Harder math problems

Boys and girls
There are eight boys and nine girls in the class. There were six children on the trip from this class. What is the probability that: a) only boys went on the field trip b) just 2 boys went on the field trip
Cylinder
Calculate the dimensions of a cylindrical container with a volume of 10 litres if its height equals its base diameter.
Steeple
A church tower is seen from the road at an elevation angle of 52°. When we move back a further 29 metres, it is seen at an elevation angle of 21°. How tall is the tower?
Green - Red
We have 4 bags. Each consists of one green and 2 red balls. From each, we pull just one ball. What is the probability that we don't pull any green ball?
Diofant equation
In the set of integers (Z), solve the equation: 212x +316y =0 Write result with integer parameter t in Z (parameter t = ...-2,-1,0,1,2,3... if equation has infinitely many solutions)
Gutter
How much metal is needed to produce 60 pieces of gutter pipes with the diameter 17 cm and length of 6 m? The plate bends add 6% of the material.
Heron backlaw
Calculate the length of the unknown side of a triangle with sides 39 and 38 and area 438.6.
Disco
At the disco, there are 12 boys and 15 girls. In how many ways can we select four dancing couples?
Euclid3
Calculate the height and sides of the right triangle if one leg is a = 100 km and the section of hypotenuse adjacent to the second leg c_b = 14 km.
Train
The train is running at speeds of 98 km/h. From the beginning of braking to full stop, the train runs for 2 minutes. If the train slows the braking equally, calculate the distance from the location where you need to start to brake.
Tangents
From point R, two tangents are drawn to a circle with a radius of 41 cm. The distance between the two points of tangency is 16 cm. Calculate the distance from point R to the centre of the circle.
Rhombus 2
Calculate the rhombus area with a height v=48 mm and shorter diagonal u = 60 mm long.
Steps
How many steps do you save by walking diagonally across a square plot instead of walking along two of its sides, if the full perimeter takes 458 steps?
N-gon II
What is the side length of the regular 9-gon circumscribed circle of radius 13 cm?
Circle in rhombus
A circle is inscribed in a rhombus. The points of tangency divide each side into segments of length 14 mm and 9 mm. Calculate the area of the circle.
Cube - angles
Calculate the angle alpha (α) between the face diagonal and the base of a cube. Calculate the angle beta (β) between the space diagonal and the base of the cube.
Diagonals of the rhombus
Calculate the height of a rhombus whose diagonals are 18 cm and 6 cm.
Isosceles trapezoid
The bases of the isosceles trapezoid are in the ratio of 5:3. The arms have a length of 5 cm and height = 4.8 cm. Calculate the circumference and area of a trapezoid.
4s pyramid
A regular tetrahedral pyramid has a base edge a=8 and a collateral edge length b=20. What is its height?
Angle between lines
Calculate the angle between the following two lines: p: -4x +7y +7 =0 q: -x +4y +7=0

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