The five-number summary for the number of males (in thousands an a company's fleet of cars is {7, 49, 66, 72, 98}. Are there any outliers? Explain.

True or false: Two points may be collinear and also noncoplanar.

Use an algebraic method to find a partial fraction decomposition. $\frac{x+17}{2 x^{2}+5 x-3}$

(a) List in spectroscopic notation all levels with n = 7. (b) An electron is initially in the state with n = 7, l = 2. List in spectroscopic notation all lower states to which transitions are allowed.

Consider the predator-prey model $x^{\prime}(t)=-4 x+2 x y, y^{\prime}(t)=5 y-x y$. a. Does x represent the population of the predator species or the prey species? b. Find the lines along which $x^{\prime}(t)=0$ Find the lines along which $y^{\prime}(t)=0$. c. Find the equilibrium points for the system. d. Identify the four regions in the first quadrant of the xy-plane in which $x^{\prime}$ and $y^{\prime}$ are positive or negative. e. Sketch a typical solution curve in the xy-plane. In which direction does the solution evolve?

Match the equation with the degenerate conic section dint would describe its graph. The matching is one-to-one. $y^{2}-4 x^{2}=0$. A. A single point. B. Two intersecting lines. C. Two parallel lines. D. The empty set.

Consider the function

$$f(x)=\tan \frac{1}{x}.$$

Show that f(x) = 0 for

$$4x=\frac{1}{\pi}, \frac{1}{2 \pi}, \frac{1}{3 \pi}, \ldots$$

For the following exercises, solve each equation for x. $\log _{3}(3 x)-\log _{3}(6)=\log _{3}(77)$

Prove that the circle group is a subgroup of $\mathbb {C}^{*}$.

Find the measure of a supplement of each angle. $83^{\circ}$

Create a geometric pattern for each number pattern. $1,8,27,64, \dots$

For the following exercises, find the decomposition of the partial fraction for the nonrepeating linear factors. $\frac{4 x-1}{x^{2}-x-6}$

Evaluate each expression when a=-5 and b=4. $\left(a^{2}-b^{3}\right)^{2}$

Each sampling method suffers from a form of bias. Identify the bias, tell how the sample statistic might deffer significantly from the population parameter, and suggest how the problem might be corrected. The dining committee of the student council surveys students in the lunch hall, asking them, "Do you prefer eating in the lunch hall to eating off campus or bringing your own lunch?" They are mildly surprised to learn that 93% of the students surveyed prefer the lunch hall.