# Examples for secondary school students - page 68

- Express train

International express train drove from Kosice to Teplice. In the first 279 km, the track was repaired, and therefore it was moving at a speed of 10km/h less than it was scheduled to drive. The rest of the 465 km trip has increased the speed by 8 km/h than. - Hemispherical hollow

The vessel hemispherical hollow is filled with water to a height of 10 cm =. How many liters of water are inside if the inside diameter of the hollow is d = 28cm? - Tractors

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? - Deviation of the lines

Find the deviation of the lines AG, BH in the ABCDEFGH box-cuboid, if given | AB | = 3cm, | AD | = 2cm, | AE | = 4cm - Flowers 2

Cha cruz has a garden. The ratio roses to tulips is 2 : 5, the ratio of roses to orchids is 7 : 6. Cha cruz wonders what the ratio of tulips to orchids is. If Cha cruz has 183 plants, how many of each kind are there? - Three workplaces

How many ways can we divide nine workers into three workplaces if they need four workers in the first workplace, 3 in the second workplace and 2 in the third? - Final exam

There are 5 learners in a class that has written a final exam Aleta scored 55% vera scored 36% and Sibusiso scored 88% if Thoko scored 71% and the class average was 63%. What was Davids score as a percentage? - Spherical tank

The tank of a water tower is a sphere of radius 35ft. If the tank is filled to one quarter of full, what is the height of the water? - Median and modus

Radka made 50 throws with a dice. The table saw fit individual dice's wall frequency: Wall Number: 1 2 3 4 5 6 frequency: 8 7 5 11 6 13 Calculate the modus and median of the wall numbers that Radka fell. - Subsets

How many 19 element's subsets can be made from the 26 element set? - 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? - Geometric progression

In geometric progression, a1 = 7, q = 5. Find the condition for n to sum first n members is: sn≤217. - The mast

The top of the pole we see at an angle of 45°. If we approach the pole by 10 m, we see the top of the pole at an angle of 60°. What is the height of the pole? - Peaches

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? - 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. - Same area

There is a given triangle. Construct a square of the same area. - Overload

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? - Square root 2

If the square root of 3m^{2}+22 and -x = 0, and x=7, what is m? - Desks

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

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