Find the inverse of the function.

$$f(x) = x^3 - 2$$

$$\begin{array} { l } { \text { Let } R \text { be a ring. The center of } R \text { is the set } \{ x \in R | a x = x a \text { for all } } \\ { a \text { in } R \} . \text { Prove that the center of a ring is a subring. } } \end{array}$$

You are given a number of

$$10 \Omega$$

resistors, each capable of dissipating only 1.0 W without being destroyed. What is the minimum number of such resistors that you need to combine in series or in parallel to make a

$$10 \Omega$$

resistance that is capable of dissipating at least 12 W?

Find each GCF.

$$24,42$$

Subtract. −20 − (−4)

Find ƒ(g(x)) and g(ƒ(x)). State the domain of each.

$$ƒ(x) = x³; g(x) =^3√1-x³$$

The path followed by a baseball after it is hit can be modeled by the equation

$$2 x ^ { 2 } - 800 x + 1000 y - 4000 = 0$$

measured in feet. What was the height of the ball when it was hit?

At a particular temperature, a 2.00-L flask at equilibrium contains

$$2.80 \times 10 ^ { - 4 } \text { mole of } N _ { 2 }, 2.50 \times 10 ^ { - 5 } \text { mole of } \mathrm { O } _ { 2 } , \\ \text { and } 2.00 \times 10 ^ { - 2 } \text { mole of } \mathrm { N } _ { 2 } \mathrm { O }$$

Calculate K at this temperature for the reaction

$$2 \mathrm { N } _ { 2 } ( g ) + \mathrm { O } _ { 2 } ( g ) \rightleftharpoons 2 \mathrm { N } _ { 2 } \mathrm { O } ( g )$$

If

$$\left[ \mathrm { N } _ { 2 } \right] = 2.00 \times 10 ^ { - 4 } \mathrm { M } , \left[ \mathrm { N } _ { 2 } \mathrm { O } \right] = 0.200 \mathrm { M } , \mathrm { and } \left[ \mathrm { O } _ { 2 } \right] =0.00245 M$$

does this represent a system at equilibrium?

Simplify the expression. 8s - 4(2s + 3)

How can you use probability to make decisions$?$

Solve the equation. Check your solution. 44 = t - 72

Explain the following statement: The smallest particles unique to a compound cannot be atoms.

Evaluate the limit of the following sequences or state that the limit does not exist.

$$a _ { n } = \cos \left( 0.99 ^ { n } \right) + \frac { 7 ^ { n } + 9 ^ { n } } { 63 ^ { n } }$$

A particular 12 V car battery can send a total charge of 84 A$\cdot$h (ampere-hours) through a circuit, from one terminal to the other. How many coulombs of charge does this represent?