# Examples for 9th grade - page 37

1. Tachometer
Tatra's tachometer shows the initial state 886123 km this morning. Tatra today travel at an average speed of 44 km/h. Determine the function that describes the Tatra's tachometer depending on the time. What is the state of tachometer after 4 hours?
2. Alloy
The first alloy is a mixture of two metals in the ratio 1:2, the second is a mixture of same metals in the ratio 2:3. At what ratio we have these two alloys put into the furnace to obtain a new metal alloy with ratio 17:27? (All three ratios correspond to.
Two fifth-graders teams competing in math competitions - in Mathematical Olympiad and Pytagoriade. Of the 33 students competed in at least one of the contest 22 students. Students who competed only in Pytagoriade was twice more than those who just competed
4. Two workers
Two workers make 138 parts/items. The first one produces 30% more than the second. How many items will each produce?
5. Arc
Convert to arc measures (radians): 924 ° Result write as a multiple of π
6. Sphere area
A cube with edge 1 m long is circumscribed sphere (vertices of the cube lies on the surface of a sphere). Determine the surface area of the sphere.
7. Workhorses
A team of colleagues done the work in 20 days. After adding 2 colleagues from the beginning the work was completed in 15 days. How many members has the colleague team?
8. TV commercials
For the typical one-hour prime-time television slot, the number of minutes of commercials is 3/8 of the minutes of the actual program. Determine how many minutes of the program are shown in that one hour.
9. Hiker and cyclist
At 7 PM hiker started at 6 km/h to hike. After 3 hrs. later started on the same trip cyclist at speed of 15 km/h. After an hour of driving a flat tire and take him half hours to correct defect. At what time catch up cyclist with hiker?
10. Rope
How many meters of rope 10 mm thick will fit on the bobbin diameter of 200 mm and length 350 mm (central mandrel have a diameter 50 mm)?
11. Distance
Wha is the distance between the origin and the point (18; 22)?
12. Pot
Calculate the height of 3 liter pot with shape cylinder with a diameter of 10 cm.
13. Scouts
Three scouts went on a three day trip. The second day went 4 km more than the first day. The third day went two times less than the first day. They went along 54 km. How many kilometers went every day together?
14. Journey
Charles and Eva stands in front of his house, Charles went to school south at speed 5.4 km/h, Eva went to the store on a bicycle eastwards at speed 21.6 km/h. How far apart they are after 10 minutes?
15. Bases
The length of the bases trapezium are in ratio 4:5. Length of midline is 15. How long are the bases of a trapezoid?
16. Pool 2
The first supply by the pool fill for five hours and the second fill for six hours, drain should be drained for 15 hours. For how many hours the pool is full, when we open both inlet now and outlet open two hours later?
17. Similarity
Rectangle ABCD has dimensions of 7 cm and 6 cm. Rectangle PQRS has dimensions 14 cm and 12 cm. Determine coefficient of the similarity k of the rectangles, if they aren't similar enter zero as the coefficient of similarity.
18. Acreage
What acreage has a rectangular plot whose diagonal is 34 meters long and one side has a length of 16 meters. ?
19. Hop-garden
The length of the rectangular hop garden Mr. Smith increased by 25% and its width by 30%. What is the percentage change in area of hop garden?
20. Sheep
Shepherd tending the sheep. Tourists asked him how much they have. The shepherd said, "there are fewer than 500. If I them lined up in 4-row 3 remain. If in 5-row 4 remain. If in 6-row 5 remain. But I can form 7-row." How many sheep have herdsman?

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