Grade - examples - page 188

1. 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?
2. 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?
3. Fractions Three-quarters of an unknown number are 4/5. What is 5/6 of this unknown number?
4. Regular prism The regular four-sided prism has a base of 25 cm2 and a surface of 210 cm2. Find its volume.
5. Vertices of a right triangle Show that the points D(2,1), E(4,0), F(5,7) are vertices of a right triangle.
6. The Stolen Money A man walks into a store and steals a \$100 bill. 5 minutes later, he returns to the store and buys stuff worth \$70. He pays with the bill that he had stolen, so the owner of the store returns him \$30. How many dollars did the store owner lose?
7. Discount sale After the discount, the computer costs 9600, - CZK. How much did it cost when the price was reduced: a) by half b) by a third c) by one fifth and then by 160 CZK 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? Find the roots of the quadratic equation: 3x2-4x + (-4) = 0.
10. Inlet minus outlet Water flows into the tank through two pipes and flows out of the third pipe spontaneously. The pipe A itself would fill the tank in 3 hours, the pipe B itself would fille in 4 hours, and the pipe C itself would flow out in 12 hours. How long will the tank. Combine like terms 4c+c-7c
12. A pizza A pizza place offers 14 different toppings. How many different three topping pizzas can you order?
13. Variability In the table bellow the number of wrong produced goods in two shifts: morning shift: 2; 0; 6; 10; 2; 2; 4; 2; 5; 2; afternoon shift: 4; 4; 0; 2; 10; 2; 6; 2; 3; 10; Compare the variability in both shifts, compare the average number of wrong goods on both
14. Mushrooms Fresh mushrooms contain 88% water, dried 14% water. How many kilograms of fresh mushrooms should be collected to get 3 kg of dried?
15. Slant height The slant height of cone is 5cm and the radius of its base is 3cm, find the volume of the cone
16. Body diagonal Calculate the cube volume, whose body diagonal size is 75 dm. Draw a picture and highlight the body diagonal.
17. Rhombus 29 One of the diagonals of a rhombus is equal to a side of the rhombus. Find the angles of the rhombus.
18. 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.
19. Fruits Amy bought a basket of fruits 1/5 of them were apples,1/4 were oranges, and the rest were 33 bananas. How many fruits did she buy in all?
20. The King The King wants to divide his sons equally. He has 42 rubies and 45 diamonds. How many sons and how will they share them?

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