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Poisson distribution : a probability distribution for discrete random variables used to calculate probabilities for a certain number of successes in a specific interval
https://openstax.org/books/principles-data-science/pages/9-key-terms
quartiles : numbers that divide an ordered dataset into quarters; the second quartile is the same as the median
https://openstax.org/books/principles-data-science/pages/9-key-terms
scatterplot (or scatter diagram) : a graphical display that shows the relationship between a dependent variable and an independent variable
https://openstax.org/books/principles-data-science/pages/9-key-terms
spatial heatmap : a data visualization method used to represent the density or intensity of data points within a geographical area using coloring and shading to represent densities of various attributes
https://openstax.org/books/principles-data-science/pages/9-key-terms
univariate data : observations recorded for a single characteristic or attribute
https://openstax.org/books/principles-data-science/pages/9-key-terms
actionable advice : recommendations or guidance in a report, particularly in an executive summary, providing practical ways to apply the report's findings or insights
https://openstax.org/books/principles-data-science/pages/10-key-terms
alt text : brief descriptions of images that accompany the image or may be embedded within the image data, meant to aid readers who are not able to view the images and graphics due to disability or other limitations
https://openstax.org/books/principles-data-science/pages/10-key-terms
assumption : statement that is thought to be true without being verified or proven; foundational hypotheses or beliefs about the structure, relationships, or distribution of data that guide the analytical approach and model selection for a project
https://openstax.org/books/principles-data-science/pages/10-key-terms
audience : the person or group that will be reading the report
https://openstax.org/books/principles-data-science/pages/10-key-terms
bootstrap samples : multiple samples taken from a dataset with duplicates permitted
https://openstax.org/books/principles-data-science/pages/10-key-terms
codebook : data dictionary to detail the variables, their units, values, and labels within the dataset used in the project
https://openstax.org/books/principles-data-science/pages/10-key-terms
constraint : limitation or restriction that is imposed on a project or its solution
https://openstax.org/books/principles-data-science/pages/10-key-terms
cross-validation : validation method that divides the training set into multiple subsets and iteratively trains and evaluates the model on different combinations of these subsets
https://openstax.org/books/principles-data-science/pages/10-key-terms
executive (or data) dashboard : a visual representation tool designed to provide a quick, real-time overview of an organization's key performance indicators (KPIs) and metrics to senior management, often updated in real time or at regular intervals
https://openstax.org/books/principles-data-science/pages/10-key-terms
executive summary : concise, standalone document that encapsulates the essence of a data science report
https://openstax.org/books/principles-data-science/pages/10-key-terms
executives : decision-makers such as managers, CEOs, or others who may not have detailed technical knowledge but need an understanding of the implications of the information for strategic decision-making
https://openstax.org/books/principles-data-science/pages/10-key-terms
experts : individuals with an advanced understanding of the subject matter, often with specialized knowledge or education in the topic at hand
https://openstax.org/books/principles-data-science/pages/10-key-terms
fold : one of a set of equally sized subsets used in k-fold cross-validation
https://openstax.org/books/principles-data-science/pages/10-key-terms
hyperparameter tuning : fine-tuning of certain constants that affect the performance of a model
https://openstax.org/books/principles-data-science/pages/10-key-terms
jargon : specialized and/or technical terms in a given field
https://openstax.org/books/principles-data-science/pages/10-key-terms
k-fold cross-validation : cross-validation strategy that works by dividing the dataset intokkequally sized subsets or folds, where the model is trained onk−1k−1of the folds and tested on the remaining fold, a process that is repeatedkktimes with each fold serving as the test set once
https://openstax.org/books/principles-data-science/pages/10-key-terms
key performance indicators (KPIs) : quantifiable metrics used to evaluate the success of an organization, employee, or process in achieving specific objectives and goals
https://openstax.org/books/principles-data-science/pages/10-key-terms
layered approach : writing strategy in which a report is organized into sections or appendices that provide different levels of detail and complexity for different audiences
https://openstax.org/books/principles-data-science/pages/10-key-terms
leave-one-out cross-validation (LOOCV) : special case of k-fold cross-validation wherekkis set to the number of data points in the dataset so that the model is trained on all data points except one, which is used as the validation set, and this process is repeated for each data point in the dataset
https://openstax.org/books/principles-data-science/pages/10-key-terms
mean percentage error (MPE) : average of the percentage errors between predicted(y^i)(y^i)and actual(yi)(yi)value:MPE=1n∑i=1nyi−y^iyiMPE=1n∑i=1nyi−y^iyi
https://openstax.org/books/principles-data-science/pages/10-key-terms
Monte Carlo simulation : random sampling and statistical modeling to estimate the probability of different outcomes under uncertainty
https://openstax.org/books/principles-data-science/pages/10-key-terms
multi-way sensitivity analysis : explores the effects of simultaneous changes in multiple input parameters on the outcome
https://openstax.org/books/principles-data-science/pages/10-key-terms
neurodiversity : normal variation of individual cognitive abilities, especially in realms of communication and processing in formation
https://openstax.org/books/principles-data-science/pages/10-key-terms
