 6 goals. Czech played against Finland. Czechs won 4:2. In what order to fall goals? How many game sequence was possible during the game? - Cross-country competition

Cross-country competition was attended by 76% of pupils of class 9.B. Class consis of 16 boys, two of whom did not run and 4 girls did not run. How many girls go to class 9.B? - Gear

Two gears, fit into each other, has transfer 1:5. Centres of gears are spaced 28 cm. What are the radii of the gears? - Hockey match

The hockey match ended with result 3:1. How many different storylines may have the match? - Raffle

How many raffle tickets must be purchased by Peter in raffle with issued 200 tickets if he wants to be sure win at least 3 price? In the raffle draws 30 prices. - Painters

One painter could paint a school for 7 days. The second one for 6 days. It was necessary to paint the school in two days. Next painter was invited and all worked together. How long would this painter painted the school itself? - Pumps

First pump flows 16 liters per second into the basin by the second pump 75% of the first and by third pump half more than the second. How long will take fill basin by all three pumps simultaneously volume 15 m^{3}(cubic meters)? - Tank and water

Cylindrical tank were poured with 3.5 liters of water. If tank base diameter is 3 dm, how height is water level in? - Painters

First painter painted fence himself for 12 hours, the second painter 3 hours sooner than first, and the third painters slowest up to 20 hours. How long took them paint fence if worked together? - Bottle

Bottle with wine costs 61 USD. Wine is 11 USD more expensive than the empty bottle. How much is the bottle itself? - Workers

Workers A and B will done work together for 20 days. They worked together 18 days. Then A worker became ill and worker B finish the job alone for 11 days. If every worker was working alone, how many days took whole work for worker A and B? - Pyramid roof

1/3 of area of the roof shaped regular tetrahedral pyramid with base edge 10 m and height of 4 m is already covered with roofing. How many square meters still needs to be covered? - Maximum area of rhombus

Calculate the interior angles at which equilateral rhombus has maximum area. - Umbrella

Can umbrella 75 cm long fit into a box of fruit? The box has dimensions of 390 mm and 510 mm. - Cuboid

Cuboid ABCDEFGH with 10 cm height has a base edge length 6 cm and 8 cm. Determine angle between body diagonal and the base plane (round to degrees). - Two workers

Two workers carry will do certain work for 12 days. After 8 days of working was one removed, and then the other finished the job alone in 10 days. For how many days would do this work alone each worker? - Building

How high is the building that throws horizontal shadow 58.5 m long at angle 36°36'? - Camel

Camel owner wants to get out of the city into oasis. He bought 3000 bananas, which wants to sell in oasis. However oasis from the city divided 1,000 kilometers of desert. Camel can carry at one time up to 1000 bananas, and for every kilometer traveled, ea - Chocholate pyramid

How many chocolates are in the third shelf when at the 8th shelf are 41 chocolates in any other shelf is 7 chocolates more the previous shelf.

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