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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.)
What is the exact area of a circle with a diameter of 29 inches? In an 8 inch square cake pan and a 10 inch square cake pan, what is the difference in volume each pan will hold? Assume each pan is 1.5 inches high. Show step by step work. Include co..
use 3.14 for pi. please show how to solve. A one-story building is 130 ft by 390 ft. if a square patio with sides 27 ft occupies the center of building, how much area remains for offices?
Probability Distribution: Mean, Variance & S.D. A frequency distribution is shown below. Complete parts (a) through (e). The number of dogs per household in a small town
Consider a Lagrangian system, with configuration space R^n, given by (x^1, ... x^n); and Lagrangian L(x', ..., x^n; v^1, ... v^n). Now consider a new system of coordinates, (y^1,... ^n),
What is the marginal cost per bicycle?
Prove the Second Isomorphism Theorem: If A is an ideal of R and S is a subring of R, then S+A is a subring, A, and (S intersecting A) are ideals of S+A and S, respectively, and (S+A)/A isomorphic to A/(S intersecting A).
Show that if R and S are commutative rings with 1, phi:R-->S is a homomorphism of R onto S, and I is an ideal of R, then phi[I]={phi(r): r included in I} is an ideal of S.
State whether each of the following fraction is a terminating or repeating decimal. If the decimal terminates, state the number of decimal places and show how you decided.
If the farmer can make a profit of $140 per acre on crop A, $200 per acre on crop B and $150 per acre on crop C how many acres of each crop should be palnted to mazimize profit?
The times were approximately Normal and the standard deviation of all such corrections was known to be 1.3 days. What is the rejection point at α = 0.001 to testHo:μ=8vs. Ha:μ>8?
At the first tri-city meeting, there were 8 people from town A, 7 people from town B, and 5 people from town C
Vital information about Quantitative analysis:Networks, PERT, critical path. A project was planned using PERT with three times estimates. The expected completion time of the project was determined to br 40 weeks
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