ratio - indicates how many times one number contains another

12 students want pancakes and 14 students want waffles. What is the ratio of the number of students

12 students want pancakes and 14 students want waffles. What is the ratio of the number of students who want pancakes to the total number of students?
12/14 is the initial ratio. However, we can simplify this. [URL='https://www.mathcelebrity.com/fraction.php?frac1=12%2F14&frac2=3%2F8&pl=Simplify']So we type 12/14 into our search engine and choose simplify.[/URL] We get:
6/7

2 times the sum of 3 and 5 divided by 10

2 times the sum of 3 and 5 divided by 10
The sum of 3 and 5 is written as:
3 + 5
2 times this sum:
2(3 + 5)
Then, we divide this by 10:
[B]2(3 + 5)/10[/B]
[B][/B]
If the problem asks you to simplify this, you [URL='https://www.mathcelebrity.com/order-of-operations-calculator.php?num=2%283%2B5%29%2F10&pl=Perform+Order+of+Operations']type this expression into our search engine[/URL] and get:
[B]1.6[/B]

3 boys share 100 in the ratio 1:2:2. how much each boy will get?

3 boys share 100 in the ratio 1:2:2. how much each boy will get?
Given the ratio 1 : 2 : 2, calculate the expected number of items from a population of 100
A ratio of 1 : 2 : 2 means that for every of item A, we can expect 2 of item B and 2 of item c
Therefore, our total group is 1 + 2 + 2 = 5
[SIZE=5][B]Calculate Expected Number of Item A:[/B][/SIZE]
Expected Number of Item A = 1 x 100/5
Expected Number of Item A = 100/5
Using our [URL='http://mathcelebrity.com/gcflcm.php?num1=100&num2=5&pl=GCF']GCF Calculator[/URL], we see this fraction can be reduced by 5
Expected Number of Item A = 20/1
Expected Number of Item A = [B]20[/B]
[SIZE=5][B]Calculate Expected Number of Item B:[/B][/SIZE]
Expected Number of Item B = 2 x 100/5
Expected Number of Item B = 200/5
Using our [URL='http://mathcelebrity.com/gcflcm.php?num1=200&num2=5&pl=GCF']GCF Calculator[/URL], we see this fraction can be reduced by 5
Expected Number of Item B = 40/1
Expected Number of Item B = [B]40[/B]
[SIZE=5][B]Calculate Expected Number of Item C:[/B][/SIZE]
Expected Number of Item C = 2 x 100/5
Expected Number of Item C = 200/5
Using our [URL='http://mathcelebrity.com/gcflcm.php?num1=200&num2=5&pl=GCF']GCF Calculator[/URL], we see this fraction can be reduced by 5
Expected Number of Item C = 40/1
Expected Number of Item C = [B]40[/B]
[B]Final Answer:[/B]
(A, B, C) =[B] (20, 40, 40)[/B] for 1:2:2 on 100 people

4 times 8 to the sixth power

4 times 8 to the sixth power
8 to the 6th power:
8^6
4 times this amount:
4 * 8^6
To evaluate this expression, we [URL='https://www.mathcelebrity.com/order-of-operations-calculator.php?num=4%2A8%5E6&pl=Perform+Order+of+Operations']type it in our search engine[/URL] and we get:
1,048,576

5/8 Of a class are boys. what fraction of the class are girls

5/8 Of a class are boys. what fraction of the class are girls?
The total class equals 1. Since 5/8 are boys, we subtract 5/8 from 1:
1 - 5/8
But we can write 1 as 8/8. So we have
8/8 - 5/8
[URL='https://www.mathcelebrity.com/fraction.php?frac1=8%2F8&frac2=5%2F8&pl=Subtract']Type this fraction operation into our search engine[/URL] and we get:
[B]3/8[/B] are girls

63 oranges is shared among 3 boys in the ratio of 2:3:4 how many oranges will the second boy receive

63 oranges is shared among 3 boys in the ratio of 2:3:4 how many oranges will the second boy receive?
Total sharing is 2 + 3 + 4 = 10.
[LIST]
[*]Boy 2 = 3/10 * 63 = [B]18.9 oranges[/B]
[/LIST]

7 multiplied by the quantity 7 take away 6

7 multiplied by the quantity 7 take away 6
Take this algebraic expression in pieces:
[LIST]
[*]7 take away 6: 7 - 6
[*]7 multiplied by the quantity: [B]7(7 - 6)[/B]
[/LIST]
This is our algebraic expression.
If you need to evaluate this expression, we [URL='https://www.mathcelebrity.com/order-of-operations-calculator.php?num=7%287-6%29&pl=Perform+Order+of+Operations']type it in the search engine[/URL] and we get;
[B]7[/B]

A 5 foot ladder is leaning against a wall. If the bottom of the ladder is 3 feet from the base of th

A 5 foot ladder is leaning against a wall. If the bottom of the ladder is 3 feet from the base of the wall, how high up the wall is the top of the ladder?
The answer is [B]4[/B]. Since we have a right triangle, with special ratio 3-4-5.
The ladder represents the hypotenuse.

