10A Coreq

In the next preview assignment and in the next class, you will need to label intervals on  number lines and use ± notation.

Labeling Intervals on Number Lines

Suppose you want to buy a pair of jeans. At department stores, the average cost of  jeans may be $30. Suppose at some stores the cost may be up to $5 over that cost,  while at other stores the cost may be up to $5 lower than that cost.

We can write this using [latex]\pm[/latex] notation as $30 [latex]\pm[/latex] $5. If we subtract 5 from 30, we get $25 [latex](30 – 5 = 25)[/latex], and if we add 5 to 30, we get $35 [latex](30 + 5 = 35)[/latex].

This makes our cost range for department store jeans $25 to $35. This can be  represented on a number line by putting a dot in the center at 30 and drawing a line that  extends 5 in both directions.

Question 1

Suppose for a more expensive style of jeans, the average cost is $50 and the cost  changes by up to $7 between stores. In other words, suppose that at some stores  jeans cost up to $7 more, while in other stores jeans cost up to $7 less.

  1. Use the number line provided to represent the corresponding cost range for these jeans.
  2. Using your answer from Part a, would $63 be considered within the upper and lower bounds of the cost interval? Explain.

Question 2

Suppose you want to buy jeans somewhere a bit more expensive, where the  average cost is $70. These jeans cost up to $9 more at some stores and up to $9  less at other stores.

  1. Use the number line provided to represent the corresponding cost range for these jeans.
  2. Would $75 be within the upper and lower bounds of the cost interval?  Explain.

Question 3

The weight of a box of cereal filled by a machine is 16 ounces (oz). However,  sometimes the box is overfilled by up to 0.5 oz, and sometimes the box is underfilled  by up to 0.5 oz.

  1.  We could represent the weight of the box of cereal (in oz) as 16 [latex]\pm[/latex] ____.
  2. The weight of the box of cereal filled by the machine is between ____ and  _____.
  3. Write your answer from Part b in interval notation form, which is: (lower  bound, upper bound).

Question 4

Use the number line provided to represent the interval for the weight of the box of cereal. Use a dot for the center of the interval and parentheses for the upper and  lower bounds.

Question 5

Which of the following values are contained in the interval? Choose all that apply.

  1.  15.2
  2. 15.4
  3. 15.8
  4. 16.4
  5. 16.6

Question 6

Intervals can also be made for proportions. To answer the following questions, use  the following expression: 0.35 [latex]\pm[/latex] 0.08.

  1. Subtract 0.08 from 0.35; we call this the lower bound.
  2. Add 0.35 to 0.08; we call this the upper bound.
  3. Plot the interval on the number line provided using a dot for the center of the  interval and parentheses for the upper and lower bounds.