Examples for secondary school students - page 118 of 229
Number of problems found: 4578
- Probability 7991
We have the numbers 4, 6, 9, 13, and 15. What is the probability that these will be the lengths of the sides of the triangle? (Consider only scalene triangles.) - Equilibrium 7990
At the end of one arm of the equilibrium scales, which are in equilibrium, a lead body with a volume V1 is suspended in the air. At the end of the other arm is an aluminum body with a volume of V2. The balance arms have sizes l1 and l2, lead density h1 = - Distribute 7988
Tomas was to distribute 259 cards with pictures of football players among three friends. And each subsequent friend had to get 2x more cards than the previous one. How many cards did the other friend receive? - 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? - The father wanted
The father wanted to divide the inheritance equally among all his sons and ordered: the eldest son would receive 1000 CZK and one eighth of the remainder, the second would receive 2000 CZK and one eighth of the new remainder, the third would receive 3000 - Triangle 42
Triangle BCA. Angles A=119° B=(3y+14) C=4y. What is the measure of triangle BCA=? - The pool - optimization
A block-shaped pool with a volume of 200 m³ is to be built in the recreation area. Its length should be 4 times the width, while the price of 1 m² of the pool bottom is 2 times cheaper than 1 m² of the pool wall. What dimensions must the pool have to make
- Tournament 7975
Eight players took part in the table tennis tournament. The tournament system allows players to play with each other only once. How many matches will take place in this tournament? - Unhatched 7969
92% of the eggs hatched in the incubator. 168 eggs remained unhatched. How many eggs have initially been in the incubator? - Equilateral 7962
After a long dinner, inside a lounge in the shape of a square ABCD, a drunken shopper E lies in such a way that the triangle DEC is equilateral. Spy F lies on the edge of BC, with |EB|=|EF|. What is the size of the angle CEF? - Hyperbola equation
Find the hyperbola equation with the center of S [0; 0], passing through the points: A [5; 3] B [8; -10] - Coordinates of square vertices
The ABCD square has the center S [−3, −2] and the vertex A [1, −3]. Find the coordinates of the other vertices of the square. - Prism diagonal
The body diagonal of a regular square prism has an angle of 60 degrees with the base, and the edge length is 10 cm. What is the volume of the prism? - Four-digit 7953
How many four-digit codes on the wheel lock can we create from the digit 0,1,2,3,4,5,6,7,8,9 if it is true that we cannot repeat the numbers? - Rectangle
There is a rectangle with a length of 12 cm and a diagonal 8 cm longer than the width. Calculate the area of a rectangle.
- Rabbits 7948
Hens and rabbits, 22 heads and 62 feet, run around the garden. How many? - Rotating 7947
In the rotating cone = 100π S rotating cone = 90π v =? r =? - Schoolchildren 7938
There are 350 boys in the school, 56% of all schoolchildren. How many students are there at school, and how many girls are there? - A pizza
A pizza place offers 14 different toppings. How many different three-topping pizzas can you order? - 600 pencils
Six hundred pencils we want to be divided into three groups. The biggest groups have ten pens more than the smallest. How many ways can this be done?
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