<ol>
<li>Each of the following inequalities is true for some values of x EXCEPT:
A. X<X^2<X^3
B. X<X^3<X^2
C. X^2<X^3<X
D. X^3<X<X^2
E. X^3<X^2<X</li>
</ol>
<p>RIGHT ANSWER : C
2. Carol has 5 scarves and 5 sweaters, and each scarf matches a different sweater. If he chooses one of these scarves and one of these sweaters at random , what is the probability that they will not match ?? </p>
<p>Thanks ! :)</p>
<p>For your first question,
A is true if x=any positive integer, like 2
B is true if x=any number -1<x<0, like -0.5
C is never true
D is true if x=any negative integer, like -2
E is true if x=any number 0<x<1, like 0.5</p>
<p>Question 1:
We can simply rule out all other answers by finding an example that works for each of them.</p>
<p>a) X< X^2 < X^3 Pick X = 2
b) X < X^3 < X^2 Pick X = -0.5
d) X^3 < X < X^2 Pick X = -2
e) X^3 < X^2 < X Pick X = 0.5</p>
<p>So, we have given examples for a,b,d,e, and thus we can rule these choices out and pick C.</p>
<p>Question 2. I believe the answer is 4/5. Think of it this way. Let’s first pick a scarf. Then, given this scarf choice, there are 5 sweaters we can pick from. Only one of these sweaters matches the scarf we chose, and there is a 1/5 chance that we pick this sweater. Therefore, there is a 1 - 1/5 chance that it does not match. This is 4/5.</p>
<p>For your second question:
There are 25 possible scarf/sweater combinations (5 scarfs * 5 sweaters).
There are 5 times when the scarf will match the sweater.
So if in 5 of 25 cases the sweater and scarf DO match, then they do not match 20 of 25 times, or 80% of the time.
Hope this helps! :)</p>