nonspecialists : nonexpert audience without specialized knowledge of the subject but with some need to understand the basics of a data science report for a particular reason
https://openstax.org/books/principles-data-science/pages/10-key-terms
one-way sensitivity analysis : examines how changes in one input parameter at a time affect the outcome of a model
https://openstax.org/books/principles-data-science/pages/10-key-terms
scenario analysis : evaluates the outcomes under different predefined sets of input parameters, representing possible future states or scenarios
https://openstax.org/books/principles-data-science/pages/10-key-terms
sensitivity analysis : technique used to determine how different values of an independent variable affect a particular dependent variable under a given set of assumptions
https://openstax.org/books/principles-data-science/pages/10-key-terms
technicians : practical users of information in a data science report who may apply the knowledge in a hands-on manner
https://openstax.org/books/principles-data-science/pages/10-key-terms
validation : evaluation of multiple predictive models and/or hyperparameter tuning
https://openstax.org/books/principles-data-science/pages/10-key-terms
version control system : a software tool that helps keep track of changes to files, code, or any type of digital content over time
https://openstax.org/books/principles-data-science/pages/10-key-terms
Rational numbers may be written as fractions or terminating or repeating decimals. SeeExample 1andExample 2.
https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-key-concepts
Determine whether a number is rational or irrational by writing it as a decimal. SeeExample 3.
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The rational numbers and irrational numbers make up the set of real numbers. SeeExample 4. A number can be classified as natural, whole, integer, rational, or irrational. SeeExample 5.
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The order of operations is used to evaluate expressions. SeeExample 6.
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The real numbers under the operations of addition and multiplication obey basic rules, known as the properties of real numbers. These are the commutative properties, the associative properties, the distributive property, the identity properties, and the inverse properties. SeeExample 7.
https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-key-concepts
Algebraic expressions are composed of constants and variables that are combined using addition, subtraction, multiplication, and division. SeeExample 8. They take on a numerical value when evaluated by replacing variables with constants. SeeExample 9,Example 10, andExample 12
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Formulas are equations in which one quantity is represented in terms of other quantities. They may be simplified or evaluated as any mathematical expression. SeeExample 11andExample 13.
https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-key-concepts
Products of exponential expressions with the same base can be simplified by adding exponents. SeeExample 1.
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Quotients of exponential expressions with the same base can be simplified by subtracting exponents. SeeExample 2.
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Powers of exponential expressions with the same base can be simplified by multiplying exponents. SeeExample 3.
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An expression with exponent zero is defined as 1. SeeExample 4.
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An expression with a negative exponent is defined as a reciprocal. SeeExample 5andExample 6.
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The power of a product of factors is the same as the product of the powers of the same factors. SeeExample 7.
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The power of a quotient of factors is the same as the quotient of the powers of the same factors. SeeExample 8.
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The rules for exponential expressions can be combined to simplify more complicated expressions. SeeExample 9.
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Scientific notation uses powers of 10 to simplify very large or very small numbers. SeeExample 10andExample 11.
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Scientific notation may be used to simplify calculations with very large or very small numbers. SeeExample 12andExample 13.
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The principal square root of a numberaais the nonnegative number that when multiplied by itself equalsa.a.SeeExample 1.
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Ifaaandbbare nonnegative, the square root of the productababis equal to the product of the square roots ofaaandbbSeeExample 2andExample 3.
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Ifaaandbbare nonnegative, the square root of the quotientababis equal to the quotient of the square roots ofaaandbbSeeExample 4andExample 5.
https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-key-concepts
We can add and subtract radical expressions if they have the same radicand and the same index. SeeExample 6andExample 7.
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Radical expressions written in simplest form do not contain a radical in the denominator. To eliminate the square root radical from the denominator, multiply both the numerator and the denominator by the conjugate of the denominator. SeeExample 8andExample 9.
https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-key-concepts
The principalnth root ofaais the number with the same sign asaathat when raised to thenth power equalsa.a.These roots have the same properties as square roots.SeeExample 10.
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Radicals can be rewritten as rational exponents and rational exponents can be rewritten as radicals. SeeExample 11andExample 12.
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The properties of exponents apply to rational exponents. SeeExample 13.
