Examples for secondary school students - page 103 of 214
Number of problems found: 4261
- STRESSED word
Each letter in STRESSED is printed on identical cards, one letter per card, and assembled in random order. Calculate the probability that the cards spell DESSERTS when assembled. - Direction 7999
A (5; -4) B (1; 3) C (-2; 0) D (6; 2) Calculate the direction vector a) a = AB b) b = BC c) c = CD - Classroom
Of the 26 pupils in the classroom, 12 boys and 14 girls, four representatives are picked to the odds of being: a) all the girls b) three girls and one boy c) there will be at least two boys - Spherical cap
Place a part of the sphere on a 4.6 cm cylinder so that the surface of this section is 20 cm². Determine the radius r of the sphere from which we cut the spherical cap.
- 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? - Triangle 42
Triangle BCA. Angles A=119° B=(3y+14) C=4y. What is the measure of triangle BCA=?
- Block-shaped 7976
A block-shaped pool with a volume of 200m³ 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?
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