Examples for secondary school students - page 99 of 232
Number of problems found: 4622
- Ball color probability
Determine the probability that three balls, ten red, and ten blue balls, will be drawn from 3 balls of the same color. - Cup saucer price
Four cups and one porcelain saucer cost € 140. Two cups and five saucers cost € 160. How much is a cup? - Five-gon
Calculate the side a, the circumference, and the area of the regular 5-angle if Rop = 6cm. - Fall sum or same
Find the probability that if you roll two dice, the sum of 10 will fall, or the same number will fall on both dice. - Four equation system
Solve a system of equations with four unknowns: 2a + 2b-c + d = 4 4a + 3b-c + 2d = 6 8a + 5b-3c + 4d = 12 3a + 3b-2c + 2d = 6 - Annulus
Two concentric circles with radii 1 and 9 surround the annular circle. This ring is inscribed with n circles that do not overlap. Determine the highest possible value of n. - Coordinates of a centroind
Let A = [3, 2, 0], B = [1, -2, 4], and C = [1, 1, 1] be 3 points in space. Calculate the coordinates of the centroid of △ABC (the intersection of the medians). - Roof metal consumption
The roof is a regular hexagonal pyramid shell with a wall height of v = 5 m and a base edge of a = 4 m. Calculate the consumption of sheet metal to cover the roof, assuming 15% losses. - Shop weekly earnings
They earned CZK 113,400 in the shop in four weeks. The first and fourth-week sales were the same, the second week 10% higher than the first week and the third week 5% lower than the first week. How much did they earn each week? - Powder box distribution
The store stacked two hundred boxes of washing powder in three piles. There were 13 more boxes in the first pile than in the second pile, one-fifth more in the second pile than in the third pile. How many boxes were in which pile? - Coal cart calculation
The miner removed 135 carts of coal in 5 days so that the next day he removed three carts of coal more. How many carts did he drive on the first day? - Money distribution calculation
Honza, Lucas, and David are to split CZK 5,400 so that Lucas receives CZK 400 more than Honza and David CZK 400 less than Honza. How much will each of them receive? - Number selection probability
If we choose four numbers from 1 - 20, what is the probability that 6 or 10 will be among them? - Aircraft altitude calculation
The aircraft flying just above point A can be seen from observation B, 2,400 meters away from point A, at an altitude of 52°30'. How high does the plane fly? - Corona virus
Calculate an estimate of the GDP (Gross Domestic Product) percentage that declined due to the quarantine related to the corona COVID-19 virus that lasted for two months. During this time, economic activity is down by 80%. - Wall thickness
The hollow metal ball has an outside diameter of 40 cm. Determine the wall thickness if the weight is 25 kg and the metal density is 8.45 g/cm³. - Big Earth
What percentage of the Earth's surface is seen by an astronaut from a height of h = 350 km? Take the Earth as a sphere with a radius R = 6370 km. - Railway vibration speed
The period of the natural oscillation of the railway car is 1.25s. The length of the rails is 25 m. At what speed does the vibration, caused by the impact of the wheels on the joints between the rails, reach a maximum? Give the result in m/s. - Self-oscillation period
The water in the vessel carried by the boy has a self-oscillation period of 0.8 s. What is the size of the boy's movement speed when the length of the boy's step is 60 cm? Give the result in m/s. - Tropics and polar zones
What percentage of the Earth's surface lies in the tropical, temperate, and polar zones? Tropics border individual zones at 23°27' and polar circles at 66°33'.
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