The function $T(g)=1670+0.15(g-16,700)$ represents the 2009 federal income tax T (in dollars) due for a “married filing jointly” filer whose modified adjusted gross income is g dollars, where $16,700 \leq g \leq 67,900.$ Find adjusted gross income g as a function of federal income tax T. What are the domain and the range of this function?

Which postulate explains the fact that two straight roads cannot cross each other more then once?

Write each phrase as an algebraic expression. Use n for "a number." seven less than five times a number

A triangle has two angles with a measure of $60 ^ { \circ }$ and one side with a length of 12. What is the perimeter of the triangle?

Naman and Ada disagree about how to find an equivalent expression for 2(4x − 3) + 6. Who is correct? How do you know? Use properties of operations and the order of operations to justify your response.

$$\begin{matrix} \text{Naman} & \text{Ada}\\ \text{2(4x − 3) + 6} & \text{2(4x − 3) + 6}\\ \text{6 + 2(4x − 3)} & \text{8x − 6 + 6}\\ \text{8(4x − 3)} & \text{8x + 0}\\ \text{32x − 24} & \text{8x}\\ \end{matrix}$$

Rewriting an expression in a different form can show how quantities are related.

Nielsen Research provides weekly ratings of nationally broadcast television programs. The ratings of the 84 prime-time programs broadcast by the four major televisions networks (ABC, CBS, FOX, and NBC) for the week of April 14–20, 2008, are provided in the file named NielsenResearch. The ratings range from 1 to 103. Shown are the ratings for 12 shows in the file (days and times for shows that aired multiple episodes are shown). Do these data suggest that the overall ratings for the four networks differ significantly? Use the Kruskal-Wallis test with a .10 level of significance. What is the p-value and what is your conclusion?

$$\begin{matrix} \text{Program} & \text{Network} & \text{Rating}\\ \hline \text{20/20} & \text{ABC} & \text{60}\\ \text{30 Rock} & \text{NBC} & \text{44}\\ \text{48 Hours Mystery (Sat. 10:00 P.M)} & \text{CBS} & \text{51}\\ \text{48 Hours Mystery (Sat. 9:00 P.M)} & \text{CBS} & \text{78}\\ \text{48 Hours Mystery (Tues. 10:00 P.M)} & \text{CBS} & \text{63}\\ \text{60 Minutes} & \text{CBS} & \text{13}\\ \text{According to Jim (Tues. 8:00 P.M)} & \text{ABC} & \text{89}\\ \text{According to Jim (Tues. 8:30 P.M)} & \text{ABC} & \text{91}\\ \text{American Dad (Sun. 7:30 P.M)} & \text{FOX} & \text{100}\\ \text{American Dad (Sun. 9:30 P.M)} & \text{FOX} & \text{65}\\ \text{American Idol (Tues. 8:00 P.M)} & \text{FOX} & \text{1}\\ \text{American Idol (Wed. 9:00 P.M)} & \text{FOX} & \text{2}\\ \end{matrix}$$

The vertical line passing through the vertex of a parabola is called the _____.

Locate the given numbers in the complex plane. $10$

Use atomic properties to explain why xenon is 11 times as soluble as helium in water at $0 ^ { \circ } \mathrm { C }$ on a mole basis.

Solve each system of equations. If the system has no solution, say that it is inconsistent.

$$\left\{\begin{aligned} 3 x-2 y+2 z=& 6 \\ 7 x-3 y+2 z=&-1 \\ 2 x-3 y+4 z=& 0 \end{aligned}\right.$$

A Major League baseball diamond is actually a square 90 feet on a side. The pitching rubber is located 60.5 feet from home plate on a line joining home plate and second base. If a pitcher faces home plate, through what angle does he need to turn to face first base?

Use identities to write each expression as a single function of x or $\theta$. $\tan \left(360^{\circ}-\theta\right)$

Identify each sequence as arithmetic, geometric, or neither. If possible, determine the 50th term of each sequence. a. $-5, -1, 3, 7 , 11, 15, 19, 23$ . . . Type of Sequence:............ 50th term: .............
b. $0, 1 , 1, 2, 3, 5, 8 ,13$ ..... Type of Sequence: ..... 50th term: ..... c. $27 , 9 , 3 , 1 , \dfrac{1}{3} , \dfrac{1}{9} , \dfrac{1}{27}$ Type of Sequence: ............. 50th term:..............

Discuss the parts of a typical rib.