The rate constant for the decomposition of acetaldehyde, $\mathrm{CH}_3 \mathrm{CHO}$, to methane, $\mathrm{CH}_4$, and carbon monoxide, $\mathrm{CO}$, in the gas phase is $1.1 \times 10^{-2} \mathrm{~L} \mathrm{~mol}^{-1} \mathrm{~s}^{-1}$ at $703 \mathrm{~K}^{\text {and }} 4.95 \mathrm{~L} \mathrm{~mol}^{-1} \mathrm{~s}^{-1}$ at $865 \mathrm{~K}$. Determine the activation energy for this decomposition.

Find the geometric mean of 9 and 25.

What does it mean to solve a right triangle?

In an attempt to determine the factors that affect the amount of energy used, 200 households were analyzed. In each, the number of occupants and the amount of electricity used were measured. Determine the regression line and interpret the results.

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form.

$$\text { Slope } = - 4 , \text { passing through } ( - 4,0 )$$

In the earlier problem, suppose that the mean amount of juice squeezed is 5.0 ounces. The probability is 77% that the sample mean amount of juice will be greater than what value?

What does the term infatuation mean?

Determine whether each statement is always, sometimes, or never true. Explain your reasoning. The geometric mean for consecutive positive integers is the mean of the two numbers.

Give an answer to the following question.

How could you prove $\sqrt[3]{x y z} \leq \frac{1}{3}(x+y+z)$ (geometric mean $\leq$ arithmetic mean)?

Given the following values for the changes in enthalpy ($\Delta$ H) and entropy ($\Delta$ S), which of the following processes can take place at 298 K without violating the Second Law of Thermodynamics?

(a) $\Delta$ H = -84 kJ mol$^{-1}$ (-20 kcal mol$^{-1}$),

$\Delta$ S=+125 J mol$^{-1}$ K$^{-1}$(+30 cal mol$^{-1}$ K$^{-1}$)

(b) $\Delta$ H= -84 kJ mol$^{-1}$ (-20 kcal mol$^{-1}$),

$\Delta$ S= -125 J mol$^{-1}$ K$^{-1}$ (-30 cal mol$^{-1}$ K$^{-1}$)

(c) $\Delta$ H= +84 kJ mol$^{-1}$ (+20 kcal mol$^{-1}$),

$\Delta$ S= -125 J mol$^{-1}$ K$^{-1}$ (+30 cal mol$^{-1}$ K$^{-1}$)

(d) $\Delta$ H= +84 kJ mol$^{-1}$ (+20 kcal mol$^{-1}$),

$\Delta$ S= -125 J mol$^{-1}$ K$^{-1}$ (-30 cal mol$^{-1}$ K$^{-1}$)

Write an equation in point-slope form for the line that passes through the given point with the slope provided. Then graph the equation.

$$(-2, -8), slope \frac{5}{6}$$

Find the slope of the line passing through the given points using the slope formula. Describe the slope as positive, negative, zero, or undefined. (-3, -10) and (-1, -1)

What is the aqueous humor, where is it located, and what are its functions?

Find the partial fraction decomposition for each rational expression. $\frac{-x^{4}-8 x^{2}+3 x-10}{(x+2)\left(x^{2}+4\right)^{2}}$