ANSWER
Find out the customer was the first to get both items
To proof
As given
During a promotional event
sporting goods store gave every 14th customer a free shirt and a free bottle to every 18th customer.
Least common factor of ( 14 , 18 )
L.C.M (14,18) = 2 ×7 ×9
= 126
Also as shown in the table given below
in the table
the common value in the shirt and bottle is 126.
i.e 126 th the customer was the first to get both items.
Hence proved
Answer:
C: I and III only.
Step-by-step explanation:
We have two numbers x and y such that:
And we want to determine which of the following conditions must be true.
First, let's examine the third condition. We have:
To see if this is true, let's try a negative value for y. So, let's use -7. This will give:
Simplify:
This is saying we need a number less than -7 and greater than 7.
This is impossible. So, y <em>must be</em> greater than 0.
Therefore, Condition III must be true.
Next, let's see this compound inequality visually.
Picture the following number-line:
<----------(-y)----------0----------y---------->
Whatever y is, -y is just y on the negative side.
Now, since our condition is that -y<x<y, this means that our x can be anywhere between -y and y. Namely:
<----------(-y)----------0----------y---------->
To determine our correct condition, let's picture x anywhere on the bolded lines. I'm just going to put x here...
<----------(-y)-------(x)--0----------y---------->
Now, remember the alternative definition for absolute value. Namely, the absolute value of x is also the <em>distance</em> from 0 to x. And this distance is always positive.
Since our x is between -y and y, our distance from 0 to x will always be less than the distance from 0 to either y.
Therefore, Condition I is also true.
Let's try an example. Let's let y = 9. So, -y=-9. And let's let x be between 9 and -9, say, -2. So:
<---(-9)-----(-2)--0--------(9)------>
We can see that:
Also, this example counters Condition II, as our x can indeed be negative if we desire it.
Algebraically, if we have a negative x such that:
We can divide everything by -1 to obtain:
We can flip this to get:
Which is our original inequality. So, Condition II does not need to be true.
So, the two conditions that <em>must</em> be true is I and III.
So, our answer is C.