Examples for secondary school students - page 24 of 231
Number of problems found: 4620
- From experience
From the experience of an insurance company employee, it turned out that the insurance benefit under household insurance is more than 25,000 CZK with a probability of 0.3. What is the probability that among the next ten insurance claims there will be: a) - Function inverse square
The inverse function to the function f(x) = √(x-3) for x ≥ 3 is the function: - Cube small diagonal
The cube comprises 64 small cubes, each with an edge length of 15 mm. Calculate the wall length and body diagonals. - Point collinear coordinates
Given are points A [1;a2;a3], B [3;-4;-1], C [-3;-1;8]. Points A, B, and C lie in a straight line. Calculate the coordinates a2, a3 - Function graph intersection Determine the value of the number a so that the graphs of the functions f: y = x² and g: y = 2x + a have exactly one point in common.
- Centimeters - trapezoid
The area of the trapezoid is 132 cm². The difference in the length of both bases is 6 cm, and the height is 2 cm longer than the shorter base. Find the height of the trapezoid in centimeters. - Line perpendicular coordinate
The straight line p is given by the formula y = 1/2 x - 1 . The line q is perpendicular to the line p and passes through the point A [1; 5]. Determine the y-coordinate of the point that intersects the line q with the y-axis. - Avocado seed probability
The probability of sprouting each avocado pit is 0.9. We planted 3 stones. What is the probability that exactly two of them will grow? - Calculate cuboid
Given cuboid ABCDEFGH. We know that |AB| = 1 cm, |BC| = 2 cm, |AE| = 3 cm. Calculate in degrees the angle size formed by the lines BG and FH . - Cylinder express radius
Please express r from the formula for the surface of the cylinder. - Circle line intersection
Calculate the sum of the x-coordinates of the intersections of the circle given by the equation (x - 1)²+ y² = 1 and the line given parametrically x = t, y = t , where t∈R. - Radiation shield
Determine what thickness of the shielding material will be required if we reduce the radiation to 3% of the original value if we know that a thickness of 6 mm will reduce the level of the same radiation by 9%. Round up to the whole value in millimeters (t - Odd number sum
Determine the sum of all positive odd numbers less than 78 - Conductor charge transfer
Conductor A has an electrical potential of +140V concerning the Earth; conductor B has a potential of -60V. How much electric charge will we transfer from wire B to wire A if we do the work of 4.10-4 Joules? - Circle distance ratio
What is the ratio of the distance of the nearest and farthest point of the circle described by the equation x2+y2-16x-12y+75=0 from the origin of the coordinate system? - Editor bonus division
To the three editors - Brandon, Lubosh, and Lucy - the publishing house owner wants to divide the extraordinary bonus of 1000 euros so that Lubosh gets twice as much as Lucy and Lucy receives three times as much as Brandon. How many euros will each of the - Geometric sequence sum
Calculate the sum of the first 9 terms of the geometric sequence if a3 equals 2 and a4 equals 8. - Height of poplar
From the 40 m high observation deck, you can see the top of the poplar at a depth angle of 50°10' and the bottom of the poplar at a depth angle of 58°. Calculate the height of the poplar. - Probability - shelf
Ten books are placed randomly on one shelf. Find the probability that certain three books are placed next to each other. - Strudel piece length
Mom divided the strudel among her three sons. First, she cut off 1/3 of the strudel. She split the rest in a ratio of 2:3. The difference between the longest and shortest pieces is 4 cm. Determine the length of the strudel in cm.
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