# Examples for 9th grade - page 29

- 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? - Retail

At what price bought retail 1 kg goods from wholesale, if lost in the distribution is 3.9% of weight of the goods and retail still have a profit of 13.2%? Goods are sold at retail for 17 euro per kg. - Square

If the length of the sides of the square we decrease by 25% decrease the content area of 28 cm^{2.}Determine the side length of the original square. - Pyramid

Cuboid ABCDEFGH has dimensions AB 3 cm, BC 4 cm, CG 5 cm. Calculate the volume and surface area of a triangular pyramid ADEC. - Sequence

Write the first 7 members of an arithmetic sequence: a_{1}=8, d=-9. - Triangle

Calculate heights of the triangle ABC if sides of the triangle are a=48, b=81 and c=98. - Paul and Honza

Honza went to chat on a bike without a break 3.0 hours. Paul the same way without breaks 30 minutes longer. The difference between the speeds of the two boys was the one kilometer per hour. How fast was Paul, if you know that the speed of the boys did not. - Mountain railway

Height difference between points A, B of railway line is 38.5 meters, their horizontal distance is 3.5 km. Determine average climb in permille up the track. - Swing

A child weighing 12 kg is sitting on a swing at a distance of 130 cm from the axis of rotation. How far away from the axis of rotation (center) must sit down his mother weighs 57 kg if she wants to be swing in balance? - The professor's birthday

Professor of mathematics had 48 birthdays. The director congratulated him. The professor asked the director: "And how old are you?" The director replied: "I'm exactly twice as many years than you were when I was old as to you today." How old is the direc - Cuboids in cube

How many cuboids with dimensions of 6 cm, 8 cm and 12 cm can fit into a cube with side 96 centimeters? - Gasholder

The gasholder has spherical shape with a diameter 23 m. How many m^{3}can hold in? - Gon functions

Decide which of the numbers (values of trigonometric functions) are positive and which are negative (or zero). Positive mark +1 and negative -1. - ISO Triangle V2

Perimeter of RR triangle (isosceles) is 474 m and the base is 48 m longer than the arms. Calculate the area of this triangle. - Password

The voltage station is every day changing the master password, which consists of three letters. Code generation process does not change and is based on the following procedure: The following letters (A) to (I) correspond to different numbers from 1 to 9. I - Examination

The class is 22 students. How many ways can choose four to examination? - Compare II

Which of the numbers 15^{8}, 8^{15}is greater? - Invitations

For every 5 minutes writes Dana 10 invitations, while Anna 14 invitations. How long will write together 120 invitations? - Again saw

From the trunk of the tree we have to a sculpture beam with rectangular cross-section with dimensions 128 mm and 140 mm. What is the trunk smallest diameter? - Train from Brno

First train started from Brno at 8 am at 60 km per hour. Second train started from Opava at 7 o'clock at the speed of 40 kilometers per hour. In how many hours and how far from cities trains meet when the distance of cities is 200 kilometers.

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