A character trait is a habit, a physical attribute, or an attitude that helps define a character. Why might Ortiz Cofer have given Eugene's mother the character traits of a face like a doll and a tiny, sweet-sounding voice?

Simplify the expression. -5t + 12 + 8 - 7t

Dennis owns 24% of a partnership. Bob owns 48% of the partnership. If Rich is the third partner, what percent of the partnership does he own? Write a simplified ratio to represent their investments in the partnership.

For aspartic and glutamic acids, the isoelectric point occurs at a pH where the net charge on the two carboxyl groups is -1 and balances the charge of +1 on the $\alpha-$amino group. Calculate pI for these amino acids.

How does caffeine reach the brain after someone drinks a cup of coffee or tea? In your answer, be sure to identify the systems involved.

When the author says "But it says nothing," does she really mean that "Sayonara" has no meaning? Explain.

Write each exponential equation in logarithmic form. $\left( a ^ { 2 } \right) ^ { 2 } = a ^ { 4 }$

An astronaut with a mass of $90 \mathrm{kg}$ (including spacesuit and equipment) is drifting away from his spaceship at a speed of $0.20 \mathrm{m} / \mathrm{s}$ with respect to the spaceship.The astronaut is equipped only with a $0.50-\mathrm{kg}$ wrench to help him get back to the ship. With what speed and in what direction relative to the spaceship must he throw the wrench for his body to acquire a speed of $0.10 \mathrm{m} / \mathrm{s}$ and direct him back toward the spaceship? Explain.

The Burden Corporation manufactures racquets. The racquets have the expense equation $E=r q+f$. What is the average cost of producing x racquets?

In an investigation of thermophysical properties of methylbenzene R.D. Goodwin (J. Phys. Chem. Ref. Data 18, 1565 (1989)) presented expressions for two phase boundaries. The solid-liquid boundary is given by $p / bar =p_{3} / bar + 1000(5.60+11.727 x) x$ where $x=T / T_{3}-1$ and the triple point pressure and temperature are $p_{3}= 0.4362\ \mu b a r$ and $T_{3}=178.15\ \mathrm{K}.$ The liquid-vapour curve is given by $\ln (p / bar) = -10.418 / y+ 21.157-15.996 y + 14.015 y^{2} - 5.0120 y^{3} + 4.7334(1-y)^{1.70}$ where $y=T / T_{e}=T /(593.95\ K).$ (a) Plot the solid-liquid and liquid-vapour phase boundaries. (b) Estimate the standard melting point of methylbenzene. (c) Estimate the standard boiling point of methylbenzene. (The equation you will need to solve to find this quantity cannot be solved by hand, so you should use a numerical approach, e.g. by using mathematical software.) (d) Calculate the standard enthalpy of vaporization of methylbenzene at the standard boiling point, given that the molar volumes of the liquid and vapour at the standard boiling point are $0.12\ \mathrm{dm}^{3}\ \mathrm{mol}^{-1}$ and $30.3\ \mathrm{dm}^{3}\ \mathrm{mol}^{-1},$ respectively.

One end of a cantilever beam of length L is built into a wall and the other end is supported by a single post. The deflection, or "sag," of the beam at a point located x units from the built-in end is modeled by the formula

$$D=k\left(2 x^{4}-5 L x^{3}+3 L^{2} x^{2}\right)$$

where k is a positive constant. Where does the maximum deflection occur on the beam?

Write the prime factorization of 5000 using exponents.

Describe how product yield affects unit cost.

After the Challenger disaster in 1986, a study was made of the 23 launches that preceded the fatal flight. A mathematical model was developed involving the relationship between the Fahrenheit temperature x around the O-rings and the number y of eroded or leaky primary O-rings. The model stated that $y=\frac{6}{1+e^{-(5.085-0.1156 x)}}$ where the number 6 indicates the 6 primary O-rings on the spacecraft. Graph the equation using a graphing utility. At what temperature is the predicted number of eroded or leaky O-rings 1? 3? 5?