# Grade - examples - page 71

1. Parallelogram +ľ
| AB | = 76cm, | BC | = 44cm, angle BAD = 30 °. Find the area of the parallelogram.
2. Three numbers
The sum of the three numbers is 287. These numbers are in a ratio of 3: 7: 1/4 Define these numbers
3. Two boxes-cubes
Two boxes cube with edges a=38 cm and b = 81 cm is to be replaced by one cube-shaped box (same overall volume). How long will be its edge?
4. Medal
Calculate the approximate weight of the gold Olympics medal, if its diameter is 8 cm and a thickness 6 mm. The density of gold find out in the tables or on the Internet.
5. Popsicles
Francis went to buy ice lollies. If he buy 8 popsicles he missed 4 USD. When he buy 7 popsicles, got back 1 USD. How many USD was a popsicle?
6. Daughters
The man conducting the census asks a woman to age of three daughters. Woman says when multiply the age getnumber 72; if their ages add up, get a number of our house, as you see. The man says: That is not enough to calculate their ages. She says: my oldes
7. Nuts, girl and boys
Milena collected fallen nuts and called a bunch of boys let them share. She took a condition: the first boy takes one nut and tenth of the rest, the second takes 2 nuts and tenth new rest, the third takes 3 nuts and tenth new rest and so on. Thus managed.
8. Bicycles
You're the owner of the transport 's learning playground. Buy bicycles of two colors but you've got to spend accurately 120000 Kč. Blue bike costs 3600Kč and red bicycle 3200Kč.
9. Acute angles
Sizes of acute angles in the right-angled triangle are in the ratio 1: 3. What is size of the larger of them?
10. Equator
Suppose that tourist went on foot over the Globe equator. How many meters more track made ​​his hat on his head as the shoes on your feet? The radius of the earth is 6378 km and height of the tourist is 1.7 m.
11. Motion 2
At 10 o'clock started from place A car speed at 90 km/h. 20 minutes after started from the place B at speed 60 km/h another car. Distance places A and B is 120 kilometers. What time and where they meet?
12. Cuprum
From 1600 mm long sheet of copper plate 2 mm thickness we have separated over the whole length the belt weighing 6000 g. Calculate belt width if 1 dm3 copper weighs 8.9 kg.
13. Decibel
A circuit has an input power of 58 mW. Its output power is 6 mW. What is the loss in decibels?
14. One and a half chicken
One and a half chicken bears one and a half egg in one and a half day. How many eggs can withstand from 6 chicken in 6 days?
15. Freight and passenger car
The truck starts at 8 pm at 30 km/h. Passenger car starts at 8 pm at 40 km/h. Passenger arrives in the destination city 1 hour and 45 min earlier. What is the distance between the city of departure and destination city?
16. Scale of the map
Determine the scale of the map, which is the actual distance of 120 km l represented by segment long 6 cm.
17. 3d vector component
The vector u = (3.9, u3) and the length of the vector u is 12. What is is u3?
18. Concentric circles
In the circle with diameter 19 cm is constructed chord 9 cm long. Calculate the radius of a concentric circle that touches this chord.
19. Isosceles IV
In an isosceles triangle ABC is |AC| = |BC| = 13 and |AB| = 10. Calculate the radius of the inscribed (r) and described (R) circle.
20. Digging companies
Company A would dig a pit for 12 days, company B for 15 days, company C for 20 days and the company D for 24 days. Work began together companies C and D, but after three days joined them other two companies. How long took to dig a pit?

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