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A 41-year-old male presents to the ED for complaints of right foot pain and foul odor to a sore that does not seem to be healing. You observe a nickel sized open area to right foot with yellow purulent drainage and foul odor. Past medical history of hypertension and diabetes. Vital signs: Temp 99.9, BP 112/64, HR 96, RR 16. Took 1g Tylenol an hour prior to arrival for pain. Pain currently 5/10. What is this patient’s ESI level?

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In order to calculate ΔG of a reaction, what must we know? Question 6 options: a) The equilibrium constant b) Concentration of reactants only c) Whether a reaction is thermodynamically favorable or not d) Concentration of products only Is related to the change in free energy of the reaction

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Let \[ f(x)=\sqrt{x+2} \] and \[ g(x)=x^{2}-5 \] .Evaluate $ (f \circ g)(\sqrt{39}) $.

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1. For a measurable function $f: X \rightarrow C$, where $X, \mathcal{M}, \mu$ is a measure space, we define $\|f\|_{\infty} := \inf \{M \in \mathbb{R} : |f| \le M$ a.e.$ \}$. For $f \in L^1(X, d\mu)$, prove that $\lim_{p \rightarrow \infty} \|f\|_p = \|f\|_{\infty}$, (Hint: treat $\lim \sup$ and $\lim \inf$ separately.)

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2. (a) Ralph has utility function is $u(x) = x$, so he is risk neutral. Ralph is facing a potential loss of $L, which has a probability of $\frac{1}{10}$ of happening. He can choose to insure this loss at a price of $\gamma$ for each dollar of risk insured. For what prices $\gamma$ does Ralph choose to buy full insurance (i.e., buy $L of insurance)? (b) Priya has a linear value function $v(x) = x$ but evaluates lotteries using probability weighting. Her probability weighting function satisfies $\pi(\frac{1}{10}) > \frac{1}{10}$. Priya is facing a potential loss of $L, which has a probability $\frac{1}{10}$ of happening. She can choose to insure this loss at a price of $\gamma$ for each dollar of risk insured. For what prices $\gamma$ does Priya choose to buy full insurance (i.e., buy $L of insurance)? Express your answer in terms of $\pi(\frac{1}{10})$. (c) Is Ralph or Priya's demand for insurance higher?

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Question 2 (30 points) For the directed graph below A B E C D G F J I a. find the strongly connected components. b. draw a DAG from strongly connected components the strongly connected components formed in part a. c. Provide a valid topological sort for the directed acyclic graph (DAG) that you created in part b.

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Problem 6. Let $f(x) = \begin{cases} \frac{-1 + \sqrt{1 + 2x^2}}{x + \sin(\pi x)}, & x \neq 0, \\ 0, & x = 0. \end{cases}$ (a) Find $f'(2)$. Write your answer in the form $ax + b$, where $a$ and $b$ are some rational numbers. (b) Find $f'(0)$

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The point P is on the unit circle. Find P(x, y) from the given information. The x-coordinate of P is positive, and the y-coordinate of P is $\frac{-\sqrt{10}}{10}$. P(x, y) = (\boxed{0, -1})$

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4. Complex conjugate poles. Answer the following. Caution: one of the three parts is a trick question. When you reach the trick question, briefly discuss the trick. [a] Consider the continuous linear system characterized by the transfer function Determine $\omega_n$ and $\zeta$. $H_a(s) = \frac{10^5}{s^2 + 5s + 100}$ [b] Repeat part a for $H_b(s) = \frac{10^5}{s^2 + 20s + 100}$ [c] Repeat part a for $H_c(s) = \frac{10^5}{s^2 + 52s + 100}$

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2. Analyze the network below (assume $V_{BE} = 0.7V$, $V_T = 26 mV$, $\beta = 100$ and $r_e = 10k\Omega$). a. Draw the d.c. biasing circuit; calculate the quiescent collector current $I_C$ b. Draw the a.c. equivalent circuit (use the mid-frequency a.c. model for the BJT). c. Calculate small signal a.c. voltage gain $V_{out}/V_{sig}$. Show all work.

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william c.