In Exercises $6-14, x=12, y=10,$ and $z=24 .$ Write each ratio in simplest form. $z : x : y$

In Exercises $6-14, x=12, y=10,$ and $z=24 .$ Write each ratio in simplest form. $x :(x+y) :(y+z)$

Exercises $15-20$ refer to a triangle. Express the ratio of the height to the base in simplest form. $$\begin{array}{|c|c|}\hline \text { height } & {5 \mathrm{km}} \\ \hline \text { base } & {45 \mathrm{km}} \\ \hline\end{array}$$

Exercises $15-20$ refer to a triangle. Express the ratio of the height to the base in simplest form. $$\begin{array}{|c|c|}\hline \text { height } & {1 \mathrm{m}} \\ \hline \text { base } & {0.6\mathrm{m}} \\ \hline\end{array}$$

Exercises $15-20$ refer to a triangle. Express the ratio of the height to the base in simplest form. $$\begin{array}{|c|c|}\hline \text { height } & {0.6 \mathrm{km}} \\ \hline \text { base } & {0.8\mathrm{km}} \\ \hline\end{array}$$

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In Exercises $6-14, x=12, y=10,$ and $z=24 .$ Write each ratio in simplest form. $x : y : z$

$6 : 5 : 12$

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In Exercises $6-14, x=12, y=10,$ and $z=24 .$ Write each ratio in simplest form. $\frac{y+z}{x-y}$

In Exercises $6-14, x=12, y=10,$ and $z=24 .$ Write each ratio in simplest form. $\frac{x}{x+z}$

In Exercises $6-14, x=12, y=10,$ and $z=24 .$ Write each ratio in simplest form. $=$ to $x$

For the following exercises, solve each system by Gaussian elimination.$$\begin{aligned} 10 x+2 y-14 z &=8 \\-x-2 y-4 z &=-1 \\-12 x-6 y+6 z &=-12 \end{aligned}$$

(a) If you combine two atomic orbitals on two different atoms to make a new orbital, is this a hybrid orbital or a molecular orbital? (b) If you combine two atomic orbitals on one atom to make a new orbital, is this a hybrid orbital or a molecular orbital? (c) Does the Pauli exclusion principle(Section 6.7) apply to MOs? Explain.

According to an article in the Economist about the healthcare system in the United Kingdom: "A defining principle of the National Health Service is that it is "free at the point of delivery." What does "free at the point of delivery" mean? Is health care actually free to residents of the United Kingdom? Briefly explain.

In Exercises 47-56, (a) use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant, and (b) make a table of values to verify whether the function is increasing, decreasing, or constant over the intervals you identified in part (a).

$g(x) = x$

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In Exercises $6-14, x=12, y=10,$ and $z=24 .$ Write each ratio in simplest form.

$z : x : y$

In Exercises $6-14, x=12, y=10,$ and $z=24 .$ Write each ratio in simplest form.

$\frac{y+z}{x-y}$

In Exercises $6-14, x=12, y=10,$ and $z=24 .$ Write each ratio in simplest form.

$\frac{x}{x+z}$

In Exercises $6-14, x=12, y=10,$ and $z=24 .$ Write each ratio in simplest form.

$=$ to $x$

For the following exercises, solve each system by Gaussian elimination.

$$

\begin{aligned} 10 x+2 y-14 z &=8 \\-x-2 y-4 z &=-1 \\-12 x-6 y+6 z &=-12 \end{aligned}

$$

(a) If you combine two atomic orbitals on two different atoms to make a new orbital, is this a hybrid orbital or a molecular orbital? (b) If you combine two atomic orbitals on one atom to make a new orbital, is this a hybrid orbital or a molecular orbital? (c) Does the Pauli exclusion principle

(Section 6.7) apply to MOs? Explain.

According to an article in the Economist about the healthcare system in the United Kingdom: "A defining principle of the National Health Service is that it is "free at the point of delivery." What does "free at the point of delivery" mean? Is health care actually free to residents of the United Kingdom? Briefly explain.

In Exercises 47-56, (a) use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant, and (b) make a table of values to verify whether the function is increasing, decreasing, or constant over the intervals you identified in part (a).

$g(x) = x$