Use a graphing utility to graph the function. Find the domain and range of the function. $f(x)=\sqrt{16-x^{2}}$

Write the quotient in scientific notation: (4 × 10^12)/(8 × 10^4)

Simplify the factorial expression. $\frac{2 n !}{(n+1) !}$

Let f(x)=

$$x^8$$

-2x+3; find

$$\lim _ { w \rightarrow 2 } \frac { f ^ { \prime } ( w ) - f ^ { \prime } ( 2 ) } { w - 2 }$$

Mr. Doody, at age 70, is expected to live for 15 years. If he can invest at 4% per annum compounded monthly, how much does he need now to guarantee himself $300 every month for the next 15 years?

In an ideal Brayton cycle, air is compressed from 100 kPa and $25^{\circ} \mathrm{C}$ to 1 MPa, and then heated to $927^{\circ} \mathrm{C}$ before entering the turbine. Under cold-air-standard conditions, the air temperature at the turbine exit is (a) $349^{\circ} \mathrm{C}$ (b) $426^{\circ} \mathrm{C}$ (c) $622^{\circ} \mathrm{C}$ (d) $733^{\circ} \mathrm{C}$ (e) $825^{\circ} \mathrm{C}$

Use an inverse matrix to solve the linear system. 4x + y = - 2, -6x + y = 18

Use cylindrical coordinates to find the centroid of the solid. The solid that is bounded by the cone

$$z = \sqrt { x ^ { 2 } + y ^ { 2 } }$$

and the plane z=2.

Engineers must consider the breadths of male heads when designing motorcycle helmets. Men have head breadths that are normally distributed with a mean of 6.0 in. and a standard deviation of 1.0 in.. Due to financial constraints, the helmets will be designed to fit all men except those with head breadths that are in the smallest 2.5% or largest 2.5%. Find the minimum and maximum head breadths that the helmets will fit.

Find the mean, median, mode, and range of each data set. 19, 25, 31, 19, 34, 22, 31, 34

Write each polynomial in standard form. Then give the leading coefficient.

$$4 d + 3 d ^ { 2 } - d ^ { 3 } + 5$$

Determine whether each statement is sometimes, always, or never true. Justify your reasoning using a counterexample or proof. In an isosceles triangle, the perpendicular bisector of the base is also the angle bisector of the opposite vertex.

Multiply.

$$( 3 y + 1 ) \left( 2 y ^ { 2 } + 3 y + 2 \right)$$

Determine whether the product exists.

$$F=\left[\begin{array}{ll}{2} & {3} \\ {6} & {9}\end{array}\right] \quad G=\left[\begin{array}{rr}{-3} & {6} \\ {2} & {-4}\end{array}\right] \quad H=\left[\begin{array}{r}{-5} \\ {6}\end{array}\right] \quad I=\left[\begin{array}{ll}{0} & {7}\end{array}\right]$$

HG