The number of cars sold weekly by a new automobile dealership grows according to a linear growth model. The first week the dealership sold four cars (Po = 4). The second week the dealership sold nine cars ( P = 9). Write the recursive formula for the number of cars sold, P,, in the (n + 1)th week. Pn = Pn -1+ 5 v Write the explicit formula for the number of cars sold, Pn, in the (n + 1)th week. P, = 4+5(n – 1) × If this trend continues, how many cars will be sold in the 4th week? 19 v cars
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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![### Understanding Linear Growth in Car Sales at a Dealership
The number of cars sold weekly by a new automobile dealership grows according to a linear growth model. Here is a breakdown of the sales trend:
- **First week:** The dealership sold four cars. This is represented as \( P_0 = 4 \).
- **Second week:** The dealership sold nine cars. This is represented as \( P_1 = 9 \).
### Recursive Formula
**Task:** Write the recursive formula for the number of cars sold, \( P_n \), in the \( (n + 1) \)th week.
The recursive formula is:
\[ P_n = P_{n-1} + 5 \]
This indicates that each week, the number of cars sold increases by 5 compared to the previous week.
✔️ Correct answer.
### Explicit Formula
**Task:** Write the explicit formula for the number of cars sold, \( P_n \), in the \( (n + 1) \)th week.
An initial incorrect formula given is:
\[ P_n = 4 + 5(n - 1) \]
✘ Incorrect answer.
### Predicting Future Sales
**Question:** If this trend continues, how many cars will be sold in the 4th week?
Using the recursive formula, we can predict the number of cars sold in the 4th week:
\[ 19 \] cars
✔️ Correct answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd10f884b-6753-44fe-997f-af50a8e0d0d1%2F158eea22-2cd8-41d7-a859-03a1424bda9b%2Fu014m0r.png&w=3840&q=75)
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