The most difficult problems

Number of problems found: 6044

  • Cancel fractions
    zlomky_15 Compress the expression of factorial: (n+6)!/(n+4)!-n!/(n-2)!
  • Normal distribution GPA
    normal_d_3 The average GPA is 2.78 with a standard deviation of 4.5. What are students in the bottom the 20% having what GPA?
  • Overload
    aircraft-02_10 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
    jehlan_4b_obdelnik_2 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
    triangle_bac_1 A triangle has a hypotenuse of 55 and an altitude to the hypotenuse of 33. What is the area of the triangle?
  • Hexagon ABCDEF
    hexagon_2 In the regular hexagon ABCDEF, the diagonal AE has a length 8cm. Calculate the circumference and the hexagon area.
  • The sides
    rectangle_9 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
    right_triangle_3 Side b = 1.5, hypotenuse angle A = 70 degrees, Angle B = 20 degrees. Find its unknown sides length.
  • Water flow 2
    water3_9 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
    trains_9 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
    teplomer_6 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
    rectangle_5 Calculate the area of a rectangle in which the length of the diagonal is 10 cm.
  • Curve and line
    parabol 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
    radium A radioactive material loses 10% of its mass each year. What proportion will be left there after n=6 years?
  • Equilateral triangle
    vpisany_stvorec A square is inscribed into an equilateral triangle with a side of 10 cm. Calculate the length of the square side.
  • Ruler and compass
    triangle_bac Use a ruler and compass to construct a triangle ABC with AB 5cm BAC 60° and ACB 45°.
  • Bitoo and Reena
    apples_10 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
    meter_9 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
    stromy_9 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
  • Raffle
    tombola_3 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?

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