Math practice for 13 year olds - page 47 of 424

Number of problems found: 8477

Books in Slovak and English
Vera has 4 Czech and 3 English books. She wants to arrange them on a shelf so that the Czech books come first and the English books second. In how many ways can this be done?
Birthday boy 2
In how many ways can seven people be seated around a table if the birthday boy must sit at the head?
HAMMER 3
Determine in how many ways the letters of the word HAMMER can be rearranged so that some group of consecutive letters in the rearrangement forms the word WATER.
Base RR odd
The base of a 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 surface area of the prism if its height is 35 cm.
Relay
A relay race will be run by the class team of Kate, Alice, Michaela, and Erica. Determine how many different running orders are possible, given that each of them can run in any position.
Police on time
A boat carrying smugglers has left the shore and is travelling at 85 km/h. After 10 minutes, a police boat starts chasing it at 110 km/h. International waters, where the possibility of apprehending the smugglers ends, begin 30 km from the coast. Will the
Map - route
A map has a scale of 1:40,000. How many centimetres will a route of 4.8 km be shown as on the map?
Tanker 3
A full fuel tank weighs 4,500 kg. If we pump out 30% of the gasoline, it will weigh 3,900 kg. How many kilograms does the empty tank weigh?
RR trapezoid 12
In an isosceles trapezoid ABCD, calculate the missing side lengths given a = 46 cm, b = 85 cm, and height = 84 cm.
Perimeter 59
The circumference of a circular bed is 36 m. Find the length of the arc corresponding to the following central angles: 90°, 45°30′, 120°, 15°.
Beads
We have 4 beads: one green, one yellow, and 2 pink. In how many possible ways can we string them onto a string?
Segments 6
Express the ratio of 1 cm to 1 m.
Competitor 2
In a race, 1/12 of the competitors finished ahead of me and 7/8 of the competitors finished behind me. How many of us ran in total?
Calculate
A cone has a base diameter of 16 cm and a slant height of 10 cm. Calculate its surface area and volume.
Mirror
The dimensions of a mirror are 750 mm × 700 mm, and the mirror is to be tilted 8° away from the wall. How many centimetres must the bottom of the mirror protrude from the wall?
Reduced - rectangles
The dimensions of a rectangle are a = 42 cm and b = 91 cm. Determine the perimeter and area of the rectangle after it is scaled down in the ratio 6:7 compared to the original.
Segment - ratio
Calculate the length of a new segment created by scaling 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 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 the ratio 3:2. How much will we now pay for a dining set (6 chairs and a table) if a chair originally cost €44 and the table €232?
Princess 2
A very overweight princess weighed 168 kg on 5 October. By 10 November, her weight had changed in the ratio 7:4. How much did she weigh on 10 November? Did she gain or lose weight?

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