1. (20 pts) Given n is a positive integer, prove that n is odd if and only if n² + 3 is even. You must use definitions of even (and odd, if needed). Do not use "even plus even is even" or similar rules of thumb.

Q: Prove: Given a polynomial p(x) with degree n and cЄ R, we have n p(x) = p(c) + Σ p(k) (c) k! k=1 -(x…

A: Detailed explanation:We shall utilize the following properties of polynomials and their derivatives…

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Q: 1. Digicel's profit function for the sale of S21 is as follows: л(q)=-2q²+350q - 150 The selling…

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Q: Form Three Consumer Arithmetic Assignment You are now twenty-six years old with a first degree, and…

A: Conclusion:Based on the calculations, renting a studio apartment is the more financially economical…

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Q: Calculate the missing values. Express dollar values rounded to two decimal places and break-even…

A: To solve the missing values, we will use the following formulas depending on the given and the…

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Q: Two sides and an angle​ (SSA) of a triangle are given. Determine whether the given measurements…

A: The objective of the question is to determine whether the given measurements can form a triangle,…

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A: step: 1In given question  is solved ,so it's solution is as follows; (b). Define G:R→Rby the rule…

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A: gcd(1,769,2,378)=1,769*x+2,378*y2,378=1*1,769+6091,769=2*609+gcd(1,769,2,378)=1,769*x+2,378*y2,378=1…

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A: The objective of the question is to prove that the given relation R is an equivalence relation. An…

Q: write 49D2 fourteen in the base ten system

A: The objective of this question is to convert a number from base fourteen to base ten. The number…

Q: b) iv)

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Q: Calculate the limits of the following progressions

A: Step 1:Step 2:Step 3: Step 4:

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A: To find f'(1), we need to differentiate the given function f(p) with respect to p and then evaluate…

Q: 4) Let VM2x2(F) be the set of all matrices of size 2 × 2 and let U and W be two subspaces of V such…

A: Step 1: Step 2: Step 3: Step 4:

Q: Let H be the function from the space of 3 × 1 matrices by itself defined by the formula: H a Show…

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Q: Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it…

A: Of the four options provided, the correct answer is the first parametrisation:(2 sin(πt), 2 cos(πt),…

Q: Fixed Cost (FC) per month Variable Cost (VC) per unit Selling Price (S) Break-even Volume (x) Total…

A: a. break even volume = fixed cost/(selling price-variable cost)=8,800/(37-23)=628.57 or 629Total…

Q: washer-dryer combination can be purchased from a department store by making monthly credit card…

A: referencesRivaldo, Y., Kamanda, S. V., & Yusman, E. (2022). The Effect Of Products, Promotions…

Q: 1. Digicel's profit function for the sale of S21 is as follows: π(q)=-2q²+350q - 150 The selling…

A: a:Given information:Profit function: π(q) = -2q^2 + 350q - 150Price function: p = 600 - 2qStep 1:…

Q: 1348 trays of food are at the cafeteria if the trays of food are spread out evenly onto eight…

A: Total number of trays = 1348  Number of different tables = 8  We need to find out how many trays of…

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A: Step 1: First find out the (m,n) which belong to the equivalence classes R for x, y ∈ A. As mRn ⟺…

Q: (3) (a) Find Taylor polynomial of degree three at x0 = 0, for f(x) = 2x·

A: The objective of this question is to find the Taylor polynomial of degree three for the function…

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Q: (a) Consider the equation y = x² - 2x. What curve does this represent in R²? Make a sketch of the…

A: Step 1: Analyze the equation for y (part (a))The equation y = x^2 - 2x represents a parabola in…

Q: Calculate the convergence of the following progressions

A: 1. To calculate the convergence of the given sequence:lim n->∞ (sqrt(n) - sqrt(n+1)) / (sqrt(n) +…

Q: E 28° 14 58° F 28+58-86-180=-9 olve for x. R H P 30° 8+6x 4x+2 0

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Q: 3/2 What is the value of fff e(x² + y²+2²)³½³ dV, where B is the unit ball, x² + y² + z² ≤ 1? 4 (π…

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Q: f(x) = 4x³-3x²+7x-11 Draw or add images here Question Details Done 1 19. Find an equation for the…

A: Original function:f(x)=4x3−3x2+7x−11 1. Identify the Function and the Derivative:We are given the…

Q: Three vectors V1, V2, and V3 are given. If they are linearly independent, show this; otherwise, find…

A: The given three vectors are v1​=⎣⎢⎡​103​⎦⎥⎤​,v2​=⎣⎢⎡​3−512​⎦⎥⎤​ and v3​=⎣⎢⎡​3−714​⎦⎥⎤​.Writing them…

Q: Question Content Area Computer equipment was acquired at the beginning of the year at a cost of…

A: Given information, Equipment cost or Book value of the equipment at the beginning of Year 1=…

Q: Prepare á frequency distribution of the following data, showing the number of popsicles produced:…

A: For any query with the solution, please ask in the comment box.

Q: 10 points eBook Print References Classify the situation as stratified random sampling, systematic…

A: Step 1: Define the common sampling techniques*Simple sampling is where samples are chosen entirely…

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Q: Suppose you are shopping for a gift and see the item you want at 35% off. The price is usually $150.…

A: The objective of this question is to find out the sale price of an item after a discount of 35% on…

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A: Step 1:Step 2:

Q: 2 Question 14, 4.6.6 Find a general solution to the differential equation using the method of…

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Q: 1 2. Can c = 1 be written as a linear combination of a1, a2, a3 ? explain why or 1 why not?

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Q: dx d (2² dy) + + λxy = 0, y(1) = 0, y′(2) = 0, form a regular Sturm-Liouville system. Show further…

A: Step 1: Step 2: Step 3: Step 4:

Q: A diagonalization of the matrix A is given in the form P-1AP = D. List the eigenvalues of A and…

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A: Here, if the height of rock is y and the time is x seconds, y belong to 0.81, and x belongs to 0.3…

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A: a.n=8r=29the number of vertical lines is 8-1= 7 vertical linesThe number of crosses is equal to…

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A: Step 1:Given:Total numbers (n) =17,Selected number =9  formula is used:…

Q: The veterinarian prescribes prednisone to Murphy the dog at 1.5mg/kg. The prednisone comes in…

A: Approach to solving the question:Calculate Murphy's Prednisone Dose: Determine Murphy's weight and…

Q: Solve the following trigonometric equation 2sim20+ cose-1 = 0; 0≤0< 2π

A: Step 1: Step 2: Step 3: Step 4:

Q: Use residues to establish the following integration formul

A: Step 1: Step 2: Step 3: Step 4:

Q: Let G be the function from the space of 2 × 2 matrices to itself defined by: a b G (2) - [d 3a+c -b…

A: Step 1: Step 2: Step 3: Step 4: