Make a chart that compares the structure and function of viruses with prokaryotes and eukaryotes.

Calculate the triple scalar products $\mathbf { v } \cdot ( \mathbf { u } \times \mathbf { w } )$ and $\mathbf { u } \cdot ( \mathbf { w } \times \mathbf { v } )$, where $\mathbf { u } = \langle 4,2 , - 1 \rangle$, $\mathbf { v } = \langle 2,5 , - 3 \rangle$, and $\mathbf { w } = \langle 9,5 , - 10 \rangle$.

Find the sale price of the following item. Round to two decimal places when necessary: Original price: $45.00; Markdown : 22%.

Fill in the blank. The functions f and

$$f ^ { - 1 }$$

are _____.

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

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.

$$24,42$$

Queen, Inc., a tennis racket manufacturer, determines that the annual cost C of making x rackets is $\$23$ per racket plus $\$125,000$ in fixed overhead costs. It costs the company $\$8$ to string a racket. Find a function

$$y_3=R_u(x)$$

that models the revenue generated by selling x unstrung rackets.

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?

Bacteria can be grown in the laboratory on synthetic media. Can bacteriophages be grown on cultures of bacteria? Can bacteriophages be grown on synthetic media? Explain your answer.

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?

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

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