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Dad made cookies. Dad ate 1 cookie. Dave ate 1/2 dozen cookies. Kate ate 1/2 of what Dave ate. Henry & Julie each ate 1/3 of what was left.
A large purse is full of coins. If you count them by 13's, 23's, or 31's, there will be one left over. If you count them by 73's there will be none left over.
Show that if {an} ? H, then the power series S8n=0 anzn has radius of convergence > 1.
If we assign number values to letters in the following way: A = 26, B = 25, C = 24 and so on until Y = 2 and Z =1
Describe all subgroups of S5 which are Galois groups of irreducible polynomials of degree 5.
Describe all nonisomorphic central extensions of Z_n by Z_2 x Z_2 meaning central group extensions of the form.
You have three thousand bananas that you have to get to a destination 1000 miles away. You can only carry 1000 bananas at a time.
If n is even, then f is strictly increasing hence one-to-one, on [0,infinity) and f([0,infinity)) = [0,infinity).
At Very Long Hotel in Florida, there are n rooms located along a very long corridor and numbered consecutively from 1 to n.
Suppose we have a building with a floor shaped like an isosceles right triangle. The two sides adjacent to the right triangle have length 100 feet.
Show the existence of an extension of Fq of order l for any prime l.Provide complete and step by step solution for the question.
Let K be obtained as a field Q(a) where a is a root of P(x) = x3 - 3. Find an irreducible polynomial which defines the splitting field of P(x).
Bijection between open interval and half-open interval.Please help with the following problem. Provide step by step calculations.
The endpoints of the diameter of a circle are P=(-3,2) and Q=(5,-6). Find: (i) The center of the circle.
Systems of Linear Equations : Row Operations and Solutions.Find the augmented matrix for each system of linear equations:
Prove that (n + 1)!>2^(n+3) for n>=3 Hint: try using mathematical induction. Provide complete and step by step solution for the question.
The sales S (in thousands of units) of a product after x hundred dollars is spent on advertising is: S = 10(1-e^kx).
Determine the level of sound (in decibels) for the given sound intensity. I=10^-3.5 watt per m^2 (jet 4 miles from takeoff)
Show that the gap between two consecutive squarefree numbers can be arbitrary large.
Use the definition of a logarithm to write the equation in logarithm form. (For instance, the logarithm form of 23 = 8 is log28 = 3.) 93/2 = 27.
Define a universal set U as the set of counting numbers. Form a new set that contains all possible subsets of U.
Leontief Input-Output Model and Real-World Applications.Why did Leontief use linear algebra techniques to create his model?
Solve the following quadratic equations by factorization. Provide complete and step by step solution for the question.
Find how long it takes her to row upstream, how long to row downstream, and how many kilometers she rows?
What do they have in common and how do they help solve systems of linear equations?What is an Eigenvalue? What is an Eigenvector?