Sophia College Algebra MM212 Final Milestone

Sophia College Algebra MM212 Final Milestone 20/25 that's 80% 20 questions were answered correctly. 5 questions were answered incorrectly. 1 Geri runs a total of 3.1 miles in a cross-country race. How many feet is this equivalent to? • 5,280 feet • 16,368 feet • 4,989 feet • 15,840 feet RATIONALE In general, we use conversion factors to convert from one unit to another. A conversion factor is a fraction with equal quantities in the numerator and denominator, but written with different units. We want to convert miles to feet. We know how many feet are in 1 mile. We will use this fact to set up a conversion factor. There are 5280 feet in 1 mile. To convert 3.1 miles into feet, multiply by the fraction . Notice how the fractions are set up. The units of miles will cancel, leaving only feet. Finally we can evaluate the multiplication by multiplying across the numerator and denominator. In the numerator, 3.1 times 5280 equals 16368. 3.1 miles is equivalent to 16,368 feet. CONCEPT Converting Units 2 Perform the indicated operations and write your result as a single number. R ATIONALE For this expression, there is a lot to consider here. Follow the order of operations, and evaluate anything inside parentheses and other grouping symbols first. There are two groups. First, the radical symbol groups (11 × 2 – 6), and a set of parentheses groups . Let's evaluate what is under the radical first. Under the radical, there is multiplication and subtraction. Multiplication comes before subtraction in the order of operations, so we multiply 11 by 2 to get 22. Next, evaluate the subtraction. 22 minus 6 is 16. Now we can take the square root of 16. The square root of 16 is 4. This is the simplified expression underneath the radical. Next, we have to evaluate the operations in the set of parentheses. Exponents comes before subtraction in the order of operations, so we square 4 first. 4 squared equals 16. Next, we subtract 9 from 16. 16 minus 9 equals 7. Now that we have eliminated the grouping symbols, we can evaluate the multiplication of 5 and 7. 5 times 7 equals 35. Finally, we can add 4 and 35. 4 plus 35 is equal to 39. The expression simplifies to 39. CONCEPT Order of Operations: Exponents and Radicals 3