Math practice for 13 year olds - page 67 of 428

Number of problems found: 8559

Number ratio subtraction
I think two numbers. Their ratio is 5:7. If 3 is subtracted from the first and 7 from the second, then the ratio is 6:7. What number was I thinking?
Triangle sides - natural
In triangle ABC, side a = 30 cm b = 7 cm. The length of the third side in cm is a natural number. What is the least and what is the greatest length that side c can have?
Cube triangle volume
In the cube ABCDEFGH, the area of triangle ABK is √20 cm². How much cm² is the volume of ABGH in a cube if you know that K is the midpoint of edge CG?
Tetrahedron segment midpoint
The sum of the lengths of all the edges of the regular tetrahedron ABCD is 48 cm. How many cm is the segment XY if you know that X is AB's midpoint and Y is CD's midpoint?
Triangle area side
Calculate the area of an isosceles triangle ABC with a base of 10 cm and a side of 7 cm. Sketch a picture.
Trapezoid perimeter base
An isosceles trapezoid has one base twice as short as the other. Its area is 42 cm², and its height is 4 cm. Calculate its circumference if you know that the arm is 5.3 cm long.
Prism pyramid ratio
For the volumes of a perpendicular prism and a pyramid with the same base and height: A) the volumes are equal B) the volume of a pyramid is three times smaller than the volume of a prism C) the ratio of the volumes of the prism and the pyramid is 1:3 D)
Peter example solving
Peter solves 40 examples. For a correctly solved example, he receives CZK 5 from his mother. For example, in a poorly solved case, he will pay 20 CZK to his mother. After solving all the examples, he had CZK 25 more than when he started counting. How many
Banknote payment count
CZK 8,000 was paid out in fifty pieces of banknotes in denominations of CZK 100 and CZK 200. How many were there?
Triangle height line
In the right triangle KLM, the hypotenuse l = 9 cm and the perpendicular k = 6 cm. Calculate the size of the height vl and the line tk.
Building shadow height
The school building casts a shadow 16 m long on the plane of the yard, and at the same time, a vertical meter pole casts a shadow 132 cm long. Determine the height of the building.
Glass cocktail level
The cone-shaped glass has a volume of 2.5 dl and a diameter of 13 cm. How much cocktail is left in the glass if the level only reaches half the height of the glass?
Segment ratio reduction
I will reduce a segment of length 16 cm in the ratio 7:8, what will its length be in cm?
Angular velocity
Determine the difference in angular velocities of the clock hands. [rad/s] ω of clock hands =? ω minute hands =? ω second hands =?
Diagonal of a cube
Calculate the volume of a cube with a wall diagonal of u = 20 cm.
Rectangle perimeter ratio
The sides of the rectangle are in the ratio of 5 : 8. Its perimeter measures 208 cm. Determine the area of this rectangle.
Stipend double increase
University students increased their stipend by 20% and then again by 10%. Now he gets 99 euros. What was his original scholarship?
Flag color combinations
How many 4 colored flags can be made from 5 colors so that each flag consists of three different colors?
Motorcycle acceleration time
Motorcyclist Arnošt begins to move on his motorcycle in a uniformly accelerated motion with an acceleration of 1.6 m/s². At what time will it reach a speed of 50 km/h? What distance will it travel at this time?
Number sum puzzle
I think of three numbers. When I add them, I get 15. When I subtract the third number from the sum of the first two numbers, I get 10. When I subtract the second number from the sum of the first and third numbers, I get 8. What number do I think?

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