For the following problem, find the third direction cosine and the two possible values of the third direction angle.

$$c_1=\frac{18}{23}, c_2=-\frac{13}{23}$$

Give an example of a situation in which two variables have no causal connection but are highly correlated because they are both related to a third variable. Explain what the third variable is.

List some possible ways to choose random samples for each study. A study of the opinions of people toward Medicare.

Risk of harm in social and behavioral sciences generally fall in three categories, which are:

A. Breach of confidentiality, loss of autonomy, and study procedures

B. Study procedures, breach of confidentiality, and loss of employment

C. Invasion of privacy, adverse reaction to study drug, and discrimination

D. Invasion of privacy, breach of confidentiality, and study procedures

The first number plus the third number is equal to the second number. The sum of the first number and the second number is six more than the third number. Three times the first number minus two times the second number is equal to the third number. What is the sum of the three numbers?

A study of the U.S. Office of Science and Technology in 1972 estimated the cost of reducing automobile emissions by certain percentages. Find a model that captures the "diminishing returns" trend of these data.

$$\begin{array}{|c|c|} \hline \text { Reduction in emissions ( in percentage) } & \text { Cost per car (in dollars) } \\ \hline 50 & 45 \\ 55 & 55 \\ 60 & 62 \\ 65 & 70 \\ 70 & 80 \\ 75 & 90 \\ 80 & 100 \\ 85 & 200 \\ 90 & 375 \\ 95 & 600 \\ \hline \end{array}$$

scribit is third person singular in present tense. scribit means s/he writes. scripsit is third person singular in perfect tense. spripsit means s/he wrote. scripserat is third person singular in plupercfect tense. scripserat means s/he had written.

Complete the sentence in a way that shows you understand the meaning of the italicized vocabulary word.

If Pat bungles the science project, he ...

What does it mean when an observational study is retrospective? What does it mean when an observational study is prospective?

The famous formula

$$e^{a+bi}=e^{a(\cos b+i\sin b)}$$

is called Euler's Formula,after the Swiss mathematician Leonhard Euler $(1707–1783)$. This formula gives rise to one of the most wonderful equations in mathematics.

$$e^{\pi i}+1=0$$

This elegant equation relates the five most famous numbers in mathematics

$$0, 1, \pi, e,\ \text{and}\ i$$

in a single equation. Show how Euler’s Formula can be used to derive this equation.

Evaluate the determinant by a cofactor expansion along (a) the first row. (b) the first column. (c) the second row. (d) the second column. (e) the third row. (f) the third column.

List some possible ways to choose random samples for each study. A study to determine favorite brands of cereal.

How might someone who unknowingly is committing the fundamental attribution error explain Stanley Milgram’s obedience study?

a. Subjects in that study were highly influenced by the power of Milgram and his team. b. Subjects in that study desired a high degree of positive reinforcement. c. Subjects in that study wanted to be part of Milgram’s group. d. Subjects in that study must have been the kind of people that like to hurt others.

Draw a triangle ABC. a. Construct the line parallel to B̅C̅ through point A. b. Use measurement to justify that the line you constructed is parallel to B̅C̅. c. Use mathematics to justify this construction.