<p>The weights of 10 bags of apples range from 2.75 pounds to 3.15 pounds. If w is the weight, in pounds, of one of these bags, which of the following must be true?</p>
<p>A. | w 2.75 | less than or equal to 0.2
B. | w 2.95 | less than or equal to 0.2
C. | w + 2.95 | less than or equal to 0.2
D. | w 0.2 | less than or equal to 2.75
E. | w 10 | less than or equal to 2.95</p>
<p>How do you solve it? And where do the 2.95 and 0.2 come from?</p>
<p>if you take out the absolute value and solve it, you end up with w<3.15 and w>2.75</p>
<p>Ermm…clarify a bit more please.</p>
<p>if you take the absolute value of something, you are calculating how far left or how far right it is.</p>
<p>for example on a number line, -9 and 9 are both 9 units away from 0
if you pick any number between -9 and 9, its distance from 0 is at MOST 9.</p>
<p>-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
take the absolute value of any number and the most it can be is 9. so, it would be less than or equal to 9</p>
<p>the average between 2.75 and 3.15 is 2.95</p>
<p>if you pick a number between 2.75 and 3.15 and find the distance from it to 2.95, it will never be more than 0.2</p>
<p>2.75 —> 2.95 —> 3.15</p>
<p>you can only go 0.2 to the left of 2.95 (stopping at 2.75)
you can only go 0.2 to the right of 2.95 (stopping at 3.15)</p>
<p>so you can only go an amount less than or equal to 0.2 away from 2.95</p>
<p>l w - 2.95 l is > or = to 0.2</p>
<p>endpoints of the interval would be
l 2.75 - 2.95 l = 0.2
l 3.15 - 2.95 l = 0.2</p>
<p>^^^ you mean < or = to 0.2</p>
<p>yea my bad</p>
<p>Can someone entertain my dumb question…
what if | w – 2.95 | greater than or equal to 0.2 was an answer choice
Would that work as well?</p>
<p>No.</p>
<p>2.95-2.95 = 0 = smaller than .2</p>