The most difficult problems
Number of problems found: 6044
- Cancel fractions
Compress the expression of factorial: (n+6)!/(n+4)!-n!/(n-2)!
- Normal distribution GPA
The average GPA is 2.78 with a standard deviation of 4.5. What are students in the bottom the 20% having what GPA?
What overload in g (g-force) has passed the pilot if he accelerated from 0 to 600 km/h in 3 seconds?
- The Scout Tent
The Scout Tent has a rectangular wooden underlay with dimensions of 220 cm and 150 cm. How much canvas is needed for a 170 cm high of pyramid roof?
- Hypotenuse - RT
A triangle has a hypotenuse of 55 and an altitude to the hypotenuse of 33. What is the area of the triangle?
- Hexagon ABCDEF
In the regular hexagon ABCDEF, the diagonal AE has a length 8cm. Calculate the circumference and the hexagon area.
- The sides
The sides of a rectangle are in a ratio of 2:3, and its perimeter is 1 1/4 inches. What are the lengths of its side? Draw it.
- Right angled triangle 3
Side b = 1.5, hypotenuse angle A = 70 degrees, Angle B = 20 degrees. Find its unknown sides length.
- Water flow 2
How many litres of water will flow in 7 minutes from a cylindrical pipe 1 cm in diameter, if the water flows at a speed of 30 km per hour
- Train speed
Two guns were fired from the same place at an interval of 10 minutes and 30 seconds, but a person in a train approaching the place hears second shot 10 minutes after the first. The speed of the train (in km/hr), supposing that sound travels at 340 m/s is:
- Exponential warm
Suppose that a body with temperature T1 is placed in surroundings with temperature T0 different from that of T1. The body will either cool or warm to temperature T(t) after time t, in minutes, where T(t)=T0 + (T1-T0)e^(-kt) . If jello salad with 30 degree
- Diagonal to area
Calculate the area of a rectangle in which the length of the diagonal is 10 cm.
- Curve and line
The equation of a curve C is y=2x² -8x+9 and the equation of a line L is x+ y=3 (1) Find the x co-ordinates of the points of intersection of L and C. (2) Show that one of these points is also the stationary point of C?
- Radioactive material
A radioactive material loses 10% of its mass each year. What proportion will be left there after n=6 years?
- Equilateral triangle
A square is inscribed into an equilateral triangle with a side of 10 cm. Calculate the length of the square side.
- Ruler and compass
Use a ruler and compass to construct a triangle ABC with AB 5cm BAC 60° and ACB 45°.
- Bitoo and Reena
Bitoo ate 3/5 part of an apple and the remaining part was eaten by his sister Reena. How much part of an apple did Renna eat? Who had the larger share? By how much?
- Tallest and shortest
Jenn is the tallest on the team. He is 1 1/2 times as tall as the shortest girl whom is 4 1/4 feet tall. How tall is Jebb?
Twelve students work on a week forestry brigade. One hundred spruces will receive x CZK, one hundred pine y CZK. How many receive each one students did in one day if they planted a total of 25,000 spruces per week and 30,000 pine trees? Express by express
There are 200 draws in the raffle, but only 20 of them win. What is the probability of at least 4 winnings for a group of people who have bought 5 tickets together?