Harder math problems - page 2 of 5

Event probability
The probability of event P in 8 independent experiments is 0.33. What is the probability that the event P occurs in one experiment (chance is the same)?
Cylinder - basics
Cylinder with base radius r = 54 cm and height h=35 cm. Calculate: a) Area of the base
Sphere in cone
A sphere of radius 3 cm describes a cone with minimum volume. Determine cone dimensions.
Motion
If you go at speed 5.5 km/h, you come to the station 33 minutes after leaving the train. If you bike to the station at speed 29 km/h, you come to the station 52 minutes before its departure. How far is the train station?
Tetrahedral pyramid
Calculate the volume and surface area of a regular tetrahedral pyramid, its height is $b cm, and the length of the edges of the base is 6 cm.
Earth parallel
Earth's radius is 6370 km long. Calculate the length parallel to latitude 50°.
Dices throws
What is the probability that the two throws of the dice: a) Six falls even once b) Six will fall at least once
Pairs
At the table sit 10 people, 5 on one side and 5 on the other side. Among them are 3 pairs. Every pair wants to sit opposite each other. How many ways can they sit?
Euclid3
Calculate the height and sides of the right triangle if one leg is a = 81 cm and the section of hypotenuse adjacent to the second leg c_b = 39 cm.
Bridge
The bridge arc has a span of 72 m and height 5 m. Calculate the radius of the circle arc of this bridge.
Interested 7090
We call a natural number N bombastic if it contains no zero in its notation and if no smaller natural number has the same product of digits as the number N. Charles first became interested in bombastic prime numbers and claimed that there were not many of
Components
The 8 white, 4 blue, and 2 red components are in the box. What is the probability that we pull one white, one blue, and one red component without returning it?
One green
In the container are 45 white and 15 green balls. We randomly select five balls. What is the probability that there will be one green ball maximally?
R Trapezium
Rectangular trapezium has bases 21 and 10 and area 92 cm². What is its perimeter?
Circle arc
The circle segment has a circumference of 135.26 dm and 2096.58 dm² area. Calculate the radius of the circle and the size of the central angle.
Hypotenuse and height
In a right triangle is length of the hypotenuse c = 56 cm and height h_c = 4 cm. Determine the length of both triangle legs.
Peroxide
How much-distilled water (in liters) must pharmacists pour into 300 ml of 23.6% solution of hydrogen peroxide to get 2.7% solution to gargle?
Tower
The top of the tower is a regular hexagonal pyramid with a base edge 6.1 meters long and a height 11.7 meters. How many m² of the sheet is required to cover the top of the tower? We must add 9% of metal for waste.
Hands
The clock shows 12 hours. After how many minutes will the angle be between the hour and minute hand 90°? Consider the continuous movement of both hands for hours.
Rotating cone II
Calculate the area of the surface of a rotating cone with base radius r=15 cm and height h=13 cm.

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