$$\begin{array} { r } { \text { Find a Hamiltonian circuit in } } \\ { \quad \operatorname { Cay } \left( \{ ( a , 0 ) , ( b , 0 ) , ( e , 1 ) \} : Q _ { 4 } \oplus Z _ { 2 } \right) } \end{array}$$

For the following key term or person, write a sentence explaining its significance: weapons of mass destruction (WMD)

An auto repair shop’s records show that 15% of the cars serviced need minor repairs averaging $100, 65% need moderate repairs averaging$550, and 20% need major repairs averaging $1100. (a) What is the expected cost of repair of a car selected at random? (b) The shop has 125 cars scheduled for repair. What is the total expected repair cost of these cars?

The diameter of a tire on the car was 24 inches. Find the circumference of the tire to the nearest inch. (Use 3.14 for

$$\pi$$

.)

(a) If $-10\cos \omega t + 4\sin \omega t = A \cos (\omega t + \Phi)$, where $A>0$ and $-180^\circ< \Phi \leq 180^\circ$, find $A$ and $\Phi$. (b) If $200 \cos (5t + 130^\circ) = F \cos 5t + G\sin 5t$, find $F$ and $G$. (c) Find three values of $t$, $0\leq t \leq 1\text{ s}$, at which $i(t) = 5 \cos 10t - 3 \sin 10t = 0$. (d) In what time interval between $t = 0$ and $t = 10$ ms in $10 \cos \pi t \geq 12 \sin 100 \pi t$?

Express all z scores with two decimal places. For the Verizon airport data speeds (Mbps), the highest speed of 77.8 Mbps was measured at Atlanta's (ATL) international airport. The complete list of 50 Verizon data speeds has a mean of i = 17 .60 Mbps and a standard deviation of s = 16.02 Mbps. What is the difference between Verizon 's data speed at Atlanta's international airport and the mean of all ofVerizon's data speeds?

Use slopes and the distance formula to show that the quadrilateral whose vertices are (0,0),(1,3),(4,2) and (3,-1) is a square.

Determine whether the given random variable X is discrete or continuous. X counts the number of players on a hockey team who are injured in a randomly selected game.

Describe the differences between the graphs of y = (x + 6)^2 and y = (x - 6)^2 + 7.

Evaluate without using a calculator by using ratios in a reference triangle. sin 11π/3

Let

$$\mathbf{v}_{1}=\left[ \begin{array}{r}{2} \\ {3} \\ {-5}\end{array}\right], \mathbf{v}_{2}=\left[ \begin{array}{r}{-4} \\ {-5} \\ {8}\end{array}\right]$$

, and

$$\mathbf{w}=\left[ \begin{array}{r}{8} \\ {2} \\ {-9}\end{array}\right]$$

. Determine if w is in the subspace of $\mathbb{R}^{3}$ generated by $\mathbf{v}_{1}$ and $\mathbf{v}_{2}$.

Find a formula for $s_{n}, n \geq 1.$ 2, 5, 10, 17, 26, ...

Graph each equation. $\frac{x^{2}}{16}+\frac{y^{2}}{9}=1$

(a) If b is a positive constant and x > 0, find all critical points of f(x) = x - b ln x. (b) Use the second-derivative test to determine whether the function has a local maximum or local minimum at each critical point.