Latest word problems
- 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´?
- 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?
- 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.
- 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.
- The piglet
The weight of the piglet grew regularly by five kilograms for four months. Determine the proportion by weight of the piglet in each month, if the first weighed 35 kg.
- The dough
The dough contains water, flour, and sugar. Water and flour in a ratio of 2: 3, flour, and sugar in a ratio of 2: 1. Determine the ratio of all three components of the dough.
- Two parallel chords
In a circle 70 cm in diameter, two parallel chords are drawn so that the center of the circle lies between the chords. Calculate the distance of these chords if one of them is 42 cm long and the second 56 cm.
- Water percent
A 15 g sample of the substance contains 70% water. After drying, the weight was reduced to 9 g. What percentage of water is now in the sample?
- Birthday paradox
How large must the group of people be so that the probability that two people have a birthday on the same day of the year is greater than 90%?
- The water tank
The water tank has the shape of a sphere with a radius of 2 m. How many liters of water will fit in the tank? How many kilograms of paint do we need to paint the tank, if we paint with 1 kg of paint 10 m2?
The lifetime of a light bulb is a random variable with a normal distribution of x = 300 hours, σ = 35 hours. a) What is the probability that a randomly selected light bulb will have a lifespan of more than 320 hours? b) Up to what value of L hours can th