Men have heights with a mean of 176 cm and a standard deviation of 7 cm. Charles Darwin had a height of 182 cm. Convert Darwin's height to a z score.

Using Capitals for Proper Adjectives. Complete each of the following sentences by supplying a proper adjective that is correctly capitalized. _____ winters are usually long and cold.

(a) Find $\mathbf{r}(a)$ and $\mathbf{r}'(a)$ at the given value of $a$.

(b) Sketch the curve defined by $\mathbf{r}$ and the vectors $\mathbf{r}(a)$ and $\mathbf{r}(a)$ on the same set of axes.

$$\mathbf{r}(t)=t^2\mathbf{i}+t^3\mathbf{j};\hspace{6pt} a=1$$

Two similar hexagonal prisms have volumes of 250 cubic feet and 2 cubic feet. What is the ratio of the height of the large cylinder to the height of the small cylinder?

For the following question,

Find the dimensions of the box described.

The length is three times the height and the height is one inch less than the width. The volume is $108$ cubic inches.

Differentiate the function below using the Chain Rule.

$$f(x)=\left(\frac{2 x}{x^2+1}\right)^3$$

Prove the said theorem. (Hint for Property $1$: If the limit equals $r<1$, choose a real number $R$ such that $r<R<1$. By the definitions of the limit, there exists some $N>0$ such that $\sqrt[n]{\left|a_n\right|}<R$ for $n>N$.)

Determine the symmetry of $r$ the maximum value of $|r|$ and any zeros of $r$. Then sketch the graph of the polar equation (plot additional points if necessary).

$$r= \cos5\theta$$

Consider a transition matrix T for a Markov chain with entries $a_{i j}$, where $1 \leq i \leq n$ and $1 \leq j \leq n$.

a. If there are $n$ states associated with the Markov chain, what is the size of the matrix $T$ ?

b. Describe the probability that each entry represents. Can an entry be negative?

c. What is the sum of the entries in each column of $T$ ?

Calculate the value of the multiple integral.

$$∫∫∫H z^3√x^2+y^2+z^2 dV,$$

where H is the solid hemisphere that lies above the xy-plane and has center the origin and radius 1

Draw the structure of leu-enkephalin, a pentapeptide that acts as an analgesic and opiate, and has the following sequence: Tyr–Gly–Gly–Phe–Leu.

Write a function rule for the area of a triangle with a base 2 m less than 4 times its height. What is the area of the triangle when its height is 8 m?

A ball of mass m is thrown straight up into the air with an initial speed $v_{i}.$ Find the momentum of the ball (a) at its maximum height and (b) halfway to its maximum height.

An inclined ramp is to be built so that it reaches a height of 6.00 ft over a 15.00 ft run. Braces are placed every 5.00 ft. Find the height of braces x and y.