Numerade

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16. There are three vessels of identical volume, which contain a mixture of wine and water. The ratio of wine to water in each vessel is $ 2: 3,4: 5 $ and $ 5: 7 $, respectively. The mixture of all the three vessels is poured into a big pot. The ratio of wine to water in the new mixture is a) $ 212: 321 $ b) $ 181: 189 $ c) $ 227: 313 $ d) $ 342: 341 $

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1. Two forces are applied as shown in figure 1 to a bracket support. Determine the magnitude and direction of their resultant using trigonometric solution. Figure 1

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Prepare an article on the importance of coral reefs and their significance in the marine ecosystem of the Andaman and Nicobar Islands

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14. At the end of maximum Inspiration: a) Intra-alveolar pressure is zero b) Intra-pleural pressure is zero c) Recoil force of the chest is greater than the recoil force of the lung d) Surface tension is lowest e) Average alveolar PO2 is lower than at the end of maximum expiration

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1. Meaning of \"Extensive\" (20 pts): Consider the Helmholz Free energy $F(N, V, T)$. The fact that $F$ is extensive can be expressed mathematically as, $F(\lambda N, \lambda V, T) = \lambda F(N, V, T)$ (1) From this show that $G = F + PV = N \frac{\partial F}{\partial N}_{V, T} = \mu N$ (2) Hint: Take derivative with respect to $\lambda$ on both sides of equation (1).

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Problem 11 Intro A stock just paid an annual dividend of $5.4. The dividend is expected to grow by 4% per year for the next 4 years. In 4 years, the P/E ratio is expected to be 18 and the payout ratio to be 60%. The required rate of return is 8%. Part 1 What is the intrinsic value of the stock?

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1. Shaquille O'Neal has a 0.53 probability of making a free throw. Assume independence from attempt to attempt. In three attempts, find the following probabilities (give numerical answers to four decimal places): • He made exactly two. • He missed all three. 2. A coin is flipped 8 times: • What is the probability it landed heads 5 times? • What is the probability it landed heads at least once?

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3. A car suspension, as following, can be modeled using a 2DOF system. Car mass $m_1$ = 2000 kg, tire mass $m_2$ = 40 kg, car spring stiffness $k_1$ = 1000 N/m, tire stiffness $k_2$ = 10000 N/m. Calculate a) (10 points) natural frequencies $\omega_1$ and $\omega_2$ b) (15 points) vectors $u_1$ and $u_2$ c) (15 points) Given the initial condition $x_0 = \begin{bmatrix} 0 \\ 1 \end{bmatrix}$ and $v_0 = \begin{bmatrix} 0 \\ 0.5 \end{bmatrix}$, calculate the free response of the system.

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1. (6 points) The time in days between breakdowns of a machine is exponentially distributed with $\lambda = 0.25$. (a) What is the median time between machine breakdowns? (b) What is the probability that after the machine is repaired it lasts at least a week before failing again? (c) If the machine has performed satisfactorily for six days, what is the probability that it lasts at least three more days before breaking down?

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Please help me with this statistics question. A 40-kN axial load is applied to a short wooden post that is supported by a concrete footing resting on undisturbed soil. Determine a) the maximum bearing stress (in MPa) on the concrete footing, and b) the size of the footing (in mm) for which the average bearing stress in the soil is 150 kPa. P = 40 kN v = d^2Fm Farw 121002,000 Sol = 1150 Pa d = ballow N(e01)0h = (50(104)

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colin a.