Answer:
This is actually a reduction, and the scale factor of this dilation is 0.5.
When a line is given in the form
The slope of the line is m. So, in this case, the slope of 
is 1.
Given a slope 
, you find the slope of a perpendicular line 
by imposing
So, if the given line has slope 1, a perpendicular line has slope given by
and thus 
So, we want a line with slope -1 and passing through (12,-1). Using the fomula
we get
Say, for example, you have an improper fraction (it usually is if you're trying to convert to a mixed number) like: 55/7
You would take the highest number that is divisible by the denominator, which in this case is 7 (7x7=49; 7x8 would be 56 and we don't want that)
You subtract the number you got (49) from the original numerator (55).
That will give you 6.
Now, you put the whole number (7) before the fraction (6/7)
Pet show has stations for each animal. There are 5 rabbits, 7 cats, 8 dogs, and 4 hamsters.
1. How many cats need to be added to make the probability 1/2.
For the probability to be 1/2, we need there to be 1 cat for every 2 animals. There are 5+8+4 = 17 other animals besides cats so we need to increase the amount of cats to 17 so that it is 1/2 of the total. We already have 7 so we need 17-7 = 10 more cats.
2. Assume we added the cats. What's the probability of picking a dog?
Since we added the cats, the total number of animals is now 17+17 = 34
There are 8 dogs, so the probability of picking a dog will be 8/34 which will reduce to 8/34 = 4/17 (you will pick 4 dogs every 17 attempts).
3. No more animals added. What is the probability of picking a rabbit or hamster?
Total rabbits and hamsters is 5+4 = 9 so there is a 9/34 chance of picking a rabbit or hamster. (you will pick a rabbit or hamster 9/34 attempts).
4. What is the probability of NOT picking a goldfish?
Be careful here... the question is what is the probability that you won't pick a goldfish? Well there are no goldfish, so there is a 34/34 (100%) chance that you won't pick a goldfish. You will NOT pick a goldfish 34 out of 34 times.
