Keegan and Jeff did some research and found that there are approximately 7,492,000,000,000,000,000 grains of sand on Earth. Jeff says that it is about $7 \times 10^{15}$ grains of sand. Keegan says that this is about $7 \times 10^{18}$ grains of sand. Whose estimate, Jeff's or Keegan's, is more logical? Explain.

Evaluate. (-7)$^{0}$

The table shows the results of the draw. The students who drew rational numbers will form the team called the Tigers. The students who drew irrational numbers will form the team called the Lions. List the members of each team.

$$\begin{array}{|l|c|} \hline \text { Student } & \text { Number Draw } \\ \hline \text { Lydia } & \sqrt{38} \\ \hline \text { Marcy } & 6.3\overline{4} \\ \hline \text { Caleb } & \sqrt{36} \\ \hline \text { Ryan } & 6.343443444 \ldots \\ \hline \text { Anya } & 6.\overline{34} \\ \hline \text { Chan } & \sqrt{34} \\ \hline \end{array}$$

Those powers held by the States, not granted specifically to the National Government by the Constitution

Sofia wrote a decimal as a fraction. Her classmate Nora says that her method and answer are not correct. Sofia disagrees and says that this is the method she learned.

$$\begin{array}{c} 0.12112111211112 = \\ x=0.12 \\ 100 \cdot x=100 \cdot 0.12 \\ 100 x=12.12 \\ 99 x=12 \\ x=\frac{12}{99} \end{array}$$

Is Nora or Sofia correct? Explain your reasoning.

The table shows the results of the draw. The students who drew rational numbers will form the team called the Tigers. The students who drew irrational numbers will form the team called the Lions. List the members of each team.

$$\begin{array}{|l|c|} \hline \text { Student } & \text { Number Draw } \\ \hline \text { Lydia } & \sqrt{38} \\ \hline \text { Marcy } & 6.3\overline{4} \\ \hline \text { Caleb } & \sqrt{36} \\ \hline \text { Ryan } & 6.343443444 \ldots \\ \hline \text { Anya } & 6.\overline{34} \\ \hline \text { Chan } & \sqrt{34} \\ \hline \end{array}$$

Calvin and Mike do sit-ups when they work out. They start with 64 sit-ups for the first set and do half as many each subsequent set. What representation can you use to show the relationship between the set number and the number of sit-ups?

Cassify the following numbers as rational or irrational.

$$\begin{array}{cccccc} \frac{8}{5} & \pi & 0 & \sqrt{1} & 4.46466 \ldots & -6 & \sqrt{2} \end{array}$$

Simplify the expression. (6 $\cdot$ 100) - (1 $\cdot$ 10)

Alberto incorrectly stated that

$$\frac{5^{7}}{5^{4}}=1^{3}$$

What was Alberto's error? Explain your reasoning and find the correct answer.

Manolo says that the solution of the equation g$^{2}$ = 36 is g = 6 because 6 $\times$ 6 = 36. Is Manolo's reasoning complete? Explain.

Find

$$\left(2.2 \times 10^{5}\right) \div\left(4.4 \times 10^{-3}\right)$$

When you regroup the factors, what do you notice about the quotient of the decimal factors? How does this affect the exponent of the quotient?

A survey of 1,000 U.S. government employees who have an advanced college degree produced the following responses to the offering of a promotion to a higher grade position that would involve moving to a new location.Use the results of the survey to estimate the following probabilities.a. What is the probability that a randomly selected government employee having an advanced college degree would accept a promotion?b. What is the probability that a randomly selected government employee having an advanced college degree would not accept a promotion?c. What is the probability that a randomly selected government employee having an advanced college degree has a spouse with a professional position?

$$\begin{matrix} \text{Promotion} & \text{Married Both Spouses Professional} & \text{Married One Spouse Professional} & \text{Unmarried} & \text{Total}\\ \text{Rejected} & \text{184} & \text{56} & \text{17} & \text{257}\\ \text{Accepted} & \text{276} & \text{314} & \text{153} & \text{743}\\ \text{Total} & \text{460} & \text{370} & \text{170} & \text{1000}\\ \end{matrix}$$

Simplify the expression. Assume that x is nonzero. Your answer should have only positive exponents. $x^{-10} \cdot x^{6}$