Examples for secondary school students - page 69
There are 20 peaches in the pocket. 3 peaches are rotten. What is the probability that one of the randomly picked two peaches will be just one rotten?
Wheel and belt tractors each day plow 8 ha of fields. For plow 76 hectares, the wheel would have to work for 12 days and 8 days with the belt tractor together. How many hectares do each day of each tractor?
95% of the components manufactured on the lathe comply with the standard, of which 80% of the components are first-class. How likely can we expect a manufactured part to be first class?
How many 19 element's subsets can be made from the 26 element set?
- Cube cut
In the ABCDA'B'C'D'cube, it is guided by the edge of the CC' a plane witch dividing the cube into two perpendicular four-sided and triangular prisms, whose volumes are 3:2. Determine in which ratio the edge AB is divided by this plane.
- Geometric progression
In geometric progression, a1 = 7, q = 5. Find the condition for n to sum first n members is: sn≤217.
- Same area
There is a given triangle. Construct a square of the same area.
- Boys to girls
The ratio of boys to girls in a party is 3:5 . If 6 more boys arrived and 4 girls left the party, the ratio of boys to girls would be 5:6 . How many are in the party originally?
What overload in g (g-force) has passed the pilot if he accelerated from 0 to 600 km/h in 3 seconds?
- Mixing water
The 30-liter container should we fill with water at 60 degrees Celsius. How many liters of water 80 degrees C hot and how many liters of water 20 degrees Celsius warm we have to mix?
- Diagonals of pentagon
Calculate the diagonal length of the regular pentagon: a) inscribed in a circle of radius 12dm; b) a circumscribed circle with a radius of 12dm.
- Mast shadow
Mast has 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 15°. Determine the height of the mast, if the sun above the horizon is at angle 33°. Use the law of sines.
- Square root 2
If the square root of 3m2 +22 and -x = 0, and x=7, what is m?
A class has 20 students. The classroom consists of 20 desks, with 4 desks in each of 5 different rows. Amy, Bob, Chloe, and David are all friends, and would like to sit in the same row. How many possible seating arrangements are there such that Amy, Bob, C
12, 60, -300,1500 need next 2 numbers of pattern
- The swimmer
The swimmer swims at a constant speed of 0.85 m/s relative to water flow. The current speed in the river is 0.40 m/s, the river width is 90 m. a) What is the resulting speed of the swimmer with respect to the tree on the riverbank when the swimmer motion
- SSA and geometry
The distance between the points P and Q was 356 m measured in the terrain. The PQ line can be seen from the viewer at a viewing angle of 107° 22 '. The observer's distance from P is 271 m. Determine the viewing angle of P and observer.
- Barrel with water
The water barrel has a weight of 52 kg. When we pour a quarter of the water, the weight of the barrel is reduced to 40 kg. Determine the weight of the empty barrel.
- Bridge cards
How many bridge hands are possible containing 4 spades,6 diamonds, 1 club, and 2 hearts?
- Expressions 3
If k(x+6)= 4x2 + 20, what is k(10)=?