Is conjecture $(1)$ in the text (that the $n$th perfect number contains exactly $n$ digits) true or false? Explain.

Draw a Venn diagram showing the members of Congress of the United States, the members of the House of Representatives, and the members of the Senate.

Compile a list of all the various techniques for factoring a polynomial that have been covered so far in the text. Give an example illustrating each technique and write a paragraph discussing when the use of each technique is appropriate.

As discussed in this lecture, what is augmented cognition?

Which principle is most important for a nurse to follow when using a clinical practice guideline for an assigned patient?

1. Knowing the source of the guideline
2. Reviewing the evidence used to develop the guideline
3. Individualizing how to apply the clinical guideline for a patient
4. Explaining to a patient the purpose of the guideline

Explain why the empty set cannot be put in a one-to-one correspondence with any non-empty set.

Show that 2047 passes Miller's test to the base 2, but that it is composite. A composite positive integer n that passes Miller's test to the base b is called a strong pseudoprime to the base b. It follows that 2047 is a strong psuedoprime to the base 2.

Which of the following sets are equal?

$$A = {a,b,c,d}$$

$$B = {d,e,a,c}$$

$$C = {d,b,a,c}$$

$$D = {a,a,d,e,c,e}$$

Draw a Venn diagram showing the relationship between the set of natural numbers and the set of whole numbers.

Which symbol will make the following statement true? Write >, <, or =.

$$58.827 \bigcirc 58.91$$

A student claims that she has found an easy way to find the number of terms in an arithmetic sequence: “You take the difference between the last and first terms and divide by the common difference.” How do you respond?

Use the approach in Gauss's Problem to find the following sums of arithmetic sequences: a. 1+2+3+4+...+998 b. 1+3+5+7+...+ 101 c. 4+9+14+19 +... +494 d. 881+872+863+854+..+8

a. The sum of the sequence is $\square$.

Prove Fermat's Little Theorem: If p is a prime and $a \in \mathbb{Z},$ then $a^{p} \equiv a(\bmod p)$. If a is relatively prime to p, then $a^{p-1} \equiv 1(\bmod p).$

Mr. Marcos organizes a classroom game for 16 students. Each student is randomly assigned a different numbers from 1 to 16. Students assigned a multiple of 4 or 9 are on Team A. Students assigned a multiple of 5 or 7 are on Team B. Students assigned any other number are on Team C. Find each probability. P(Nicole was assigned 7|Nicole is on Team B) A. 1/16, B. 1/5, C. 5/16, D. 3/8