# Examples for secondary school students - page 22

- Components

In the box are 8 white, 4 blue and 2 red components. What is the probability that we pull one white, one blue and one red component without returning? - Sphere

Intersect between plane and a sphere is a circle with a radius of 60 mm. Cone whose base is this circle and whose apex is at the center of the sphere has a height of 34 mm. Calculate the surface area and volume of a sphere. - Diameter

If the endpoints of a diameter of a circle are A(10, -1) and B (3, 10), what is the radius of the circle? - Vacation

Parents piggybacking children on vacation to its grandmother and grandfather at a city distant 150 kilometers. They agreed to meet halfway. Parents will be travel at 90 km/h, grandmother and grandfather at 60 km/h. Parents depart at 12:00 hours. When grand - Cube - wall

V kocke ABCDEFGH je ?. Aký je povrch kocky? - Paper box

Calculate the consumption of paper on the box-shaped quadrangular prism with rhombic footstall, base edge a=6 cm and the adjacent base edges forms an angle alpha = 60 °. Box height is 10 cm. How many m^{2}of the paper consumed 100 such boxes? - RT 11

Calculate the area of right tirangle if its perimeter is p = 45 m and one cathethus is 20 m long. - Abyss

Stone was pushed into the abyss: 2 seconds after we heard hitting the bottom. How deep is the abyss (neglecting air resistance)? (gravitational acceleration g = 9.81 m/s^{2}and the speed of sound in air v = 343 m/s) - Journey

The road from A to B measures 11.5 km. Firstly up the hill, then by level plane and then downhill. Tourist goes uphill at 3 km/h, on the plane 4 km/h and downhill 5 km/h. From point A to B went 2h 54 min back 3h 6 min. How long is the segment of level pla - Combi-triangle

On each side of the square is marked 10 different points outside the vertices of the square. How many triangles can be constructed from this set of points, where each vertex of the triangle lie on the other side of the square? - Gauss

Help little C.F. Gauss sum all the integers from 1 to 420. - Angles in triangle

The triangle is ratio of the angles β:γ = 6:8. Angle α is 40° greater than β. What are the size of angles of the triangle? - Bulbs

The probability that the bulb can operate 5000 hours is 0.16. What is the probability that exactly one of three bulbs can operate 5000 hours? - Unit vector 2D

Determine coordinates of unit vector to vector AB if A[-6; 8], B[-18; 10]. - Diagonals

Calculate the length of the diagonals of the rhombus if its side is long 5 and one of its internal angle is 80°. - Volume and surface

Calculate the volume and surface area of the cylinder when the cylinder height and base diameter is in a ratio of 3:4 and the area of the cylinder jacket is 24 dm^{2}. - Moon

We see Moon in the perspective angle 28'. Moon's radius is 1740 km at the time of the full moon. Calculate the mean distance of the Moon from the Earth. - JUDr. Usury

Judge JUDr. Usury approved the agreement on guilt and punishment where confessed to pay daily interest 0.18%. How big is a yearly interest? Year has 360 days. - Square pyramid

Calculate the volume of the pyramid with the side 5cm long and with a square base, side-base has angle of 60 degrees. - Tourist Jirka

Distance between the points A and B is 13.5 km. Jirka went from point A to point B unknown speed and for an unknown period of time. Back to the point A went slower by 3 km/h which means that went 20 minutes more. How long Jirka took the return journey?

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