New data from DESI suggests a link between dark energy and string theory. Discoveries could offer the first observational evidence.
Dark Energy and String Theory: New Evidence from DESI
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PROBABILITY
Recent Articles in Mathematics
Scientists Discover Seven Thousand Year Old Mummies in Sahara Desert
Scientists have discovered 7000-year-old mummies in the Sahara Desert revealing new insights into ancient history and genetic lineages.
Understanding Ordered Pairs: Definition Examples and Applications
Learn the definition of an ordered pair in mathematics including its key characteristics and applications. Explore examples and understand how it’s used.
Meteorite from Lost Planet: New Discovery Reveals Ancient Solar System Secrets
Scientists have discovered a meteorite NWA 15915 that originated from a lost planet offering insights into the early solar system.
Solving Polynomial Equations: Finding q(uv) = 0
Discover how to solve polynomial equations and find q(uv) = 0. Learn techniques for determining polynomial relationships between variables. Polynomial Equation Solver.
Understanding Inequalities in Harmonic Homogeneous Polynomials
Explore the inequality concerning the dimension of harmonic homogeneous polynomials. Learn about the relationship between homogeneous polynomials and their Laplacian. Harmonic Homogeneous Polynomials explained.
Polynomial Ratio Image: Exploring the Image of a Ratio of Polynomials in â„‚
Investigating the image of a ratio of polynomials with affine coefficients. Does the image lie within a complex polytope defined by vertices? Polynomial Ratio Image.
Chebyshev Polynomials Series: Exploring Patterns in Polynomial Coefficients
Discover the fascinating relationship between Chebyshev polynomials of the second kind and binomial coefficients in this exploration of series. Chebyshev Polynomials Series.
Calculating the Change of Basis Matrix for Linear Maps on Polynomials
Learn how to calculate the change of basis matrix for linear maps on polynomials. This guide clarifies common discrepancies and misunderstandings. Change of Basis Matrix explained.
Understanding the Luhn Algorithm for Credit Card Validation
Learn how the Luhn algorithm validates credit card numbers and other identification codes. Discover the steps and applications of this essential checksum formula.
Understanding Open and Closed Intervals: Definitions and Examples
Learn about open and closed intervals in mathematics including definitions and examples. Essential for understanding calculus.
Understanding Sequences and Limits: A Comprehensive Guide
Learn about sequences their limits and how they differ from functions. Discover convergence and divergence and essential theorems.
Understanding Open and Closed Intervals in Mathematics
Learn about open and closed intervals in mathematics including definitions and examples using mathjax notation.
Does a Series Converge? Understanding Convergence in Mathematics
Learn what it means for a series to converge to a specific value in mathematics. Explore the concept of convergence.
Can Subsets of Natural Numbers Have Equal Harmonic Series Sums?
Explore if disjoint subsets of natural numbers exist where the sum of harmonic series terms over each subset is equal. Investigate the harmonic series and its subset sums.
Can Natural Numbers Be Partitioned by Equal Digit Sum?
Can natural numbers be divided into two sets with equal sums of their digits? Explore this intriguing partitioning problem.
Solving the Distinct Real Numbers Problem with Equations
Explore the solutions for distinct real numbers satisfying specific equations in this insightful blog post.
Calculating Distance in 3D: Understanding Triangular Relationships
Learn how to calculate distance in 3D using triangular relationships and trigonometric ratios.
How to Find the Remainder of Polynomial Division
Learn how to find the remainder of polynomial division using standard and alternate methods.
Proving the Generalized Function Equality for Cosine Series
Prove the equality of cosine series in generalized functions. Learn how to manipulate trigonometric series for advanced applications.
Solving the Surjective Function Equation f(x) for Positive Real Numbers
Discover the surjective functions f(x) that satisfy the equation 2xf(f(x)) = f(x)(x + f(f(x))) for all positive real numbers x.
Solving Surjective Functions: A Functional Equation Approach
Discover how to find all surjective functions f:R→R satisfying a specific functional equation. Learn the key steps and techniques.
Solving Projectile Motion: Finding Maximum Height and Time of Flight Using a Quadratic Equation
Learn how to solve projectile motion problems using quadratic equations. Find the maximum height and time of flight for a projectile launched at a 45-degree angle.
Proving Mathematical Propositions: Direct Indirect and Other Methods
Learn various methods for proving mathematical statements including direct proof indirect proof (contradiction and contrapositive) proof by cases and mathematical induction. Explore examples and applications.
Navigating the CBSE Board Exams 2025: A Comprehensive Guide
Conquer the CBSE Board Exams 2025 with our guide! Learn effective study strategies, time management tips, and overcome exam anxiety for success.
Multiplication Rule in Probability
The multiplication rule in probability is used to find the probability of the intersection of two or more independent event
Addition Rule in Probability
Addition Rule calculates the probability of one or more events occurring. For mutually exclusive events, add individual probabilities. For non-mutually exclusive events, add individual probabilities and subtract the probability of both events occurring.
Suppose the diameter of aerosol particles in a particular application is uniformly distributed between 2 and 6 nanometers. Find the probability that a randomly measured particle has diameter greater than 3 nanometers.
uniformly distributed aerosol particles between 2 and 6 nanometers
Random Event
A random event refers to an unpredictable occurrence that has no discernible pattern or predetermined outcome. It is an event whose outcome cannot be reliably predicted or determined based on prior information or knowledge. Random events are commonly encountered in...