Numbers - examples
- Sum of inner angles
Prove that the sum of all inner angles of any convex n-angle equals (n-2) . 180 degrees.
Show that if x, y, z are 3 consecutive nonzero digits, zyx-xyz = 198, where zyx and xyz are three-digit numbers created from x, y, z.
- Simplify 3
Simplify mixed numerals expression: 8 1/4- 3 2/5 - (2 1/3 - 1/4) Show your solution.
- Scientific notation
Approximately 7.5x105 gallons of water flow over a waterfall each second. There are 8.6x104 seconds in 1 day. Select the approximate number of gallons of water that flow over the waterfall in 1 day.
The perimeter of a rectangle is 90 m. Divide it into three rectangles, the shorter side has all three rectangles the same, their longer sides are three consecutive natural numbers. What is the dimensions of each rectangle?
- Three friends
Three friends had balls in ratio 2: 7: 4 at the start of the game. Could they have the same number of balls at the end of the game? Write 0, if not, or write the minimum number of balls they had together.
One brick is 6 kg and half a brick heavy. What is the weight of one brick?
Area of square garden is 4/5 of triangle garden with sides 24 m, 15 m and 15 m. How many meters of fencing need to fence a square garden?
If water flows into the pool by two inlets, fill the whole for 18 hours. First inlet filled pool 10 hour longer than second. How long pool is filled with two inlets separately?
Juan bought 9 same chocolates for 9 Eur. How many euros he pay for 29 chocolates?
- Forestry workers
In the forest is employed 43 laborers planting trees in nurseries. For 6 hour work day would end job in 35 days. After 11 days, 8 laborers go forth? How many days is needed to complete planting trees in nurseries by others, if they will work 10 hours a da
Gross wage was 1430 USD including 23% bonus. How many USD were bonuses?
- Right Δ
Right triangle has length of one leg 51 cm and length of the hypotenuse 85 cm. Calculate the height of the triangle.
Route is long 147 km and the first day first regiment went at an average speed 12 km/h and journey back 21 km/h. The second day went second regiment same route at an average speed 22 km/h there and back. Which regiment will take route longer?
Is the number 146025 divisible by 6?
- Motion problem
From Levíc to Košíc go car at speed 81 km/h. From Košíc to Levíc go another car at speed 69 km/h. How many minutes before the meeting will be cars 27 km away?
Mr. Billy calculated that excavation for a water connection dig for 12 days. His friend would take 10 days. Billy worked 3 days alone. Then his friend came to help and started on the other end. On what day since the beginning of excavation they met?
A man drinks a barrel of water for 32 days, woman for 54 days, for how many days they drink barrel together?
After three 10° beers consumed in a short time there are 6.2 g of alcohol in 5 kg adult human blood. How much is it per mille?
- Cube in a sphere
The cube is inscribed in a sphere with volume 5951 cm3. Determine the length of the edges of a cube.