Examples for secondary school students - page 85 of 231

Number of problems found: 4613

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?
Bulb switch puzzle
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
Diagonal of the diamond
The ABCD diamond shape is known as diagonal u2 and a height v. Do an analysis.
Stoaches
Stoaches are fictional creatures distantly related to bigfoot and yeti. Stoach weights are normally distributed, with a mean of 904g and a standard deviation of 104g. State the probability that the sample mean of a random sample of 36 stoach weights excee
Kohlrabies
The price of one kohlrabi increased by € 0.40. The number of kohlrabies a customer can buy for € 4 has thus decreased by 5. Find out the new price of one kohlrabi in euros.
Temperature conversion calculation
When converting degrees Celsius (C) to degrees Fahrenheit (F), the relationship is used: F = C . 9/5 + 32. How many degrees Celsius are they in New York City if the thermometer reads 23 degrees Fahrenheit?
Shop weekly earnings
They earned CZK 98,400 in the shop in three weeks. The second week's sales were 20% higher than the first. The third week was 10% lower than the second week. How much did they earn each week?
Student math probability
There are 25 students in the class, 12 of whom are not ready for math. There are five students in the math class. What is the probability of at least 3 being math-ready?
Area and perimeter of rectangle
The rectangle area is 3000 cm², and one dimension is 10 cm larger than the other. Determine the perimeter of the rectangle.
Component deviation probability
There are 200 components in the production batch, of which 26 have a plus deviation from the nominal value. Calculate the probability that none of the 10 products selected will have a positive variance if we make selections without repetition
Larger perimeter
A square and a circle pass through two adjacent vertices of the square (endpoints of side a) and the center of the opposite side (c). Which of the plane shape has a larger perimeter?
The shooter
The shooter shoots at the target, assuming that the individual shots are independent of each other and the probability of hitting them is 0.2. The shooter fires until he hits the target for the first time, then stops firing. (a) What is the most likely nu
Side effect probability
The probability of an adverse drug reaction is 2.1%. How many people need to be prescribed for one patient to experience side effects with a chance of 90%?
Isosceles triangle
In an isosceles triangle ABC with base AB; A [3,4]; B [1,6] and the vertex C lies on the line 5x - 6y - 16 = 0. Calculate the coordinates of vertex C.
Inscribed and described circle
Find the radii of a circle inscribed and circumscribed by a regular pentagon whose side measures 3 cm.
Lesson variability comparison
In September, students missed the following number of lessons: Girls: 2; 0; 7; 8; 2; 2; 4; Boys: 4; 4; 0; 3; 10; 3; 8; Compare the variability of both statistical files.

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