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1 answer:
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Answer:
a) Side Parallel to the river: 200 ft
b) Each of the other sides: 400 ft
Step-by-step explanation:
Let L represent side parallel to the river and W represent width of fence.
The required fencing (F) would be .
We have been given that field must contain 80,000 square feet. This means area of field must be equal to 80,000.
We are told that the fence on the side opposite the river costs $20 per foot, and the fence on the other sides costs $5 per foot, so total cost (C) of fencing would be .
From equation (1), we will get:
Upon substituting this value in cost equation, we will get:
To minimize the cost, we need to find critical points of the the derivative of cost function as:
Since width cannot be negative, therefore, the width of the fencing would be 400 feet.
Now, we will find the 2nd derivative as:
Now, we will substitute in 2nd derivative as:
Since 2nd derivative is positive at , therefore, width of 400 ft of the fencing will minimize the cost.
Upon substituting in
, we will get:
Therefore, the side parallel to the river will be 200 feet.
Answer:
The score that cuts off the bottom 2.5% is 48.93.
Step-by-step explanation:
When the distribution is normal, we use 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.
In this question, we have that:
What is the score that cuts off the bottom 2.5%
This is X when Z has a pvalue of 0.025, so X when Z = -1.96.
The score that cuts off the bottom 2.5% is 48.93.