The economic advisor of a large tire store proposes the demand function D(p)=

$$\frac { 1800 } { p - 40 }$$

, where D(p) is the number of tires of one brand and size that can be sold in one day at a price p. For what prices is the demand elastic? Inelastic?

What fraction of the air molecules in a house must be pushed outside while the furnace raises the inside temperature from

$$16.0 ^ { \circ } \mathrm { C }$$

to

$$20.0 ^ { \circ } \mathrm { C }$$

? The pressure does not change since the house is not airtight.

Write the power of 10 in standard form. Then multiply the factors. $7.83 \times 10 ^ { 0 }$

(a) If a is a unit vector perpendicular to b, find the value of

$$a \cdot ( 2 a - 3 b )$$

. (b) If p is a unit vector making a 45° angle with vector q, and

$$p \cdot q = 3 \sqrt { 2 }$$

, find |q|.

Make a sketch in the xy-plane in order to determine the number of solutions to the given linear system.

$$\left. \begin{array} { l } { 3 x - 4 y = 12 }, \\ { 6 x - 8 y = 24 }. \end{array} \right.$$

State the domain and range of the function and sketch a graph showing four periods.

$$y=-tan^2x$$

Is the value t = 1.82 significant at the 5% level? Is it significant at the 1% level?

Find the inverse of the matrix. For what value(s) of x, if any, does the matrix have no inverse?

$$\left[ \begin{array} { l l } { 2 } & { x } \\ { x } & { x ^ { 2 } } \end{array} \right]$$

Factor the trinomial.

$$5 w ^ { 2 } - 6 w + 1$$

Give an example of a

$$3 \times 3$$

matrix A that has a generalized eigenvector that is not an eigenvector, and exhibit such a generalized eigenvector.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Over the life of an installment loan, the interest portion increases and the portion applied to paying off the principal decreases with each successive payment.

A set of data pairs has a correlation coefficient r = 0.3. Your friend says that because the correlation coefficient is positive, it is logical to use line of best fit to make predictions. Is your friend correct? Explain your reasoning.

Translate each open sentence into a statement involving distance. |3-s|=4

Write each trigonometric expression as an algebraic expression in u. $\cos \left(\sin ^{-1} u\right)$