Using calculus, it can be shown that if a ball is thrown upward with an initial velocity of 16 ft/s from the top of a building 7
04 ft high, then its height h above the ground t seconds later will be h = 704 + 16t − 16t2. During what time interval (in seconds) will the ball be at least 32 ft above the ground? (Enter your answer using interval notation.)
1 answer:
Answer:
[0, 7]
Step-by-step explanation:
We want the height to be greater than or equal to 32 ft, so ...
704 +16t -16t^2 ≥ 32
t^2 -t -42 ≤ 0 . . . . . . . . . . . subtract 32, divide by -16
(t -7)(t +6) ≤ 0
This inequality will be true for values of t between -6 and +7. Since we're only concerned with times t ≥ 0, the appropriate solution interval is ...
0 ≤ t ≤ 7 . . . . [0, 7] in interval notation
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Answer:
The level L such that there is probability only 0.01 that the mean glucose level of 6 test results falls above L is L = 127.1 mg/dl.
Step-by-step explanation:
To solve this problem, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central limit Theorem
The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation
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In this problem, we have that:
What is the level L such that there is probability only 0.01 that the mean glucose level of 6 test results falls above L ?
This is the value of X when Z has a pvalue of 1-0.01 = 0.99. So X when Z = 2.33.
By the Central Limit Theorem
The level L such that there is probability only 0.01 that the mean glucose level of 6 test results falls above L is L = 127.1 mg/dl.
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