Examples for secondary school students - page 48 of 213
Number of problems found: 4256
- Poisson distribution - daisies
The meadow behind FLD was divided into 100 equally large parts. Subsequently, it was found that there were no daisies in ten of these parts. Estimate the total number of daisies in the meadow. Assume that daisies are randomly distributed in the meadow. - Three sigma rule
The height of trees in a given stand is known to be a quantity with a normal probability distribution with a mean value of 15 m and a variance of 5 m². Determine the interval in which there will be tree heights in such a stand with a probability of 90% - Seedlings
The meadow was divided into 30 equally large parts, and then it was calculated how many seedlings were in each part. It was found that there were no seedlings in six parts. Five parts contained one seedling, twelve parts two seedlings, and seven parts thr - The surface
The surface of the cylinder is 1570 cm²; its height is 15 cm. Find the volume and radius of the base.
- Above water surface
If we remove the stone from the water, we apply a force of 120N. How much force will we exert if we move the stone above the water? The stone's density is 5000 kg/m³. - Two workers
One worker makes a part 4 hours and the second 9 hours later than they would make the same part together. How long does it take for each worker to make the part himself? - Hockey Championships
At the 2021 World Hockey Championships, there are eight teams in Group A, each playing seven matches. There are 4 points for each team to gain points (3-2-1-0), but it is always paired with the opponent's points ( 0-1-2-3). How many points are there possi - Indistinguishable 48981
How many ways can we build eight indistinguishable towers on an 8 × 8 board, so they don't endanger each other? - Two cars
Two cars (trucks and passengers) drove simultaneously from two places 50 km away. If they go against each other, they will meet in 30 minutes. If they follow each other in the same direction, the car will catch up with the truck in 2.5 hours. What is the
- Oscillation 48961
Write the equation of harmonic oscillation if the amplitude of the oscillation is 5 cm and its period is 0.5 s. - Bottle, cup and jug
The bottle and the cup have the same weight as the jug. The bottle has the same weight as the cup and plate. Two jugs have the same weight as three plates. What is the weight of the bottle if the weight of the cup is 100g? - Siblings 48821
Three siblings saved CZK 1,445. Adela saved 10% less than Martin and David 10% more than Adela. How many crowns did each of them save? - Oscillations 48711
The time signal in the radio consists of four sound marks with a frequency of 1,000 Hz, of which the first three have a duration of 100 ms and the fourth 500 ms. How many oscillations will occur at each mark? - Two pendulums
In 24 s, the first pendulum performed 12 oscillations and the second 16 oscillations. Determine the periods and frequencies of both pendulums.
- Suspended 48691
A body weighing 400 kg is suspended at a distance of 1 m from one end of the beam on a beam weighing 100 kg and 5 m. How large do forces act at the ends of the beam? - Isosceles trapezoid
Find the height in an isosceles trapezoid if the area is 520 cm² and the base a = 25 cm and c = 14 cm. Calculate the interior angles of the trapezoid. - Isosceles 48443
Three equal positive charges Q are located at the vertices of an isosceles right triangle ABC. The right angle is at vertex A. The length of side AB is 1m. What is the electric field strength at the center S of side BC, i.e., what force would act on a pos - School model
The beech school model of a regular quadrilateral pyramid has a base 20 cm long and 24 cm high. Calculate a) the surface of the pyramid in square decimeters, b) the mass of the pyramid in kilograms if the density of the beech is ρ = 0,8 g/cm³ - A machine
A machine produces steel rods of normally distributed length, the mean length and the standard deviation being 50.0 cm and 0.5 cm, respectively. The rods do not conform to safety standards if they are either shorter than 49.1 cm or longer than 50.7 cm in
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