Math practice for 13 year olds - page 44 of 420

Number of problems found: 8399

Two Sections
A sphere with a radius of 5 cm was divided into two spherical sections. The height of the smaller section is 1cm. Determine the volume of the smaller section to the nearest hundredth of a cm³.
To the cinema 2
On Tuesday, 20 more visitors came to the cinema than on Monday. On Wednesday, half as many visitors came as on Tuesday. There were a total of 175 visitors to the cinema during these three days. How many were there each day?
Members 2
The members of a housing cooperative elected a seven-member board. In how many ways can a chairman, vice-chairman, treasurer, and recorder be chosen from among them?
Books in Slovak and English
Vlasta has 4 Czech and 3 English books. She wants to arrange them on a shelf so that Slovak books are first and then English books are second. How many ways are there to do this?
Birthday boy 2
In how many ways can seven people be seated around a table so that the birthday boy sits at the head?
HAMMER 3
Determine how many ways it is possible to rearrange the letters of the word HAMMER so that in this rearrangement some group of consecutive letters forms the word WATER.
Base RR odd
The base of the prism is an isosceles trapezoid ABCD with bases AB = 12 cm, and CD = 9 cm. The angle at vertex B is 48° 10'. Determine the volume and area of the prism if its height is 35 cm.
Relay
The relay race will be run for the class of Katka, Alice, Michaela, and Erika. Determine how many different orders there are in which the girls can run, as long as each of them can run in any position.
Police on time
A boat with smugglers has left the shore and is traveling at a speed of 85 km/h. In 10 minutes, a police boat starts chasing it at a speed of 110 km/h. International waters, where the possibility of apprehending smugglers ends, begin 30 km from the coast.
Map - route
The map has a scale of 1:40000. In how many centimeters will the route, which measures 4.8 km, be shown on it?
Tanker 3
A gasoline tank weighs 4500kg. If we pump 30% of the gasoline out of the tank, it will weigh 3900kg. How many kilograms does an empty tank weigh?
RR trapezoid 12
In an isosceles trapezoid ABCD, calculate the missing lengths of the sides when a=46cm, b=85cm height=84cm.
Perimeter 59
The perimeter of a circular bed is 36m. Find the length of the part of its perimeter that corresponds to the given central angles: 90°, 45°30', 120°, 15°
Beads
We have 4 beads. One is green, one is yellow, and 2 are pink. In how many possible ways can we string them on a string?
Competitor 2
In the race, 1 twelfth of the competitors finished ahead of me and 7 eighths of the competitors finished behind me. How many of us ran?
Calculate
A rotating cone has a diameter of 16 cm and a side of 10 cm. Calculate the surface area and volume of the solid.
Mirror
The dimensions of the mirror are 750mm x 700mm, the mirror should be tilted 8° from the wall. How many cm must it be tilted from the wall?
Reduced - rectangles
The dimensions of the rectangle are a = 42 cm, and b = 91cm. Determine the perimeter and area of the rectangle, which is reduced in size compared to the original rectangle in the ratio 6:7.
Segment - ratio
Calculate the size of the new segment that is created by changing the segment CD = 12 cm in the ratio 4 : 3.
Price increase
As part of a packaging innovation, the price of mineral water, which previously cost €0.68, was changed in the ratio of 11:8. How much will we pay for a bottle of mineral water now?

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