# Examples for secondary school students - page 65

- Three students

Three students independently try to solve the problem. The first student will solve a similar problem with a probability of 0.6, the second student will solve at a probability of 0.55, and the third will solve at a probability 0.04. The problem is resolved - Peroxide

How many ml 30% of peroxide (H2O2) should be poured into 100ml H2O to give a 20% solution? - Tetrahedron

What is the angle of the sides from the base of a three-sided pyramid where the sides are identical? - Exponential equation

Determine the value of having y in the expression (3^y): (4^-1)=36.Y is a natural number greater than zero. - Diagonals

What x-gon has 54 diagonals? - Average age

The company of five people has an average age of 46 years. The average age of the first four is 43 years. How many years has the fifth member of this company? - Utopia Island

A probability of disease A on the island of Utopia is 40%. A probability of occurrence among the men of this island, which make up 60% of all the population (the rest are women), is 50%. What is the probability of occurrence of A disease among women on Uto - Cube edges

If the edge length of the cube increases by 50%, how does the volume of this cube increase? - Two diggers

Two diggers should dig a ditch. If each of them worked just one-third of the time that the other digger needs, they'd dig up a 13/18 ditch together. Find the ratio of the performance of this two diggers. - Six terms

Find the first six terms of the sequence a1 = -3, an = 2 * an-1 - PIN code

PIN on Michael credit card is a four-digit number. Michael told this to his friend: • It is a prime number - that is, a number greater than 1, which is only divisible by number one and by itself. • The first digit is larger than the second. • The second. - Hyperbola

Find the equation of hyperbola that passes through the point M [30; 24] and has focal points at F1 [0; 4 sqrt 6], F2 [0; -4 sqrt 6]. - Functions f,g

Find g(1) if g(x) = 3x - x^{2}Find f(5) if f(x) = x + 1/2 - Pravoúhly trojúhelník

Určete obsah pravoúhlého trojúhelníku, jehož délky stran tvoří po sobě jdoucí členy aritmetické posloupnosti a poloměr kružnice opsané tomuto trojúhelníku je 5 cm. - Right angled triangle 3

Side b = 1.5, hypotenuse angle A = 70 degrees, Angle B = 20 degrees - Variability

In the table bellow the number of wrong produced goods in two shifts: morning shift: 2; 0; 6; 10; 2; 2; 4; 2; 5; 2; afternoon shift: 4; 4; 0; 2; 10; 2; 6; 2; 3; 10; Compare the variability in both shifts, compare the average number of wrong goods on both - Isosceles triangle

The leg of the isosceles triangle is 5 dm, its height is 20 cm longer than the base. Calculate base length z. - Quadratic equation

Find the roots of the quadratic equation: 3x^{2}-4x + (-4) = 0. - Population growth

How many people will be on Earth from two people for 5,000 years, if every couple has always 4 children, (2 boys and 2 girls) at the age of 25-35, and every man will live 75 years? - Sixty

Sixty percent of one-fifteen of the total is equal to thirty. What are two percent of the total?

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