# Grade - examples - page 126

1. Water channel
The cross section of the water channel is a trapezoid. The width of the bottom is 19.7 m, the water surface width is 28.5 m, the side walls have a slope of 67°30' and 61°15'. Calculate how much water flows through the channel in 5 minutes if the water flow
2. Octagonal mat
Octagonal mat formed from a square plate with a side of 40 cm so that every corner cut the isosceles triangle with leg 3.6 cm. What is the content area of one mat?
3. Three friends
Three friends divided the profit 104,650 CZK, so that for every 4 CZK, which got the first friend equals 5 crowns for second and for every 9 CZK, which got the second equals 16 CZK for third. Question: Who got the most and how much.
4. Positive number z
Positive number z is 10% greater than the number y. How many % is y smaller than z? Report the result rounded to one decimal place.
5. Roots
Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
6. Value of teeth
To know value to the healthy teeth we discover only when we take care about tooth caries followed by loss of teeth and think how to replace missing teeth... Calculate the value (cost of money) healthy teeth, if we assume that man has with 32 teeth and rep
7. Pitcher
Matthew picked up half-pitcher of raspberry in 45 minutes. Find how long three children filled the pitcher if each of them working at the same pace as Matthew.
8. Water tank
The water tank has a cylindrical shape with a base diameter of 4.2 m and is 80 cm deep. How many minutes will take fill it 10 cm below the edge of the tank if water flowing 2 liters per second?
9. LCM
Common multiple of three numbers is 3276. One number is in this number 63 times, second 7 times, third 9 times. What are the numbers?
10. Two rulers
We have two rulers. Scale interval on first rulers are a spaced 1 cm and on second spaced 15 mm. Rulers are attached to each other so that they match initial divider commas. What next dividers commas coincide? Find at least three cases.
11. Costume
Denisa is preparing for a goldsmith's costume carnival. During the preparations, she thought she would let her hair wipe instead - she would apply a 5 μm thick layer of gold to each hair. How much gold would Denisa need? Assume that all hundred thousand De
12. Concrete pipe
How much will cost cover a 6 m long concrete pipe with an outer radius 1.5 m and inner radius 0.8 meters if 1 m2 paint costs 24 €.
13. Six years
In six years Jan will be twice as old as he was six years ago. How old is he?
14. Pulley
On wheels with a diameter of 40 cm is fixed rope with the load. Calculate how far is load lifted when the wheel turns 7 times?
15. Internal angles
One internal angle of the triangle JAR is 25 degrees. The difference is the size of the two other is 15°. Identify the size of these angles.
16. Store
Peter paid in store 3 euros more than half the amount that was on arrival to the store. When he leave shop he left 10 euros. How many euros he had upon arrival to the store?
17. Four sided prism
Calculate the volume and surface area of a regular quadrangular prism whose height is 28.6cm and the body diagonal forms a 50 degree angle with the base plane.
18. Star equation
Write digits instead of stars so that the sum of the written digits is odd and is true equality: 42 · ∗8 = 2 ∗∗∗
19. Bridge piers
One quarter of the bridge pier is sunk into the ground. Two thirds are in the water. Protruding above the water is 1.20 m long. Determine the height of bridge piers.
20. Mom and daughter
Mother is 39 years old. Her daughter is 15 years. For many years will mother be four times older than the daughter?

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