Each year a college awards five merit-based scholarships to members of the entering freshman class who have exceptional high school records. The initial pool of applicants for the upcoming academic year has been reduced to a “short list” of eight men and ten women, all of whom seem equally deserving. If the awards are made at random from among the eighteen finalists, what are the chances that both men and women will be represented?

A college wants to survey its graduating seniors to find out how many have already found jobs in their field of study after graduation. a. What is the objective of the survey? b. Describe the population for the survey. c. Write two unbiased questions for the survey.

Given f$(x) = x² - 1$,

find $f(-5)$.

Express in the form $k \sqrt[3]{3}$ (a) $\sqrt[3]{24}$, (b) $\sqrt[3]{81}+\sqrt[3]{3}$, (c) $(\sqrt[3]{3})^{4}$, (d) $\sqrt[3]{3000}-\sqrt[3]{375}$.

To get to work, a commuter must cross train tracks. The time the train arrives varies slightly from day to day, but the commuter estimates he'll get stopped on about 15% of work days. During a certain 5-day work week, what is the probability that he a) gets stopped on Monday and again on Tuesday? b) gets stopped for the first time on Thursday? c) gets stopped every day? d) gets stopped at least once during the week?

The Virginia Cooperative Extension reports that the mean weight of yearling Angus steers is 1152 pounds. Suppose that the standard deviation is 84 pounds. How many standard deviations from the mean would a steer weighing 1000 pounds be?

A 1 $\mathrm{M} \Omega$ resistor is formed by a cylinder of graphite-clay mixture having a length of2 cm and a radius of 4 mm. Determine the conductivity of the resistor.

Control rods slow nuclear reactions by (a) reducing the amount of fuel available. (b) absorbing the heat produced. (c) increasing the rate heat transfers to the water. (d) absorbing excess neutrons.

(a) State Biot-Savart's law. (b) The y- and z-axes, respectively, carry filamentary currents 10 A along $\mathbf{a}_{y}$ and 20 A along $-\mathbf{a}_{z}$. Find Hat ( -3, 4, 5).

The points A(2, 1), B(6, 10) and C(10, 1) form an isosceles triangle with AB and BC of equal length. The point G is (6, 4). (a) Write down the coordinates of M, the mid-point of AC. (b) Show that BG = 2GM and that BGM is a straight line. (c) Write down the coordinates of N, the mid-point of BC. (d) Show that AGN is a straight line and that AG = 2GN.

Different numbers x, y and z are the first three terms of a geometric progression with common ratio r, and also the first, second and fourth terms of an arithmetic progression. (a) Find the value of r. (b) Find which term of the arithmetic progression will next be equal to a term of the geometric progression.

Use first and second derivatives to locate and describe the stationary points on the graphs of the following functions and equations. If this method fails, then use the change of sign of $\frac{d y}{d x}$or f'(x) to distinguish maxima, minima and points of inflexion. (a) $y=3 x^{4}-4 x^{3}-12 x^{2}-3$ (b) $y=x^{3}-3 x^{2}+3 x+5$ (c) $y=16 x-3 x^{3}$ (d) $y=\frac{4}{x^{2}}-x$ (e) $y=\frac{4+x^{2}}{x}$ (f) $y=\frac{x-3}{x^{2}}$ (g) $y=2 x^{5}-7$ (h) $y=3 x^{4}-8 x^{3}+6 x^{2}+1$

Find an article in a newspaper, magazine, or the Internet that compares two or more groups of data. a) Does the article discuss the W's? b) Is the chosen display appropriate? Explain. c) Discuss what the display reveals about the groups. d) Does the article accurately describe and interpret the data? Explain.

Find the impulse responses of the systems described by these equations. (a) $\mathrm{y}^{\prime}(t)+5 \mathrm{y}(t)=\mathrm{x}(t)$ (b) $\mathrm{y}^{\prime \prime}(t)+6 \mathrm{y}^{\prime}(t)+4 \mathrm{y}(t)=\mathrm{x}(t)$ (c) $2 \mathrm{y}^{\prime}(t)+3 \mathrm{y}(t)=\mathrm{x}^{\prime}(t)$ (d) $4 y^{\prime}(t)+9 y(t)=2 x(t)+x^{\prime}(t)$