수와 연산 전체 문제

For the following exercises, solve the given problem.

According to the U.S. Mint, the diameter of a quarter is 0.955 inches. The circumference of the quarter would be the diameter multiplied by $\pi .$ Is the circumference of a quarter a whole number, a rational number, or an irrational number?

For the following exercises, solve the given problem.

Jessica and her roommate, Adriana, have decided to share a change jar for joint expenses. Jessica put her loose change in the jar first, and then Adriana put her change in the jar. We know that it does not matter in which order the change was added to the jar. What property of addition describes this fact?

For the following exercises, consider this scenario: There is a mound of $g$ pounds of gravel in a quarry. Throughout the day, 400 pounds of gravel is added to the mound. Two orders of 600 pounds are sold and the gravel is removed from the mound. At the end of the day, the mound has 1,200 pounds of gravel.

Write the equation that describes the situation.

For the following exercises, consider this scenario: There is a mound of $g$ pounds of gravel in a quarry. Throughout the day, 400 pounds of gravel is added to the mound. Two orders of 600 pounds are sold and the gravel is removed from the mound. At the end of the day, the mound has 1,200 pounds of gravel.

Solve for g.

For the following exercise, solve the given problem.

Ramon runs the marketing department at their company. Their department gets a budget every year, and every year, they must spend the entire budget without going over. If they spend less than the budget, then the department gets a smaller budget the following year. At the beginning of this year, Ramon got $2.5 million for the annual marketing budget. They must spend the budget such that $2,500,000-x=0.$ What property of addition tells us what the value of x must be?

For the following exercises, use a graphing calculator to solve for x. Round the answers to the nearest hundredth.

$0.5{(12.3)}^{2}-48x=\frac{3}{5}$

For the following exercises, use a graphing calculator to solve for x. Round the answers to the nearest hundredth.

${(0.25-0.75)}^{2}x-7.2=9.9$

If a whole number is not a natural number, what must the number be?

Determine whether the simplified expression is rational or irrational: $\sqrt{-18-4(5)(-1)}.$

Determine whether the simplified expression is rational or irrational: $\sqrt{-16+4(5)+5}.$

The division of two natural numbers will always result in what type of number?

What property of real numbers would simplify the following expression: $4+7(x-1)?$

Is ${2}^{3}$ the same as ${3}^{2}?$ Explain.

When can you add two exponents?

What is the purpose of scientific notation?

Explain what a negative exponent does.

For the following exercises, simplify the given expression. Write answers with positive exponents.

${9}^{2}$

For the following exercises, simplify the given expression. Write answers with positive exponents.

${15}^{-2}$

For the following exercises, simplify the given expression. Write answers with positive exponents.

${3}^{2}\times {3}^{3}$

For the following exercises, simplify the given expression. Write answers with positive exponents.

${4}^{4}\div 4$