a) Construct a regular hexagon with sides of length 3 cm. b) Calculate its area, showing your method clearly.

Find the LCM for the given group of numbers.

8,12

A regular polyhedron has axis symmetry of order 3, but does not have plane symmetry. What is the figure? Explain.

Predict the Output:

ListNode *p = new ListNode(56.4, new ListNode(31.5));
ListNode *q = p;
while (q->next->next != NULL)
q = q->next;
cout << q->value;

Equation E_t=$\frac{\sigma}{2 \epsilon_0}$shows that $E_t$ has the same value for all points in front of an infinite uniformly charged sheet. Is this reasonable? One might think that the field should be stronger near the sheet because the charges are so much closer.

$$\text { Show that conjugacy is an equivalence relation on a group. }$$

Prove.

The group G consists of exactly n permutations.

The measure of an exterior angle of a regular polygon is given. Find the measure of an interior angle. Then find the number of sides. 72

A regular polygon has an angle of rotational symmetry of $5^\circ.$ How many sides does the polygon have?

Find the area of each regular polygon with the given apothem a and side length s. decagon, a = 19 m, s = 12.3 m

Many traffic experts argue that the most important factor in accidents is not the average speed of cars but the amount of variation. Suppose that the speeds of a sample of 200 cars were taken over a stretch of highway that has seen numerous accidents. Compute the variance and standard deviation of the speeds, and interpret the results.

Make a multiplication table for the symmetric group S_3.

Let G be an r-regular graph with n vertices and m edges. Find (and prove) a simple algebraic relation between r, n, and m.

Describe the group sometimes referred to as Middle America.