# Examples for secondary school students - page 45

1. Book
Alena read a book at speed 15 pages per day. If she read twice as fast she should read a book four days earlier. How many pages have a book?
2. Bearing
A plane flew 50 km on a bearing 63°20' and the flew on a bearing 153°20' for 140km. Find the distance between the starting point and the ending point.
3. Debt
Joe and Caryl have a debt of \$100,500. Joe makes \$90,000 per year, and Caryl makes \$35,000 per year. How much should both pay to zero out the debt fairly, based on their salaries?
4. The city
At the end of 2010 the city had 248000 residents. The population increased by 2.5% each year. What is the population at the end of 2013?
5. Class - boys and girls
In the class are 60% boys and 40% girls. Long hair has 10% boys and 80% girls. a) What is the probability that a randomly chosen person has long hair? b) The selected person has long hair. What is the probability that it is a girl?
6. Water reservoir
The cuboid reservoir contains 1900 hectoliters of water and the water height is 2.5 m. Determine the dimensions of the bottom where one dimension is 3.2 m longer than the second one.
7. Diamond
Calculate the length of the two diagonals of the diamond if: a = 13 cm v = 12 cm
8. Car and cyclist
Cyclist started from town at speed 18 km/h. After 1 hour 30 min started the car from town and caught up with the cyclist in 50 minutes. How fast was a car?
9. Scalar dot product
Calculate u.v if |u| = 5, |v| = 2 and when angle between the vectors u, v is: a) 60° b) 45° c) 120°
10. Enterprise
The value of annual production enterprise is 7.1 million USD. The average annual growth rate is 1.5%. What will be value of production at the end of the fifth year?
11. Medians and sides
Determine the size of a triangle KLM and the size of the medians in the triangle. K=(-5; -6), L=(7; -2), M=(5; 6).
12. Wavelength
Calculate the wavelength of the tone frequency 11 kHz if the sound travels at speeds of 343 m/s.
13. Bank
Paul put 10000 in the bank for 6 years. Calculate how much you will have in the bank if he not pick earned interest or change deposit conditions. The annual interest rate is 3.5%, and the tax on interest is 10%.
14. Triangle KLM
In the rectangular triangle KLM, where is hypotenuse m (sketch it!) find the length of the leg k and the height of triangle h if hypotenuse's segments are known mk = 5cm and ml = 15cm
15. Confectionery
The village markets have 5 kinds of sweets, one weighs 31 grams. How many different ways a customer can buy 1.519 kg sweets.
16. Interesting property
Plot a rectangular shape has the interesting property that circumference in meters and the area in square meters are the same numbers. What are the dimensions of the rectangle?
17. Average mark
Calculate average mark in English, if a student got a couple of 3's, 20% less 2 than 3, and 50% more 1's than the 2's.
18. Average age
The average age of all people at the celebration was equal to the number of people present. After the departure of one person who was 29 years old, average age was again equal to the number present. How many people were originally to celebrate?
19. Gain
Find the gain whenever the output power is 21x the input power.
20. Unions now
The plant has 1,250 employees. The Trade Unions (former ROH, OH) is 18% male, 23% female. Plant management reported that in the trade union is 20% of all employees. How many men and women are in plant and how many are men and women in trade unions?

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