Draw the directional field for the following differential equations. What can you say about the behavior of the solution? Are there equilibria? What stability do these equilibria have? y’ = y - x

Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. A study of seat belt use involved chjldren who were hospitalized after motor vehicle crashes. For a group of 123 children who were wearing seat belts, the number of days in intensive care units (ICU) has a mean of 0.83 and a standard deviation of 1.77. For a group of 290 children who were not wearing seat belts, the number of days spent in ICUs has a mean of 1.39 and a standard deviation of 3.06 (based on data from "Morbidity Among Pediatric Motor Vehicle Crash Victims: The Effectiveness of Seat Belts," by Osberg and Di Scala, American Journal of Public Health, Vol. 82, No. 3). Construct a confidence interval appropriate for the hypothesis: Children wearing seat belts have a lower mean length of time in an ICU than the mean for children not wearing seat belts.

Write the chemical formula for each of the following compounds. (a) magnesium chloride (b) aluminum sulfide (c) tin(II) sulfate (d) iron(III) oxide (e) lead(II) nitrate (f) silver phosphate (g) sulfuric acid (h) hydrochloric acid (i) chlorine dioxide (j) dinitrogen monoxide

Simplify.

$$\frac { - 3 + 11 } { - 1 - 3 }$$

A large research balloon containing $2.00 \times 10^{3} \mathrm{m}^{3}$ of helium gas at 1.00 atm and a temperature of $15.0^{\circ} \mathrm{C}$ rises rapidly from ground level to an altitude at which the atmospheric pressure is only 0.900 atm. Assume the helium behaves like an ideal gas and the balloon’s ascent is too rapid to permit much heat exchange with the surrounding air. Calculate the temperature of the gas at the higher altitude.

$$\begin{array} { l } \text{ Animal physiologists use the formula} \\ \qquad { S = k W ^ { 2 / 3 } } \\ { \text { to calculate an animal's surface area (in square meters) from } } \\ { \text { its weight } W ( \text {in kilograms), where } k \text { is a constant that } } \\ { \text { depends on the animal under consideration. Suppose a phys- } } \\ { \text { iologist calculates the surface area of a horse } ( k = 0.1 ) . \text { If the } } \\ { \text { horse's weight is estimated at } 300 \text { kg } , \text { with a maximum error } } \\ { \text { in measurement of } 0.6 \text { kg } , \text { determine the percentage error in } } \\ { \text { the calculation of the horse's surface area. } } \end{array}$$

evaluate (if possible) the function at each specified value of the independent variable and simplify. f(x) = √x+8 + 2 , f(-8)

Find the relationship between the circumference and area of a circle.

A block in the shape of a rectangular solid has a cross-sectional area of 3.50 cm$^2$ across its width, a front-to-rear length of 15.8 cm, and a resistance of 935 $\Omega$. The block’s material contains $5.33 \times 10^{22}$ conduction electrons/m$^3$. A potential difference of 35.8 V is maintained between its front and rear faces. What is the current in the block?

Write the equation in standard form.

$$- x ^ { 2 } = 15$$

Use the data to make a box-and-whisker plot. 62, 63, 62 ,64, 68, 62, 62

Square root functions and cube root functions are examples of ______ functions.

Evaluate the expression if a = 8, b = 4, and c = 16.

$$\frac{3ab + c^2}{a}$$

At 800 K, the equilibrium constant for the reaction $\mathrm { A } _ { 2 } ( g ) \rightleftharpoons 2 \mathrm { A } ( g ) \text { is } K _ { c } = 3.1 \times 10 ^ { - 4 }$ If the value of $k_f = 0.27 s^{- 1},$ what is the value of $k_r$ at 800 K?