Numerade

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Birth weights of babies in the United States can be modeled by a normal distribution with mean 3250 grams and standard deviation 550 grams. Those weighing less than 2500 grams are considered to be of low birth weight.

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A nation has a(n)________________ if it is the only source of a particular product or if it can make more of a product using fewer resources than other countries.

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As light enters the eye, what is the first structure through which it must pass? the lens the cornea the iris the aqueous humor

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Write the expression $i(t)$ if $v(t) = 200(e^{-3000t})u(t)$ V. Show all steps.

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The two areas of the brain thought to be overactive in people with autism spectrum disorder are the ____ and the ____. O amygdala, prefrontal cortex O amygdala, fornix O cerebellum, striatum O prefrontal cortex, hippocampus O thalamus, cingulate cortex

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Exercise 4.8.24 Let $\Omega$ have n elements. How many partitions are there of $\Omega$ into exactly k sets, for each $k \in \{1, \dots, n\}$? Conditional Probability, Independence, and Bayes' Theorem $\cdot$ 155 Exercise 4.8.25 Let's revisit the previous exercise. Assume all possible partitions of $\Omega$ are equally likely. If n = 4 what is the probability that all sets in the partition have the same number of elements? Can you answer this for general n? Exercise 4.8.26 We flip a coin that is heads with probability .2 and tails with probability .8. We then roll two fair (and independent) die if the coin comes up heads, or roll three fair die if it comes up tails. What is the probability the sum of the dice is 3?

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Rewrite without parentheses: 2x^2z^4 - 7z^6 * -3x^5z Simplify your answer as much as possible: -6x^7z^5 + 21x^5z^7

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(a) As suggested in class one can model two adjacent inert gas atoms as linear oscillating electric dipoles. Fill in the mathematics between the following two equations: $H_1 = \frac{e^2}{4\pi\epsilon_0} \left[ \frac{1}{R} + \frac{1}{R + x_1 - x_2} - \frac{1}{R + x_1} - \frac{1}{R - x_2} \right]$ and $H_1 \approx -\frac{e^2}{4\pi\epsilon_0} \frac{2x_1x_2}{R^3}$ (b) As suggested in the lecture, a normal mode transformation can change the coupled oscillating dipole problem into a sum of two independent oscillators with slightly modified energies and spring constants. Do the math which uses the normal mode approximation to go from the coupled oscillator hamiltonian $H_0 + H_1 = \frac{p_1^2}{2m} + \frac{Cx_1^2}{2} + \frac{p_2^2}{2m} + \frac{Cx_2^2}{2} - \frac{2e^2x_1x_2}{4\pi\epsilon_0R^3}$ to two uncoupled oscillators $H_0 + H_1 = \frac{P_a^2}{2m} + \frac{C_ax_a^2}{2} + \frac{P_s^2}{2m} + \frac{C_sx_s^2}{2}$ (c) In lecture we argued that the coupling lowers the ground state energy of the two oscillator system as follows: $\hbar\omega_s + \hbar\omega_a = \hbar\omega_0 - \frac{\hbar\omega_0}{8} \left[\frac{2e^2}{\pi\epsilon_0CR^3}\right]^2 = \hbar\omega_0 - \frac{A}{R^6}$ Prove this statement.

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Consider the Job Market Signalling model discussed in the slides. a) Suppose that the costs of education for low type workers are 60,000 for every year of education. For which values of $y^*$ do we obtain a Separating equilibrium? Compared to the original case, what happens to Pareto efficiency? Provide an intuitive explanation of your answers. b) Suppose that the costs of education for high type workers are 30,000 per year (and for low type 40,000/year). For which values of $y^*$ do we obtain a Separating equilibrium? Compared to the original case, what happens to Pareto efficiency? Provide an intuitive explanation of your answers. c) Suppose that the costs of education are the same for both workers. Can education still be used as a productivity signal? Explain your answer carefully.

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Show that the absorption coefficient of a Lorentz oscillator at the line centre does not depend on the value of ?0.

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josefina k.