# Examples for 9th grade - page 92

1. Two diggers Two diggers should dig a ditch. If each of them worked just one-third of the time that the other digger needs, they'd dig up a 13/18 ditch together. Find the ratio of the performance of this two diggers.
2. PIN code PIN on Michael credit card is a four-digit number. Michael told this to his friend: • It is a prime number - that is, a number greater than 1, which is only divisible by number one and by itself. • The first digit is larger than the second. • The second.
3. Body diagonal - cube Calculate the surface and cube volume with body diagonal 15 cm long.
4. Quadrangular pyramid The regular quadrangular pyramid has a base length of 6 cm and a side edge length of 9 centimeters. Calculate its volume and surface area.
5. Four numbers The first number is 50% second, the second number is 40% third, the third number is 20% of the fourth. The sum is 396. What are the numbers?
6. Cross road From the junction of two streets that are perpendicular to each other, two cyclists (each on another street) walked out. One ran 18 km/h and the second 24 km/h. How are they away from a) 6 minutes, b) 15 minutes?
7. Electric input power Solve problems related to electric power: a) U = 120 V, I = 0.5 A, P =? b) P = 200 W, U = 230 V, I =? c) I = 5 A, P = 2200W, U =?
8. Vertices of a right triangle Show that the points D(2,1), E(4,0), F(5,7) are vertices of a right triangle.
9. Mushrooms Fresh mushrooms contain 88% water, dried 14% water. How many kilograms of fresh mushrooms should be collected to get 3 kg of dried?
10. Sum of squares The sum of squares above the sides of the rectangular triangle is 900 cm2. Calculate content of square over the triangle's hypotenuse.
11. Body diagonal Calculate the cube volume, whose body diagonal size is 75 dm. Draw a picture and highlight the body diagonal.
12. Granules Katy had two dogs. The first one ate a pack of granules a week and the other two times longer. Katka bought them two bags of granules. How long does it last for both dogs?
13. Slant height The slant height of cone is 5cm and the radius of its base is 3cm, find the volume of the cone
14. Cube diagonals Calculate the length of the side and the diagonals of the cube with a volume of 27 cm3.
15. Two buses The first bus runs 15 minutes the second bus runs after 21 minutes. Together they both leave at 7:00 on Monday. When and what day will they meet?
16. Prism diagonal The body diagonal of a regular square prism has an angle of 60 degrees with the base, the edge length is 10 cm. What is the volume of the prism?
17. Functions f,g Find g(1) if g(x) = 3x - x2 Find f(5) if f(x) = x + 1/2
18. Bulbs There are 875 identical light bulbs in the sports hall lightning for 2 hours. How long does it lightning 100 this light bulbs?
19. Pupils There are 32 pupils in the classroom, and girls are two-thirds more than boys. a) How many percents are more girls than boys? Round the result to a whole percentage. b) How many are boys in the class? c) Find the ratio of boys and girls in the class. Wr
20. Iron ball The iron ball has a weight of 100 kilograms. Calculate the volume, radius, and surface if the iron's density is h = 7.6g/cm3.

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