Examples for secondary school students - page 111 of 213
Number of problems found: 4256
- Mixing water
We should fill the 30-liter container with water at 60 degrees Celsius. How many liters of water is 80 degrees C hot, and how many liters of water 20 degrees Celsius warm do we have to mix? - Effective and mean voltage
A voltage divider consisting of resistors R1 = 103000 Ω and R2 = 197000 Ω is connected to the ideal sine wave voltage source, R2 is connected to a voltmeter which measures the mean voltage and has an internal resistance R3 = 200300 Ω, the measured value i - Three unknowns
Solve the system of linear equations with three unknowns: A + B + C = 14 B - A - C = 4 2A - B + C = 0 - Pooja
Pooja and Deepa's age is 4:5, and four years back, it was 8:11. What is the age of Pooja now?
- Standard deviation
Find the standard deviation for the dataset (grouped data): Age (years); No. Of Persons 0-10 ; 15 10-20 ; 15 20-30 ; 23 30-40 ; 22 40-50 ; 25 50-60 ; 10 60-70 ; 5 70-80 ; 10 - Hexagon in circle
Calculate the radius of a circle whose length is 10 cm greater than the circumference of a regular hexagon inscribed in this circle. - Kilograms 7343
Max and Katy together weigh 75 kg. Katy and Tina are 71 kilograms. Max and Tina 80 kilograms. How many kilograms does each of the children weigh? - Symmetry by plane
Determine the coordinates of an image of point A (3, -4, -6) at a symmetry that is determined by the plane x-y-4z-13 = 0 - Non linear eqs
Solve the system of non-linear equations: 3x²-3x-y=-2 -6x²-x-y=-7
- Water reservoir
One drain hole emptied the water from the tank for 20 hours, with the second drain for 30 hours. How long will the water drain from this tank if we open two drains simultaneously? - Competition 7328
Adam was practicing for a darts competition in class. Every day at home, he threw darts at a target in which the individual fields were worth 1,3 and 5 points. He threw 9 darts every day and always scored 27 points. He is in good form and never missed a t - Three-digit numbers
Use the number 4,5,8,9 to write all three-digit numbers without repetition. How many such numbers are there? - Inequality 7320
Let a, b, and c be positive real numbers whose sum is 3, each of which is at most 2. Prove that the inequality holds: a2 + b2 + c2 + 3abc - Confectionery 7318
The confectioner needs to carve a cone-shaped decoration from a ball-shaped confectionery mass with a radius of 25 cm. Find the radius of the base of the ornament a (and the height h). He uses as much material as possible is used to make the ornament.
- Determine 7314
The hiker went from A to B and back in 3 hours and 41 minutes. The road from A to B is first uphill, then flat, and finally downhill. A hiker walked up a hill at a speed of 4 km/h, on a flat surface at a speed of 5 km/h, and down a hill at a speed of 6 km - Kindergarten 7313
The children in the kindergarten drank 20% of the prepared tea in the morning. They drank another 10% of the left tea afternoon. After the whole day, there were still 9 liters of tea left. How many liters of tea was prepared in the kindergarten in the mor - Odd/even number
Pick any number. If that number is even, divide it by 2. If it's odd, multiply it by three and add one. Now, repeat the process with your new number. If you keep going, you'll eventually end up at one every time. Prove. - Rectangular trapezoid
The ABCD rectangular trapezoid with the AB and CD bases is divided by the diagonal AC into two equilateral rectangular triangles. The length of the diagonal AC is 62cm. Calculate the trapezium area in cm square and calculate how many different perimeters - Std-deviation
Calculate standard deviation for file: 63,65,68,69,69,72,75,76,77,79,79,80,82,83,84,88,90
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