# Examples for secondary school students - page 49

1. Dollars Mama split 760 dollars Jane, Dane and Eva as follows: Jane got three times more than Dane and Dane and got 40 more than Eva. How much does get each of them?
2. Cuboid and ratio Cuboid has dimensions in ratio 1:2:6 and the surface area of the cuboid is 1000 dm2. Calculate the volume of the cuboid.
3. Ten dices When you hit ten dices at the same time you get average 35. How much do you hit if every time you get six, you're throwing the dice again?
4. One green In the container are 45 white and 15 balls. We randomly select 5 balls. What is the probability that it will be a maximum one green?
5. Consecutive numbers Sum of ten consecutive numbers is 105. Determine these numbers (write first and last).
6. Students In the front row sitting three students and in every other row 11 students more than the previous row. Determine how many students are in the room when the room is 9 lines, and determine how many students are in the seventh row.
7. Insert into GP Between numbers 5 and 640 insert as many numbers to form geometric progression so sum of the numbers you entered will be 630. How many numbers you must insert?
8. Asymptote What is the vertical asymptote of ?
9. Owner of the company The owner of the company with extensive administrative activity wants to sell the obsolete 3 machines at the price of CZK 1000 per 1 machine with a six-month warranty period. If the machine breaks down during this period, the owner will return the employe
10. Sum or product What is the probability that two dice fall will have the sum 7 or product 12?
11. Pears Andrew, Lenka and Rasto have together 232 pears. Lenka has 28 more than Rasto and Rasto pears have 96 more than Andrew. Determine how much each of them has pears.
12. Class pairs In a class of 34 students, including 14 boys and 20 girls. How many couples (heterosexual, boy-girl) we can create? By what formula?
13. Hollow sphere The volume of the hollow ball is 3432 cm3. What is its internal radius when the wall thickness is 3 cm?
14. Cards The player gets 8 cards of 32. What is the probability that it gets a) all 4 aces b) at least 1 ace
15. Sides ratio Calculate the circumference of a triangle with area 84 cm2 if a:b:c = 10:17:21
16. Dividing money Thomas, Honza and Vasek are to divide 1220kč. Honza got 25% more than Thomas. Vasek 20% less than Thomas. How CZK each got?
17. Points on circle In the Cartesian coordinate system with the origin O is a sketched circle k /O; r=2 cm/. Write all the points that lie on a circle k and whose coordinates are integers. Write all the points that lie on the circle I / O; r=5 cm / and whose coordinates are i
18. Square and rectangle Calculate the side of a square which content area equals area of the rectangle having a length of 3 cm greater and by 2 cm smaller than the side of the square. Write the equation of the quadratic function which includes points A (-1, 10), B (2, 19), C (1,4) Output Controller of the company in the control of 50 randomly selected products found that 37 of them had no defect 8 has only one flaw, three had two defects, and two products had three defects. Determine the standard deviation and coefficient of variati