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2 number Word Problems

This calculator handles word problems in the format below:

* Two numbers have a sum of 70 and a product of 1189 What are the numbers?

* Two numbers have a sum of 70. Their difference 32

* Two numbers have a sum of 70 and a product of 1189 What are the numbers?

* Two numbers have a sum of 70. Their difference 32

Algebraic Expressions

This calculator builds algebraic expressions based on word representations of numbers using the four operators and the words that represent them(increased,product,decreased,divided,times)

Binomial Multiplication (FOIL)

Multiplies out the product of 2 binomials in the form (a + b)(c + d) with 1 unknown variable.

This utilizes the First-Outside-Inside-Last (F.O.I.L.) method.

This utilizes the First-Outside-Inside-Last (F.O.I.L.) method.

Boolean Algebra Multiplication

Determines the product of two expressions using boolean algebra.

Cartesian Product

Given a Set A and Set B, this calculates the Cartesian Product A × B

Cross Product A × B

Given two vectors A and B in R^{3}, this calculates the cross product A × B as well as determine if the two vectors are parallel

Estimating Reasonableness of Products

Given a product of 2 numbers and an estimated product, this will check to see if it is reasonable

Fundamental Rule of Counting

Given a set of items, this calculates the total number of groups/choices that can be formed using the rule of product.

Gross Domestic Product (GDP)

Solves for all items of the Gross Domestic Product (GDP) equation:

GDP

Consumption (C)

Investment (I)

Government Spending (G)

Exports (X)

Imports (I).

GDP

Consumption (C)

Investment (I)

Government Spending (G)

Exports (X)

Imports (I).

Imaginary Numbers

Calculates the imaginary number i where i = √-1 raised to any integer power as well as the product of imaginary numbers of quotient of imaginary numbers

Rational Exponents - Fractional Indices

This calculator evaluates and simplifies a rational exponent expression in the form a^{b/c} where a is any integer *or* any variable [a-z] while b and c are integers. Also evaluates the product of rational exponents

Sales Price Variance

Calculates the Sales Price Variance and Total Variance for a group of products

Set Notation

Given two number sets A and B, this determines the following:

* Union of A and B, denoted A U B

* Intersection of A and B, denoted A ∩ B

* Elements in A not in B, denoted A - B

* Elements in B not in A, denoted B - A

* Symmetric Difference A Δ B

* The Concatenation A · B

* The Cartesian Product A x B

* Cardinality of A = |A|

* Cardinality of B = |B|

* Jaccard Index J(A,B)

* Jaccard Distance J_{σ}(A,B)

* Dice's Coefficient

* If A is a subset of B

* If B is a subset of A

* Union of A and B, denoted A U B

* Intersection of A and B, denoted A ∩ B

* Elements in A not in B, denoted A - B

* Elements in B not in A, denoted B - A

* Symmetric Difference A Δ B

* The Concatenation A · B

* The Cartesian Product A x B

* Cardinality of A = |A|

* Cardinality of B = |B|

* Jaccard Index J(A,B)

* Jaccard Distance J

* Dice's Coefficient

* If A is a subset of B

* If B is a subset of A

Square Roots and Exponents

Given a number (n), or a fraction (n/m), and/or an exponent (x), or product of up to 5 radicals, this determines the following:

* The square root of n denoted as √n

* The square root of the fraction n/m denoted as √n/m

* n raised to the x^{th} power denoted as n^{x} (Write without exponents)

* n raised to the x^{th} power raised to the yth power denoted as (n^{x})^{y} (Write without exponents)

* Product of up to 5 square roots: √a√b√c√d√e

* Write a numeric expression such as 8x8x8x8x8 in exponential form

* The square root of n denoted as √n

* The square root of the fraction n/m denoted as √n/m

* n raised to the x

* n raised to the x

* Product of up to 5 square roots: √a√b√c√d√e

* Write a numeric expression such as 8x8x8x8x8 in exponential form

Sum to Product and Product to Sum Formulas

Given two angles in degrees of u and v, this determines the following:

* Sin(u) ± Sin(v)

* Cos(u) ± Cos(v)

* Sin(u)Sin(v)

* Cos(u)Cos(v)

* Sin(u)Cos(v)

* Cos(u)Sin(v)

* Sin(u + v)

* Sin(u - v)

* Cos(u + v)

* Cos(u - v)

* Tan(u + v)

* Tan(u - v)

* Sin(u) ± Sin(v)

* Cos(u) ± Cos(v)

* Sin(u)Sin(v)

* Cos(u)Cos(v)

* Sin(u)Cos(v)

* Cos(u)Sin(v)

* Sin(u + v)

* Sin(u - v)

* Cos(u + v)

* Cos(u - v)

* Tan(u + v)

* Tan(u - v)

Units of Output (Service Output) Depreciation

Given an asset value, salvage value, production units, and units per period, this calculates the depreciation per period using the units of output depreciation (service output depreciation)

Vectors

Given 2 vectors A and B, this calculates:

* Length (magnitude) of A = ||A||

* Length (magnitude) of B = ||B||

* Sum of A and B = A + B (addition)

* Difference of A and B = A - B (subtraction)

* Dot Product of vectors A and B = A x B

A ÷ B (division)

* Distance between A and B = AB

* Angle between A and B = θ

* Unit Vector U of A.

* Determines the relationship between A and B to see if they are orthogonal (perpendicular), same direction, or parallel (includes parallel planes).

* Cauchy-Schwarz Inequality

* The orthogonal projection of A on to B, proj_{B}A and and the vector component of A orthogonal to B → A - proj_{B}A

Also calculates the horizontal component and vertical component of a 2-D vector.

* Length (magnitude) of A = ||A||

* Length (magnitude) of B = ||B||

* Sum of A and B = A + B (addition)

* Difference of A and B = A - B (subtraction)

* Dot Product of vectors A and B = A x B

A ÷ B (division)

* Distance between A and B = AB

* Angle between A and B = θ

* Unit Vector U of A.

* Determines the relationship between A and B to see if they are orthogonal (perpendicular), same direction, or parallel (includes parallel planes).

* Cauchy-Schwarz Inequality

* The orthogonal projection of A on to B, proj

Also calculates the horizontal component and vertical component of a 2-D vector.

3 more than the product of 7 and a number x is less than 26

The product of 8 and a number k is greater than 4 and no more than 16

8 increased by the product of a number and 7 is greater than or equal to -18

12 plus the product of 4 and a number is greater than 72

Melinda is paid 17000 per year. She is also paid a sales commission of 5% of the value of her sales.

Seven subtracted from the product of 3 and a number is greater than or equal to -26

Nine less than the product of 2 and y is not less than 15

Ten subtracted from the product of 9 and a number is less than ?24

The product 18 And q

The product of two positive numbers is 96. Determine the two numbers if one is 4 more than the other

A bag contains 3 red marbles and 4 blue marbles. a marble is taken at random and replaced. another m

A random sample of n = 10 flash light batteries with a mean operating life X=5 hr. And a sample stan

From a standard 52 card deck, how many 6-card hands will have 2 spades and 4 hearts?

Let P(n) and S(n) denote the product and the sum, respectively, of the digits of the integer n. For

The product of x and u is not greater than 21

The product of x and 7 is not greater than 21

A manufacturer has a monthly fixed cost of $52,500 and a production cost of $8 for each unit produce

Serial numbers for a product are to made using 4 letters followed by 4 numbers. If the letters are t

1 integer is 7 times another. If the product of the 2 integers is 448, then find the integers.

When 3 consecutive positive integers are multiplied, the product is 16 times the sum of the 3 intege

A manufacturer has a monthly fixed cost of $25,500 and a production cost of $7 for each unit produce