Which is larger: the number of meters across the Milky Way, or the number of cells in all humans? Explain or show your reasoning.

Some useful information:

• The Milky Way is about 100,000 light years across.
• There are about 37 trillion cells in a human body.
• One light year is about \(10^{16}\) meters.
• The world population is about 8 billion.

What information would you need to know in order to solve the following problem?

Suppose that someone leaves all the lights on at your school. Before leaving for the day, the principal goes around and turns off all the lights. How long does this take?

Lin’s mother has a car that she uses for work, shopping, and trips. About how many times does one tire on her car revolve in a year? Explain or show your reasoning.

Some useful information:

• The diameter of her tire is 27 inches.
• She drives about 10,000 miles in one year.
• There are 5,280 feet in one mile.
• There are 12 inches in one foot.

Ecologists measure the body length and wingspan of 127 butterfly specimens caught in a single field.

1. Draw a line that you think is a good fit for the data.
2. Write an equation for the line.
   
3. What does the slope of the line tell you about the wingspans and lengths of these butterflies?

Diego was solving an equation, but when he checked his answer, he saw his solution was incorrect. He knows he made an error, but he can’t find it. Where is Diego’s error and what is the solution to the equation?

\(\displaystyle \begin{align} \text-4(7-2x)=3(x+4)\\ \text-28-8x=3x+12\\ \text-28=11x+12\\ \text-40=11x\\ \text{-}\frac {40}{11}=x\ \end{align}\)

 

The two triangles are similar. Find \(x\).