Graph by hand the standard normal distribution by using the formula derived in the Previous Exercise. Let $\pi \approx 3.14$ and $e \approx 2.718$. Use $X$ values of $-2,-1.5,-1,-0.5,0,0.5$, $1,1.5$, and $2.$ (Use a calculator to compute the $y$ values.)

On the lines provided, rewrite the following phrases and short sentences so that the possessive forms are correct. If an item is already correct, write $C$.

Example 1. Casey's and Marcos grades $\underline{\text{Casey's and Marcos's grades}}$

6. Chris and Lindas' conversation $\underline{\phantom{\text{The horse with the sllvery mane and white tall was chosen by the photographer.}}}$

Reduce $[A | I]$ to find $A^{−1}$. In each case, check your calculations by multiplying the given matrix by the derived inverse.

$$\left[\begin{array}{lll} 1 & 3 & 5 \\ 0 & 1 & 4 \\ 0 & 2 & 7 \end{array}\right]$$

On the line provided, write each of the following words, using hyphens to show how the word could be divided at the end of a line. If a word should not be divided, write do not divide.

Example 1. frankly $\underline{\text{frank-ly}}$

plunge $\underline{\phantom{\text{The horse with the sllvery mane and white tall was chosen by the photographer.}}}$

On the line provided, write each word syllable-by-syllable. Draw a vertical line between syllables. Check a dictionary if you are unsure of a word's division.

Example thoroughly $\underline{\text{thor I ough I ly}}$

calendar $\underline{\phantom{\text{The horse with the sllvery mane and white tall was chosen by the photographer.}}}$

Why is urethritis, an infection of the urethra, frequently preliminary to further infections of the urinary tract?

Which of the following units are derived units? Explain.

$$\mathrm{kL} \mathrm{Mg} \mathrm{Gm} \mathrm{kg} / \mathrm{L} \quad \mathrm{mg} / \mathrm{cm}^3$$

The value of $g$ at any latitude $\phi$ may be obtained from the formula

$$g=32.09\left(1+0.0053 \sin ^2 \phi\right) \mathrm{ft} / \mathrm{s}^2$$

which takes into account the effect of the rotation of the earth, as well as the fact that the earth is not truly spherical. Determine to four significant figures $(a)$ the weight in pounds, $(b)$ the mass in pounds, $(c)$ the mass in $\mathrm{lb} \cdot \mathrm{s}^2 / \mathrm{ft}$, at the latitudes of $0^{\circ}, 45^{\circ}, 60^{\circ}$, of a silver bar, the mass of which has been officially designated as $5\ \mathrm{lb}$.

Reduce $[A | I]$ to find $A^{−1}$. In each case, check your calculations by multiplying the given matrix by the derived inverse.

$$\left[\begin{array}{lll} 1 & 4 & 2 \\ 0 & 2 & 1 \\ 3 & 5 & 3 \end{array}\right]$$

Find ${\vec{f}} \ '(t)$ for the vector function, and state the domain of each derived function.

$$\vec{f}(t)=3^{2 t^2} \bar{i}+\dfrac{2 t-3}{2 t+4} \hat{j}$$

For this exercise, you will sketch the graph of the function.

$$f(x)= \begin{cases}-x & \text { if } x<0 \\ x^2 & \text { if } 0 \leqslant x<2 \\ 1 & \text { if } x \geqslant 2\end{cases}$$

Benito has $x$ applos. He cuts each apple in half and gives each half to a different horse. Which expression represents the number of horses Benito feeds? (A) $x \cdot \frac{1}{2}$ (C) $x=1 \frac{1}{2}$ (B) $x \div \frac{1}{2}$ (D) $x \div 1 \frac{1}{2}$

A person sitting at the beach is wearing a pair of Polaroid sunglasses and notices little discomfort due to the glare from the water on a bright sunny day. When she lies on her side, however, she notices that the glare increases. Why?

The period of a pendulum is given by $T = 4 \sqrt { \frac { \ell } { g } } \int _ { 0 } ^ { \pi / 2 } \frac { d \theta } { \sqrt { 1 - k ^ { 2 } \sin ^ { 2 } \theta } } = 4 \sqrt { \frac { \ell } { g } } F ( k )$, where $\ell$ is the length of the pendulum, $g \approx 9.8 \mathrm { m } / \mathrm { s } ^ { 2 }$ is the acceleration due to gravity, k=sin $\left( \theta _ { 0 } / 2 \right)$, and $\theta _ { 0 }$ is the initial angular displacement of the pendulum (in radians). The integral in this formula F(k) is called an elliptic integral, and it cannot be evaluated analytically.

Approximate F(0.1) by expanding the integrand in a Taylor (binomial) series and integrating term by term.