Units - math word problems

30-60-90
The longer leg of a 30°-60°-90° triangle measures 5. What is the length of the shorter leg?
Angle between vectors
Find the angle between the given vectors to the nearest tenth of a degree. u = (-22, 11) and v = (16, 20)
Sales off
If a sweater sells for $ 19 after a 5% markdown, what was its original price?
Rhombus diagonal
Area of rhombus is 224. One diagonal measures 33, find length of other diagonal.
Gasholder
The gasholder has spherical shape with a diameter 20 m. How many m³ can hold in?
Scouts
The boys from scout group traveled 5 days distance 115 km. Every day walked 1.5 km less than the previous day. How many kilometers scouts walked in the first day?
Carpenter
From wooden block carpenter cut off a small cuboid block with half the edge length. How many percent of wood he cut off?
Dog
Man goes with a dog on a long walk 17 km from the house. Man is walking at speed 4.9 km/h and a dog that constantly running between house and man at 12.6 km/h. How many kilometers will run the dog when they reach their destination?
Truncated cone
Calculate the height of the rotating truncated cone with volume V = 1115 cm³ and a base radii r₁ = 7.9 cm and r₂ = 9.7 cm.
Bases
The length of the bases trapezium are in ratio 4:5. Length of midline is 15. How long are the bases of a trapezoid?
Racer
The first racer run at a speed 20 m/s and is 750 meters before the finish and ahead 79 meters before second competitor. At what speed must run the second racer to catch first racer at the finish line?
Flowerbed
Flowerbed has the shape of an isosceles obtuse triangle. Arm has a size 5.5 meters and an angle opposite to the base size is 94°. What is the distance from the base to opposite vertex?
Sales vs profit
Apple sells 22 percent less computes than the Acer but the profit from their sales is 2.2 times higher than Acer. How many times are Apple computer more expensive than Acer?
Divers
20-member group of divers carries the air for 15 hours of diving. 4 members of the expedition sick or wasn't came. How many hours is sufficient air to other divers?
TV commercials
For the typical one-hour prime-time television slot, the number of minutes of commercials is 3/8 of the minutes of the actual program. Determine how many minutes of the program are shown in that one hour.
The professor's birthday
Professor of mathematics had 57 birthdays. The director congratulated him. The professor asked the director: "And how old are you?" The director replied: "I'm exactly twice as many years than you were when I was old as to you today." How old is the dire
Car
The driver of a car is to get to 608 km distant city. From atlas found that 162 km will have to pass through the cities at average speed 48 km/h. Remainder of the journey pass outside the cities at average speed 116 km/h. Calculate how many hours it will
Ice cream in cone
In the ice cream cone with a diameter of 5.7 cm is 0.8 dl of ice cream. Calculate the depth of the cone.
Painter Pavel
Painter Pavel painted the fence for 16 hours and painter Petr the same fence painted for 13 h. How long should take painted the fence together?
Cable car 2
Cable car rises at an angle 41° and connects the upper and lower station with an altitude difference of 1175 m. How long is the track of cable car?

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