Examples for secondary school students - page 17 of 213
Number of problems found: 4253
- Five-minute 80951
Karel has an average grade of exactly 1.12 from five-minute episodes. Prove that at least 22 of them have one. - Elevation 80869
We can see the top of the tower standing on a plane from a certain point A at an elevation angle of 39° 25''. If we come towards its foot 50m closer to place B, we can see the top of the tower from it at an elevation angle of 56° 42''. How tall is the tow - Elevation 80866
Find the height of the tower when the geodetic measured two angles of elevation α=34° 30'' and β=41°. The distance between places AB is 14 meters. - Probability 80860
During the exam, the student takes 3 questions out of 20. He is ready for 14 of them. Find the probability that he draws at least one that he knows. - Centimeters 80859
Triangle ABC and triangle ADE are similar. Calculate in square centimeters the area of triangle ABC if the length of side DE is 12 cm, the length of side BC is 16 cm, and the area of triangle ADE is 27 cm². - Probability 80858
During the exam, the student takes 3 questions out of 30. He is ready for 20 of them. Find the probability that he draws at most 2 that he knows. - Probability 80857
During the exam, the student answers 4 questions out of 25. He is ready for 20 of them. Find the probability that he draws exactly one that he does not know. - Probability 80856
The probability of occurrence of a certain phenomenon is the same in all trials and is equal to 0.7. Attempts are repeated until this phenomenon occurs. What is the probability that we will have to make a fifth trial? - Probability - coin toss
A coin is tossed 24 times. Find the probability of getting 16 heads. (The probability of getting a head is 0.5) - Longitudinal 80822
How does the rail lengthen when the temperature changes from -30°C to 30°C if it is 25 m long at 0°C? The temperature coefficient of longitudinal expansion is 12.10na-6Kna-1. - Transported 80813
Three Tatras transported 22.2 tons of sand. The second Tatra transported 20% more than the first, and the third Tatra 25% more than the second. How much did each Tatra take? - Effectiveness 80811
According to clinical studies, the effectiveness of the drug is 90%. The doctor prescribed the medicine to eight patients. What is the probability that the drug will be effective in all these patients? - Manufacturer 80810
The manufacturer indicates that the germination rate of the pepper seeds is 68%. What is the probability that a) out of ten seeds sown, at least 8 will germinate? b) will at most 3 sprouts out of ten seeds be sown? - Trapezoid 80809
The house's roof is a trapezoid of the same name, with 85 tiles at the ridge and 100 tiles at the bottom. There is always one more bag in each row than the previous one. How many bags do I need for the entire roof? - Arithmetic 80808
The lengths of the sides of a right triangle form the first 3 terms of the arithmetic sequence. The content is 6cm². - Calculate 80804
The school bought 20 tablets and 15 laptops for the students for a total of exactly €6,000. Calculate the amount of one tablet and the price of a laptop if the tablet was €50 cheaper than the laptop. - Differential 80799
Kerosene (ρ1 = 830 kg . m-3) flows through the pipe. Calculate the pressure difference in the given sections when the mercury level difference (ρ2 = 13600 kg . m-3) in the mercury differential manometer is h = 2.2 dm. - Hydrostatic 80798
Calculate the depth of water at which the hydrostatic pressure is equal to 100870 N/m². We only consider hydrostatic pressure. - Grandmother 80795
The grandmother is 4 times older than the grandson. In 7 years, it will be only 3 times. How old is grandma? - Probability 80785
We roll the dice and then toss the coin as many times as the number that came up on the dice. What is the probability that the coin lands head at least once?
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