# Harder math problems - page 4 of 5

- IS trapezoid

Calculate the length of diagonal u and height v of isosceles trapezoid ABCD, whose bases have lengths a = |AB| = 37 cm, c = |CD| = 29 cm and legs b = d = |BC| = |AD| = 28 cm. - Cone in cylinder

The cylinder is an inscribed cone. Find the ratio of the volume of the cone and cylinder. Please write the ratio as a decimal number and as a percentage. - School trip

The class has 19 students. How can students be accommodated in the hostel, where available 3× 2-bed, 3× 3-bed and 1× 4-bed rooms? (Each room has its unique number) - Pediatrician

Pediatrician, this month of 24 working days takes 6 days holidays. What is the probability that on Monday it will be at work? - Pizza

A school survey found that 10 out of 15 students like pizza. If 5 students are chosen randomly, what is the probability that all 5 students like pizza? - Fertilizer

Mr. Gherkin uses for fertilization 7% solution of fertilizer. 17 liters of it still left. How much water must be added to the solution to make only the 3% solution? - Tanks

The fire tank has a cuboid shape with a rectangular floor measuring 13.7 m × 9.8 m. Water depth is 2.4 m. Water was pumped from the tank into barrels with a capacity of 2.7 hl. How many barrels were used if the water level in the tank fell 5 cm? Wri - Free fall

Pavel fall from height 9 m. Calculate the speed he hit the ground when falling with acceleration g = 9.81 m/s² - Painting school

Redecoration school had scheduled for four crew to 10 days. After two days, a single worker was ill. For how many days was the school painted when remain workers working with the same tempo? - Cube in a sphere

The cube is inscribed in a sphere with a volume 7253 cm³. Determine the length of the edges of a cube. - Strawberries

Father collects strawberries himself in 4 hours, son in 14 hours. How long will it take them along when dad comes to help his son collect strawberries after 3 hours? - Euclid1

The right triangle has hypotenuse c = 27 cm. How large sections cuts height h_{c}=3 cm on the hypotenuse c? - Vector sum

The magnitude of the vector u is 12 and the magnitude of the vector v is 8. The angle between vectors is 61°. What is the magnitude of the vector u + v? - Two doctors

Doctor A will determine the correct diagnosis with a probability of 89% and doctor B with a probability of 75%. Calculate the probability of proper diagnosis if both doctors diagnose the patient. - Clock

What time is now if the time elapsed afternoon is 2/10 of time that elapses before midnight? - Insurance

The house owner is insured against natural disasters and pays 0.04% annually of the value of the house 53 Eur. Calculate the value of the house. Calculate the probability of disaster if you know that 41% of the insurance is to pay damages. - Tiles

From how many tiles, 20 cm by 30 cm, we can build a square of maximum dimensions if we have maximum 881 tiles. - RT - hypotenuse and altitude

The right triangle BTG has hypotenuse g=117 m, and the altitude to g is 54 m. How long are hypotenuse segments? - Balls

Three metal balls with volumes V_{1}=81 cm³ V_{2}=96 cm³ and V_{3}=28 cm³ melted into one ball. Determine its surface area. - Plastic pipe

Calculate the plastic pipe's weight with diameter d = 70 mm and length 380 cm if the wall thickness is 4 mm and the density of plastic is 1367 kg/m³.

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