A 50-pound bowling ball and an 8-pound bowling ball are dropped from a tall building. Which ball wil

A 50-pound bowling ball and an 8-pound bowling ball are dropped from a tall building. Which ball will hit first?
[B]They will land at the same time[/B]
[B]How fast something falls due to gravity is determined by a number known as the "acceleration of gravity", which is 9.81 m/s^2 at the surface of our Earth. In one second, [I]any object[/I]’s downward velocity will increase by 9.81 m/s because of gravity. This is just the way gravity works - it accelerates everything at exactly the same rate.[/B]

A bag contains 120 marbles. Some are red and the rest are black. There are 19 red marbles for every

A bag contains 120 marbles. Some are red and the rest are black. There are 19 red marbles for every black marble. How many red marbles are in the bag?
Using our [URL='https://www.mathcelebrity.com/ratio.php?simpratio=100%3A350&rs=19%3A1&rtot=120&pl=Calculate+Ratio']ratio calculator[/URL], we get:
[LIST]
[*]Red = 114
[*]Black = 6
[/LIST]

A car is traveling on a freeway at 50 mph with the cruise control set at 50 mph. Another car is trav

A car is traveling on a freeway at 50 mph with the cruise control set at 50 mph. Another car is traveling at 90 mph with the cruise control set at 90 mph. Which car has a higher acceleration?
Acceleration means a change in speed.
Neither car has a change in speed, [B]so both cars have the same acceleration which is 0[/B]

A cup that is filled with equal parts red, green, and blue dye spills half of its contents. Enough g

A cup that is filled with equal parts red, green, and blue dye spills half of its contents. Enough green dye is then poured into the cup to fill it again. What is the ratio of red to green to blue dye now?
Original Cup:
[LIST=1]
[*]Blue
[*]Green
[*]Red
[/LIST]
Spilled Cup
[LIST=1]
[*]Empty
[*]Blue
[*]Green
[*]Red
[/LIST]
Refilled Cup
[LIST=1]
[*]Green
[*]Blue
[*]Green
[*]Red
[/LIST]
[B]1:4:1[/B]

A fruit basket contains 2 red apples and 2 green apples. What is the ratio of the number of red appl

A fruit basket contains 2 red apples and 2 green apples. What is the ratio of the number of red apples to the total number of apples?
2:2 = [B]1:1[/B] simplified

A helicopter rose vertically 300 m and then flew west 400 m how far was the helicopter from it’s sta

A helicopter rose vertically 300 m and then flew west 400 m how far was the helicopter from it’s starting point?
The distance forms a right triangle. We want the distance of the hypotenuse.
Using our [URL='http://www.mathcelebrity.com/pythag.php?side1input=300&side2input=400&hypinput=&pl=Solve+Missing+Side']right triangle calculator[/URL], we get a distance of [B]500[/B].
We also could use a shortcut on this problem. If you divide 300 and 400 by 100, you get 3 and 4. Since we want the hypotenuse, you get the famous 3-4-5 triangle ratio. So the answer is 5 * 100 = 500.

a manufacturing company has a debt to equity ratio of 3 to 2. if the company has a debt of $12 milli

a manufacturing company has a debt to equity ratio of 3 to 2. if the company has a debt of $12 million, how much does it have in equity?
Set up a proportion of debt to equity
3/2 = 12/x
Using our [URL='http://www.mathcelebrity.com/prop.php?num1=3&num2=12&den1=2&den2=x&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get:
x = 8

A metal block is made of nickel and copper. The weight of metals in the block are in a ratio of 2:9.

A metal block is made of nickel and copper. The weight of metals in the block are in a ratio of 2:9. The weight of the block is 407 pounds. What is the weight of the nickel?
Using our [URL='https://www.mathcelebrity.com/ratio.php?simpratio=100%3A350&rs=2%3A9&rtot=407&pl=Calculate+Ratio']ratio calculator[/URL], we get:
[B]74 pounds[/B]

A national political party has a budget of $30,000,000 to spend on the inauguration of the new presi

A national political party has a budget of $30,000,000 to spend on the inauguration of the new president. 16% of the costs will be paid to personnel, 12% of the costs will go toward food, and 10% will go to decorations. How much money will go for personnel, food, and decorations?
[LIST]
[*]Personnel Costs = 0.16 * 30,000,000 = $4,800,000
[*]Food Costs = 0.12 * 30,000,000 = $3,600,000
[*]Decoration Costs = 0.10 * 30,000,000 = $3,000,000
[/LIST]

A new company is projecting its profits over a number of weeks. They predict that their profits each

A new company is projecting its profits over a number of weeks. They predict that their profits each week can be modeled by a geometric sequence.
Three weeks after they started, the company's projected profit is $10,985.00
Four weeks after they started, the company's projected profit is $14,280.50
Let Pn be the projected profit, in dollars, n weeks after the company started tracking their profits.
a. What is the common ratio of the sequence?
b. Calculate the initial value
c. Construct a recurrence relation that can be used to model the value of Pn
a. 14,280.50/10,985.00 = [B]1.3[/B]
b. 3 weeks ago, the Initial value is 10,985/1.3^3 = [B]$5,000
c. Pn = 5000 * 1.3^n[/B]

A pet supply chain called pet city has 15 hamsters and 12 gerbils for sale at its seaside location.

A pet supply chain called pet city has 15 hamsters and 12 gerbils for sale at its seaside location. At its livingston location there are 19 hamsters and 10 gerbils. Which location has a lower ratio of hamsters to gerbils?
Seaside ratio
15/12 = 1.25
Livingston ratio
19/10 = 1.9
Since 1.25 < 1.9, Seaside has the lower ratio of hamsters to gerbils

A rational expression is undefined when what is 0?

A rational expression is undefined when what is 0?
The [B]denominator[/B]. Because division by zero is undefined.

A rational number is such that when you multiply it by 7/3 and subtract 3/2 from the product, you ge

A rational number is such that when you multiply it by 7/3 and subtract 3/2 from the product, you get 92. What is the number?
Let the rational number be x. We're given:
7x/3 - 3/2 = 92
Using a common denominator of 3*2 = 6, we rewrite this as:
14x/6 - 9/6 = 92
(14x - 9)/6 = 92
Cross multiply:
14x - 9 = 92 * 6
14x - 9 = 552
To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=14x-9%3D552&pl=Solve']type this equation into our search engine [/URL]and we get:
x = [B]40.07[/B]

A right triangle has legs of 9 feet and 12 feet. How long is the hypotenuse?

