# Basic functions - problems

1. Lathe
95% of the components manufactured on the lathe comply with the standard, of which 80% of the components are first-class. How likely can we expect a manufactured part to be first class?
2. Former price
The price of an article is cut by 10℅, to restore it to the former value, by what percent the new price must be increased?
3. Percent change
If the length of a rectangle is increased by 25% and the width is decreased by 10%, the area of the rectangle is larger than the area of the original rectangle by what percent?
4. Tourist
A tourist walked an average speed of 3.5 km/h route in 6 hours. Calculate how many hours he would have passed at an average speed of 5.5km/h.
5. Pupils
There are 27 pupils in the classroom. They can swim 21 and ski nine pupils. Neither swim nor ski three pupils. How many pupils can swim and ski?
6. Down syndrome
Down syndrome is one of the serious diseases caused by a gene mutation. Down syndrome occurs in approximately every 550-born child. Express the incidence of Down's syndrome in newborns at per mille.
Marie wants to make a cone-shaped witch's hat for a masquerade ball. How much material will it need if it counts on an annular rim with diameters of 28cm and 44cm? Hat side length is 30cm. Add 5% of the material to the bust. Round to cm2.
8. Dog price
Tereza agreed to get a dog and 6000 crowns a year for help in a dachshund breeding station. After eight months she had to finish work and got a dog and 2000 crowns. What price does a dog have?
9. Castle tower
The castle tower has a cone-shaped roof with a diameter of 10 meters and a height of 8 meters. Calculate how much m² of coverage is needed to cover it if we must add one-third for the overlap.
10. Probability of intersection
Three students have a probability of 0.7,0.5 and 0.4 to graduated from university respectively. What is the probability that at least one of them will be graduated?
11. Friction coefficient
What is the weight of a car when it moves on a horizontal road at a speed of v = 50 km/h at engine power P = 7 kW? The friction coefficient is 0.07
12. Medians 2:1
Median to side b (tb) in triangle ABC is 12 cm long. a. What is the distance of the center of gravity T from the vertex B? b, Find the distance between T and the side b.
Lucy, Tereza, and Petra decided to compile the compulsory reading records together. It would take 30 days for Lucia alone, 36 for Tereza and 45 for Petra. How long will take make records if they will work together?
14. Iron pole
The iron pole is in the ground 2/5 of its length, partly above the ground 1/3 is yellow, and the unpainted section is 6 m long. How long is the entire column?
15. Cyclist
Cyclist drives 5 km in half an hour, how long will drive in 3 hours?
16. Cook on gas
The gas cylinder will last for 30 weekends for 2 hours of daily cooking. How many days will we be able to cook on a new cylinder when we cook 3 hours a day?
17. Dance group
The dance group formed groups of 4, 5, and 6 members. Always one dancer remains. How many dancers were there in the whole group?
18. A jackpot
How many times must I play this jackpot to win? A jackpot of seven games having (1 X 2), i. E. , home win or away win.
19. Barter
There is exchange trade on the market. We know that for two sheepskins we get three goat skins. We also know that for six rabbits skins we get four goat skins. How many rabbit's skins we get for four sheepskins?
20. Uphill and downhill
The cyclist moves uphill at a constant speed of v1 = 10 km/h. When he reaches the top of the hill, he turns and passes the same track downhill at a speed of v2 = 40 km/h. What is the average speed of a cyclist?

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