Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
![**Dividing Rational Expressions Step-by-Step Solution**
This guide will walk you through the steps necessary to divide the rational expressions provided:
Given:
\[ \frac{x^2 - x - 42}{2x^2 + 4x} \div \frac{x - 7}{x + 2} \]
Step 1: Change Division to Multiplication
Rewrite the expression:
\[ \frac{x^2 - x - 42}{2x^2 + 4x} \times \frac{x + 2}{x - 7} \]
Step 2: Factorize the Numerator and Denominator
Factor each part of the expression.
The numerator \(x^2 - x - 42\) factors to \((x - 7)(x + 6)\).
The denominator \(2x^2 + 4x\) factors to \(2x(x + 2)\).
Thus, the expression becomes:
\[ \frac{(x - 7)(x + 6)}{2x(x + 2)} \times \frac{x + 2}{x - 7} \]
Step 3: Combine and Simplify the Expression
Combine the factored expressions:
\[ \frac{(x - 7)(x + 6)(x + 2)}{2x(x + 2)(x - 7)} \]
Step 4: Cancel Common Factors
Cancel out the common factors in the numerator and denominator:
- Cancel \((x + 2)\) from the numerator and denominator.
- Cancel \((x - 7)\) from the numerator and denominator.
The simplified expression is:
\[ \frac{x + 6}{2x} \]
Step 5: Final Answer
Thus, the completely simplified form of the expression is represented as:
\[ \frac{x + 6}{2x} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F758f6220-2c9c-498c-a499-60dbbe8461af%2F21f00207-7d1f-4d04-a18b-b3ecbed63990%2Fhmijvxa_processed.png&w=3840&q=75)
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