According to psychological theory, each negative emotion one has is linked to some thought (appraisal) about the environment. This theory was tested in the journal Cognition and Emotion (Vol. 24, 2010). Over a period of two days, undergraduate students were asked to respond to events that occurred within the past 15 minutes. Each student rated the negative emotions he or she felt (e.g., anger, sadness, fear, or guilt) and gave an appraisal of the event (e.g., unpleasant or unfair). A total of 10,797 responses was evaluated in the study, of which 594 indicated a perceived unfairness appraisal. Of these unfairness appraisals, the students reported feeling angry in 127 of them. Consider a response randomly selected from the study. a. What is the probability that the response indicates a perceived unfairness appraisal? b. Given a perceived unfairness appraisal, what is the probability of an angry emotion?

The average adult male has a total blood volume of 5.0 L. After drinking a few beers, he has a BAC of 0.10. What mass of alcohol is circulating in his blood?

Compare and contrast using a graph and a table to approximate the solution of a system of one linear equation and one quadratic equation.

A friend would like you to build an “electronic eye” for use as a fake security device. The device consists of three lights lined up in a row, controlled by the outputs Left , Middle, and Right, which, if asserted, indicate that a light should be on. Only one light is on at a time, and the light “moves” from left to right and then from right to left , thus scaring away thieves who believe that the device is monitoring their activity. Draw the graphical representation for the finite-state machine used to specify the electronic eye. Note that the rate of the eye’s movement will be controlled by the clock speed (which should not be too great) and that there are essentially no inputs.

According to the National Highway Traffic and Safety Administration’s National Center for Statistics and Analysis (NCSA), “Speeding is one of the most prevalent factors contributing to fatal traffic crashes” ( NHTSA Technical Report , Aug. 2005). The probability that speeding is a cause of a fatal crash is .3. Furthermore, the probability that speeding and missing a curve are causes of a fatal crash is .12. Given that speeding is a cause of a fatal crash, what is the probability that the crash occurred on a curve?

Drivers stopped by police. According to the Bureau of Justice Statistics (September 2013), 80% of all licensed drivers stopped by police are 25 years or older. Give a percentile ranking for the age of 25 years in the distribution of all ages of licensed drivers stopped by police.

Use a graphing calculator for the following. Graph

$$y = \sqrt { x } , y = \frac { 1 } { 2 } \sqrt { x } , y = 2 \sqrt { x } , y = 3 \sqrt { x }$$

, and

$$y = 4 \sqrt { x }$$

on the same screen. b. What is the domain of each function? c. What is the range of each function? d. Describe the characteristics of

$$y= a \sqrt { x }$$

for a>0.

In each case, find the approximate sample size required to construct a 95% confidence interval for p that has sampling error SE = .06. a. Assume that p is near .3. b. Assume that you have no prior knowledge about p , but you wish to be certain that your sample is large enough to achieve the specified accuracy for the estimate.

Prove that matrix addition is associative for

$$2 \times 2$$

matrices.

What is the difference between an observational study and an experiment?

Solve the inequality. Then graph the solution set. |c + 2| > -2

The Alan Guttmacher Institute Abortion Provider Survey is a survey of all 358 known nonhospital abortion providers in the United States (Perspectives on Sexual and Reproductive Health, Jan./Feb. 2003). For one part of the survey, the 358 providers were classified according to case load (number of abortions performed per year) and whether they permit their patients to take the abortion drug misoprostol at home or require the patients to return to the abortion facility to receive the drug. The responses are summarized in the accompanying table. Suppose we select, at random, one of the 358 providers and observe the provider's case load (fewer than 50, or 50 or more) and home use of the drug (yes or no). Number of Abortions

$$\begin{matrix} \text{Permit Drug at Home} & \text{Fewer than 50} & \text{50 or More} & \text{Totals}\\ \text{Yes} & \text{170} & \text{130} & \text{300}\\ \text{No} & \text{48} & \text{10} & \text{58}\\ \text{Totals} & \text{218} & \text{140} & \text{358}\\ \end{matrix}$$

a. Find the probability that the provider permits home use of the abortion drug. b. Find the probability that the provider permits home use of the drug or has a case load of fewer than 50 abortions. c. Find the probability that the provider permits home use of the drug and has a case load of fewer than 50 abortions.

The system of linear equations has a unique solution. Find the solution using Gaussian elimination or Gauss-Jordan elimination.

$$\left\{ \begin{array} { l } { x + y + 6 z = 3 } \\ { x + y + 3 z = 3 } \\ { x + 2 y + 4 z = 7 } \end{array} \right.$$

Describe the transformations required to obtain the graph of

$$y_2$$

from the graph of

$$y_1$$

.

$$y_1=2cosπx$$

and

$$y_2=2cos2πx$$