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A polynomial is a sum of terms each consisting of a variable raised to a non-negative integer power. The degree is the highest power of the variable that occurs in the polynomial. The leading term is the term containing the highest degree, and the leading coefficient is the coefficient of that term. SeeExample 1.
https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-key-concepts
We can add and subtract polynomials by combining like terms. SeeExample 2andExample 3.
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To multiply polynomials, use the distributive property to multiply each term in the first polynomial by each term in the second. Then add the products. SeeExample 4.
https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-key-concepts
FOIL (First, Outer, Inner, Last) is a shortcut that can be used to multiply binomials. SeeExample 5.
https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-key-concepts
Perfect square trinomials and difference of squares are special products. SeeExample 6andExample 7.
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Follow the same rules to work with polynomials containing several variables. SeeExample 8.
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The greatest common factor, or GCF, can be factored out of a polynomial. Checking for a GCF should be the first step in any factoring problem. SeeExample 1.
https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-key-concepts
Trinomials with leading coefficient 1 can be factored by finding numbers that have a product of the third term and a sum of the second term. SeeExample 2.
https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-key-concepts
Trinomials can be factored using a process called factoring by grouping. SeeExample 3.
https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-key-concepts
Perfect square trinomials and the difference of squares are special products and can be factored using equations. SeeExample 4andExample 5.
https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-key-concepts
The sum of cubes and the difference of cubes can be factored using equations. SeeExample 6andExample 7.
https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-key-concepts
Polynomials containing fractional and negative exponents can be factored by pulling out a GCF. SeeExample 8.
https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-key-concepts
Rational expressions can be simplified by cancelling common factors in the numerator and denominator. SeeExample 1.
https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-key-concepts
We can multiply rational expressions by multiplying the numerators and multiplying the denominators. SeeExample 2.
https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-key-concepts
To divide rational expressions, multiply by the reciprocal of the second expression. SeeExample 3.
https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-key-concepts
Adding or subtracting rational expressions requires finding a common denominator. SeeExample 4andExample 5.
https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-key-concepts
Complex rational expressions have fractions in the numerator or the denominator. These expressions can be simplified. SeeExample 6.
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a m ⋠a n = a m + n a m ⋠a n = a m + n
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a m a n = a m − n a m a n = a m − n
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( a m ) n = a m ⋠n ( a m ) n = a m ⋠n
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a 0 = 1 a 0 = 1
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a − n = 1 a n a − n = 1 a n
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( a ⋠b ) n = a n ⋠b n ( a ⋠b ) n = a n ⋠b n
https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-key-equations
( a b ) n = a n b n ( a b ) n = a n b n
https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-key-equations
( x + a ) 2 = ( x + a ) ( x + a ) = x 2 + 2 a x + a 2 ( x + a ) 2 = ( x + a ) ( x + a ) = x 2 + 2 a x + a 2
https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-key-equations
( a + b ) ( a − b ) = a 2 − b 2 ( a + b ) ( a − b ) = a 2 − b 2
https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-key-equations
a 2 − b 2 = ( a + b ) ( a − b ) a 2 − b 2 = ( a + b ) ( a − b )
https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-key-equations
a 2 + 2 a b + b 2 = ( a + b ) 2 a 2 + 2 a b + b 2 = ( a + b ) 2
https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-key-equations
a 3 + b 3 = ( a + b ) ( a 2 − a b + b 2 ) a 3 + b 3 = ( a + b ) ( a 2 − a b + b 2 )
https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-key-equations
a 3 − b 3 = ( a − b ) ( a 2 + a b + b 2 ) a 3 − b 3 = ( a − b ) ( a 2 + a b + b 2 )
https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-key-equations
algebraic expression : constants and variables combined using addition, subtraction, multiplication, and division
https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-key-terms
associative property of addition : the sum of three numbers may be grouped differently without affecting the result; in symbols,a+(b+c)=(a+b)+ca+(b+c)=(a+b)+c
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associative property of multiplication : the product of three numbers may be grouped differently without affecting the result; in symbols,aâ‹(bâ‹c)=(aâ‹b)â‹caâ‹(bâ‹c)=(aâ‹b)â‹c
https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-key-terms
base : in exponential notation, the expression that is being multiplied
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binomial : a polynomial containing two terms
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coefficient : any real numberaiaiin a polynomial in the formanxn+...+a2x2+a1x+a0anxn+...+a2x2+a1x+a0
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commutative property of addition : two numbers may be added in either order without affecting the result; in symbols,a+b=b+aa+b=b+a
https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-key-terms
commutative property of multiplication : two numbers may be multiplied in any order without affecting the result; in symbols,aâ‹b=bâ‹aaâ‹b=bâ‹a
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constant : a quantity that does not change value
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degree : the highest power of the variable that occurs in a polynomial
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