A square and a circle are placed so that the circle is outside the square and tangent to a side of the square. The sum of the length of one side of the square and the circle's diameter is 12 feet, as shown in figure 1. Suppose the length of one side of the square is a feet. 12 Figure 1 (a) Write a formula for f(x), the sum of the total area of the square and the circle. What is the domain of this function when used to describe this problem? (The domain should be related to the problem statement.) Sketch a graph of f(x) on its domain. (b) Suppose that the object (square or circle) with larger area is painted red, and the object (square or circle) with smaller area is painted green. The cost of red paint to cover 1 square foot is $4, and the cost of green paint to cover 1 square foot is $10. Let g(x) be the function which gives the cost of painting the squares. Describe the function g(x). Sketch a graph of g(x) on its domain. Hint: Read the question carefully. The answer will be a piecewise-defined function. A complete answer should give all relevant information (c) Where is the function g(x) continuous? Where is it differentiable? Which value of a gives the least cost?
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.
Problem 2 Parts A, B, and C
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