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Let n be a positive integer. If T is a subset of {1,...,n} we say that T is an n-palindrome if, for every i in {1,...,n}, if i is in T then n+1-i is in T. For instance, {1,2,4,5} is a 5-palindrome, but is not a 6-palindrome. Examples of 6-palindromes include {2,5} andthe empty set. Show with a combinatorial proof that the number of n-palindromes equals 2^(n/2) for n even, and 2^(n+1/2) for n odd. (Hint: A set of cardinality k has 2k subsets.)
A 180-lb person compresses a bathroom scale 0.060 in. If the scale obeys Hooke's law, how much work is done compressing the scale if a 90-lb person stands on it?
two straight roads intersect to form an angle of 75. find the shortest distance from one road to a gas station on the other road 1000 ft from the junction.
Use Gauss's law to find the charge enclosed by the cube with vertices {(+/-)1,(+/-)1,(+/-)1} if the electric field is E(x,y,z) = 4xi+2yj+1zk
If you know the order of the normalizer N of can you find the generators for N? Give a solid math argument why this is correct and please keep the answer as simple as possible at the same time.
Suppose instead of making monthly deposits, Mary decides to deposit a "lump sum" into the account. How much must she deposit? What is this value also called?
The perimeter of a rectangle is 42 m. The Length of the rectangle is 3 m more than twice the width. Find the dimensions of the rectangle.
the length of a wall in a floor plan is 6 an a half in . the actual wall is 78 ft long . find the scale of the floor plan.
Apples sell for $2 per pound and oranges for $3 per pound. suppose Ben bought 5 pounds of fruit at the cost of $12. how many pounds of each kind of fruit did ben buy.
The measure of three of the angles of a quadrilateral are 67, 112, and 55 degree. What is the measure of the fourth angle?
Given that the necessary assumptions are satisfied, can it be concluded, at the 2.5% level of significance, that not all mean times to relieve pain are equal ? Formulate and test the appropriate hypotheses. Use the critical value approach.
The marketing research department for a computer company used a large city to test market their new product. They found that the demand equation was p= 1296-0.12 x^2.
An employee receives a weekly salary of $310 and a 4% commision on all sales
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