Grade - math word problems

A farmer's heritage
A farmer died leaving his 17 horses to his 3 sons. When his sons opened up the Will it read: My eldest son should get 1/2 (half) of total horses; My middle son should be given 1/3rd (one-third) of the total horses; My youngest son should be given 1/9th (
Quadrilateral prism
The surface of the regular quadrilateral prism is 8800 cm², the base edge is 20 cm long. Calculate the volume of the prism
Columns of two and three
When students in one class stand in columns of two there is none left. When he stands in columns of three, there is one student left. There are 5 more double columns than three columns. How many students are in the class?
TV tower
Calculate the height of the television tower if an observer standing 430 m from the base of the tower sees the peak at an altitude angle of 23°?
The ladder
The ladder touch on a wall at a height of 7.5 m. The angle of the inclination of the ladder is 76°. How far is the lower end of the ladder from the wall?
Cutting cone
A cone with a base radius of 10 cm and a height of 12 cm is given. At what height above the base should we divide it by a section parallel to the base so that the volumes of the two resulting bodies are the same? Express the result in cm.
Telegraph poles
The bases of two adjacent telegraph poles have a height difference of 10.5 m. How long do the wires connect the two poles if the slope is 39° 30´?
Surface of pyramid
In a regular quadrilateral pyramid, the height of the sidewall is equal to the length of the edge of the base. The content of the sidewall is 32 cm². What is the surface of the pyramid?
Electric work
Calculate the work done by the electric forces passing the current of 0.2 A through the bulb in 10 minutes if the bulb is connected to a 230 V power supply.
Two resistors
Two resistors 20 Ω and 60 Ω are connected in series and an external voltage of 400 V is connected to them. What are the electrical voltages on the respective resistors? Please comment!
Diamond area from diagonals
In the diamond ABCD is AB = 4 dm and the length of the diagonal is 6.4 dm long. What is the area of the diamond?
Lowest voltage
Three resistors with resistors R1 = 10 kΩ, R2 = 20 kΩ, R3 = 30 kΩ are connected in series and an external voltage U = 30 V is connected to them. On which resistor is the lowest voltage?
Height of pyramid
The pyramid ABCDV has edge lengths: AB = 4, AV = 7. What is its height?
What time is it?
What time is it, when there is 4 times less time left until midnight than the time that has elapsed since noon? What time is it, when one-fifth of the hours that have passed since midnight is equal to one-third of the hours that are missing by 12 o'clock?
Circle and square
An ABCD square with a side length of 100 mm is given. Calculate the radius of the circle that passes through the vertices B, C and the center of the side AD.
Double ratio
The mobile phone was twice gradually discounted in the ratio of 3: 2 1 half: 5 quarters. How much did it originally cost if the price was CZK 4,200 after a double discount?
Copper Cu wire
Copper wire with a diameter of 1 mm and a weight of 350 g is wound on a spool. Calculate its length if the copper density is p = 8.9 g/cm cubic.
Recruitment
The circumference
The circumference and width of the rectangle are in a ratio of 5: 1. its area is 216cm2. What is its length?
Probability of failures
In certain productions, the probability of failures is 0.01. Calculate the probability that there will be more than 1 failure among the 100 selected products if we return the selected products to the file after the check.

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