Ratio + mean - practice problems
Number of problems found: 17
- Divide line segment
Find the point P on line segment AB, such that |AP| = r |AB|. Coordinates of endpoints: A = (−2, 0, 1), B = (10, 8, 5), ratio r = 1/4. - Length 26
The length of the median of the trapezoid is 10 inches. The median divides the trapezoid into two areas whose ratio is 3:5. The length of the shorter base is: - Pentagon
The signboard has the shape of a pentagon ABCDE, in which line BC is perpendicular to line AB, and EA is perpendicular to line AB. Point P is the heel of the vertical starting from point D on line AB. | AP | = | PB |, | BC | = | EA | = 6dm, | PD | = 8.4dm - Lengths of medians from coordinates
There is a triangle ABC: A [-6.6; 1.2], B [3.4; -5.6], C [2.8; 4.2]. Calculate the lengths of its medians.
- Gas prices 2021
According to the SPP price list in 2021, the price of natural gas, together with its supply, is as follows: D1 - we cook. Fix 3.34 euros/month and 0.0479 euros/kWh (1 cubic meter of gas is approximately 10.555 kWh. It is called combustion heat and changes - An architect 2
An architect is designing a house. He wants the bedroom to have the dimensions of 8 ft by 4 ft by 7 ft. The architect doubles all three dimensions to create the den. Does that mean the den will have double the volume of the bedroom? First, find the volume - Two cables
On a flat plain, two columns are erected vertically upwards. One is 7 m high, and the other 4 m. Cables are stretched between the top of one column and the foot of the other column. At what height will the cables cross? Assume that the cables do not sag. - Distribute 32451
The king cannot decide how to distribute 4 cubes of pure gold, which have edges of length 3cm, 4cm, 5cm, and 6cm, to two sons as fairly as possible. Design a solution so that the cubes do not have to be cut. - Mixture of nuts
We should prepare the mixture of nuts from almonds, peanuts, and nuts cashew ratio of 1:2:3 (respectively). The price of almonds is 150 CZK/kg, the price of peanuts is 140 CZK/kg, and the price of cashew nuts is 180 CZK/kg. The price of the mixture is det
- Five numbers in ratio
Five integers are in the ratio 1: 2: 3: 4: 5. Their arithmetic mean is 12. Determine the smallest of these numbers. - Ten cashiers
Ten cashiers are open at Tesco. Customers wait an average of 15 minutes. How many other cashiers have to open to reduce the waiting time by 4 minutes? - Identical 7683
In a hotel pool, the pool manager drains the water through two identical drains every 10 hours. How much time would he save in draining the pool if the water was drained through three more drains at the same flow rate? - Twenty-three-year-old 6317
The average age of the first five hockey players was 22 years. The coach replaced the twenty-three-year-old player with a younger one, which lowered the average age of the first five hockey players to 21 years. How old is the new player? - Bases
The length of the bases trapezium is in ratio 4:5. The length of the midline is 15. How long are the bases of a trapezoid?
- Cyclist
The cyclist goes uphill 10 km for 50 minutes and downhill minutes for 29 minutes. Both applied to the pedals with the same force. How long does he pass 10 km by plane? - Daily average
Calculate the average temperature during the day, when 14 hours were 24 °C and 10 hours was 14 °C. - Tractors
Fields go plow two tractors with various performances. The first tractor plows the whole field in 11 hours. The second tractor plows the whole field 19 hours longer. How long does it take to plow the whole field with two tractors?
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