Examples for secondary school students - page 161 of 230
Number of problems found: 4597
- Combinations
If the number of elements increases by 3, it increases the number of combinations of the second class of these elements five times. How many are the elements? - A goat
In the square garden of side (a), a goat is tied in the middle of one side. Calculate the length of the rope (r) so that the goat grazes exactly half the garden. If r = c * a, find the constant c. - Doubling
The message is spreading that each day has doubled the number of people who know about it. All know a message for 20 days. How long known it, eighth people? - Modulo
Find x in the modulo equation: 47x = 4 (mod 9) Hint - read as what number 47x divided by 9 (modulo 9) gives remainder 4. - Represented 4324
A bag contains 20 candies in five different flavors: cherry, lemon, orange, mango, and cola. We know that there is at least one of each flavor in the pocket and that there are twice as many lemons as cherry ones. How many ways can different flavors be rep - Determinant 4320
Calculate the value of the determinant of a unit matrix with 11 rows. - Sharpeners 4318
Pavel bought three pencils and a sharpener in a stationery store and paid 29 CZK. Jane ordered two pencils and two sharpeners, and her purchase price was CZK 46. How much cheaper is a pencil than a sharpener? - One percent
One percent of all the lights in the city are LED, and the remaining 99% are conventional. Other types are not there. John counted them honestly, but he had counted only conventional. After a good dinner, he registered numbers, and he gave notice that fro - Determine 4314
Find the rank of each null matrix. - There
There were 12 members on the commission. Five members were in favor, and seven members were against the proposal. In how many ways could it help the commission vote? - Rectangle pool
Find the dimensions of an open pool with a square bottom and a capacity of 32 m³ that can have painted/bricked walls with the least amount of material. - Probably member
Look at the series 2,6,25,96,285, ? What number should come next? - Minimum of sum
Find a positive number that the sum of the number and its inverted value was minimal. - Inverse matrix
Find how many times the larger determinant is the matrix A, which equals 9 as the determinant of its inverse matrix. - Vineyard
While visiting a winery, the family bought a total of 32 liters of wine in bottles of 0.7 liters and 1 liter. The ratio of the number of larger bottles to smaller bottles is 9:10. The price of a smaller bottle of wine was 120 CZK and a larger bottle was 1 - Resultant force
Calculate mathematically and graphically the resultant of three forces with a common center if: F1 = 50 kN α1 = 30° F2 = 40 kN α2 = 45° F3 = 40 kN α3 = 25° - Originally 4292
The weight of the water container is 2.48 kg. If we pour 75% of the water, the container with water weighs 0.98 kg. Find the weight of the empty container. How much water was originally in the container? - Subsequent 4290
The bonuses were paid to four people in sequence, with each subsequent person receiving double what the previous person received. How many crowns in premiums did each person receive, if a total of 2625 CZK was paid for all premiums? - Gasoline canisters
Thirty-five liters of gasoline is to be divided into four canisters so that the third canister will have 5 liters less than the first canister, the fourth canister 10 liters more than the third canister, and the second canister half of that in the first c - Variation equation
Solve combinatorics equation: V(2, x+8)=72 V(2,x+8) is variations, second class, from x+8 items.
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