Math practice for 13 year olds - page 44 of 422

Number of problems found: 8424

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.
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?
Segments 6
Compare the ratio of 1cm and 1m.
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?
New Year's price increase
After the New Year, the prices of goods changed in a ratio of 3 : 2. How much will we now pay for a dining set (6 chairs and a table), if the chair originally cost €44 and the table €232?
Princess 2
The fat princess weighed 168kg on October 5. By November 10, her weight had changed in the ratio of 7:4. How much did she weigh on November 10? Did she gain or lose weight?

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