A right triangle has legs of 9 feet and 12 feet. How long is the hypotenuse?
A common right triangle ratio is 3:4:5
9 = 3 * 3
12 = 3 * 4
3 * 5 = 15, so we have [B]15 feet[/B]

A school has a boy to girl ratio of 6:7. If there are 288 boys, how many girls are there?

A school has a boy to girl ratio of 6:7. If there are 288 boys, how many girls are there?
6 boys/7 girls = 288 boys/g girls
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=6&num2=288&den1=7&den2=g&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get:
g = [B]336
[MEDIA=youtube]P7x_u9oAkEc[/MEDIA][/B]

A softball player had 13 hits in 25 times at bat. What percent of her times at bat resulted in hits?

We take the ratio of hits to at bats:
13/25 = 0.52
To get the percent, we multiply by 100:
100 * 0.52 = 52%

A stack of boards is 21 inches high. Each board is 1¾ inches thick. How many boards are there?

A stack of boards is 21 inches high. Each board is 1¾ inches thick. How many boards are there?
We want 21 / 1 & 3/4
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=21&frac2=1%263%2F4&pl=Divide']fraction operation calculator[/URL], we get:
[B]12 boards[/B]

Acceleration

Free Acceleration Calculator - Solves for any of the 4 items in the acceleration equation including initial velocity, velocity, and time.

Add 8 and 7, and then multiply by 2.

Add 8 and 7, and then multiply by 2.
Add 8 and 7:
8 + 7
Then multiply by 2:
2(8 + 7)
If you want to evaluate this order of operations, then [URL='https://www.mathcelebrity.com/distributive-property.php?a=2&b=8&c=7&pl=Distributive']type it in our search engine[/URL] to get:
[B]30[/B]

An operation is defined by a*b=3a-b.Calculate the exact value of 2*3

An operation is defined by a*b=3a-b.Calculate the exact value of 2*3
We're given a = 2 and b = 3. So the operator says:
3(2) - 3
6 - 3
[B]3[/B]

Angelica’s financial aid stipulates that her tuition cannot exceed $1000. If her local community col

Angelica’s financial aid stipulates that her tuition cannot exceed $1000. If her local community college charges a $35 registration fee plus $375 per course, what is the greatest number of courses for which Angelica can register?
We set up the Tuition function T(c), where c is the number of courses:
T(c) = Cost per course * c + Registration Fee
T(c) = 35c + 375
The problem asks for the number of courses (c) where her tuition [I]cannot exceed[/I] $1000. The phrase [I]cannot exceed[/I] means less than or equal to, or no more than. So we setup the inequality for T(c) <= 1000 below:
35c + 375 <= 1000
To solve this inequality for c, we [URL='https://www.mathcelebrity.com/1unk.php?num=35c%2B375%3C%3D1000&pl=Solve']type it in our search engine and we get[/URL]:
c <= 17.85
Since we cannot have fractional courses, we round down and get:
c[B] <= 17[/B]

Angle Ratio for a Triangle

Free Angle Ratio for a Triangle Calculator - Given an angle ratio for a triangle of a:b:c, this determines the angle measurements of the triangle.

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Approximations of Interest Rate

Free Approximations of Interest Rate Calculator - Interest Rate Approximations: Approximates a yield rate of interest based on 4 methods:

1) Max Yield denoted as i_{max}

2) Min Yield denoted as i_{min}

3) Constant Ratio denoted as i_{cr}

4) Direct Ratio denoted as i_{dr}

1) Max Yield denoted as i

2) Min Yield denoted as i

3) Constant Ratio denoted as i

4) Direct Ratio denoted as i

at a party, there are 72 people. The ratio of men to ladies to kids is 4 to 3 to 2.

at a party, there are 72 people. The ratio of men to ladies to kids is 4 to 3 to 2.
[LIST]
[*]How many men at the party?
[*]How many ladies at the party?
[*]How many kids at the party?
[/LIST]
Our total ratio denominator is 4 + 3 + 2 = 9. To find the number of each type of person, we take their ratio divided by their ratio numerator times 72 people at the party
[U]Calculate ratios:[/U]
[LIST]
[*]Men: [URL='https://www.mathcelebrity.com/fraction.php?frac1=4%2F9&frac2=72&pl=Multiply']4/9 * 72[/URL] = [B]32[/B]
[*]Ladies: [URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F9&frac2=72&pl=Multiply']3/9 * 72[/URL] = [B]24[/B]
[*]Kids: [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F9&frac2=72&pl=Multiply']2/9 * 72[/URL] = [B]16[/B]
[/LIST]
[U]Check our work:[/U]
Men + Ladies + Kids = 32 + 24 + 16
Men + Ladies + Kids = 72 <-- This checks out!

Balancing Equations

Free Balancing Equations Calculator - Given 4 numbers, this will use the four operations: addition, subtraction, multiplication, or division to balance the equations if possible.

Base Conversion Operations

Free Base Conversion Operations Calculator - This calculator allows you to add, subtract, multiply, and divide two numbers with different bases.

Basic m x n Matrix Operations

Free Basic m x n Matrix Operations Calculator - Given 2 matrices |A| and |B|, this performs the following basic matrix operations

* Matrix Addition |A| + |B|

* Matrix Subtraction |A| - |B|

* Matrix Multiplication |A| x |B|

* Scalar multiplication rA where r is a constant.

* Matrix Addition |A| + |B|

* Matrix Subtraction |A| - |B|

* Matrix Multiplication |A| x |B|

* Scalar multiplication rA where r is a constant.

