Examples for secondary school students - page 19 of 229
Number of problems found: 4578
- Two workshops
Two workshops were supposed to produce 4000 sets of kitchen utensils together. After completing this task, it was found that the first workshop produced 534 sets more than was originally set for it, while the second workshop fulfilled its task by 80%. How - Shear friction
How much force must we apply to a box weighing 300 kg to move it uniformly along a horizontal floor if the coefficient of shear friction between the box's edge and the floor is 0.5? - Hockey - game
A hockey goalkeeper has a save success rate of 93.5%. What is the probability that he will keep a clean sheet in a match when facing 25 shots? What is the probability that he will concede a maximum of 2 goals? - Four-digit number
Juraj is thinking of a four-digit number that he told us about: (a) Its digit sum is one hundredth of the number that I get by rounding the imaginary number to hundreds. (b) Its last digit is 1 more than the second-to-last. (c) The sum of its last two dig - Maturitný - RR - base
In an isosceles triangle ABC with base AB, ∠BAC = 20°, AB = 4. The axis of the interior angle at vertex B intersects side AC at point P. Calculate the length of the segment AP. Give the result to two decimal places. - Segments on the hypotenuse
A right triangle ABC has a hypotenuse of c=26cm. How many segments does the height vc=12 cm cut out on the hypotenuse c? What are the lengths of the sides a and b? What are the angles at the vertices A and B? - In trapezoid 3
In a trapezoid ABCD, the elements are given - lengths of bases a= 20cm, c= 11 cm, angle α = 63°36’ and angle β=79°36’. Calculate the lengths of the other sides and the sizes of the angles.
- Given is
Given is the circle x²+y²-4x+2y-11=0. Calculate the area of the regular hexagon inscribed in the given circle. - Missile 3
The missile penetrated the embankment to a depth of 1.2 m. What was its speed when it hit the surface of the embankment if the movement of the missile in the ground lasted 0.021 seconds and if the movement was uniformly slowed down? - Angles alpha 2
Angles alpha and beta are adjacent. Calculate their sizes if the angle alpha is 50 degrees less than the angle beta. - Acceleration 84024
What distance will a car travel with an acceleration of 10m/s² in 5 seconds? - Target - shooting
A shooter hits the target with a probability of 78%. Determine the probability that, in a competition where 3 shots are fired in a row, he misses only the first shot. Round the result to two decimal places. - Interest 83990
The deposit is €1000. The interest is 7.36% per year. What is the amount after 3 years and 9 months? - Timetable
If a train traveling between two cities increases the speed specified in the timetable by 5 km/h, it will arrive 20 minutes earlier. If it decreases it by 5 km/h, it will arrive 25 minutes later. How long is the route between the cities? - To a wholesaler
A farmer sold 10% of last year's corn crop to a wholesaler and a third of the rest to small buyers. He stored the remaining 270 tons of corn. How many tons of last year's corn crop did he sell?
- In a right triangle 13
The height of the hypotenuse is 4.8cm. The hypotenuses are in the ratio 4:3. Calculate the perimeter and area of a triangle. - Decadal - flower bed
The castle park includes a flower bed in the shape of a regular decagon with an area of 432.8 m². Determine the distance between the adjacent vertices of the flower bed. - Aluminum ignote
At what temperature did the temperature stabilize if an aluminum ignote weighing 45 kg and at a temperature of 15°C received 4.8 MJ of heat? The specific heat capacity of aluminum is 896 J/kg°C. - Specific heat
How much heat must we add to turn 25 kg of ice at a temperature of -15 degrees Celsius into water with a temperature of 23 degrees? Specific heat of fusion 333 kJ/kg. - By mass
How much heat must we supply to completely convert potassium weighing 45 kg at a temperature of 22.4 °C into potassium at a temperature of 98 °C? The specific heat of fusion is 25.5 kJ/kg, the melting point is 63.32 °C. The specific heat capacity of potas
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