The following two sets are given: G = {1, 2, 3; 4, 6, 12} , H = {1, 2, 4, 8, 16}.

Determine the elements of the following two sets: $G\cap H$ and $H\setminus G$!

If 1 kg of salami is 2800 HUF, how much will cost 35 dkg salami?

Solve the following equation on the set of real numbers!

Round your answer to three decimal places!

${2}^{x}=10$

Enter the logical value (true or false) of the following statements.

A: If a number is divisible by 6 and 8, it can also be divisible by 48.

B: If every digit of a positive integer is divisible by 3, then the number can also be divisible by 3.

C: The largest common divisor of 48 and 120 is 12.

The fourth member of the arithmetic series is 7, and the fifth is -5.

Determine the first member of the series!

Draw the graph of the function $x\to \left|x-2\right|-3$ on interval [–3; 6]!

Solve the equation sin x = 1 over a set of real numbers!

The class organizes a lottery with three numbers from numbers: 1, 2, 3, 4, 5 . Tom markes 2, 3 and 5 number on the coupon.

Calculate the probability that Tom will have a total win!

Solve the following equation on the set of real numbers!

$$7-2\left(x+5\right)=\frac{x+6}{4}+\frac{x+2}{2}$$

Length of the sides of cyclic trapezoid are: AB = 5 cm, BC = 2,5 cm, CD = 2 cm and DA = 2,5 cm.

a) Calculate the angles of the trapezoid!

b) Determine the ratio of ABC and ACD triangles!

c) The inner angles of the trapezoid are marked with an arc of 5 mm radius. Calculate the sum of the four arc lengths!