Examples for secondary school students - page 95 of 237
Number of problems found: 4730
- In the dairy
The dairy had three times more milk packages than half a liter. Four times more liters remained when sold in 10 liters and 10 half-liter containers than in half-liter packages. How many packages were there originally? - Resistor parallel connection
Three resistors with resistances of 200 Ω, 400 Ω, and 600 Ω are connected next to each other (parallel). A current of 1.8 A flows through the first 200 Ω resistor. a) What current passes through the second and what current through the third resistor? b) W - Lowest voltage
Three resistors with resistors R1 = 10 kΩ, R2 = 20 kΩ, R3 = 30 kΩ are connected in series and an external voltage U = 30 V is connected to them. On which resistor is the lowest voltage? - Hospital death probability
Statistically, in a city of 100,000 inhabitants, 600 people die in one year. During the year, 2,000 people received hospital treatment, and 120 of them died there. Calculate the probability that a citizen who comes to the hospital for treatment will die t - Marathon training distance
Peter trains for a half marathon every day. He ran 1,000 m on the first day and increased the training length by 250 m daily. On a certain day, Peter ran 21 km in training. That day, he calculated the total distance he had run since the start of training. - Aircraft climbing
The average climb angle of the aircraft is 11° 20', and its average speed is 400 km/h. How long does it take to climb to a height of 3000 m? - Quadratic function graph
The quadratic function has the formula y = x²-2x-3. Sketch a graph of this function. Find the intersections with the axes. Find the vertex coordinates. - 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 - Scrap probability
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 at a speed of v₁ = 5 km/h. After 3 hours, a cyclist sets off from the same place at a speed of v₂ = 20 km/h. At the same time as the cyclist, a car starts from point B, which is 50 km away. Calculate the distance and time at wh - Birthday paradox
How large must a group of people be so that the probability of at least two people sharing a birthday is greater than 90%? - Probability - products
Based on previous inspection, it is known that 3% of defective products occur during the manufacturing of a certain product. a) Calculate the probability that among 100 randomly selected products there are exactly 2 defective ones, assuming each product i - 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? - Component failure probability
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.
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