Use the graph to determine a. open intervals on which the function is decreasing, if any. b. open intervals on which the function is increasing, if any. c. open intervals on which the function is constant, if any. 2 3 a. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The function is decreasing on the interval(s) (Type your answer in interval notation. Use a comma to separate answers as needed.) O B. The function is never decreasing.
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.
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![### Using Graphs to Determine Function Behavior
#### Problem Statement
Use the graph to determine:
a. Open intervals on which the function is decreasing, if any.
b. Open intervals on which the function is increasing, if any.
c. Open intervals on which the function is constant, if any.
#### Graph Description
A graph of a function is provided on a Cartesian plane. The x-axis is labeled from 0 to 6, and the y-axis is labeled from -5 to 5. The function is represented by a blue line that starts from the point (0, -3) and ends at the point (6, 3).
- The graph shows a continuous, linear increase in the function from left to right.
#### Questions and Answers
**a. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.**
- **A. The function is decreasing on the interval(s) [_].**
*(Type your answer in interval notation. Use a comma to separate answers as needed.)*
- **B. The function is never decreasing.**
From the provided graph, the function does not show any intervals where it is decreasing. Therefore, the correct choice is:
**B. The function is never decreasing.**
#### Explanation
- **Increasing Intervals:**
The function is increasing over the entire domain shown in the graph, which can be observed from the continuous upward sloping line from (0, -3) to (6, 3).
- **Decreasing Intervals:**
There are no decreasing intervals observed on the graph since the function is always moving upwards.
- **Constant Intervals:**
There are no intervals where the function is constant since the function does not stay flat at any point.
Understanding how to interpret a graph and identify intervals where a function is increasing, decreasing, or constant is a fundamental skill in calculus and algebra.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F61114f5f-1857-43f7-9640-cf88fdfe990f%2Ff6eed008-729a-4721-bc8f-3dcbbe852b18%2Fu5vyuho_processed.png&w=3840&q=75)
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