Solve the equation using the square root property.

$$m ^ { 2 } + 4 = 0$$

Let $Y_1 < Y_2 < ... < Y_n$ be the order statistics of a random sample from a $N \left( \theta , \sigma ^ { 2 } \right) , - \infty < \theta < \infty$ distribution. Show that the distribution of $Z = Y _ { n } - \overline { X }$ does not depend upon $\theta.$ Thus $\overline { Y } = \sum _ { 1 } ^ { n } Y _ { i } / n,$ a complete sufficient statistic for $\theta$ is independent of Z.

Find the interval of convergence. $\sum_{k=0}^{\infty} 3^{k}(x-2)^{k}$

Suppose A has position vector 3i + 2j - k, B has position vector 2i - j - 8k, and C has position vector i + j + ak. Find the unit vector u in the direction of $\overrightarrow{\mathrm{BA}}$.

The width of a particular microwave oven is exactly right to support a standing-wave mode. Measurements of the temperature across the oven show that there are cold spots at each edge of the oven and at three spots in between. The wavelength of the microwaves is 12 cm. How wide is the oven?

A patient can’t see objects closer than 40.0 cm and wishes to clearly see objects that are 20.0 cm from his eye. Find the power of the lens in diopters.

Find the vertex and the axis of symmetry of the graph of the function. $f ( x ) = 5 ( x - 2 ) ^ { 2 }$

Explain why cos $\theta=\cos \left(\theta+n \cdot 360^{\circ}\right)$ for any angle $\theta$ and any integer n.

Change the order of integration by integrating first with respect to z, then x, then y. $\int _ { - 1 } ^ { 2 } \int _ { 1 } ^ { 3 } \int _ { 0 } ^ { 4 } \left( x ^ { 2 } z + \frac { 1 } { y } \right) d x d y d z$

Convert the polar equation to rectangular form and sketch its graph. $r=4 \sin \theta$

Determine the angular momentum ${H}_{P}$ of the 6-lb particle about point P .

Given M, find $M^{-1}$ and show that $M^{-1} M=I$.

$$\left[\begin{array}{rrr}{2} & {3} & {0} \\ {1} & {2} & {3} \\ {0} & {-1} & {-5}\end{array}\right]$$

Solve each inequality. Check to justify your answer. Then graph the solution set. $10 + c \leq 9$

When using a function to model a situation like the fee per camper, you only use those values that make sense in the context of the situation. We will consider the rational function

$$f(x) = \frac{12,000 + 45x}{x – 30}$$

over a broader range of values. Graph the function on a graphing calculator, using the viewing window

$$[ - 450,450 ] \text { by } [ - 400,400 ]$$

Use your calculator to approximate the x- and y-intercepts. Find the exact values of the x- and y-intercepts, using the function. Show your work. Division of a nonzero quantity by zero is undefined. Name the value(s) for which the function is not defined and explain how you determined the value(s). What is the domain of the function? Write your answer using set notation, interval notation, and inequalities. What is the range of the function? Write your answer using set notation, interval notation, and inequalities.