Basic Math Operations

Free Basic Math Operations Calculator - Given 2 numbers, this performs the following arithmetic operations:

* Addition (Adding) (+)

* Subtraction (Subtracting) (-)

* Multiplication (Multiplying) (x)

* Long division (Dividing) with a remainder (÷)

* Long division to decimal places (÷)

* Partial Sums (Shortcut Sums)

* Short Division

* Duplication and Mediation

* Addition (Adding) (+)

* Subtraction (Subtracting) (-)

* Multiplication (Multiplying) (x)

* Long division (Dividing) with a remainder (÷)

* Long division to decimal places (÷)

* Partial Sums (Shortcut Sums)

* Short Division

* Duplication and Mediation

Basic Statistics

Free Basic Statistics Calculator - Given a number set, and an optional probability set, this calculates the following statistical items:

Expected Value

Mean = μ

Variance = σ^{2}

Standard Deviation = σ

Standard Error of the Mean

Skewness

Mid-Range

Average Deviation (Mean Absolute Deviation)

Median

Mode

Range

Pearsons Skewness Coefficients

Entropy

Upper Quartile (hinge) (75th Percentile)

Lower Quartile (hinge) (25th Percentile)

InnerQuartile Range

Inner Fences (Lower Inner Fence and Upper Inner Fence)

Outer Fences (Lower Outer Fence and Upper Outer Fence)

Suspect Outliers

Highly Suspect Outliers

Stem and Leaf Plot

Ranked Data Set

Central Tendency Items such as Harmonic Mean and Geometric Mean and Mid-Range

Root Mean Square

Weighted Average (Weighted Mean)

Frequency Distribution

Successive Ratio

Expected Value

Mean = μ

Variance = σ

Standard Deviation = σ

Standard Error of the Mean

Skewness

Mid-Range

Average Deviation (Mean Absolute Deviation)

Median

Mode

Range

Pearsons Skewness Coefficients

Entropy

Upper Quartile (hinge) (75th Percentile)

Lower Quartile (hinge) (25th Percentile)

InnerQuartile Range

Inner Fences (Lower Inner Fence and Upper Inner Fence)

Outer Fences (Lower Outer Fence and Upper Outer Fence)

Suspect Outliers

Highly Suspect Outliers

Stem and Leaf Plot

Ranked Data Set

Central Tendency Items such as Harmonic Mean and Geometric Mean and Mid-Range

Root Mean Square

Weighted Average (Weighted Mean)

Frequency Distribution

Successive Ratio

Bitwise Operations

Free Bitwise Operations Calculator - Performs bitwise operations between two decimal or binary numbers:

* Bitwise OR

* Bitwise AND

* Bitwise XOR

Also performs Bitwise NOT on 1 number

* Bitwise OR

* Bitwise AND

* Bitwise XOR

Also performs Bitwise NOT on 1 number

Cards in a pack are either orange or purple. 80% of the cards are orange. Write the ratio of orange

Cards in a pack are either orange or purple. 80% of the cards are orange. Write the ratio of orange cards to purple cards.
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=+90&den1=+80&pct=80&pcheck=4&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']80% as a fraction [/URL]is 4/5.
Fractions to ratios can be written as numerator : denominator, so we have:
[B]4:5[/B]

Centripetal Acceleration

Free Centripetal Acceleration Calculator - Solves for any of the 3 items in the centripetal acceleration formula, centripetal acceleration, rotational speed, and radius.

Combined Ratio

Free Combined Ratio Calculator - Given a ratio a:b and a ratio b:c, this determines the combined ratio a:c

Complex Number Operations

Free Complex Number Operations Calculator - Given two numbers in complex number notation, this calculator:

1) Adds (complex number addition), Subtracts (complex number subtraction), Multiplies (complex number multiplication), or Divides (complex number division) any 2 complex numbers in the form a + bi and c + di where i = √-1.

2) Determines the Square Root of a complex number denoted as √a + bi

3) Absolute Value of a Complex Number |a + bi|

4) Conjugate of a complex number a + bi

1) Adds (complex number addition), Subtracts (complex number subtraction), Multiplies (complex number multiplication), or Divides (complex number division) any 2 complex numbers in the form a + bi and c + di where i = √-1.

2) Determines the Square Root of a complex number denoted as √a + bi

3) Absolute Value of a Complex Number |a + bi|

4) Conjugate of a complex number a + bi

Compound Interest and Annuity Table

Free Compound Interest and Annuity Table Calculator - Given an interest rate (i), number of periods to display (n), and number of digits to round (r), this calculator produces a compound interest table. It shows the values for the following 4 compound interest annuity functions from time 1 to (n) rounded to (r) digits:

v^{n}

d

(1 + i)^{n}

a_{n|}

s_{n|}

ä_{n|i}

s_{n|i}

Force of Interest δ^{n}

v

d

(1 + i)

a

s

ä

s

Force of Interest δ

Cubic Equation

Free Cubic Equation Calculator - Solves for cubic equations in the form ax^{3} + bx^{2} + cx + d = 0 using the following methods:

1) Solve the long way for all 3 roots and the discriminant Δ

2) Rational Root Theorem (Rational Zero Theorem) to solve for real roots followed by the synthetic div/quadratic method for the other imaginary roots if applicable.

1) Solve the long way for all 3 roots and the discriminant Δ

2) Rational Root Theorem (Rational Zero Theorem) to solve for real roots followed by the synthetic div/quadratic method for the other imaginary roots if applicable.

