Determine whether the following statements are true and give an explanation or counterexample. In general, f(g(x))=g(f(x)).

Let p be the population proportion for the situation. Find point estimates of p and q. In a survey of 800 U.S. adults, 90 are making the minimum payment(s) on their credit card(s).

Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum values of f. f(x)=2-1/3x, x>=-2

Which element is oxidized, and which is reduced in the following reactions?

$$3 \mathrm { Fe } \left( \mathrm { NO } _ { 3 } \right) _ { 2 } ( a q ) + 2 \mathrm { Al } ( s ) \longrightarrow 3 \mathrm { Fe } ( s ) + 2 \mathrm { Al } \left( \mathrm { NO } _ { 3 } \right) _ { 3 } ( a q )$$

Graph the inequality. 2x + 2y < 18

Find each difference. Express your answer in lowest terms. $\frac { 4 } { 13 } - \left( \frac { - 7 } { 26 } \right)$

Let $\mathcal { A } \subseteq \mathbf { R }$ be nonempty and bounded above, and let $S$ be the union of all $A \in \mathcal { A }$

$$\begin{array} { l } { \text { (a) First, prove that } S \in \mathbf { R } \text { by showing that it is a cut. } } \\ { \text { (b) Now, show that } S \text { is the least upper bound for } \mathcal { A } \text { . } } \end{array}$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. If an event is certain to occur, its probability is 1.

$$\begin{array} { l } { \text { Prove that isomorphism is an equivalence relation. That is, for any } } \\ { \text { groups } G , H , \text { and } K , G \approx G , G \approx H \text { implies } H \approx G , \text { and } G \approx H \text { and } } \\ { H \approx K \text { implies } G \approx K } \end{array}$$

Compare how the skin interrelates with other organ systems to maintain a constant body temperature.

Iron corrodes to produce rust, $Fe_2O_3,$ but other corrosion products that can form are $Fe(O)(OH),$ iron oxyhydroxide, and magnetite, $Fe_3O_4.$ The oxidation number for Fe in magnetite was controversial for a long time. If we assume that oxygen's oxidation number is - 2, and Fe has a unique oxidation number, what is the oxidation number for Fe in magnetite?

A QR factorization of A is given. Use it to find a least squares solution of

$$A \mathbf { x } = \mathbf { b }.$$

$$A = \left[ \begin{array} { l l } { 2 } & { 1 } \\ { 2 } & { 0 } \\ { 1 } & { 1 } \end{array} \right] , Q = \left[ \begin{array} { r r } { \frac { 2 } { 3 } } & { \frac { 1 } { 3 } } \\ { \frac { 2 } { 3 } } & { - \frac { 2 } { 3 } } \\ { \frac { 1 } { 3 } } & { \frac { 2 } { 3 } } \end{array} \right] , R = \left[ \begin{array} { l l } { 3 } & { 1 } \\ { 0 } & { 1 } \end{array} \right] , \mathbf { b } = \left[ \begin{array} { r } { 2 } \\ { 3 } \\ { - 1 } \end{array} \right]$$

Find the P-value for the hypothesis test with the standardized test statistic z. Decide whether to reject

$$H _ { 0 }$$

for the level of significance

$$\alpha$$

. Right-tailed test z = 2.46

$$\alpha = 0.01$$

Sketch a sinusoidal function that passes through (0, -4) and has a period of 20, an amplitude of 3, and an equation of the axis y = -1.