A jug of water is pierced and begins to drip. The number of seconds between each drip is recorded. Estimate the probability the
next drip will occur in under 5 seconds. 1 3 2 1 1 4 6 5 6 7 7 8 9 6 9 8 6
2 answers:
The attached figure shows a point diagram that represents the situation. In this diagram the frequency in which the time between dripping was 1 2 3 4 5 6 7 8 and 9 seconds is observed.
we see that more often, the time between drips is 6 seconds.
However, we want to estimate the probability that the next drip occurs in less than 5 seconds.
The probability that the time between drips will be x seconds is:
P (t = x) = m / n
Where m is the number of times recorded in which the time between dripping was x seconds, and n is the total number of recorded data.
So, the probability that the time between drips is 5 seconds is:
P (t = 5) = 1/17
The probability that the time between drips is less than 5 is:
P (t <5) = P (t = 1) + P (t = 2) + P (t = 3) + P (t = 4)
P (t <5) = 3/17 + 1/17 + 1/17 + 1/17
P (t <5) = 6/17 = 0.3529
P (t <5) = 35.3%
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Answer: 58 ft × 58 ft
Step-by-step explanation:
Let the length of the region = x feet
And, the width of the region = y feet
Since, the perimeter of the region = 234 feet ( Given )
⇒
⇒
⇒
Again the area of the region, A = xy
⇒
⇒
By differentiating the above equation with respect to x,
⇒
For maxima or minima,
Again differentiating equation A'(x) with respect to x,
We get, A''(x) = -2
Hence, For x = 58.5 A''(x) = negative
⇒ For x = 58.5 feet the area A(x) is maximum,
⇒ The length of the region having maximum area = x = 58.5 feet
And, the width of the region having maximum area = y = 117-x= 117 - 58.5=58.5 feet,
⇒ The dimension of the region having the maximum area = 58.5 ft × 58.5 ft