Determine a conversion ratio that could be used to convert miles to inches

Determine a conversion ratio that could be used to convert miles to inches.
We know that 1 mile equals 5,280 feet.
We know that 1 foot equals 12 inches.
So 1 miles = 5,280 feet * 12 inches per foot= [B]63,360 inches[/B]

Electrons have a charge of -1. Protons have a charge of 1. The total charge of an atom is the sum of

Electrons have a charge of -1. Protons have a charge of 1. The total charge of an atom is the sum of its electron charges and proton charges. Find the total charge of an atom with 24 protons and 32 electrons
We use sign operations to get:
+24 - 32 = [B]-8[/B]

Factoring and Root Finding

Free Factoring and Root Finding Calculator - This calculator factors a binomial including all 26 variables (a-z) using the following factoring principles:

* Difference of Squares

* Sum of Cubes

* Difference of Cubes

* Binomial Expansions

* Quadratics

* Factor by Grouping

* Common Term

This calculator also uses the Rational Root Theorem (Rational Zero Theorem) to determine potential roots

* Factors and simplifies Rational Expressions of one fraction

* Determines the number of potential*positive* and *negative* roots using Descarte’s Rule of Signs

* Difference of Squares

* Sum of Cubes

* Difference of Cubes

* Binomial Expansions

* Quadratics

* Factor by Grouping

* Common Term

This calculator also uses the Rational Root Theorem (Rational Zero Theorem) to determine potential roots

* Factors and simplifies Rational Expressions of one fraction

* Determines the number of potential

Falling Object

Free Falling Object Calculator - Calculates any of the 3 items in the falling object formula, distance (s), acceleration (a), and time (t).

Finance

1. Spend 8000 on a new machine. You think it will provide after tax cash inflows of 3500 per year for the next three years. The cost of funds is 8%. Find the NPV, IRR, and MIRR. Should you buy it?
2. Let the machine in number one be Machine A. An alternative is Machine B. It costs 8000 and will provide after tax cash inflows of 5000 per year for 2 years. It has the same risk as A. Should you buy A or B?
3. Spend 100000 on Machine C. You will need 5000 more in net working capital. C is three year MACRS. The cost of funds is 8% and the tax rate is 40%. C is expected to increase revenues by 45000 and costs by 7000 for each of the next three years. You think you can sell C for 10000 at the end of the three year period.
a. Find the year zero cash flow.
b. Find the depreciation for each year on the machine.
c. Find the depreciation tax shield for the three operating years.
d. What is the projects contribution to operations each year, ignoring depreciation effects?
e. What is the cash flow effect of selling the machine?
f. Find the total CF for each year.
g. Should you buy it?

Fractions

Free Fractions Calculator - Calculates things like fraction to percent, fraction to decimal, unit fraction, ratios, and more

Fractions and Mixed Numbers

Free Fractions and Mixed Numbers Calculator - Given (improper fractions, proper fraction, mixed numbers, or whole numbers), this performs the following operations:

* Addition (Adding)

* Subtraction (Subtracting)

* Positive Difference (Absolute Value of the Difference)

* Multiplication (Multiplying)

* Division (Dividing: complex fraction division is included)

* Compare Fractions

* Simplifying of proper and improper fractions as well as mixed numbers. Fractions will be reduced down as far as possible (Reducing Fractions).

* Reciprocal of a Fraction

* Find all fractions between two fractions

* reduce a fraction

* Addition (Adding)

* Subtraction (Subtracting)

* Positive Difference (Absolute Value of the Difference)

* Multiplication (Multiplying)

* Division (Dividing: complex fraction division is included)

* Compare Fractions

* Simplifying of proper and improper fractions as well as mixed numbers. Fractions will be reduced down as far as possible (Reducing Fractions).

* Reciprocal of a Fraction

* Find all fractions between two fractions

* reduce a fraction

Gamma Constant γ

Free Gamma Constant γ Calculator - This calculator generates 5000 iterations for the development of the gamma constant γ

Golden Ratio

Free Golden Ratio Calculator - Solves for 2 out of the 3 variables for a segment broken in 2 pieces that satisfies the Golden Ratio (Golden Mean).

(a) Large Segment

(b) Small Segment

(a + b) Total Segment

(a) Large Segment

(b) Small Segment

(a + b) Total Segment

I am thinking of a number.i multiply it by 5 and add 139. I get the same number if I multiply by 13

I am thinking of a number.i multiply it by 5 and add 139. I get the same number if I multiply by 13 and subtract 13.What is my number?
Take a number (n):
The first operation is multiply 5 times n, and then add 39:
5n + 139
The second operation is multiply 13 times n and subtract 13:
13n - 13
Set both operations equal to each other since they result in [I]the same number[/I]
5n + 139 = 13n - 13
[URL='https://www.mathcelebrity.com/1unk.php?num=5n%2B139%3D13n-13&pl=Solve']Type this equation into our search engine[/URL] and we get:
[B]n = 19[/B]

if 200 is divided in the ratio of 1:3:4 , what is the greatest number

if 200 is divided in the ratio of 1:3:4 , what is the greatest number
Determine the ratio denominator by adding up the ratio amounts:
1 + 3 + 4 = 8
So we have the following ratios and ratio amounts with our greatest number in bold:
[LIST]
[*]1/8 * 200 = 25
[*]3/8 * 200 = 75
[*]4/8 * 200 = [B]100[/B]
[/LIST]

if the ratio of 2x to 5y is 3 to 4, what is the ratio of x to y?

if the ratio of 2x to 5y is 3 to 4, what is the ratio of x to y?
Set up our given ratio:
2x/5y = 3/4
Cross multiply:
2x * 4 = 5y * 3
8x = 15y
Divide each side by 8:
8x/8 = 15y/8
x = 15y/8
Now divide each side by y to find x/y:
x/y = 15y/8y
x/y =[B] 15/8[/B]

If the ratio of private school students to public school students in a city is 4 to 15 and there is

If the ratio of private school students to public school students in a city is 4 to 15 and there is a total of 18,601 students, how many students are in public schools?
Since 4 out of 15 are public school students, this means (15 - 4)/15 = 11/15 are public school students.
The total public school students are (11/15) * 18601 = 13,640.73. Rounded up, it is [B]13,641[/B].

