# Examples for 9th grade - page 67

- Dices throws

What is the probability that the two throws of the dice: a) Six falls even once b) Six will fall at least once - Semicircle

To a semicircle with diameter 10 cm inscribe square. What is the length of square sides? - 3s prism

It is given a regular perpendicular triangular prism with a height 19.0 cm and a base edge length 7.1 cm. Calculate the volume of the prism. - Throw

We throw 2 times with 2 dices. What is the probability that the first roll will fall more than sum of 9 and the second throw have sum 3 or does not have the sum 4? - 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. - Repairman

Repairman has vowed to do repair work at the plant for 25 days. However work had to be shortened, and therefore he took helper worker. Together they made all the corrections for the whole days. How long it would take work to helper worker? - Triangular pyramid

Calculate the volume and surface area of a regular triangular pyramid whose height is equal to the length of the base edges 10 cm. - Park

In the park is marked diamond shaped line connecting locations A, D, S, C, B, A. Calculate its length if |AB| = 108 m, |AC| = 172.8 m. - Rain

How many mm of water rained the roof space 75 m^{2}if the empty barrel with a radius of 8 dm and height 1.2 m filled to 75% its capacity? :-) - Alfa, beta, gama

In the triangle ABC is the size of the internal angle BETA 8 degrees larger than the size of the internal angle ALFA and size of the internal angle GAMA is twice the size of the angle BETA. Determine the size of the interior angles of the triangle ABC. - Lift

The largest angle at which the lift rises is 16°31'. Give climb angle in permille. - Circular pool

The base of pool is circle with a radius r = 10 m excluding circular segment that determines chord length 10 meters. Pool depth is h = 2m. How many hectoliters of water can fit into the pool? - Password dalibor

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? - Rectangular triangles

The lengths of corresponding sides of two rectangular triangles are in the ratio 2:5. At what ratio are medians relevant to hypotenuse these right triangles? At what ratio are the contents of these triangles? Smaller rectangular triangle has legs 6 and 8 c - Height difference

What height difference overcome if we pass road 1 km long with a pitch21 per mille? - Motion 2

At 10 o'clock started from place A car speed at 90 km/h. 20 minutes after started from the place B at speed 60 km/h another car. Distance places A and B is 120 kilometers. What time and where they meet? - Chord 4

I need to calculate the circumference of a circle, I know the chord length c=19 cm and the distance from the center d=33 cm chord to the circle. - Brass tube

The outer perimeter of brass tube (ρ = 8.5 g/cm^{3}) is 51 cm. Its mass is 5 kg, length 56 cm. What is the pipe wall thickness? - Rectangle and circle

The rectangle ABCD has side lengths a = 40 mm and b = 30 mm and is circumscribed by a circle k. Calculate approximately how many cm is circle long. - Blackjack TU160

Bomber Tupolev TU160 started at 9:00 from the airport and flew at average speed of 1850 km/h toward the airfield B distant 3500 km. After evaluating the danger from the airport B started at 9:45 B towards A fighter MIG 29 at an average speed 2300 km/h. At

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