# Examples for 9th grade - page 5

- Square diagonal

Calculate length of the square diagonal if the perimeter is 200 cm. - Ace

From complete sets of playing cards (32 cards) we pulled out one card. What is the probability of pulling the ace? - Numbers

Determine the number of all positive integers less than 2937474 if each is divisible by 11, 23, 17. What is its sum? - Flags

How many different flags can be made from colors white, yellow, red, blue, green, orange so that each flag consisted of three different colors? - Triangle ABC

Calculate the sides of triangle ABC with area 883 cm^{2}and if a: b: c = 15:7:19 - Ravens

The tale of the Seven Ravens were seven brothers, each of whom was born exactly 1.5 years after the previous one. When the eldest of the brothers was 4-times older than the youngest, mother all curse. How old was seven ravens brothers when their mother cur - MO SK/CZ Z9–I–3

John had the ball that rolled into the pool and it swam in the water. Its highest point was 2 cm above the surface. Diameter of circle that marked the water level on the surface of the ball was 8 cm. Determine the diameter of John ball. - Right

Determine angles of the right triangle with the hypotenuse c and legs a, b, if: ? - IS triangle

Calculate interior angles of the isosceles triangle with base 37 cm and legs 36 cm long. - Steps

How many steps you save if you go square estate for diagonal (crosswise), rather than circumvent on the two sides of its perimeter with 298 steps. - Tractors

Fields go plow two tractors with various performance. The first tractor plow whole field in 5 hours, the second tractor plow whole field 5 hours longer. How long take plow whole field with two tractors? - Gutter

How much metal is needed for production 37 pieces of gutter pipes with the diameter 16 cm and length of 1 m? The plate bends add 7% of the material. - Cuboid diagonal

Calculate the volume and surface area of the cuboid ABCDEFGH, which sides abc has dimensions in the ratio of 7:10:8 and if you know that the wall diagonal AC is 21 cm and angle between AC and the body diagonal AG is 40 degrees. - Vans

In how many ways can 8 shuttle vans line up at the airport? - Meadow

On the meadow grazing horses, cows and sheep, together less than 200. If cows were 45 times more, horses 60 times more and sheep 35 times more than there are now, their numbers would equall. How many horses, cows and sheep are on the meadow together? - Cyclist

Cyclist goes uphill 1 km for 6.3 minutes and downhill minutes for 2.1 minutes, both applied to the pedals same force. How long he pass 1 km by plane? - Slope of track

Calculate the average slope of the rail tracks between Prievidza (309 m AMSL) and Bratislava (152 m AMSL), if the track is 158 km long. - Seating

How many ways can 7 people sit on 3 numbered chairs (eg seat reservation on the train)? - Prism

Right angle prism, whose base is right triangle with leg a = 3 cm and hypotenuse c = 5 cm has same volume as a cube with an edge length of 1 dm. a) Determine the height of the prism b) Calculate the surface of the prism c) What percentage of the cube' - Z9–I–1

In all nine fields of given shape to be filled natural numbers so that: • each of the numbers 2, 4, 6 and 8 is used at least once, • four of the inner square boxes containing the products of the numbers of adjacent cells of the outer square, • in the cir

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