Maths practice for 14 year olds - page 153 of 361

Number of problems found: 7214

Three dice
The player throwing the three dice asked G. Galilei: "Should I bet on the sum of 11 or the sum of 12?" What did Galilei answer him? Hint: write down all three triples of numbers that can be thrown, have a total of 11, have a total of 12, and compare proba
Three roads
The three boys moved from start to finish on three different routes, A, B, and C, always simultaneously. Adam drove road A 1500 m long on a scooter. Blake walked route B 600 m long on foot. Cyril got on a scooter on route C after a 90 m walk, then he left
Acute triangle
In the acute triangle KLM, V is the intersection of its heights, and X is the heel of height to the side KL. The axis of the angle XVL is parallel to the side LM, and the angle MKL is 70°. What size are the KLM and KML angles?
Roads
There are four roads from city A to city B and five roads from city B to city C. How many different routes can we take from city A to city C via city B?
Even number writing
Use the digits 3, 4, 5, and 6 to write all even numbers. How many such numbers can you write when you can repeat the numbers?
Number 4
Camilla wrote all-natural numbers from 1 to 400 inclusive. How many times did she write the number 4?
Grandma grandchildren age
Grandma is 72 years old. It's four times the sum of the ages of her two grandchildren. The age of the older of them is twice of a younger grandson. How old is your younger grandson?
Double-digit number creation
How many double-digit numbers greater than 60 can we make from digits 0,5,6,7,8,9? The numerals must not be repeated.
The staircase
The staircase has a total height of 3.6 m and forms an angle of 26° with the horizontal. Calculate the length of the whole staircase.
Cone roof cost
The roof of the castle tower has the shape of a cone with a base diameter of 12 m and a height of 8 m. How many euros will we pay to cover the roof if 1 m of square roofing costs 3.5 euros?
Tower room whitewash
The castle tower room has the shape of a cylinder with a diameter of 4.6 m and a height of 2.9 m. Calculate how much it will cost to whitewash the ceiling and walls of this room if €23 is paid for 1 square meter, while windows and doors account for 15℅ of
Sphere cut
A sphere segment is cut off from a sphere k with radius r = 1. The volume of the sphere inscribed in this segment is equal to 1/6 of the segment's volume. What is the distance of the cutting plane from the center of the sphere?
Deceleration of car
The car has a speed of 60 km/h and, after a 100 m journey speed of 40 km/h. What is the deceleration of a car if we assume that its movement is constantly slowed down?
Two-element combinations
Write all two-element combinations from elements a, b, c, and d.
Fresh juice
The seller offers fresh-squeezed juice, which the customer either pours into his own containers or sells in liter plastic bottles, which the customer buys from him. A liter of juice costs 40 CZK more than a bottle. There is no charge for turning the juice
Ladder
How long is a ladder that touches a wall 4 meters high and has a lower part 3 meters away from the wall?
Quadrilateral pyramid
Find the height and surface of a regular quadrilateral pyramid with a base edge a = 8 cm and a wall height w = 10 cm. Sketch a picture.
Triangular pyramid
Calculate the volume of a regular triangular pyramid with edge length a = 12 cm and pyramid height v = 20 cm.
Roof cardboard
The roof of the prefabricated holiday cottage has the shape of a regular quadrilateral pyramid with a length of the base edge of 8 meters and a height of 9 m. How many square meters of cardboard are needed to cover the roof?
Linden tree percentage
The graph shows the distribution of the number of all trees by species that the volunteers planted in the city park. What percentage of the total number of planted trees are lindens? Oak 23 pieces Maple 12 pieces Linden 15 pieces

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