Power - high school - math problems

  1. Cube construction
    222cube A 2×2×2 cube is to be constructed using 4 white and 4 black unit cube. How many different cubes can be constructed in this way? ( Two cubes are not different if one can be obtained by rotating the other. )
  2. A rectangle 2
    rectangles A rectangle has a diagonal length of 74cm. Its side lengths are in ratio 5:3. Find its side lengths.
  3. Before yesterday
    percent He merchant adds a sale sign in his shop window to the showed pair of shoes in the morning: "Today by p% cheaper than yesterday. " After a while, however, he decided that the sign saying: "Today 62.5% cheaper than the day before yesterday". Determine the
  4. Compound interest 3
    exp_growth2 After 8 years, what is the total amount of a compound interest investment of $25,000 at 3% interest, compounded quarterly? (interest is now dream - in the year 2019)
  5. Divide 8
    powers Divide 6840 by x y and z, in such a way that x has twice as much as y, who has half as much as z
  6. Three members GP
    exp_growth The sum of three numbers in GP (geometric progression) is 21 and the sum of their squares is 189. Find the numbers.
  7. Six speeds
    gears-3 A drilling machine is to have 6 speed ranging from 50 to 750 revolution per minute. If the speed forms a geometric progression, determine their values.
  8. Eq2 2
    kardan3rd Solve following equation with quadratic members and rational function: (x2+1)/(x-4) + (x2-1)/(x+3) = 23
  9. Investment 2
    exp_growth2 Jack invested $5000 in a 5-month term deposit at 4.7% p. A. . At the end of the 5-months, jack reinvested the maturity value from the first deposit into an 11-month term deposit at 7.3% p. A. What is the maturity value at the end of the second term deposi
  10. Curiosity factor
    wwww A blogger starts a new website, initially the number of the traffic is 293 due to their curiosity factor. The business owner estimated that the traffic will increase by 2,6% per week. What will be the number of it in week 5?.
  11. Profit growth
    growth The profit of a company increased by 25% during the year 1992, increased by 40% during the year 1993, decreased by 20% in the year 1994 and increased by 10% during the year 1995. Find the average growth in the profit level over the four years periods?
  12. Substitution method
    500px-Sine_cosine_plot.svg Solve goniometric equation: sin4 θ - 1/cos2 θ=cos2 θ - 2
  13. Precious metals
    gold_3 In 2006-2009, the value of precious metals changed rapidly. The data in the following table represent the total rate of return (in percentage) for platinum, gold, an silver from 2006 through 2009: Year Platinum Gold Silver 2009 62.7 25.0 56.8 2008 -41.3
  14. Powers 3
    exp_4 2 to the power of n divided by 4 to the power of -3 equal 4. What is the vaule of n?
  15. Boys and girls
    boy_6 There are eight boys and nine girls in the class. There were six children on the trip from this class. What is the probability that left a) only boys b) just two boys
  16. Last digit
    olympics_3 What is the last number of 2016 power of 2017
  17. Geometric progression
    exp_1 In geometric progression, a1 = 7, q = 5. Find the condition for n to sum first n members is: sn≤217.
  18. Water lilies
    lekno_2 Water lilies are growing on the pond and their number is doubled every day. The whole layer is covered in 12 days. How many days will it cover 8 layers?
  19. Find the 2
    square_4 Find the term independent of x in the expansion of (4x3+1/2x)8
  20. Radioactive material
    radium A radioactive material loses 10% of its mass each year. What proportion will be left there after n=6 years?

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