# Examples for 9th grade - page 11

1. Parquet floor
Three workers laid parquet floor for 2.301 hour. The first one would do this work alone 7 hours, the second in 6 hours. For how many hours would fulfill this work the third worker, if he worked alone?
2. Hole
In the center of the cube with edge 14 cm we will drill cylinder shape hole. Volume of the hole must be 27% of the cube. What drill diameter should be chosen?
3. Tinsmith
Tinsmith construct chimney pipe 145 cm long and 15 cm wide. What are the dimensions of the sheet will have to prepare for the construction of a pipe when the plate overlap at the joint add \$x cm width of the plate?
4. Cu wire
Copper wire has a length l = 980 m and diameter d = 8 mm. Calculate the weight if density of copper is ρ = 8500 kg/m3. Result round to one decimal place.
Determine the radius of the circle, if its perimeter and area is the same number.
6. Discount
Product has been discounted twice by 19%. What is the total discount given?
7. Seedcake
Seedcake costs 44 cents. How many minimum seedcakes we must buy that we can pay in cash only whole euros?
8. Euclid1
Right triangle has hypotenuse c = 27 cm. How large sections cuts height hc=3 cm on the hypotenuse c?
9. Parallelogram
Calculate area of the parallelogram ABCD as shown if |AB| = 19 cm, |BC| = 18 cm and angle BAD = 90°
10. Phone numbers
How many 7-digit telephone numbers can be compiled from the digits 0,1,2,..,8,9 that no digit is repeated?
During the spring cleaning ladies going to wash windows. Mother takes wash all the windows 5 hours, the grandmother 3 times longer and Paula wash all windows in 2 hours. How many hours will spend washing the windows this "women's team" if working togethe
12. Diofant equation
In the set of integers (Z) solve the equation: ? Write result with integer parameter ? (parameter t = ...-2,-1,0,1,2,3... if equation has infinitely many solutions)
13. Octahedron - sum
On each wall of a regular octahedron is written one of the numbers 1, 2, 3, 4, 5, 6, 7 and 8, wherein on different sides are different numbers. For each wall John make the sum of the numbers written of three adjacent walls. Thus got eight sums, which also.
14. Cubes
Cube, which consists of 27 small cubes with edge 4 dm has volume:
15. Cuboid
Determine the dimensions of cuboid a, b, c; if diagonal d=9 dm has angle with edge a α=55° and has angle with edge b β=58°
16. Two doctors
Doctor A will determine the correct diagnosis with a probability 86% and doctor B with a probability 86%. Calculate probability of correct diagnosis if patient is diagnosed by both doctors.
17. Freedom
In the city are 3/9 of women married for 3/6 men. What proportion of the townspeople is free (not married)? Express as a decimal number.
18. 4side pyramid
Calculate the volume and surface of 4 side regular pyramid whose base edge is 4 cm long. The angle from the plane of the side wall and base plane is 60 degrees.
19. Square diagonal
Calculate the length of diagonal of the square with side a = 23 cm.
20. Map
On the tourist map at a scale of 1 : 50000 is distance between two points along a straight road 3.7 cm. How long travels this distance on a bike at 30 km/h? Time express in minutes.

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