PLSSS HELP ME PLSSS 14 POINTS!
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the "t" variable is independent, namely it can change values "freely", and a(t) is dependent, because it depends on those values on "t" to get its own value.
if we make a table of values for minutes, we know the balloon is inflating at 6000 ft³ each passing minute.
1 minute......................... 6000(1) ft³
2 minutes......................6000(2) ft³
3 minutes......................6000(3) ft³
4 minutes......................6000(4) ft³
t minutes......................6000(t) ft³
before getting in the domain and range, let's find out how much air after 6 minutes.
a(6) = 6000(6)
a(6) = 36000 ft³.
now, what domain, namely values for "t" make sense?
well, we know the balloon can only hold up to 90000 ft³, and on every passing minute is filling up by 6000 ft³, after how many minutes will it be filled up?
90000/6000 = 15, after 15 minutes.
so at 0 minutes, t = 0, the balloon is empty, and 15 minutes later, t = 15, the balloon is filled up, [ 0 , 15 ].
what values for the range, namely a(t), makes sense?
well, we know when the balloon is empty is holding 0 ft³, and when is full it has 90000 ft³, [0 , 90000].
Answer: (C) 0.1591
Step-by-step explanation:
Given : A manufacturer of radial tires for automobiles has extensive data to support the fact that the lifetime of their tires follows a normal distribution with
Let x be the random variable that represents the lifetime of the tires .
z-score :
For x= 44,500 miles
For x= 48,000 miles
Using the standard normal distribution table , we have
The p-value :
Hence, the probability that a randomly selected tire will have a lifetime of between 44,500 miles and 48,000 miles = 0.1591