# Basic functions - problems - page 27

1. Shape
Plane shape has a maximum area 677 mm2. Calculate its perimeter if perimeter is the smallest possible.
2. A family
A family of four pays for garbage collection per year 1800 Kč. How many crowns a year the waste company get from the house where lives 93 people?
3. Trains
Daily passes the same track section 8 pairs of trains with average 2400 passagers. How many people average travel in one train?
Practitioners lined up in rectangle with row with four, five or six exercisers, one always missing to full rectangle. How many exercisers were on the field, if they have estimated not been more than 100?
5. Unknown integer
Find the smallest integer that: divided by 2, the remainder is 1 divided by 3 the remainder is 2, divided by 4 remainder is 3, ... divided by eight reminder is 7, by 9 reminder is 8.
6. ICE train
German runways test a new ICE train between Munich and Berlin. The train runs to Berlin at a slow speed of 100 km/h. Back from Berlin goes faster. How quickly did the train have to go on a return trip so that the total average train speed for both journeys
7. Cinema
How many ways can be divided 11 free tickets to the premiere of "Jáchyme throw it in the machine" between 6 pensioners?
8. Brick
Isosceles scale has on one side all brick and second weight 1 kg and 1/4 of brick. The balance is in equilibrium. What is the weight of a brick?
9. Painting
Jožko with Fero painted the bench for four hours. How many hours would take work if four friends help him?
10. Automaker
The automaker now produces daily 4 new cars more than last year so the production of 360 cars will save just one full working day. How many working days to produce 360 vehicles needed last year?
11. Tournament
Determine how many ways can be chosen two representatives from 34 students to school tournament.
12. Minute hand v2
In how many minutes describe the minute hand angle 60 degrees?
13. Disinfecting solution
How much distilled water is necessary to pour into 500 ml of 33% hydrogen peroxide solution to obtain 3% disinfecting solution?
14. Seating rules
In a class are 24 seats but in 7.B class are only 18 students. How many ways can student seat? (The class has 12 benches. A bench is for a pair of students.) Result (large number) logarithm and thus write down as powers of 10.
15. Class 8.A
Three quarters of class 8.A went skiing. Of those who remained at home one third was ill and the remaining six were on math olympic. How many students have class 8.A?
16. Angles ratio
The internal angles of a triangle are in ratio 1:4:5 What kind of triangle is it? (solve internal angles and write down and discuss)
17. Angle
A straight line p given by the equation ?. Calculate the size of angle in degrees between line p and y-axis.
18. Cows
20 cows has food for 60 days. We reduce the dose to two-thirds for 18 cows. How many days will be fed?
19. Book
Calculate the thickness of the page of the collection of examples from mathematics, where 4.87 cm thick and has 451 pages.
20. Sum-log
The sum of two numbers is 32, the sum of their logarithms (base 10) is 2.2. Determine these numbers.

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