# Examples for 9th grade - page 24

- Toys

3 children pulled 9 different toys from a box. Many ways can be divided toys so that each children had at least one toy? - Geometric mean

Calculate the geometric mean of numbers a=23.4 and b=16.8. Determine the mean by construction where a and b are the length of the lines. - Rectangular trapezoid

The rectangular trapezoid having bases length 3.2 cm and 62 mm. The shorter arm has a length 0.25 dm. Calculate the lengths of the diagonals and the second arm. - Tetrahedral prism

Calculate surface and volume tetrahedral prism, which has a rhomboid-shaped base, and its dimensions are: a = 12 cm, b = 7 cm, ha = 6 cm and prism height h = 10 cm. - Segments

Line segments 52 cm and 7.6 dm long we divide into equal parts which lengths in centimeters is expressed integer. How many ways can we divide? - Hexagonal pyramid

Base of the pyramid is a regular hexagon, which can be circumscribed in a circle with a radius of 1 meter. Calculate the volume of a pyramid 2.5 meters high. - Angles in triangle

The triangle is ratio of the angles α:β = 8:3. Angle γ is 40° greater than α. What are the size of angles of the triangle? - Snowman 2

On the medal, which has the shape of a circle with a diameter 17 cm is sketched snowman so that the following requirements are met: 1. snowman is composed of three circles, 2. space over snowman is the same as under it, 3. diameters of all circles express - Diagonals in the diamond

The length of one diagonal in diamond is 25 cm greater than the length of the second diagonal and diamond area is 20 m^{2.}Determine the sizes of the diagonals. - Series

Andrew wrote this series of numbers: 1,3,7,15, .... n. Which number in the series does not belong? ? - Chord AB

What is the length of the chord AB if its distance from the center S of the circle k(S, 71 cm) is 27 cm? - Average

What is the average speed of the car, where half of the distance covered passed at speed 59 km/h and the other half at 119 km/h. - Trapezoid ABCD v2

Trapezoid ABCD has length of bases in ratio 3:2. The area of riangle ACD is 956 dm^{2.}What is the area of trapezoid ABCD? - Price of state

Estimate the cost of the state based on following reason. State price is expressed as a percentage respectively share in the redistribution of national GDP. Employee creates monthly value € 1121 (super-gross wage).Then tax him 35.2% employer contribution - The cone

The lateral surface area of the cone is 4 cm^{2,}the area of the base of the cone is 2 cm^{2.}Determine the angle in degrees (deviation) of the cone sine and the cone base plane. (Cone side is the segment joining the vertex cone with any point of the base ci - Tractors

Six tractors plowing the field for 8 days. After two days, two tractors broke down. How many days were prolonged work in the field? - Three digits number

How many are three-digit integers such that in they no digit repeats? - Chemical parison

The blown parison (with shape of a sphere) have a volume 1.3 liters. What is its surface? - Triangle

Calculate the sides of the triangle if its area S = 630 and the second cathethus is shorter by 17. - Two typists

There are two typists who are rewriting the material 705 pages. First can it handle rewrite yourself for 24 days; the second 12 days. First typist wrote material yourself 4 days rest rewrites yourself second typist. How many days will it take rewriting alt

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