answer:Technical analysts in the financial markets often find employment in the following sectors: 1. Investment banks, where they contribute to trading decisions and create research reports. 2. Asset management companies, assisting portfolio managers in making investment choices. 3. Stockbroking firms, providing analysis to support clients' trading activities. 4. Financial advisory firms, offering market insights and analysis for investment recommendations.

answer:To find the sum, combine like terms: begin{align*} p(x) + q(x) &= (11.7x^2 - 9.1x^2) + (-0.1x + 3.6x) + (12.9 - 4.9) &= (11.7 - 9.1)x^2 + (-0.1 + 3.6)x + (12.9 - 4.9) &= 2.6x^2 + 3.5x + 8.0 end{align*} So, the sum is 2.6x^2 + 3.5x + 8.0.

answer:Given Information: Confidence level: 95% Margin of error: 0.1 Population proportion (p) is unknown Since the population proportion (p) is unknown, we will use the conservative estimate of p = 0.5 to calculate the sample size. Formula: n = (Z^2 * p * (1-p)) / E^2 where: Z is the z-score corresponding to the desired confidence level p is the estimated population proportion E is the margin of error Substituting the values: Z = 1.96 (for a 95% confidence level) p = 0.5 E = 0.1 n = (1.96^2 * 0.5 * (1-0.5)) / 0.1^2 n = (3.8416 * 0.5 * 0.5) / 0.01 n = 0.9604 / 0.01 n ≈ 96 Therefore, a sample size of approximately 96 full-time students should be interviewed to achieve a 95% confidence interval with a length of no more than 0.1.

answer:In mathematics, a ring and its modules share a relationship akin to that between a field and its vector spaces. A vector space is a structure (V,mathbb{F}, +, cdot), where (V, +) is an abelian group, and mathbb{F} is a field acting on V through scalar multiplication, which is compatible with vector addition and field multiplication. A ring, on the other hand, is a triple (R, +, times), with (R, +) as an abelian group and a bilinear multiplication operation. When we replace the field in a vector space's definition with a ring, we obtain a module. For example, consider the set of smooth vector fields on a manifold M; they form a module over the ring of smooth real-valued functions C^{infty}(M). To connect the concepts of rings and vector spaces more closely, we can consider an algebra over a field. An algebra, (A, mathbb{F}, +, cdot), is a vector space (A, mathbb{F}, +) equipped with a bilinear product (ring multiplication) that is associative and unital, satisfying the following properties for all a, b in mathbb{F} and r, s in A: 1. Distributive law: a cdot (r + s) = a cdot r + a cdot s and (a + b) cdot r = a cdot r + b cdot r. 2. Associativity: (r cdot s) cdot t = r cdot (s cdot t). 3. Unit: There exists an element 1_A in A such that 1_A cdot r = r cdot 1_A = r for all r in A. Examples of algebras over a field include: 1. Square matrices of order n over mathbb{F}. 2. The polynomial ring mathbb{F}[x]. 3. The ring of continuous real-valued functions on a topological space X. 4. Clifford algebras, encompassing real numbers, complex numbers, bi-complex numbers, quaternions, and hypercomplex systems. 5. Algebras of linear operators, which are crucial in functional analysis. If we consider rings without the assumption of commutativity or associativity, we obtain non-associative algebras like Lie algebras, which are useful in differential geometry to study vector fields on manifolds. Further generalizations lead to structures like Banach algebras, C*-algebras, Poisson algebras, and Hopf algebras. As an example, every ring R is an R-module over itself, where the scalar multiplication is simply the ring multiplication itself. In this case, the module's operation is the ring's multiplication, and the identity element acts as the neutral scalar.