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Let T(n) denote an equilateral triangular board with side length of 2^n units, subdivided into 4^n equilateral triangles with side length of one unit each. A trapezoidal tile (or triangular triomino) is a tile consisting of 3 adjacent equilateral triangles, each with side length one. (See picture in the textbook on page 277) Prove, using mathematical induction, that if any corner triangle is removed from a T(n) then the rest of the triangular board can be tiled using trapezoidal tiles for any positive integer n. Use part (a) and mathematical induction to show that if all three of the corner triangles and one additional triangle is removed from T(n) then rest of the triangular board can be tiled using trapezoidal tiles for any positive integer n.
Let G be finite abelian group with this property: For each positive integer m such that m | |G|, there are exactly m elements in G with order dividing m. Prove that G is cyclic.
Identify the meaning of independent and dependent events. Calculate probabilities and joint probabilities of simple events. Explain the basic logic of probability theory
a beam is clamped horizontally at both ends and carries a concentrated load at the middle of the beam. find the static
What value would you expect to find for the standard deviation of all these sample means? (round to the nearest integer)
A salesperson receives a year-end bonus if sales credited to that person average Shs50,000 per quarter or higher. The home office informs the salesperson that sales credited in the first three quarters have averaged Shs 40,000 per quarter. What mi..
Wiiand Corporation has 50,000 shares of $10 par value common stock outstanding. It declares a 10% stock dividend on december 1 when the market value per share is $16.
find the area of the parcel of land that is , the area under the curve y=x^3+1 over the interval 0 and 1 where x and y are in hundreds of feet. If the land in the parcel is appraised at RM12 per square feet, what is the total value of the parcel? ..
one train travels 392 miles and 20 mph faster in the same time another train travels 322 miles. What is the speed of each train?
Suppose that at a certain instant the volume is 590 cubic centimeters and the pressure is 97 kPa and is decreasing at a rate of 13 kPa/minute. At what rate in cubic centimeters per minute is the volume increasing at this instant?
Find the dimensions of a right circular cylinder that is open on the top, isolated on the bottom, holds 1 liter, and uses the least amount of material.
Explain the five-steps for solving rational equations. Can any of these steps be eliminated? Can the order of these steps be changed? Would you add any steps to make it easier, or to make it easier to understand?
Calculate Clayton's profit margin and debt ratio.
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