answer:Let's break down the problem into cases depending on where Procedure A is placed:Case 1: Procedure A is at the first step.This means we have 4 remaining procedures (B, C, D, and E) to arrange, with the constraint that C and D must be consecutive.We can treat Procedures C and D as a single entity since they must be consecutive, and thus we have three entities to arrange: "CD", B, and E.There are 3! ways to arrange these three entities.For each of those arrangements, there are 2 ways to arrange C and D within the "CD" entity (CD or DC).So the number of possible arrangements for Case 1 is 3! times 2 = 6 times 2 = 12.Case 2: Procedure A is at the last step.By the same reasoning as Case 1, we again have 4 remaining procedures to arrange with the same constraints.Thus, the number of possible arrangements for Case 2 is also 3! times 2 = 12.By adding the arrangements from both cases, we get the total number of possible arrangements:Total number of arrangements = Case 1 + Case 2 = 12 + 12 = 24.So there are boxed{24} possible arrangements for the experimental sequence.

answer:First, let's find the sum of the given vectors:begin{align}overrightarrow{a} + 2overrightarrow{b} &= (cos 5^{circ},sin 5^{circ}) + 2(cos 65^{circ},sin 65^{circ}) &= (cos 5^{circ} + 2cos 65^{circ}, sin 5^{circ} + 2sin 65^{circ}). end{align}Next, we'll find the magnitude (modulus) of the resulting vector:begin{align}| overrightarrow{a} + 2overrightarrow{b} | &= sqrt{(cos 5^{circ} + 2cos 65^{circ})^2 + (sin 5^{circ} + 2sin 65^{circ})^2} &= sqrt{(cos^2 5^{circ} + 4cos^2 65^{circ} + 4cos 5^{circ}cos 65^{circ}) + (sin^2 5^{circ} + 4sin^2 65^{circ} + 4sin 5^{circ}sin 65^{circ})} &= sqrt{(cos^2 5^{circ} + sin^2 5^{circ}) + 4(cos^2 65^{circ} + sin^2 65^{circ}) + 4(cos 5^{circ}cos 65^{circ} + sin 5^{circ}sin 65^{circ})} &= sqrt{1 + 4 + 4(cos(65^{circ}-5^{circ}))} &= sqrt{5 + 4cos 60^{circ}} &= sqrt{5 + 4 left(frac{1}{2}right)} &= sqrt{7}. end{align}So, the magnitude of overrightarrow{a} + 2overrightarrow{b} is boxed{sqrt{7}}.

answer:It is obvious x, y, and z are symmetrical. We are going to solve the problem by Completing the Square.x ^ 2 + y ^ 2 + z ^ 2 - xy - yz - zx = 12x ^ 2 + 2y ^ 2 + 2z ^ 2 - 2xy - 2yz - 2zx = 2(x-y)^2 + (y-z)^2 + (z-x)^2 = 2Because x, y, z are integers, (x-y)^2, (y-z)^2, and (z-x)^2 can only equal 0, 1, 1. So one variable must equal another, and the third variable is 1 different from those 2 equal variables. So the answer is boxed{D}.~[isabelchen](https://artofproblemsolving.comhttps://artofproblemsolving.com/wiki/index.php/User:Isabelchen)

answer:(1) Since f(0) = 1, we have c = 1. Next, considering f(x + 1) - f(x) = 2x, we can expand it as:[f(x + 1) - f(x) = [a(x + 1)^2 + b(x + 1) + 1] - (ax^2 + bx + c) = 2x,]simplifying which leads to:[a(2x + 1) + b = 2x.]Comparing coefficients, we get the system of equations:[begin{cases}2a = 2a + b = 0end{cases}]From this, we deduce a = 1 and b = -1. Therefore, the expression for f(x) is:[boxed{f(x) = x^2 - x + 1}.](2) To tackle the inequality f(x) geq 2x + m, we can rewrite it as:[x^2 - x + 1 geq 2x + m,]which simplifies to:[x^2 - 3x + 1 - m geq 0 quad text{on the interval} [-1, 1].]Let g(x) = x^2 - 3x + 1 - m. The axis of symmetry for this quadratic function is x = frac{3}{2}, which is not inside the interval [-1, 1]. Hence, g(x) is decreasing on [-1, 1].The minimum value of g(x) in the given interval will occur at x = 1, so we need to guarantee that g(1) geq 0 to satisfy the inequality over [-1, 1]. We evaluate g(1):[g(1) = 1^2 - 3(1) + 1 - m geq 0,]which implies -1 - m geq 0. Solving this inequality for m, we get m leq -1.Therefore, the range for the real number m is:[boxed{m leq -1}.]

answer:Let the tangent point be (m, n),The derivative of y=- frac {1}{2}x+ln x is y'=- frac {1}{2}+ frac {1}{x},Thus, the slope of the tangent line is - frac {1}{2}+ frac {1}{m},Given the equation of the tangent line y= frac {1}{2}x-b,We have - frac {1}{2}+ frac {1}{m} = frac {1}{2},Solving this gives m=1, n=- frac {1}{2}+ln 1=- frac {1}{2},Then, b= frac {1}{2}m-n= frac {1}{2}+ frac {1}{2}=1.Therefore, the answer is: boxed{1}.By setting the tangent point as (m, n) and finding the derivative of y=- frac {1}{2}x+ln x, we can determine the slope of the tangent line. Using the given equation of the tangent line, we can solve for m=1, and by substituting into both the tangent line equation and the curve equation, we can find the value of b.This problem tests the application of derivatives: finding the slope of the tangent line, understanding the geometric meaning of derivatives, and correctly deriving and setting the tangent point are key to solving the problem. It is a basic question.

answer:From the problem statement, there are 5 gaps formed between the 6 people. To insert 3 seats into these gaps, the number of different seating arrangements can be calculated as A_{6}^{6}C_{5}^{3}=7200. Therefore, the correct answer is boxed{A}. The problem involves permutations, combinations, and simple counting, testing the students' computational skills, and is quite basic.