Numerade

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2. Danni has 650 in a savings account on 1/1/2021. At the end of the year (on 12/31/2021) she has 720 in the account. She also made the following deposits and withdrawals during the year. Date Deposit Withdrawal Value Before Transaction 3/1 50 0 655 6/15 0 30 720 8/1 0 0 680 10/31 100 0 800 Calculate the time-weighted and dollar-weighted rates of return.

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3) If the coefficient of friction is 0.18, will the block move up the plane, down the plane, or remain at rest.

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1 point) (Exercise 2.22) A bill for $300 is purchased for $294 four months before it is due. Find: a) The nominal rate of discount convertible monthly earned by the purchaser.

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Each allowed energy level of a system of non-interacting fermions has a degeneracy $ M $. If there are $ N $ fermions and $ R $ is the remainder upon dividing $ N $ by $ M $, then the degeneracy of the ground state is 1. $ R^{M} $ 2. 1 3. $ M $ 4. $ { }^{M} C_{R} $

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If the reference voltage has a short to ground, what would be the vehicle symptoms? Explain why this symptom would occur.

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The Bank of Speedy Creek has chosen the following initial balance sheet: Suppose all the banks in the banking system have the same desired reserve ratio as the Bank of Speedy Creek. If the currency drain ratio is 10 percent, the size of the money multiplier is ___.

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(AKS 11a2, DOK 2) Which statement is correct for the refraction diagram below? * incedent ray normal $\theta_1$ Medium 1 Medium 2 $\theta_2$ refracted ray Medium 1 could be air and medium 2 could be water so it travels faster in medium 1. The index of refraction of medium 1 is greater than medium 2 so it travels faster in medium 2. The light travels faster in medium 1. The light travels slower in medium 2.

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1 CSS Farms sells onions in a competitive market and hires workers from a competitive labor market. Labor is the only variable input for CSS Farms. The table below shows the workers hired per day, quantity of onions produced per day, and total costs per day for CSS Farms. The price of an onion is $.50. # of workers hired Quantity of Onions Total Cost 0 0 $10 1 45 $25 2 105 $40 3 145 $55 4 180 $70 5 195 $85 6 200 $100 (a) When the firm hires the third worker, does it experience diminishing marginal returns? (b) What is the marginal revenue product of the third worker? (c) Based on the figures in the table above, what is the wage rate? (d) What is the profit-maximizing number of workers? (e) If the demand for onions increases, will CSS Farms hire more, fewer, or the same number of workers? Explain?

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3. (35 points) A plant is controlled by a proportional controller with a unity feedback as shown below: $T(s)$ Controller Process $Y(s)$ $R(s)$ K $G(s)$ The transfer function of the process is given by $G(s) = \frac{s+2}{s(s+1)(s+b)}$. (a) Obtain the closed-loop transfer function $T(s) = \frac{Y(s)}{R(s)}$. (b) Obtain the sensitivity, $S_b$, of the closed-loop system to small change in the parameter b. (c) With $R(s) = 0$, $T_d(s) = \frac{A}{s}$ and the steady-state error $E(s) = R(s) - Y(s)$, obtain the steady state error $e_d$ due to the disturbance. (d) With $R(s) = \frac{B}{s^2}$, $T_d(s) = 0$ and the steady-state error $E(s) = R(s) - Y(s)$, obtain the steady state error $e_s$ due to the ramp input.

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(ii) $y = \log_a(\tan^{-1}2^x)$

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joseph s.