Entries by Paul

4) A fast-food restaurant wants a special container to hold coffee.

4) A fast-food restaurant wants a special container to hold coffee. The restaurant wishes thecontainer to quickly cool the coffee from 200°F to 130°F and keep the liquid between 110° and130°F as long as possible. The restaurant has three containers to select from.The CentiKeeper Company has a container that reduces the temperature of a liquid […]

1 Show, ifnNis not prime, then there exists[a],[b]Zsuch that[a][0][b], but[a][b]=[0]. Show, ifpNis prime,[a],[b]Zand[a][0][b], then[a][b][0].

1 Show, if n∈N is not prime, then there exists [a],[b]∈Z such that [a]≠[0]≠[b], but [a]⋅[b]=[0]. Show, if p∈N is prime, [a],[b]∈Z and [a]≠[0]≠[b], then [a]⋅[b]≠[0]. 2. Suppose R and S are two equivalence relations on a set A. Prove that R ∩ S is also an equivalence relation. (For an example of this, look at Figure 11.3. Observe that for the equivalence relations R2,R3 and R4, […]

Exercise 5. Consider the vector space P3 with inner product defined by (f,g) = f(-1)g(-1) + f(0)g(0) + f(1)g(1) + f(2)g(2). (a) Find an orthonormal…

Can anyone help me out with his problem? It is about Applied Linear Algebra. Exercise 5.Consider the vector space P3 with inner product defined by(f,g) = f(-1)g(-1) + f(0)g(0) + f(1)g(1) + f(2)g(2).(a) Find an orthonormal basis for the subspace spanned by 1, x, and x2.(b) Find the projection of the function 1 + 4x […]

Part of your task as a scholar-practitioner is to act as a critical consumer of research and ask informed questions of published material. Sometimes, claims are made that do not match the results of t

Part of your task as a scholar-practitioner is to act as a critical consumer of research and ask informed questions of published material. Sometimes, claims are made that do not match the results of the analysis. Unfortunately, this is why statistics is sometimes unfairly associated with telling lies. These misalignments might not be solely attributable […]