Basic operations and concepts - math word problems - page 302 of 324
Number of problems found: 6465
- Shadow - an observation tower
How tall is an observation tower if it casts a shadow 9.6 m long at the exact same moment that a half-metre pole casts a shadow 30 cm long? - Triangle similarity area
The area of a right-angled triangle KLM with a right angle at the vertex L is 60 mm square, and its hypotenuse k is 10 mm long. Triangles KLM and RST are similar. The similarity ratio is k=2.5. Calculate the area of triangle RST. - An architect 2
An architect is designing a house. He wants the bedroom to be 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 of the bedroom. Sol - Sides of the triangle
The sides of the triangle ABC have a length of 4 cm, 5 cm, and 7 cm. Construct triangle A'B'C', similar to triangle ABC, which has a circumference of 12 cm. - Similarity coefficient
Given triangle ABC with sides a = 12 cm, b = 9 cm, c = 7 cm, and triangle DEF with sides d = 8.4 cm, e = 6.3 cm, f = 4.9 cm. Determine whether triangles ABC and DEF are similar. If so, state the similarity ratio and the theorem by which they are similar. - Tree shadow length
How long is the shadow of a tree 7.6 m high, and the shadow of a 190 cm high road sign is 3.3 m long? - Shadows At the park, a young woman who is 1.72 meters tall casts a 3.5 meters shadow at a certain hour. What is the height of a tree in the park that, at the same time, casts a 12.3 meters shadow?
- Chimney shadow height
At the same time, a vertical 2-meter pole casts a shadow of 0.85 meters. At the same time, a chimney of unknown height casts a 45 m long shadow. Determine the height of the chimney. - Drug effectiveness probability
According to clinical studies, the effectiveness of the drug is 90%. The doctor prescribed the medicine to eight patients. What is the probability that the drug will be effective in all these patients? - Cylinder volume ratio
Calculate the cylinder's volume if you know that the ratio of the cylinder's height to the base's radius is 3:2 and the height is 15 dm. - Points in plane
The plane is given 12 points, 5 of which are located on a straight line. How many different lines could be drawn from these points? - Plane count
There are 12 points in space, with no three lying on a straight line. How many different planes are determined by these points? - Suppose 4
Suppose that 14% of all steel shafts produced by a certain process are nonconforming but can be reworked (rather than having to be scrapped). Consider a random sample of 200 shafts, and let X denote the number among these that are nonconforming and can be - Center of gravity
Find the set of points formed by the center of gravity of right triangles with the same hypotenuse (build several possible triangles into one image). - Cleaner injury hours
Four cleaners will clean the hotel in 15 hours. How long will they clean if, after 8 hours, one gets injured and leaves? - Diameter of a drum
Winding drum length 180 mm, initial diameter 60 mm. Using a 6 mm rope with a length of 50 m, what will be the diameter of the wound drum with the rope? - Percentage - prism and cube
Prism with square base a=25 cm, height h=45 cm. cube: b=15 cm a) what percentage of the volume of the prism is the volume of the cube? b) what height should the prism have to have the same volume as the cube? - Block dimension ratio
A cuboid has dimensions in the ratio 9:5:4. Determine its volume, given that the sum of the longest and shortest edges is 65 cm. - Equilateral triangle ABC
In the equilateral triangle ABC, K is the center of the AB side, the L point lies on one-third of the BC side near point C, and point M lies on one-third of the side of the AC side closer to point A. Find what part of the ABC triangle contains the triangl - Triangle from sticks
Bob the boulder has many sticks of lengths 3.5 and 7. He wants to form triangles, each of whose edges consists of exactly one stick. How many non-congruent triangles can be formed with the sticks?
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