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Which of the following is NOT a potential cable wiring fault detected by a wire map tester? answer Split pair Reversed pair Signal attenuation Crossed pair (TX/RX transposed)

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Find the Taylor polynomial of order 3 generated by f at a. f(x) = e^{-5x}, a = 0

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rovides a list of potential capabilities that an organization could look for in a particular attack. Based upon the capabilities discovered to be used in the attack, it may be possible to identify the adversary with a high probability of a correct attribution (the potential for false flag operations means that no attribution is ever certain).

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Interpreting a Line Graph In a line graph, a line that goes up means an increase in value while a line that goes down from its previous point means a decrease in value. Example 4 As the new librarian, Judith wants to put all things in order. She made an inventory of the monthly checkout of books for the last six months that she was not around. Let us study the graph that she made below: Answer the questions: 1. What is the line graph all about? 2. What is the scale used in the $ y $-axis? 3. In which month was checking out of books is at its highest? 4. How many books were checked out in June? 5. Which month has the lowest check out of books recorded?

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Proof that f is onto: To show that f is onto, let m be any nonnegative integer in Znonneg. On a separate piece of scratch paper, find an element of Z+ written as an expression using the variable m, with the property that when f is applied to it, the result is m. Write the expression in the box below. Incorrect: Your answer is incorrect. Show that the Proof: In order to show that f is countable we must construct a well-defined function f: Z* = Znonneg that is both one-to-one and onto. We will show that the following is a function from Z* to Znonneg that satisfies these requirements. (Choose one definition for f and use it for the rest of the proof.) - f(n) = n + 2 for each positive integer n - f(n) = n + 1 for each positive integer n - f(n) = n - 1 for each positive integer n - f(n) = n^2 for each positive integer n - f(n) = |n| for each positive integer n Proof that f is one-to-one: To show that f is one-to-one, let n and n' be any integers in Z* and assume that f(n) = f(n'). By definition of f, we have the following: f(n) = f(n') Substituting the expressions for f(n) and f(n') into the equation f(n) = f(n') and simplifying the result shows that n = n'. Thus, f is one-to-one. Proof that f is onto: By construction, the quantity in the box is a positive integer and when the function f is applied to it, the result is m. Thus we have shown that there exists an element of Z* that is sent to m by f, and so f is onto.

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(Sterling Numbers) The Sterling number $S(n, r)$ counts the number of ways $n$ people can be divided in $r$ non empty teams. (Equivalently, it is the number of ways to partition a set of size $n$ into $k$ nonempty subsets.) The teams should be considered non specific. This means that the teaming {\{a\}, \{b\}, \{c,d\}} is same as {\{b\}, \{a\}, \{c,d\}}. 1. What are the values of $S(n, n)$ and $S(n, 1)$? (1-point) 2. List all the ways one can form 3 teams from a set of 5 people. Use this to determine the value of $S(5, 3)$. (2-points) 3. Show (using a combinatorial proof or otherwise) that for any natural numbers $n$ and $r$, $S(n+1,r) = S(n, r-1) +r S(n,r)$

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3.4 Verify that the two-dimensional transformation relations giving Cartesian stresses in terms of polar components are given by $\sigma_x = \sigma_r \cos^2\theta + \sigma_\theta \sin^2\theta - 2\tau_{r\theta} \sin\theta \cos\theta$ $\sigma_y = \sigma_r \sin^2\theta + \sigma_\theta \cos^2\theta - 2\tau_{r\theta} \sin\theta \cos\theta$ $\tau_{xy} = -\sigma_r \sin\theta \cos\theta - \sigma_\theta \sin\theta \cos\theta + \tau_{r\theta} (\cos^2\theta - \sin^2\theta)$

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2. Use the following information to calculate the concentration of hydrogen gas present in the container at equilibrium. Show all of your work: Methane gas, $CH_4(g)$, can be produced in a laboratory by reacting carbon disulfide, $CS_2(g)$, and hydrogen gas, $H_2(g)$, as represented by the following equation. $CS_2(g) + 4H_2(g) \rightleftharpoons CH_4(g) + 2H_2S(g)$ Initially, at a temperature of 90 °C. 0.18 mol/L $CS_2(g)$ and 0.31 mol/L $H_2(g)$ are present in a closed container. When equilibrium is established, 0.13 mol/L $CS_2(g)$ is present.

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5. Liddle Problem 11.3: a. The temperature at the core of the Sun is around $10^7$ K. How old was the Universe when it was this hot? Was it matter dominated or radiation dominated at that time? b. At the CERN collider, typical particle energies are of order of 100 Gev. How old was the Universe when typical particle energies were around this size? What was the temperature at this time? Note: The answer in the text is not quite correct.

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The Pythagorean triple (a, b, c) is primitive if a, b, c are positive integers and gcd(a, b, c) = 1. Suppose a = 2mn, b = $m^2$ - $n^2$ and c = $m^2$ + $n^2$. Assuming that m > n, and gcd(m, n) = 1, and that m and n are of opposite parity, find all primitive Pythagorean triples such that 0 < c < 30 by filling out the following table: [Hint: Use the constraints on m and n and the fact that if c < 30, then m cannot be more than 5]. m n a b c

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claudia v.