Intersection of sets - math word problems

Number of problems found: 48

Alarm systems
What is the probability that at least one alarm system will signal the theft of a motor vehicle when the efficiency of the first system is 90% and of the independent second system 80%?
Coordinates
Determine the coordinates of the vertices and the content of the parallelogram, the two sides of which lie on the lines 8x + 3y + 1 = 0, 2x + y-1 = 0 and the diagonal on the line 3x + 2y + 3 = 0
Ten pupils
10 pupils came to the art group. 8 pupils painted with watercolors and 9 pupils painted with ink, each pupil painted with ink or watercolors. How many pupils painted water and ink at the same time?
Line intersect segment
Decide whether the line p : x + 2 y - 7 = 0 intersects the line segment given by points A[1, 1] and B[5, 3]
Eq triangle minus arcs
In an equilateral triangle with a 2cm side, the arcs of three circles are drawn from the centers at the vertices and radii 1cm. Calculate the content of the shaded part - a formation that makes up the difference between the triangle area and circular cuts
Construction of trapezoid
Construct a trapezoid if b = 4cm, c = 7cm, d = 4,5cm, v = 3 cm (Procedure, discussion, sketch, analysis, construction)
Hazard game
In the Sportka hazard game, 6 numbers out of 49 are drawn. What is the probability that we will win: a) second prize (we guess 5 numbers correctly) b) the third prize (we guess 4 numbers correctly)?
Glasses
There are 36 pupils in the class. Nine girls wear glasses. Boys with glasses are five less than girls without glasses. Boys without glasses are two times more than girls without glasses. How many boys and how many girls?
Three excursions
Each pupil of the 9A class attended at least one of the three excursions. There could always be 15 pupils on each excursion. Seven participants of the first excursion also participated in the second, 8 participants of the first excursion, and 5 participan
Double probability
The probability of success of the planned action is 60%. What is the probability that success will be achieved at least once if this action is repeated twice?
Square and circles
The square in the picture has a side length of a = 20 cm. Circular arcs have centers at the vertices of the square. Calculate the areas of the colored unit. Express area using side a.
Pupils
There are 27 pupils in the classroom. They can swim 21 and ski nine pupils. Neither swim nor ski three pupils. How many pupils can swim and ski?
Christmas or Easter
Please calculate this example by the Venn equation. They asked 73 students whether they like Christmas or Easter. 34 of them like one of the holidays. 39 loves Easter. There are twice as many students who wish both holidays than those who only love Easter
Sphere in cone
A sphere is inscribed in the cone (the intersection of their boundaries consists of a circle and one point). The ratio of the surface of the ball and the contents of the base is 4: 3. A plane passing through the axis of a cone cuts the cone in an isoscele
The box
The box contains five chocolate, three fruit, and two menthol candies. We choose sweets at random from the box. What is the probability that we will take out one chocolate, one fruit, and one menthol candy without a return?
Probability of intersection
Three students have a probability of 0.7,0.5 and 0.4 to graduated from university respectively. What is the probability that at least one of them will be graduated?
Utopia Island
A probability of disease A on the island of Utopia is 40%. A probability of occurrence among the men of this island, which make up 60% of all the population (the rest are women), is 50%. What is the probability of occurrence of A disease among women on Ut
Cutting the prism
A prism with a square base with a content of 1 cm² and a height of 3 cm was cut from a cube with an edge length of 3 cm. What is the surface of the body formed from the cube after cutting the prism?
Brothers and sisters
There are 35 children in the class, 23 of them have a brother, and 27 of them have a sister. How many children have both a brother and a sister when there are 5 children in the class who have no brother or sister?
Left handed
It is known that 25% of the population is left-handed. What is the probability that there is a maximum of three left-handers at a seminar where there are 30 participants?

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