A humor piece published in the British Medical Journal ("Parachute use to prevent death and major trauma related to gravitational challenge: systematic review of randomized control trials," Gordon, Smith, and Pell, BMJ, 2003:327) notes that we can't tell for sure whether parachutes are safe and effective because there has never been a properly randomized, double-blind, placebo-controlled study of parachute effectiveness in skydiving. (Yes, this is the sort of thing statisticians find funny . ... ) Suppose you were designing such a study: How would you randomize this "experiment"? How would you make the experiment double-blind?

A humor piece published in the British Medical Journal ("Parachute use to prevent death and major trauma related to gravitational challenge: Systematic review of randomized control trials," Gordon, Smith, and Pell, BMJ , 2003:327) notes that we can't tell for sure whether parachutes are safe and effective because there has never been a properly randomized, double-blind, placebo-controlled study of parachute effectiveness in skydiving. (Yes, this is the sort of thing statisticians find funny .... ) Suppose you were designing such a study: a) What is the factor in this experiment? b) What experimental units would you propose? c) What would serve as a placebo for this study? d) What would the treatments be? e) What would the response variable be? f) What sources of variability would you control? g) How would you randomize this "experiment"? h) How would you make the experiment double-blind?

Prove each statement by mathematical induction.

$$2 ^ { n } < ( n + 2 ) !$$

, for all integers

$$n \geq 0$$

.

A humor piece published in the British Medical Journal ("Parachute use to prevent death and major trauma related to gravitational challenge: systematic review of randomized control trials," Gordon, Smith, and Pell, BMJ, 2003:327) notes that we can't tell for sure whether parachutes are safe and effective because there has never been a properly randomized, double-blind, placebo-controlled study of parachute effectiveness in skydiving. (Yes, this is the sort of thing statisticians find funny . ... ) Suppose you were designing such a study: What experimental units would you propose?

A humor piece published in the British Medical Journal ("Parachute use to prevent death and major trauma related to gravitational challenge: systematic review of randomized control trials," Gordon, Smith, and Pell, BMJ, 2003:327) notes that we can't tell for sure whether parachutes are safe and effective because there has never been a properly randomized, double-blind, placebo-controlled study of parachute effectiveness in skydiving. (Yes, this is the sort of thing statisticians find funny . ... ) Suppose you were designing such a study: What is the factor in this experiment?

Find the polar equation of the conic with the given eccentricity and directrix, and focus at the origin.

$$e = \frac { 1 } { 2 },$$

x = -3

Suppose that f is a continuous additive function on

$$\mathbb{R}.$$

If c := f (1), show that we have f(x) = cx for all

$$x \in \mathbb{R}.$$

Find dy/dx for the following functions.

$$y = \frac { \left( x ^ { 2 } - 1 \right) \sin x } { \sin x + 1 }$$

An office employs six customer service repres entatives. Each day, two of them are randomly selected and their customer interactions are monitored for the purposes of improving customer relations. In how many ways can the repres entatives be chosen?

Suppose that a student has 500 vocabulary words to learn. If the student learns 15 words after 5 minutes, the function $L(t) = 500(1 - e^{-0.0061t})$ approximates the number of words L that the student will learn after t minutes. How many words will the student learn after 60 minutes?

How many ways can you arrange two of the first three letters of the alphabet?

Compute the first-order partial derivatives.

$$w = \frac { x } { y + z }$$

three siblings are three different ages. The oldest is twice the age of the middle sibling, and the middle sibling is six years older than one-half the age of the youngest. Write a composite function that gives the oldest sibling’s age in terms of the youngest. Explain how you arrived at your answer.

Use a graphing device to find the solutions of the equation, rounded to two decimal places.

$$\cos x = \frac { x } { 3 }$$