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Question: In a simple graph, every face has at least three edges. This means that the number of pairs of a face and an edge bordering that face is at least 3f. Use the fact that an edge borders either one or two faces to get an inequality relating the number of edges and the number of faces in a simple planar graph.
The owner has seen tomorrow's weather forecast, which predicts a high of 90° F. About how many lines of bowling can she expect? Answer using a 95% confidence level
the manager of a small business receives a shipment of five hard drives. three hard drives are good and 2 are
In write a vector equation that is equivalent to the given system of equations.
Write an algebraic expression to answer the question below.
Let D be a Euclidean ring, F its field of quotients. Prove the Gauss lemma for polynomials with coefficients in D factored as product of polynomials with coefficients in F.
The function that models the consumption of a certain medication over the years 2000-2010 is 113.19x+223.5 where x is the number of years after 2000 and y is measured in grams per 100,000 people. Find the inverse of this function.
Show that this factorization is useful when computing high powers of A. Find fairly simple formulas for A2, A3, and Ak (k a positive integer), using P and the entries in D.
Maryam pays $3000 on the 30th day of a $7,000, 120-day, and 8% loan.
Rewrite the equation with the right side completely factored.
Suppose that a matrix A has the characteristic polynomial (λ-1)^3*(a*λ+λ^2+b) for some a,b∈R.If the trace of A is 13 and the determinant of A is 21, find all eigenvalues of A.
A positive derivative
Draw recursion trees and find big-T bounds on the solutions to the following recurrences. For all of these, assume that T(1) = 1.
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