Imaginary Numbers

Free Imaginary Numbers Calculator - 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

In Trina's desk drawer, there are 15 paper clips and 18 rubber bands. In Kirk's office supply tray,

In Trina's desk drawer, there are 15 paper clips and 18 rubber bands. In Kirk's office supply tray, there are 13 paper clips and 16 rubber bands. Who has a higher ratio of paper clips to rubber bands?
Trina: 15/18
Kirk: 13/16
We want common denominators to compare, so we get a greatest common factor (GCF) for 16 and 18.
[URL='https://www.mathcelebrity.com/gcflcm.php?num1=16&num2=18&num3=&pl=GCF+and+LCM']Running this through our search engine[/URL], we get GCF(16, 18) = 144
For Trina, 144/18 = 8
For Kirk, 144/16 = 9
We multiply Trina's fraction, top and bottom by 8:
15 * 8 / 18 * 8
120/144
We multiply Trina's fraction, top and bottom by 8:
13 * 8 / 16 * 8
104/144
[B]Trina[/B] has more in her numerator, so her ratio of paper clips to rubber bands is greater.

Ina school, out of 300 students, 70% are girls and 30% are boys. if 30 girls leave and no new boy is

Ina school, out of 300 students, 70% are girls and 30% are boys. if 30 girls leave and no new boy is admitted, what is the new% of girls in the school.
Current ratios:
[LIST]
[*]Girls = 70% of 300 = 210
[*]Boys = 30% of 300 = 90
[/LIST]
Ratios after girls leave:
[LIST]
[*]Girls = 210 - 30 = 180
[*]Boys = 90
[*]Total = 180 + 90 = 270
[*]Girls Percent = 180/270 = 2/3 = [B]66 & 2/3%[/B]
[/LIST]

Inventory Turnover and Average Inventory

Free Inventory Turnover and Average Inventory Calculator - Calculates inventory turnover ratio and average inventory

Irrational Numbers Between

Free Irrational Numbers Between Calculator - This calculator determines all irrational numbers between two numbers

John has 30 marbles, 18 of which are red and 12 of which are blue. Jane has 20 marbles, all of them

John has 30 marbles, 18 of which are red and 12 of which are blue. Jane has 20 marbles, all of them either red or blue. If the ratio of the red marbles to the blue marbles is the same for both John and Jane, then John has how many more blue marbles than Jane?
John's red ratio = 18/30
Using a [URL='https://www.mathcelebrity.com/gcflcm.php?num1=18&num2=30&num3=&pl=GCF+and+LCM']GCF for (18, 30)[/URL], we get 6.
Divide top and bottom of 18/30 by 6, we get 3/5
John's blue ratio is 12/30
Using a [URL='https://www.mathcelebrity.com/gcflcm.php?num1=12&num2=30&num3=&pl=GCF']GCF of (12, 30)[/URL], we get 6.
Divide top and bottom of 12/30 by 6, we get 2/5
Use these same ratios for Jane, we get:
Red: 3(20)/5 = 12
Blue: 20 - 12 = 8
Now the problem asks how many more blue marbles John has then Jane. We have 12 - 8 = [B]4[/B].

Juliana answered 42 times correctly on an 80-item quiz, while her sister Angela answered 21 items co

Juliana answered 42 times correctly on an 80-item quiz, while her sister Angela answered 21 items correctly on a 40-item quiz. Do they have the same portion of correct answers?
Let's compare based on correct answers to questions:
Juliana = 42/80 = 0.525
Angela = 21/40 = 0.525
So yes, they do have the same portion of correct answers.
But there's another way to solve this:
[LIST=1]
[*]Divide Juliana's the top and bottom of Juliana's fraction by 2.
[*]We picked 2 as a GCF shown in our calculator.
[*]Type [URL='https://www.mathcelebrity.com/gcflcm.php?num1=42&num2=80&num3=&pl=GCF']GCF of 42 and 80[/URL].
[/LIST]
Divide top and bottom of Juliana's fraction by the GCF of 2
42/2 = 80/2 = 21/40
This ratio equals Angela's.

Lucas has nickels,dimes,and quarters in the ratio 1:3:2. If 10 of Lucas coins are quarters, how many

Lucas has nickels,dimes,and quarters in the ratio 1:3:2. If 10 of Lucas coins are quarters, how many nickels and dimes does Lucas have?
1 + 3 + 2 = 6.
Quarters account for 2/6 which is 1/3 of the total coin count. Let x be the total number of coins. We have:
1/3x = 10
Multiply each side by 3
x = 30
We have the following ratios and totals:
[LIST]
[*]Nickels: 1/6 * 30 = [B]5 nickels[/B]
[*]Dimes: 3/6 * 30 = [B]15 dimes[/B]
[*]Quarters: 2/6 * 30 = [B]10 quarters[/B]
[/LIST]

Marita's nose is 2 inches long and her head is 9 inches tall. Assume Mount Rushmore was carved using

Marita's nose is 2 inches long and her head is 9 inches tall. Assume Mount Rushmore was carved using the same ratio. If Teddy Roosevelt's head is 60 feet tall, how long should his nose be? Round to the nearest foot, if necessary.
Set up a proportion/ratio of head height to nose height where n is the nose height for 60 feet head height:
9/2 = 60/n
[U]Using our [URL='https://www.mathcelebrity.com/prop.php?num1=9&num2=60&den1=2&den2=n&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we see that:[/U]
n = [B]13.33 rounded to the nearest foot is 13 feet[/B]

Method of Equated Time-Exact Method-Macaulay Duration-Volatility

Free Method of Equated Time-Exact Method-Macaulay Duration-Volatility Calculator - Given a set of cash flows at certain times, and a discount rate, this will calculate t using the equated time method and the exact method, as well as the macaulay duration and volatility

Money Multiplier

Free Money Multiplier Calculator - Given a reserve ratio and initial deposit amount, this calculates the money multiplier and displays the re-lending process table for a bank to other banks including reserves and loans.

