Examples for secondary school students - page 83 of 229
Number of problems found: 4578
- Wedding guests
Fifteen wedding guests could not agree on who would stand in the wedding photo. The groom suggested that all possible sets of wedding guests be made in the photographs.
- Guests - party
There are 13 guests at each other's party. How many clicks will you hear?
- School committee
Seven students were elected to the school committee. How many ways can the President, Vice-President, Secretary, and Treasurer be selected?
- Participants 31351
How many ways can the first, second, and third prizes be awarded to the 15 participants in the math competition?
- General line equations
In all examples, write the GENERAL EQUATION OF a line that is given in some way. A) the line is given parametrically: x = - 4 + 2p, y = 2 - 3p B) the slope form gives the line: y = 3x - 1 C) the line is given by two points: A [3; -3], B [-5; 2] D) the lin
- Ten persons
Ten persons, each person, make a hand to each person. How many hands were given?
- Mixture of coffee
They have to prepare a coffee mixture in packing centers, so 1 kg costs 240 CZK. Two types of coffee are in stock at the prices of 220 CZK per 1 kg and 300 CZK per 1 kg. How many kilograms of each species need to be mixed to prepare 50 kg of the required
- Playing cards
From 32 playing cards containing eight red cards, we choose four cards. What is the probability that just two will be red?
- The ages
The ages of the four sons make an arithmetic sequence, the sum of which is the father's age today. In three years, the father's age will be the sum of the ages of the three eldest sons, and in the next two and three months, the father's age will be the su
- Tangents to ellipse
Find the magnitude of the angle at which the ellipse x² + 5 y² = 5 is visible from the point P[5, 1].
- Diver
Please calculate using Pascal's law. The window of the diving helmet has a surface area of about 7dm². What pressure force acts on the window at a depth of 20 meters below the water surface?
- Refractive index
The light passes through the interface between air and glass with a refractive index of 1.5. Find: (a) the angle of refraction if light strikes the interface from the air at an angle of 40°. (b) the angle of refraction when light hits the glass interface
- Probability 31101
There are 16 balls in the box, of which seven are white, and nine are blue. We randomly select two balls. What probability will there be exactly two white balls among the selected ones?
- The intersection of the diagonals
In the rectangular coordinate system, a rectangle ABCD is drawn. These coordinates determine the vertices of the rectangle: A = (2.2) B = (8.2) C = (8.6) D = (2.6) Find the coordinates of the intersection of the diagonals of the ABCD rectangle.
- Digging a pit
The pit has the shape of a regular quadrilateral truncated pyramid. The edges of the bases are 14m and 10m long. The sidewalls form an angle of 135° with a smaller base. Find how many m³ of soil were excavated when digging the pit.
- 9-gon pyramid
Calculate a nine-sided pyramid's volume and surface, the base of which can be inscribed with a circle with radius ρ = 7.2 cm and whose side edge s = 10.9 cm.
- There
There is a triangle ABC: A (-2,3), B (4, -1), C (2,5). Determine the general equations of the lines on which they lie: a) AB side, b) height to side c, c) Axis of the AB side, d) median ta to side a
- Exponential decay
A tank contains 55 liters of water. Water is flowing out at the rate of 7% per minute. How long does it take to drain the tank?
- Maximum of volume
The shell of the cone is formed by winding a circular section with a radius of 1. For what central angle of a given circular section will the volume of the resulting cone be maximum?
- Complexity 30631
Here, you have a task to think about but don't look for great complexity in it. You have 6 bulbs connected here. A to F and 6 switches No. 1 to No. 6. Your task will be to gradually determine which bulbs will always be on if any of the switches are in the
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