Maths practice for 14 year olds - page 44 of 379
Number of problems found: 7575
- Construct 83195
Two line segments of different lengths are given. Construct a circle k so that both line segments are its chords. - Central angle
A circle k with a center at point S and a radius of 6 cm is given. Calculate the size of the central angle subtended by a chord 10 cm long. - Daffodils 83181
The spring bouquet consists of 13 daffodils and 8 tulips, and the other 30% are freesias; how many flowers are there in total? - Proportional 83174
For the lever to be balanced, the arms' lengths must be inversely proportional to the weight ratio of the weights suspended on these arms. Complete the data: 30 cm, 10 cm, 4 kg, and? kg. - Original model
When drying, the modeling mass loses 36% of its original volume. If the cube's volume is 5.12 dm³ after drying, what was the original length of the edge? - Apprentice 83169
The master gave the apprentice the task of dividing the 28 m long electric cable into two parts so that the second part was 2.5 times larger than the first. How long were the cable sections supposed to be? - Afternoon 83168
In the morning, 6 liters more water was in the green canister than in the blue one. In the afternoon, the gardener poured 1 liter of water from the green canister into the blue one. There was then twice as much water in the green canister as in the blue o
- Overhangs 83158
The area of a right triangle ABC is 346 cm2, and the angle at vertex A is 64°. Calculate the lengths of the overhangs a and b. - Isosceles triangle and cosine
Using the cosine theorem, prove that in an isosceles triangle ABC with base AB, c=2a cos α. - Hypotenuses 83154
In a right-angled triangle ABC with a right angle at the vertex C, the magnitudes of the hypotenuses are given ta=5, tb=2√10. Calculate the side sizes of triangle ABC and the circle's radius described by this triangle. - Circumscribed 83152 Given is an isosceles triangle whose base is 8 cm, and the sides are 15 cm long. Calculate the area of the triangle and the radius of the inscribed and circumscribed circle.
- Students 83149
There are 30 students in the class. Five had a mark three — other twos and ones. The average grade was 1.9. How many students got mark one? - Braking 83146
A car of mass m=1t moves at a speed v0=54 km/h. What braking force must be exerted to bring the car to a stop in 10 seconds, and how far will the car travel in this time? - Tetrahedron 83144
A container shaped like a rotating cylinder with a base radius of 5 cm is filled with water. If a regular tetrahedron with an edge of 7 cm is immersed in it, how much will the water level in the container rise? - Basketball 83137
In the basketball game, the players threw 37 times, including 2-pointers and 3-pointers, for a total of 82 points. How many were 2 points, and how many were 3 points?
- Dimensions of an aquarium
The large aquarium is shaped like a cuboid and has dimensions in the ratio 5: 7: 4. The sum of the lengths of all edges is 96 dm. How many liters of water will be in the aquarium if it is filled to four-fifths? - Probability 83133
The mobile PIN has 4 characters. What is the probability that the PIN contains the number 7 and ends with the number 5? - Remaining 83116
Ondra was reading a book. On the first day, he read one-tenth. On the second day, he read half of the remainder; on the third day, he read 20% of the new remainder; and on the fourth day, he read the remaining 72 pages. Thus, the book had 72 pages. - Grandchildren 83113
The grandfather bought 10 rubbers for 10 grandchildren. In the bag were 3 blue, 2 green and the rest red. Hansel would like blue gum. What is the probability that Janek will draw a blue rubber if 2 cousins have already drawn it before him and drawn blue a - Rectangular 83112
The garden is a rectangular trapezoid a=50m, c=30m, d=15m. If we add an 8% loss to the calculated length, how many meters of mesh do we need to fence it?
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