Multiply 0 by 3 and add 4

Multiply 0 by 3 and add 4
multiply 0 by 3:
0 * 3
Then add 4:
[B]0 * 3 + 4 <--- [/B][I]This is our algebraic expression.[/I]
If we want to evaluate this expression, we [URL='https://www.mathcelebrity.com/order-of-operations-calculator.php?num=0%2A3%2B4&pl=Perform+Order+of+Operations']type it in our search engine[/URL] and we get:
[B]4[/B]

Need help quickly! My math skills are escaping me!

If I have 13 participants attending new hire class. 3 of them did not pass, 10 passed successfully. What is the percentage of success? What is the ratio of success? I don't believe there is a ratio, I could be wrong. Probably so, math does not agree with me! Please help!
Thank you!

Need help quickly! My math skills are escaping me!

Success Percentage: 3/13 = 0.2308 = 23.08%
Success to failure ratio = 3:10

Norwood High Schools jazz band includes 33 trombone players and 27 trumpet players. Meanwhile, Lakew

Norwood High Schools jazz band includes 33 trombone players and 27 trumpet players. Meanwhile, Lakewood High Schools jazz band has 37 trombone players and 28 trumpet players. Which jazz band has a lower ratio of trombone to trumpet players?
Norwood: 33 : 27, is 33 out of 60 = 55%
Lakewood: 37 : 28 = 37/65 = 57%
Since [B]Norwood[/B] is lower than Lakewood, they have the lower ratio or trombone to trumpet players

Odds Ratio

Free Odds Ratio Calculator - This calculator determines the odds ratio for 2 groups X and Y with success and failure for an outcome.

Order of Operations

Free Order of Operations Calculator - Evaluates an expression using the order of operations, or PEMDAS or PEDMAS or BEDMAS or BODMAS

PI

Free PI Calculator - This calculator performs operations with PI and gives you other options for π related calculations.

Plane Geometry Operations

Free Plane Geometry Operations Calculator - Evaluates and simplifies various plane geometry notation and operations

Pleasantburg has a population growth model of P(t)=at2+bt+P0 where P0 is the initial population. Sup

Pleasantburg has a population growth model of P(t)=at^2+bt+P0 where P0 is the initial population. Suppose that the future population of Pleasantburg t years after January 1, 2012, is described by the quadratic model P(t)=0.7t^2+6t+15,000. In what month and year will the population reach 19,200?
Set P(t) = 19,200
0.7t^2+6t+15,000 = 19,200
Subtract 19,200 from each side:
0.7t^2+6t+4200 = 0
The Quadratic has irrational roots. So I set up a table below to run through the values. At t = 74, we pass 19,200. Which means we add 74 years to 2012: 2012 + 74 = [B]2086[/B]
t 0.7t^2 6t Add 15000 Total
1 0.7 6 15000 15006.7
2 2.8 12 15000 15014.8
3 6.3 18 15000 15024.3
4 11.2 24 15000 15035.2
5 17.5 30 15000 15047.5
6 25.2 36 15000 15061.2
7 34.3 42 15000 15076.3
8 44.8 48 15000 15092.8
9 56.7 54 15000 15110.7
10 70 60 15000 15130
11 84.7 66 15000 15150.7
12 100.8 72 15000 15172.8
13 118.3 78 15000 15196.3
14 137.2 84 15000 15221.2
15 157.5 90 15000 15247.5
16 179.2 96 15000 15275.2
17 202.3 102 15000 15304.3
18 226.8 108 15000 15334.8
19 252.7 114 15000 15366.7
20 280 120 15000 15400
21 308.7 126 15000 15434.7
22 338.8 132 15000 15470.8
23 370.3 138 15000 15508.3
24 403.2 144 15000 15547.2
25 437.5 150 15000 15587.5
26 473.2 156 15000 15629.2
27 510.3 162 15000 15672.3
28 548.8 168 15000 15716.8
29 588.7 174 15000 15762.7
30 630 180 15000 15810
31 672.7 186 15000 15858.7
32 716.8 192 15000 15908.8
33 762.3 198 15000 15960.3
34 809.2 204 15000 16013.2
35 857.5 210 15000 16067.5
36 907.2 216 15000 16123.2
37 958.3 222 15000 16180.3
38 1010.8 228 15000 16238.8
39 1064.7 234 15000 16298.7
40 1120 240 15000 16360
41 1176.7 246 15000 16422.7
42 1234.8 252 15000 16486.8
43 1294.3 258 15000 16552.3
44 1355.2 264 15000 16619.2
45 1417.5 270 15000 16687.5
46 1481.2 276 15000 16757.2
47 1546.3 282 15000 16828.3
48 1612.8 288 15000 16900.8
49 1680.7 294 15000 16974.7
50 1750 300 15000 17050
51 1820.7 306 15000 17126.7
52 1892.8 312 15000 17204.8
53 1966.3 318 15000 17284.3
54 2041.2 324 15000 17365.2
55 2117.5 330 15000 17447.5
56 2195.2 336 15000 17531.2
57 2274.3 342 15000 17616.3
58 2354.8 348 15000 17702.8
59 2436.7 354 15000 17790.7
60 2520 360 15000 17880
61 2604.7 366 15000 17970.7
62 2690.8 372 15000 18062.8
63 2778.3 378 15000 18156.3
64 2867.2 384 15000 18251.2
65 2957.5 390 15000 18347.5
66 3049.2 396 15000 18445.2
67 3142.3 402 15000 18544.3
68 3236.8 408 15000 18644.8
69 3332.7 414 15000 18746.7
70 3430 420 15000 18850
71 3528.7 426 15000 18954.7
72 3628.8 432 15000 19060.8
73 3730.3 438 15000 19168.3
74 3833.2 444 15000 19277.2

Proportion

Free Proportion Calculator - 1) Calculates the missing link of 2 equivalent proportions or ratios.

