Harder math problems - last page

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 rotating cylindrical containers with volume 10 l if the container's height is equal to the base's diameter.
Steeple
The church tower is seen from the road at an angle of 52°. When we zoom out to 29 meters away, it can be seen at an angle of 21°. How high is it?
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 unknown side in 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
To circle with a radius of 41 cm from the point R guided two tangents. The distance of both points of contact is 16 cm. Calculate the distance from point R and circle center.
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 if you go square estate for diagonal (crosswise) rather than circumvent the two sides of its perimeter with 458 steps?
N-gon II
What is the side length of the regular 9-gon circumscribed circle of radius 13 cm?
Circle in rhombus
An inscribed circle is in the rhombus. Contact points of touch divide the sides into parts of length 14 mm and 9 mm. Calculate the circle's area.
Cube - angles
Calculate the angle alpha (α) between the wall diagonal and cube base. Calculate the angle beta (β) between the cube body diagonal and the cube base.
Diagonals of the rhombus
Calculate the height of the 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=17 and a collateral edge length b=32. What is its height?
Angle between lines
Calculate the angle between these two lines: p: -4x +7y +7 =0 q: -x +4y +7=0

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