Determine whether the given graph is connected or disconnected. Then determine how many components the graph has.

Construct a truth table for each statement.

$$\sim p\wedge(p\vee q)$$

Find the vector components of x along a and orthogonal to a. $\mathbf{x}=(5,0,-3,7), \mathbf{a}=(2,1,-1,-1)$

Construct a truth table for (p ↔ q) ↔ (r ↔ s).

If you "disassembled" an atom of helium into its separate components, what would you have?

A government agency takes a random sample of income tax returns to obtain information on the average income of people in different occupations. Only the incomes and occupations are recorded from the returns, not the names. Should this study require informed consent? Explain your reasoning.

Explain why women's heights are likely to have a bell shape but their ages at marriage do not.

Use the banker's rule to find the amount that may be borrowed for each annual income.

$$\$26,750$$

The annual incomes of the households in a certain community range between 5 and 25 thousand dollars. Let X represent the annual income (in thousands of dollars) of a household chosen at random in this community, and suppose that the probability density function for X is $f(x)=k x, 5 \leq x \leq 25$.

(a) Find the value of k that makes f(x) a density function.

(b) Find the fraction of households whose income exceeds $20,000.

(c) Find the mean annual income of the households in the community.

Identify at least two situations in which important changes in value are not reported in the income statement.

Which of the following statements is true? (A) If f(x) is continuous, then f(x) is differentiable. (B) If f(x) is differentiable, then f(x) is continuous.

Knowing that the tension in cable $A B$ is $285 \mathrm{~lb}$, determine the components of the force exerted on the plate at $B$.

What is the “cosmic haystack problem”? List as many of its components as you can think of.

Construct a truth table for the given statement.

$$[ ( p \rightarrow q ) \wedge p ] \rightarrow p$$