The function T(g) = 4675 + 0.25(g - 33,950) represents the 2009 federal income tax T (in dollars) due for a “single” filer whose modified adjusted gross income is g dollars, where $33,950 \leq g \leq 82,250.$ Find adjusted gross income g as a function of federal income tax T. What are the domain and the range of this function?

How did natural selection plays a role in the changing genetic traits that the Grants observed in the medium ground finch?

Express each hexadecimal number in decimal.

$$209D$$

The general form of a nonvertical line in slope-intercept form is y = mx + b. What is the general form of a line perpendicular to y = mx + b, in slope-intercept form?

The Density Property states that there is a point between any two points on the number line. Write a rational number in simplest form that is between each pair of numbers. $\frac { 4 } { 5 }$ and $\frac { 7 } { 12 }$

find values for b such that the triangle has two solutions. A = 60°, a = 10

Simplify each expression. Express your answer so that only positive exponents occur.Assume that the variables are positive. $\frac{\left(x^{2} y\right)^{1 / 3}\left(x y^{2}\right)^{2 / 3}}{x^{2 / 3} y^{2 / 3}}$

Calculate:

$$\sqrt{\dfrac{25}{64}}$$

A 0.25 -mol sample of a weak acid with an unknown $pK_a$ was combined with 10.0 mL of 3.00 M KOH, and the resulting solution was diluted to 1.500 L. The measured pH of the solution was 3.85. What is the $pK_a$. of the weak acid?

Which of the given values is a solution of the equation? m-3=8 ; 5,11

Determine the values of a for which the system has no solutions, exactly one solution, or infinitely many solutions.

$$\begin{array}{r}{x+\quad 2 y=1} \\ {2 x+\left(a^{2}-5\right) y=a-1}\end{array}$$

Solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, say so.

$$\left\{\begin{array}{r}{2 x-y=-1} \\ {x+\frac{1}{2} y=\frac{3}{2}}\end{array}\right.$$

Express each proposition as an English sentence and determine whether it is true or false, where r and s are the propositions. r: "the moon is a cube" s: "rain is wet" $r \vee s$

Show that, under these circumstances, the sum of the lengths of the intervals making up each $C _ { n }$ no longer tends to zero as $n \rightarrow \infty .$ What is this limit?