Examples for secondary school students - page 39

Tubes
Iron tubes in the warehouse are stored in layers so that each tube top layer fit into the gaps of the lower layer. How many layers are needed to deposit 100 tubes if top layer has 9 tubes? How many tubes are in bottom layer of tubes?
Annual income
The annual incomes (in thousands of $) of fifteen families is: 60, 80, 90, 96, 120, 150, 200, 360, 480, 520, 1060, 1200, 1450, 2500, 7200 Calculate harmonic and geometric mean.
James
James paints a fence. If every day instead of 14 planks painted 16 would be done on one day earlier. How many of planks has a fence altogether?
Hexagon rotation
A regular hexagon of side 6 cm is rotated through 60° along a line passing through its longest diagonal. What is the volume of the figure thus generated?
Inscribed circle
Write the equation of a incircle of the triangle KLM if K [2,1], L [6,4], M [6,1].
Square ABCD
Construct a square ABCD with cente S [3,2] and the side a = 4 cm. Point A lies on the x-axis. Construct square image in the displacement given by oriented segment SS'; S` [-1 - 4].
Equation
How many real roots has equation ? ?
Two triangles SSA
Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles. A = 59°, a = 13, b = 14
Cleaners
Milan would clean up the room for 2.5 hours, Eric would take 10 hours. How long they swept the room together?
Diamond diagonals
Calculate the diamond's diagonal lengths if its content is 156 cm² and the side length is 13 cm.
Prism
Base of perpendicular triangular prism is a right triangle with cathetuses 4.5 cm and 6 cm. What is the surface of the prism, if its volume of 54 cubic centimeters.
Four sides of trapezoid
In the trapezoid ABCD is |AB| = 73.6 mm; |BC| = 57 mm; |CD| = 60 mm; |AD| = 58.6 mm. Calculate the size of its interior angles.
Null points
Calculate the roots of the equation: ?
Clock face
clock face is given. Numbers 10 and 5, and 3 and 8 are connected by straight lines. Calculate the size of their angles.
Win in raffle
The raffle tickets were sold 200, 5 of which were winning. What is the probability that Peter, who bought one ticket will win?
Crates 2
In 6 crates is 45 kg of apples In 5 crates is equally In 1 in crate is 3 kg more How many kilograms in each crate?
Hockey game
In the hockey game was made 6 goals. Czech played against Finland. Czechs won 4:2. In what order to fall goals? How many game sequence was possible during the game?
Double-track
On double-track express met with a freight train. Express travel at speed 72 km/h, a freight train at speed 36 km/h. After what time period will be from 9 km apart?
High wall
I have a wall 2m high. I need a 15 degree angle (upward) to second wall 4 meters away. How high must the second wall?
Powers
Express the expression ? as the n-th power of the base 10.

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