<p>I'd like these explained, please.</p>
<p><a href="http://i.imgur.com/kJ0WZ.png%5B/url%5D">http://i.imgur.com/kJ0WZ.png</a>
Answer is D. I got it right, but after a while (my first answer was B).</p>
<p><a href="http://i.imgur.com/u2MFB.png%5B/url%5D">http://i.imgur.com/u2MFB.png</a>
Answer is C.</p>
<p>Thanks!</p>
<p>For (1): y = mx + b
m = -2 and (3,4) is on the line.
So: y = -2x + b. Then since (3,4) is on the line: 4 = -2*3 + b so b = 10 and the exact equation is y = -2x + 10. When x = 0, y =10.</p>
<p>For (2) you need to figure out how many of all the possible ways of assigning employees have Karen and Tina in corner offices.</p>
<p>Count the offices from left to right, so office 1 and 4 are corner offices.</p>
<p>So the total number of possible assignments is: 4<em>3</em>2<em>1 = 24 (since any of 4 can be assigned to the first office, 3 to the second, 2 to the third and 1 to the last). After I assign the first there are 3 employees left, and after the second 2, and then 1. That’s why it’s 4</em>3<em>2</em>1.</p>
<p>Of these 24 ways how many have Karen or Tina in the corner office? A total of 4. Compute it like this. Start with the first office. There are 2 possible choices (either Karen or Tina). Now the last office (we’ve placed one of the two, so the other goes here). How about the second office? Any of the other 2 employees – so 2. And the third office? The remaining employee.</p>
<p>So the answer is 4/24 or 1/6.</p>
<p>Thanks a lot!</p>
<p>For no.2, there is a much simpler way, I solved in two seconds.
So, you have 4 squares and 2 of them have Xs on them, the probability that Karen occupies
an office with an X is 2/4 or 1/2 and the probability that Tina occupies an office with an X is 1/3 (since there is one occupied by Karen) multiply the two fractions together, you get this 1/2*1/3 = 1/6</p>
<p>MathN00B. Your approach leads to the right answer in this case. I think you would have a hard time explaining why it does. You can’t really compute one probability, and at the same time mix that with a deterministic statement like “since there is one occupied by Karem” to compute another. Yes, there is such a notion as conditional probabilities which may lead to an approach such as you’ve used. But that’s pretty advanced stuff.</p>
<p>I like to use the point-slope form for number 1 (it’s quicker):</p>
<p>y-4=-2(x-3)</p>
<p>Since we’re looking for the y-intercept, plug in a 0 for x:</p>
<p>y-4=-2(0-3)=-2(-3)=6. So y=6+4=10, choice (D).</p>
<p>We can also solve this geometrically: Since the slope is -2, we must go up 2 every time we go left 1. To get to x=0 we must go left 3. Thus we must go up 6. Since we’re starting at y=4, the y-coordinate of the y-intercept is 4+6=10.</p>
