# Examples for 9th grade - page 57

1. Plan scale
At what scale is drawn plan of the building, where one side of the building is 45 meters long is on the plan expressed by a straight line 12 mm long.
2. Is right?
Determine whether the triangle with legs (catheti) 19.5 cm and 26 cm and length of the hypotenuse 32.5 cm is rectangular?
3. Triangle midpoints
Determine coordinates of triangle ABC vertices if we know tirangle sides midpoints SAB [0;3] SBC [1;6] SAC [4;5], its sides AB, BC, AC.
4. Prism
Calculate the height of the prism having a surface area 448.88 dm² wherein the base is square with a side of 6.2 dm. What will be its volume in hectoliters?
5. Three co-owners
The three co-owners of building company have earnings from a contract portioned in the ratio of 3:6:7. Each of them received the amount in whole USD. One of them on contract earned 86450 USD. What was the total earnings this order?
6. Giant coin
From coinage metal was produced giant coin and was applied so much metal, such as production of 10 million actual coins. What has this giant coin diameter and thickness, if the ratio of diameter to thickness is the same as a real coin, which has a diameter
7. Ski class
Class attend 30 boys and some number of girls. Ski training was attended by 28 boys and all the girls, which was 95% of all students. How many girls attend this class? How many percent is that?
8. School year
At the end of the school year has awarded 20% of the 250 children who attend school. Awat got 18% boys and 23% of girls. Determine how many boys and how many girls attend school.
9. Combinations
How many different combinations of two-digit number divisible by 4 arises from the digits 3, 5 and 7?
10. Combined interest
Combined interest: Carol has deposited CZK 100,000 in the bank with an annual interest rate of 1.5%. The money was put into the account 5.5.2016 and withdraw them all before Christmas 20.12.2016. How much money did she withdraw?
11. The game of blind man's buff
Slovak levy system makes the gross wage deductions from your pay state employees. It has two components - part employee pays and part pays by the employer Suppose that the super gross wage paid 23% employer. After deducting these contributions we receive g
12. Two looms
On two different looms with different performance can be make required quantity of textile in 6 hours when both work together. On the first machine this quantity of the textile can make in 10 hours. How long should take make same quantity of textile on a s
13. Inscribed circle
XYZ is right triangle with right angle at the vertex X that has inscribed circle with a radius 5 cm. Determine area of the triangle XYZ if XZ = 14 cm.
14. Lift
The largest angle at which the lift rises is 16°31'. Give climb angle in permille.
15. Tmp workers
Three temporary workers cleaned 60 m of walkway in 5 hours. How many meters of the walkway cleared seven volunteers for eight hours?
16. Roof 7
The roof has the shape of a regular quadrangular pyramid with a base edge of 12 m and a height of 4 m. How many percent is folds and waste if in construction was consumed 181.4m2 of plate?
17. Repairman
Repairman has vowed to do repair work at the plant for 25 days. However work had to be shortened, and therefore he took helper worker. Together they made all the corrections for the whole days. How long it would take work to helper worker?
18. Candies
There are two types of candies in the store at 20 CZK/kg and 80 CZK/kg. How much will be cost a mix if we mix 22kg cheaper and 4kg more expensive candies?
19. Sum on dice
We have two dice. What is the greater likelihood of fall a total sum 7 or 8 ? (write 7, 8 or 0 if the probabilities are the same)?
20. Rhumbline
Find circumference and area of the rhumbline ABCD if the short side AD of which has a length of 5 cm, and the heel of the height from D leading to the AB side divides the AB side into two sections of 3 cm and 4 cm.

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