16. Minimum fence The running yard for a dog kennel must contain at least 900 square feet. If a 20-foot side of the kennel is used as part of one side of a rectangular yard with 900 square feet, what dimensions will require the least amount of fencing? O rectangular field with one side along of
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
Question 16
![**Candidate Recognition**
14. Candidate recognition: Suppose that in an election year, the proportion \( p \) of voters who recognize a certain candidate’s name \( t \) months after the campaign started is given by:
\[
p(t) = \frac{7.2t}{t^2 + 36} + 0.2
\]
Explore how the proportion is maximized by determining the number of months required to reach this point and the maximum percentage itself.
**Minimum Fence**
15. Minimum fence: Two equal rectangular lots need enclosing by fencing the perimeter of a larger rectangular lot and partitioning it with a fence. If each lot must measure 1200 square feet, identify the least length of fencing necessary to enclose the properties.
16. Minimum fence: A dog kennel’s running yard must cover no less than 900 square feet. With a 20-foot yard side, determine the dimensions that minimize fencing needs.
**Minimum Cost**
17. Minimum cost: A rectangular field borders a river and requires fencing on only three sides. The side opposite the river incurs \( \$40 \) per foot, while the remaining sides cost \( \$10 \) per foot. If the field must measure 45,000 square feet, find the dimensions to minimize expenses.
18. Minimum cost: A developer plans to enclose and halve a rectangular land tract into two identical lots using a central fence. Suppose the exterior fence costs \( \$20 \) per foot, and the central fence costs \( \$8 \) per foot. Calculate the dimensions that minimize costs.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F82efe7f0-1674-46d0-9961-35be2e861db0%2F56779893-a916-41cc-b243-cbddc07ded30%2Fqbwd9l.jpeg&w=3840&q=75)
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