Numerade

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etermine whether or not the following languages are regu- lar. If the language is regular then give an NFA or regular expression for the language. Otherwise, use the pumping lemma for regular languages or closure properties to prove the language is not regular L = {bnak : n > 0, k > 0} ∪ {anbk : k > 0, n > 0}

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1. Markov Decision Processes (5 points) For Thanksgiving, you are trying to prepare a turkey. To prepare the turkey, one can either decrease or increase the temperature of the oven, resulting in the turkey being undercooked, cooked, or burnt. The Markov Decision Process for this scenario is provided in Figure 1. The transition probabilities for decreasing and increasing the temperature are provided in blue and red, respectively. The rewards for the transitions are underlined and green. Using value iteration on the given MDP, compute $V_1(cooked)$. Write down the intermediate steps, including the Q-values for the state-action pairs. +1 0.3 -10 0.2 Decrease +1 Increase 1.0 +1 0.7 +4 0.4 0.6 +1 0.8 +2 Undercooked Cooked Burnt Figure 1: Markov Decision Process

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1. You are asked to help dose vancomycin for a 48 year-old woman who was admitted to the medical ICU 5 days ago with a gastrointestinal bleed and altered mental status. She has been on the ventilator for 4 days now and is suspected to have ventilator associated pneumonia. She was treated for a MRSA pneumonia six months earlier in your facility (MIC = 1). Her pertinent labs/measurements are: height: 67”, weight 72 kg, SCr 0.9 mg/dL (0.8 mg/dL on admission).

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What do inversions and balanced translocations have in common? Question 23 options: They both contain a normal amount of DNA. They both tend to have mild or no phenotypic consequences. They both can cause abnormal gamete production. All of the above statements are true.

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QUESTION 31 Which of the following statements is false with regards to deglutition? The epiglottis elevates to cover the nasopharynx. Sensory receptors are stimulated resulting in a swallowing reflex. Peristalsis of the esophagus propels food toward the stomach. A bolus of food is forced into the pharynx. Tongue blocks the mouth.

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Writing Sample Complete the following in no more than seven sentences: I should be considered for admission to the Quincy College Nursing program over other applicants because

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1. A loan for $2500 with interest at 9.75% compounded semi-annually is repaid after 2 years, 4 months and 230 days. What is the amount of interest paid?

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Question 2. Express the function f(t) = \begin{cases} 0 & t < 0\\ 5 + t^2 & 0 \le t < 3\\ 0 & t \ge 3 \end{cases} in terms of unit step functions and hence determine F(s), the Laplace transform of f(t), in the form F(s) = \frac{A}{s} + \frac{B}{s^3} + \frac{C}{s^3}e^{-\omega s} + \frac{D}{s^2}e^{-\omega s} + \frac{E}{s}e^{-\omega s} Enter the values of A, B, C, D, E and \omega in the boxes below. Enter A: Enter B: Enter C: Enter D: Enter E: Enter \omega:

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A 120V source ($E_1$) [REFERENCE], with an internal impedance of 10, is connected across the primary winding of an ideal transformer with $\alpha = 0.2$ (polarity dot at the top of the winding). $I_1$ flows into the winding, which self-induces $V_1$ across the winding. With perfect magnetic coupling, $V_2$ is mutually-induced across the secondary winding (polarity dot at the top of the winding). For the purposes of this problem, $V_2$ is assumed to point towards the dot side of the secondary winding and causes $I_2$ to flow out of the dot when a series-combination of a 200$\Omega$ resistance and a 600$\Omega$ inductive reactance is connected as the load impedance. Draw the per unit impedance diagram and calculate the per unit and actual values of the: a) voltage across the primary winding b) current entering the primary winding c) voltage across the secondary winding d) current leaving the secondary winding e) voltage across the load impedance f) complex apparent power supplied by the source g) complex apparent power supplied by the transformer

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Question 2: Stress Concentration - Torsion [30 Marks] a) A stepped shaft consisting of solid circular segments having diameters $D_1 = 50$ mm and $D_2 = 60$ mm is subjected to torques $T$. The radius of the fillet is $R = 2.5$ mm. If the allowable shear stress at the stress concentration is 110 MPa, what is the maximum permissible torque $T_{max}$? (10) Figure 1: Stepped Shaft (applies to (a) and (b) above) (Source: Mechanics of Materials Gere & Goodno 7thEd p303)

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stephanie h.