In a fully developed paragraph, explain how the term republic or republican government applies to Rome during the years of its rise by explaining who Rome's leaders were and what rights people had.

What were the political and military structures of Rome during the Republic?

What was the significance of Rome's central location and geographic features?

What were the two main social classes in Rome?

Match the terms with the definition. Some terms may not be used.

a. basic needs

b. collective values

c. innovations

d. lifeenhancing wants

e. opportunity cost

f. personal preferences

g. public goods

h. sunk cost

i. trade-off

j. values

__ Getting something in return for giving up something else

Explain the ways in which Millan believes wolves, dogs, and people all take on similar roles as leaders and followers. Do you agree with his points about human society? Why or why not?

Two sources, each having a strength of $8\ \mathrm{ft}^2 / \mathrm{s}$, are located as shown. Find the $x$ and $y$ components of the velocity of a fluid particle that passes point $(8\ \mathrm{ft}, 12\ \mathrm{ft})$. Find the equation of the streamline that passes through this point.

(a) What is a pollen grain?

(b) How does it form?

(c) What is its function, and how does it accomplish this function?

(d) In an evolutionary context, why was pollen an important step in allowing seed plants to become the dominant plants?

Casual Cuts Inc. has total estimated factory overhead for the year of $225,000, divided into four activities: cutting,$90,000; sewing, $22,500; setup,$80,000; and inspection, $32,500. Casual Cuts manufactures two types of men’s pants: jeans and khakis. The activity-base usage quantities for each product by each activity are as follows:

	Cutting	Sewing	Setup	Inspection
Jeans	500 dlh	1,000 dlh	250 setups	100 inspections
Khakis	1,000	500	750	400
	1,500 dlh	1,500 dlh	1,000 setups	500 inspections

Each product is budgeted for 10,000 units of production for the year. Determine (a) the activity rates for each activity and (b) the factory overhead cost per unit for each product, using activity-based costing.

These exercises involve counting permutations. In how many different ways can first, second, and third prizes be awarded in a game with eight contestants?

Find the nth roots of the complex number for the specified value of n.

$$-2i,n=6$$

Given a list L of words such as the following and assignment to List1:

L = ['Always', 'look', 'on', 'the', 'bright', 'side', 'of', 'life.']

List1=[[i.upper(), i.lower(), len(i)] for i in L ]

(a) What is the value of List1?

(b) Write a list comprehension that uses List1 to create a list of words of length 4.

Determine whether the set $S$ spans $R^{3}$. If the set does not span $R^{3}$, then give a geometric description of the subspace that it does span.

$$S=\{(5,6,5),(2,1,-5),(0,-4, 1)\}$$

Use the matrices below to compute each product. $$ A=\left[\begin{array}11&2\\3&4\end{array}\right] $$ $$ B=\left[\begin{array}12&3\\4&5\end{array}\right] $$ $$ C=\left[\begin{array}11&0\\-1&-2\end{array}\right] $$ a. $A(BC)$ b. $(AB)C$