Examples for secondary school students - page 91 of 229
Number of problems found: 4578
- Circle and square
An ABCD square with a side length of 100 mm is given. Calculate the circle’s radius that passes through vertices B, C, and the center of the side AD. - Research in school
For particular research in high school, four pupils are selected from a class of 30 pupils. Calculate the number of all possible results of the selection and further calculate the number of all possible results if it depends on the order in which the stud - Manufacturer 24801
Five hundred of the products in the series are to be inspected with a repeat check. The manufacturer guarantees 2% scrap for a given production. Determine the probability of scraps among the 500 products reviewed between 12 and 20. - Probability of failures
The probability of failure in specific productions is 0.01. Calculate the likelihood of more than one failure among the 100 selected products if we return them to the file after the check. - Started
A pedestrian leaves point A with a speed of v1 = 5 km/h. After 3 hours, a cyclist follows him from the same place at a speed of v2 = 20 km/h. But a car starts from point B, 50 km away at the same time as the cyclist. Calculate the distance and time at whi - Birthday paradox
How large is the group of people so that the probability that two people have a birthday on the same day of the year is greater than 90%? - The tent
The tent has the shape of a regular square pyramid. The edge of the base is 3 m long, and the tent's height is 2 m. Calculate how much cover (without a floor) is used to make a tent.
- Lifespan
The lifetime of a light bulb is a random variable with a normal distribution of x = 300 hours, σ = 35 hours. a) What is the probability that a randomly selected light bulb will have a lifespan of more than 320 hours? b) To what value of L hours can the la - Slow saving in banks
How long will it take to save € 9,000 by depositing € 200 at the beginning of each year at 2% interest? - Percentage increase
What is the annual percentage increase in the city when the population has tripled in 20 years? - Functionality 24461
The daily product consists of 1000 components, and the probability of failure of any component during the use of the device is 0.001. It does not depend on other components. What is the probability of failure of two components in the investigated period o - Magnified cube
If the lengths of the cube's edges are extended by 5 cm, its volume will increase by 485 cm³. Determine the surface of both the original and the magnified cube. - Afforestation 24341
During the afforestation, 2,950 saplings were planted in three days. On the second day, 25% more saplings were planted than on the first day, and on the third day, 15% more than on the second day. How many saplings were planted on each day? - Numbers 24281
Of the four numbers, the second is five larger than the first, the third two smaller than the first, and the fourth is twice larger than the first. Find these numbers if their sum is 38. - Internal angles
In the ABC triangle, the magnitude of the inner angle beta is one-third the magnitude of the angle alpha and 20° larger than the magnitude of the gamma angle. Determine the magnitudes of the interior angles of this triangle.
- Caramels 24131
Anička and Jana shared 21 caramels, while Jana had 40% of what Anička received. How many caramels did she get? - Viewing angle
The observer sees a straight fence 60 m long at a viewing angle of 30°. It is 102 m away from one end of the enclosure. How far is the observer from the other end of the enclosure? - Forty-eight 24101
Forty-eight people were present at the reception. Among them were Czechs, Slovaks, and Germans. Slovaks were 4 more than Czechs and Germans 6 less than half Czechs and Slovaks. How many Czechs, Slovaks, and Germans were there at the reception? - Improvement 23971 Three employees received a reward of CZK 5,000 for the improvement proposal. They divided the money according to work so that the first got twice as much as the second, and the second got three times as much as the third. How many crowns did each person r
- Adam
Adam has half more money in his right pocket than in his left pocket. If he transferred 40 crowns from the left pocket to the right, he would have the same in both pockets. Calculate how many crowns Adam has in his left pocket more than in his right. How
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