Examples for secondary school students - page 22 of 231

Number of problems found: 4606

Temperature 83492
How much heat is needed to turn 1kg of ice at a temperature of -10℃ into steam at a temperature of 100℃?
Calculate
A bicycle rotates with a frequency of f= 25 Hz. By braking, its rotation can be slowed down evenly and the bicycle stops after a time of t0= 30 s from the start of braking. Calculate the angular acceleration Ԑ and the number of revolutions the bicycle mak
Coordinates of line points
I have a point A=[2,1] and a line y+x-5=0. How do I determine the coordinates of point A', which is the image of point A according to the given straight line?
Numbers 6D
Find out how many natural six-digit numbers exist whose digit sum is four.
Lifetime - bell curve
Laser lifetime follows a normal distribution with a mean of 7000 hours and a standard deviation of 600 hours. What is the probability that the laser will fail before 6000 hours? What is the probability that the laser will last at least 7500 hours?
Distance
If Danka increases her walking speed by 1km/h, she will cover a distance greater than 20 km in 4 hours. If she decreases her speed by 1km/h, she will not cover more than 20 km in 5 hours. At what speed did Danka walk? (s=v. t;s- distance, v- speed, t- tim
Circumscribed circle ABC
Triangle ABC, with sides a = 15 cm, b = 17.4 cm, and c = 21.6 cm, is circumscribed by a circle. Calculate the area of the segments determined by the sides of the triangle.
Circumscribed triangle
Calculate the radius of the circle of the circumscribed triangle, which has side dimensions of 8, 10, and 14 cm.
Playmakers + coach
In a basketball game, two pivots, two wings, and one point guard play. The coach has three pivots, four wing players, and two playmakers available on the bench. How many different five players can a coach send to the board during a game?
Components 83328
Divide the number 112 into three components, x, y, and z, so that x: y = 7: 5 and y: z = 3: 4 apply.
Refrigerator, lemonades
How many possible ways can we store three lemonades, four mineral waters, and two juices in the refrigerator next to each other?
Married pairs
In how many ways can we seat five guests at a table, two of whom are married and want to sit next to each other?
Probability - defective parts
There are 10 parts in the box, and 3 of them are defective. Let's choose 4 components at random. What is the probability that it will be among them a) 0 defective, b) just one defective component, c) just two defective components, d) exactly 4 defective c
Acceleration 83305
A body of mass 500 kg is lifted with a uniformly accelerated rectilinear motion using a rope. Determine the acceleration at which the rope breaks if it sustains a load of 15,000 N.
Acceleration 83304
The acceleration of a mass point during its rectilinear movement decreases uniformly from the initial value a0 = 10 m/s2 at time t0 = 0 to a zero value for a period of 20 s. What is the speed of the mass point at time t1 = 20 s, and what is the path of th
Arithmetic 83270
Marks with equal weight 2,1,3,2,2,3,1,3,1,1,2,4,2,2,3,1,1,2,1,3 specify: 1) arithmetic mean 2) absolute and relative frequency 3) mode and median 4) create a chart
Probability - coloured balls
The cube has 6 blue, 8 red, and 10 green balls. The player randomly draws 3 balls. Determine the probability that he draws balls of the same color.
Deposited 83235
A student deposited €500 in a savings bank at 2.5% interest. In what time (in years) will he earn as much interest as he invested?
Mechanical 83220
An airplane weighing 100 tons flies at an altitude of 11 km at a speed of 850 km/h. What is its kinetic, potential, and total mechanical energy?
CFO Director
The financial director has determined the following profitability scenarios for the profitability of the new branch of the company: Profit of 5 million CZK with probability 0.1. Profit of 3 million CZK with probability 0.3. Profit of 1 million CZK with pr

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