Examples for secondary school students - page 65 of 230
Number of problems found: 4582
- Permutations 46323
I want to find the number of permutations of the set M6 if not one element is in that position as in the original input (1 2 3 4 5 6). So I have to exclude numbers with 1 in 1st place, 2 in 2nd place, and 3 in 3rd place. - A bag
A bag contains nine blue marbles and one green marble. What is the probability of drawing a blue marble followed by a green marble without replacing the first marble before drawing the second marble? - Rectangular base
Calculate the pyramid's surface area with a rectangular base measuring 9cm, 4cm, and 6cm high. - Resistance 46111
A metal ring with a radius of 10 cm is placed in a magnetic field so that the normal to its surface makes an angle of 60° with the induction lines. The induction of the magnetic field varies uniformly and drops from 0.45 T to 0.35 T in 0.50 s. Determine t - Cylindrical magnets
Calculate the magnetic field energy of a cylindrical coil with 400 turns, a length of 0.4 m, and a radius of 20 mm. A current of 3A passes through the coil. (µo = 4π 10-7 H/m) - Self-inductance 46011
Calculate the self-inductance of the coil, which has 1,300 turns, if the inductive current through the coil changes by 6 * 10 ^ -5 Wb by a constant current change of 2A. - Surveyors
Surveyors mark 4 points on the globe's surface so their distances are the same. What is their distance from each other?
- Performance 45861 The electric motor with a power input of 25 kW works with an efficiency of 80 percent. He will do the work in 6 hours. What is the performance, and what part of the work is the loss?
- Sister 45831
Eva has a sister who is four years older. Ten years ago, she was twice as old as Eva. How old is Eva now? - Coefficient 45821
What is the smallest radius a turn must have for a car to enter safely without exceeding a speed of 50 km/h? The coefficient of shear friction between the tires and the surface is 0.4. - Edmond
Edmond Santos borrowed USD 20,000 for 18 months at 6 1/2 % per year. Find the APR (Annual Percentage Rate) if he repaid the loan monthly. The answer is: Note: APR is expressed as a percentage representing the actual yearly cost of funds over a loan term. - Three pillars
On a straight road, three pillars are 6 m high at the same distance of 10 m. At what angle of view does Vlado see each pillar if it is 30 m from the first and his eyes are 1.8 m high? - Two similar
There are two similar triangles. One has a circumference of 100 cm, and the second has sides successively 8 cm, 14 cm, and 18 cm longer than the first. Find the lengths of its sides. - Solutions 45511
Two parallel chords in a circle with a radius of 6 cm have lengths of 6 cm and 10 cm. Calculate their distance from each other. Find both solutions. - Calculate
Calculate the area of triangle ABC if given by alpha = 49°, beta = 31°, and the height on the c side is 9cm.
- Sapphires 45461
The jeweler selects three gems in the ring. It has rubies, emeralds, and sapphires. How many choices does it have? - Molecules 45441
The mean square velocity of the gas molecules is 1200 m/s. What pressure does this gas exert on the vessel wall when its density is 0.03 kg/m³? - Angle of diagonals
Calculate a rectangle's perimeter and area if its diagonal is 14 cm and the diagonals form an angle of 130°. - The surface
The surface of a truncated rotating cone with side s = 13 cm is S = 510π cm². Find the radii of the bases when their difference in lengths is 10cm. - Confidence interval
A food testing laboratory in Abu Dhabi has been commissioned to estimate the amount of olive oil contained in 1-gallon tins purchased from a range of international olive oil producers. The manufacturers state that the standard deviation of the amount of o
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