# Examples for secondary school students - page 54

- Paper box

Hard rectangular paper has dimensions of 60 cm and 28 cm. The corners are cut off equal squares and the residue was bent to form an open box. How long must be side of the squares to be the largest volume of the box? - Hockey match

The hockey match ended with result 3:1. How many different storylines may have the match? - Five members

Write first 5 members geometric sequence and determine whether it is increasing or decreasing: a_{1}= 3 q = -2 - Truncated cone 3

The surface of the truncated rotating cone S = 7697 meters square, the substructure diameter is 56m and 42m, determine the height of the tang. - Alcohol mixture

From 55% and 80% alcohol we have to produce 0.2 kg of 60% alcohol. How many of them do we use in solution? - Average

If the average(arithmetic mean) of three numbers x,y,z is 50. What is the average of there numbers (3x +10), (3y +10), (3z+10) ? - Threesome

Dana, Dalibor and Michael have a combined 57 years. Dana is five years older than Dalibor, but Dana is five years younger than Michael. Determine how old is Dana, Dalibor and Michael. - Internal angles

Find the internal angles of the triangle ABC if the angle at the vertex C is twice the angle at the B and the angle at the vertex B is 4 degrees smaller than the angle at the vertex A. - Banknotes

$ 1390 was collected. How much was in $20 notes and how many in $50 notes in that order? How many solutions exists? - Wall height

Calculate the surface and volume of a regular quadrangular pyramid if side a = 6 cm and wall height v = 0.8dm. - Repair company

The company repairs cars. The first day repair half of the contract second day, the half of the rest and third day 8 residue cars. How many total cars company repaired? - Four integers

Fnd four consecutive integers so that the product of the first two is 70 times smaller than the product of the next two. - Tenth member

Calculate the tenth member of geometric sequence when given: a_{1}=1/2 and q=2 - The swing

To swing the two girls. Aneta weight 45 kg and Simon 35 kg weight. How far should sit Simon from the middle of swing so it is balanced, if we know that Aneta is sitting at distance 1,5m? How far are girls sitting apart? - Variable

Find variable P: PP plus P x P plus P = 160 - Candy - MO

Gretel deploys to the vertex of a regular octagon different numbers from one to eight candy. Peter can then choose which three piles of candy give Gretel others retain. The only requirement is that the three piles lie at the vertices of an isosceles triang - Probability

What are the chances that the lottery, in which the numbers are drawn 5 of 50 you win the first prize? - Electricity consumption cost

Last year Karol family reduced its electricity consumption by 31% compared to the previous year and paid CZK 2883 less. How many CZK is electricity last year and how many two year ago? - Difference of two number

The difference of two numbers is 20. They are positive integers greater than zero. The first number raised to one-half equals the second number. Determine the two numbers. - Daily temperature

The average of daily temperature measurements in one week every day at the same hour was -2.8 °C. All temperatures were measured in different days are different. The highest daily maximum temperature was 2.4 °C, the lowest -6 °C. Determine the options tha

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