# Grade - examples - page 77

1. Rectangle and circle
The rectangle ABCD has side lengths a = 40 mm and b = 30 mm and is circumscribed by a circle k. Calculate approximately how many cm is circle long.
2. Vector
Determine coordinates of the vector u=CD if C[19;-7], D[-16,-5].
3. The dice
What is the probability of events that if we throw a dice is rolled less than 6?
4. Trees
Loggers wanted to seed more than 700 and less than 800 trees. If they seed in rows of 37, left them 8 trees. If they seed in rows of 43, left the 11 trees. How many trees must seed ?
5. Machines 2
2 machines for 50 hours produces 2,000 products. How many machines need to buy to make in 30 hours 15,000 products?
6. Oil tank and pipes
The underground oil tank can be filled by two oil pipelines. The first is filled in 72 hours and the second in 48 hours. How many hours from the moment when first pipeline began to fill the oil is it necessary to start filling it with the second to fill in
7. Octagon from rectangle
From tablecloth rectangular shape with dimensions of 4 dm and 8 dm we cuts down the corners in the shape of isosceles triangles. It thus formed an octagon with area 26 dm2. How many dm2 we cuts down?
8. Relay-race
Kate ran 170 meters at 29.8 seconds, Suzan at 29.3 seconds, Roza at 34 seconds and Žofka at 30.4 seconds. How long took to run 4x170 m relay-race?
9. Thales
Calculate the length of the Thales' circle described to right triangle with hypotenuse 18.4 cm.
10. Rectangle
The rectangle is 18 cm long and 10 cm wide. Determine the diameter of the circle circumscribed to rectangle.
11. Hearts
5 cards are chosen from a standard deck of 52 playing cards (13 hearts) with replacement. What is the probability of choosing 5 hearts in a row?
12. Chord MN
Chord MN of circle has distance from the center circle S 120 cm. Angle MSN is 64°. Determine the radius of the circle.
13. Chicken and rabbits (classic)
Grandmother breeding chickens and rabbits. It found that the yard has 35 heads and 108 legs. How many chickens and rabbits breeding in the yard?
14. Water in body
Water in the human organism of all the compounds represented, constitutes about 3/5 of the total weight. How many kilograms of water is in your body when you weigh 67 kg?
15. Total displacement
Calculate total displacement of the 4-cylinder engine with the diameter of the piston bore B = 6.6 cm and stroke S=2.4 cm of the piston. Help: the crankshaft makes one revolution while the piston moves from the top of the cylinder to the bottom and back.
16. Clocks
How long track travel the second hand in 46 hours, the end of which is 4 cm long.
17. Deposit 3
After a year had Martin on bank account € 2028. What was the interest rate when the initial deposit was € 1879?
18. Tractors
6 tractors started plowing the field that them together take 12 days. Agronomist hesitates to A) after 2 days to withdraw 2 tractors, or B) after 3 days to withdraw 3 tractors. Help him which of these two cases will be plowing done sooner.
19. Gravel - cone
Mound of gravel has shape of regular circular cone with a height 3.3 meter and a base circumference of 18.85 meters. How many cubic meters of gravel are in the pile? Calculate the weight of gravel if its density is p = 640 kg / cubic m.
20. Bakery
How heavy must prepare bread at a bakery if lose during baking 16% of water and after baking must have 2 kg? (Calculate to the nearest gram)

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