Numerade

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Calculate the heat capacity of 2D electrons at low temperature ($\mu >> k_BT$ or $\beta \mu >> 1$). You may need to use the following integral: $\int_{-\infty}^{+\infty} dx \frac{x^2 e^x}{(e^x + 1)^2} = \frac{\pi^2}{3}$

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A stream containing 60 wt.% styrene (MW 104) and 30 wt.% ethylbenzene, (MW 106), and the balance toluene (MW 92) is fed to a distillation column at a feed rate of 100 kg/hr. The column has two outlets: an overhead stream and a bottoms stream. The overhead stream contains 99% of the toluene that was fed to the column and 90% of the ethylbenzene feed to the column. The styrene composition in the bottoms stream is 95%. Determine the flow rates and compositions of the overhead and bottoms streams.

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If a product has several good substitutes, demand for the product is most likely to be: A. Elastic B. Inelastic C. Unit elastic D. Very inelastic

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Simplify the rational expression \frac{x^2 - x - 2}{x + 1} (a) x + 2 (b) x - 2 (c) x - 1 (d) x + 1 (e) x^2 - 2 (f) none of these

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Why is deoxyribose a good name for the 5-carbon sugar in DNA? Responses: Its 3′ carbon lacks the -OH group found in ribose (and RNA). "Deoxy" means "off-oxygen"—the name makes sense because the sugar's 2′ carbon lacks the -OH group found on ribose. The difference in sugars is the presence or absence of an -OH group on the 2′ carbon, which is the basis of polarity in nucleic acids.

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Question 12 (02.01 MC) In the cell phone market, what demand curve shift would occur if the price of cellular service decreased? Select one: ? a. The demand for cell phones would shift to the left. ? b. The demand for cell phones would shift to the right. ? c. The demand for cell phones and the quantity demanded would remain constant. ? d. The quantity demanded of cell phones would increase, but the demand curve would not shift. ? e. The quantity demanded of cell phones would decrease, but the demand curve would not shift. Clear my choice

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10. When 0.1740g of a 3d transition metal (M) is reacted with an excess of a 3.0M aqueous HCl solution, 128.8mL of hydrogen gas is released and the M3+ chloride salt is formed. The hydrogen gas is collected over water. The temperature at the time of the reaction is 24.0°C. Atmospheric pressure is 749.0 torr. Aqueous vapor pressure at this temperature is 26.7 torr. What is the SYMBOL of the metal? a. Sc b. Ni c. Cr d. Fe e. Zn f. Cu g. Ti 11. A 3.19 mole sample of an ideal gas occupies a volume of 812mL at 553°C. What pressure does it exert? Include the unit with your answer.

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Find the value of $y'$ when $x = 0$ if \\ $xy^2 + e^{y/8} = e$ \\ (A) $-\frac{8^6}{e}$ (B) $-\frac{8^4}{e}$ (C) $-\frac{8}{e}$ (D) $-\frac{8^8}{e}$ (E) $-\frac{8^5}{e}$ (F) $-\frac{8^2}{e}$ (G) $-\frac{8^3}{e}$ (H) $-\frac{8^7}{e}$

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Calculate how many moles of A- and HA are in 0.1 M, 0.01 M, and 0.001 M buffers before and after the addition of extra HCl or NaOH, based on the initial and final pH values. Calculate the theoretical number of moles based on the concentrations and the volume of HCl/NaOH added. Use the Henderson-Hasselbalch Equation to determine the number of moles before and after the addition of HCl/NaOH. To be used for the determined number of moles (before addition): - For 0.1 M, pH = 6.00, pKa = 6.10. - For 0.01 M, pH = 6.06, pKa = 6.10. - For 0.001 M, pH = 6.14, pKa = 6.10. To be used for the theoretical number of moles (after addition): - For 0.1 M, pH = 6.07, pKa = 6.10, 200 microliters of 1 M NaOH added. - For 0.01 M, pH = 7.1, pKa = 6.10, 200 microliters of 1 M NaOH added. - For 0.001 M, pH = 2.3, pKa = 6.10, 200 microliters of 1 M HCl added. Note: The total volume of each buffer solution is 50 mL. Show all work.

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Problem 4. Suppose that T: V ? V is a linear transformation and x, y are two eigenvectors for distinct eigenvalues. Prove that \{x, y\} are linearly independent. Problem 5. Suppose that A is a diagonalizable n \times n matrix. Show that A$^{2023}$ is also

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jennifer s.