How many intersections are there of the graphs of the equations below? One-halfx + 5y = 6 3x + 30y = 36 none one two infinitely
2 answers:
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Answer:
a) P=0
b) P=0.164
c) P=0.145
Step-by-step explanation:
We have 12 pieces, with 3 of each of the 4 flavors.
You draw the first 4 pieces.
a) The probability of getting all of the same flavor is 0, because there are only 3 pieces of each flavor. Once you get the 3 of the same flavor, there are only the other flavors remaining.
b) The probability of all 4 being from different flavor can be calculated as the multiplication of 4 probabilities.
The first probability is for the first draw, and has a value of 1, as any flavor will be ok.
The second probability corresponds to drawing the second candy and getting a different flavor. There are 2 pieces of the flavor from draw 1, and 9 from the other flavors, so this probability is 9/(9+2)=9/11≈0.82.
The third probability is getting in the third draw a different flavor from the previos two draws. We have left 10 candys and 4 are from the flavor we already picked. Then the third probabilty is 6/10=0.6.
The fourth probability is getting the last flavor. There are 9 candies left and only 3 are of the flavor that hasn't been picked yet. Then, the probability is 3/9=0.33.
Then, the probabilty of picking the 4 from different flavors is:
c) We can repeat the method for the previous probabilty.
The first draw has a probability of 1 because any flavor is ok.
In the second draw, we may get the same flavor, with probability 2/11, or we can get a second flavor with probability 9/11. These two branches are ok.
For the third draw, if we have gotten 2 of the same flavor (P=2/11), we have to get a different flavor (we can not have 3 of the same flavor). This happen with probability 9/10.
If we have gotten two diffente flavors, there are left 4 candies of the picked flavors in the remaining 10 candies, so we have a probabilty of 4/10.
For the fourth draw, independently of the three draws, there are only 2 candies left that satisfy the condition, so we have a probability of 2/9.
For the first path, where we pick 2 candies of the same flavor first and 2 candies of the same flavor last, we have two versions, one for each flavor, so we multiply this probability by a factor of 2.
We have then the probabilty as:
Answer:
0.3114
Option d is right
Step-by-step explanation:
Let X be the time spent on a treadmill in the health club
Given that research shows that on average, patrons spend an average of 42.5 minutes on the treadmill, with a standard deviation of 5.4 minutes
Also given that X is normal
the probability that randomly selected individual would spent between 30 and 40 minutes on the treadmill.
round off to two decimals tog et
the probability that randomly selected individual would spent between 30 and 40 minutes on the treadmill is 0.31
Hence option d is right