# Examples for 9th grade - page 58

- Task of the year

Determine the number of integers from 1 to 10^{6}with ending four digits 2001. - Average height

In a class are 34 students. The average height of students is 165 cm. What will be the average height of students in the classroom when two pupils tall 176 cm and 170 cm moved from this school/class? - The deposit

Deposit has been placed for one year at an annual rate of 4.5%. After the added interst amount rose to € 2,612.5. Determine initial deposit. - Interst on savings

The bank offers 1.6% interest. How many euros have to insert at the beginning if we received € 15 on the interest? - Apprentice

Worker and apprentice execute the work for 6 hours. Worker performs himself in 10 hours. How long do the work of an apprentice? - Coins

In ticket maschine were together one hundred coins. They were only 20 and 50 cent coins. The sum total was 29 euros and 60 cents. How many were in ticket maschine coins and which type? - The fence

I'm building a fence. Late is rounded up in semicircle. The tops of late in the field between the columns are to copy an imaginary circle. The tip of the first and last lath in the field is a circle whose radius is unknown. The length of the circle chord i - Traffic laws

Under traffic regulations, car lights can illuminate the road up to a maximum of 30 m. To check the reach of the dipped-beam lights of their car, Peter stopped car at 1.5 m from the wall. The dipped-beam headlights are 60 cm high. At what height on the wa - Painters 4

One painter will do the job for 12 days. After a 4 1/3 day he comes second to help him and complete work together for 8 days. How long would work the second painter himself? - Trapezoid thirds

The ABCD trapezoid with the parallel sides of the AB and the CD and the E point of the AB side if the segment DE divides the trapezoid into two parts with the same area. Find the length of the AE line segment. - Heating plant

Workers dump imported coke at heating plant. On the first day used half of the amount, the second day three quarters the rest and on the third day left 120 tons. How much coke they dump at heating plant? - Sweets

3 chocolate and 7 cakes cost 85, - CZK. 2 chocolates and 6 cakes cost 86, - CZK. How much is 5 chocolates and 9 cakes? I wonder how to get the result, but only by logic without the use of a system of equations - Rain

How many mm of water rained the roof space 75 m^{2}if the empty barrel with a radius of 8 dm and height 1.2 m filled to 75% its capacity? :-) - Repairman

Repairman has vowed to do repair work at the plant for 25 days. However work had to be shortened, and therefore he took helper worker. Together they made all the corrections for the whole days. How long it would take work to helper worker? - Trapezoid

How long are the trapezoid bases with area 24 cm^{2}and height 3 cm. One base is 3 times longer than the shorter. - Variations

Determine the number of items when the count of variations of fourth class without repeating is 50 times larger than the count of variations of third class without repetition. - Three shapes

1/5 of a circle is shaded. The ratio of area if square to the sum of area of rectangle and that of the circle is 1:2. 60% of the square is shaded and 1/3 of the rectangle is shaded. What is the ratio of the area of circle to that of the rectangle? - Vector - basic operations

There are given points A [13; 11] B [23; -4] C [9; -1] and D [-11; 25] a. Determine the coordinates of the vectors u=AB v=CD s=DB b. Calculate the sum of the vectors u + v c. Calculate difference of vectors u-v d. Determine the coordinates of the vector w - Triangle

Determine whether a triangle can be formed with the given side lengths. If so, use Heron's formula to find the area of the triangle. a = 177 b = 124 c = 63 - Isosceles right triangle

Contents of an isosceles right triangle is 18 dm^{2.}Calculate the length of its base.

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