Examples for secondary school students - page 38

  1. Mean
    integrales if the mean of the set of data 5, 17, 19, 14, 15, 17, 7, 11, 16, 19, 5, 5, 10, 8, 13, 14, 4, 2, 17, 11, x is -91.74, what is the value of x?
  2. Rotating cone
    kuzel_3 Calculate the volume and the surface area of a rotating cone of base radius r = 2.3 dm and a height h = 46 mm.
  3. Pine
    trees How much of a mixed forest rangers want to cut down, if their head said: "We only cut down pine trees, which in our mixed forest 98%. After cut pine trees constitute 94% of all trees left."
  4. Two pipes
    2pipes One pipe fill one-fifth volume 20 minutes before by second one. The two pipes together will fill the tank in two hours. How long is will fill tank each pipe separately?
  5. Tower model
    tower Tower height is 300 meters, weight 8000 tons. How high is the model of the tower weight 1 kg? (State the result in the centimeters). The model is made from exactly the same material as the original no numbers need to be rounded. The result is a three-digi
  6. Legs
    zidle In the room are four-legged chairs, three-legged stool, and all are sitted with (one) people. I counted all the leg room and there were a total of 39. How many are there chairs, stool and people?
  7. Three vectors
    vectors_sum0 The three forces whose amplitudes are in ratio 9:10:17 act in the plane at one point so that they are in balance. Determine the angles of the each two forces.
  8. Geometric sequence
    cralici In the geometric sequence is a4 = 20 a9 = -160. Calculate the first member a1 and quotient q.
  9. Geometric progression 2
    exp_x There is geometric sequence with a1=5.7 and quotient q=-2.5. Calculate a17.
  10. Scouts
    skauti_2 Scouts purchased for camp cans two types total cost 1460 CZK. First cans were for CZK 32 and second for 25 CZK. How many cans purchased each type?
  11. Decimal to fraction
    fractions_2 Write decimal number 8.638333333 as a fraction A/B in the basic form. Given decimal has infinite repeating figures.
  12. Profits
    podnikavec Two members will make profit 52 000, - EUR. The forst earned 8% more and the second 10% more and thus earned together 56 700, - EUR. How many will initially each earn?
  13. Parabola
    parabola_1 Find the equation of a parabola that contains the points at A[6; -5], B[14; 9], C[23; 6]. (use y = ax2+bx+c)
  14. Center of gravity
    map_1 The mass points are distributed in space as follows - specify by coordinates and weight. Find the center of gravity of the mass points system: A1 [14; -2; 5] m1 = 10.2 kg A2 [-2; -16; 7] m2 = 13.6 kg A3
  15. Two months
    mars with moons Mars has two months, Phobos and Deimos. Phobos orbits around Mars in 7 hours 39 minutes and Deimos in 30 h 14 min. How long will repeat the relative position of the three celestial bodies?
  16. Segment in a triangle
    priecka In a triangle ABC with the side/AB/ = 24 cm is constructed middle segment/DE/ = 18 cm parallel to the side AB at a distance 1 cm from AB. Calculate the height of the triangle ABC to side AB.
  17. Ratio of two unknown numbers
    numbers2_23 Two numbers are given. Their sum is 30. We calculate one-sixth of a larger number and add to both numbers. So we get new numbers whose ratio is 5:7. Which two numbers were given?
  18. MATES
    sazka In MATES (Small Television tipping) from 35 randomly numbers drawn 5 winning numbers. How many possible combinations there is?
  19. Trapezoid 15
    trapezoid3 Area of trapezoid is 266. What value is x if bases b1 is 2x-3, b2 is 2x+1 and height h is x+4
  20. Traffic laws
    car_lights Under traffic regulations, car lights can illuminate the road up to a maximum of 30 m. To check the reach of the dipped-beam lights of their car, Peter stopped car at 1.5 m from the wall. The dipped-beam headlights are 60 cm high. At what height on the wa

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