2) Also determines if two numerical proportions that you entered such as 1/10=6/12 are equivalent or*not* equivalent.
Note: You can use all allowable operators such as =,<,≤,>,≥

2) Also determines if two numerical proportions that you entered such as 1/10=6/12 are equivalent or

Prove sqrt(2) is irrational

Use proof by contradiction. Assume sqrt(2) is rational.
This means that sqrt(2) = p/q for some integers p and q, with q <>0.
We assume p and q are in lowest terms.
Square both side and we get:
2 = p^2/q^2
p^2 = 2q^2
This means p^2 must be an even number which means p is also even since the square of an odd number is odd.
So we have p = 2k for some integer k. From this, it follows that:
2q^2 = p^2 = (2k)^2 = 4k^2
2q^2 = 4k^2
q^2 = 2k^2
q^2 is also even, therefore q must be even.
So both p and q are even.
This contradicts are assumption that p and q were in lowest terms.
So sqrt(2) [B]cannot be rational.
[MEDIA=youtube]tXoo9-8Ewq8[/MEDIA][/B]

Prove the sum of any two rational numbers is rational

Take two integers, r and s.
We can write r as a/b for integers a and b since a rational number can be written as a quotient of integers
We can write s as c/d for integers c and d since a rational number can be written as a quotient of integers
Add r and s:
r + s = a/b + c/d
With a common denominator bd, we have:
r + s = (ad + bc)/bd
Because a, b, c, and d are integers, ad + bc is an integer since rational numbers are closed under addition and multiplication.
Since b and d are non-zero integers, bd is a non-zero integer.
Since we have the quotient of 2 integers, r + s is a rational number.
[MEDIA=youtube]0ugZSICt_bQ[/MEDIA]

Quadratic Equations and Inequalities

Free Quadratic Equations and Inequalities Calculator - Solves for quadratic equations in the form ax^{2} + bx + c = 0. Also generates practice problems as well as hints for each problem.

* Solve using the quadratic formula and the discriminant Δ

* Complete the Square for the Quadratic

* Factor the Quadratic

* Y-Intercept

* Vertex (h,k) of the parabola formed by the quadratic where h is the Axis of Symmetry as well as the vertex form of the equation a(h - h)^{2} + k

* Concavity of the parabola formed by the quadratic

* Using the Rational Root Theorem (Rational Zero Theorem), the calculator will determine potential roots which can then be tested against the synthetic calculator.

* Solve using the quadratic formula and the discriminant Δ

* Complete the Square for the Quadratic

* Factor the Quadratic

* Y-Intercept

* Vertex (h,k) of the parabola formed by the quadratic where h is the Axis of Symmetry as well as the vertex form of the equation a(h - h)

* Concavity of the parabola formed by the quadratic

* Using the Rational Root Theorem (Rational Zero Theorem), the calculator will determine potential roots which can then be tested against the synthetic calculator.

Quartic Equations

Free Quartic Equations Calculator - Solves quartic equations in the form ax^{4} + bx^{3} + cx^{2} + dx + e using the following methods:

1) Solve the long way for all roots and the discriminant Δ

2) Rational Root Theorem (Rational Zero Theorem) to solve for real roots followed by the synthetic div/quadratic method for the other imaginary roots if applicable.

1) Solve the long way for all roots and the discriminant Δ

2) Rational Root Theorem (Rational Zero Theorem) to solve for real roots followed by the synthetic div/quadratic method for the other imaginary roots if applicable.

ratio of the squares of t and u

ratio of the squares of t and u
Ratio is also known as quotient in algebraic expression problems.
The square of t means we raise t to the power of 2:
t^2
The square of u means we raise u to the power of 2:
u^2
ratio of the squares of t and u means we divide t^2 by u^2:
[B]t^2/u^2[/B]

ratio of x cubed and the sum of y and 5

ratio of x cubed and the sum of y and 5
x cubed means we raise x to the power of 3:
x^3
The sum of y and 5:
y + 5
ratio of x cubed and the sum of y and 5
[B]x^3/(y + 5)[/B]

Ratio Word Problems

Free Ratio Word Problems Calculator - Solves a ratio word problem using a given ratio of 2 items in proportion to a whole number.

Rational Exponents - Fractional Indices

Free Rational Exponents - Fractional Indices Calculator - 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

Rational Number Subtraction

Free Rational Number Subtraction Calculator - Subtracting 2 numbers, this shows an equivalent operations is adding the additive inverse. p - q = p + (-q)

Rational Numbers

Free Rational Numbers Calculator - This lesson walks you through what rational numbers are, how to write rational numbers, rational number notation, and what's included in rational numbers

Rational Numbers Between

Free Rational Numbers Between Calculator - This calculator determines all rational numbers between two numbers

Rational,Irrational,Natural,Integer Property

Free Rational,Irrational,Natural,Integer Property Calculator - This calculator takes a number, decimal, or square root, and checks to see if it has any of the following properties:

* Integer Numbers

* Natural Numbers

* Rational Numbers

* Irrational Numbers Handles questions like: Irrational or rational numbers Rational or irrational numbers rational and irrational numbers Rational number test Irrational number test Integer Test Natural Number Test

* Integer Numbers

* Natural Numbers

* Rational Numbers

* Irrational Numbers Handles questions like: Irrational or rational numbers Rational or irrational numbers rational and irrational numbers Rational number test Irrational number test Integer Test Natural Number Test

Ratios

Free Ratios Calculator - * Simplifies a ratio of a:b

* Given a ratio in the form a:b or a to b, and a total population amount, this calculator will determine the expected value of A and B from the ratio.

* Given a ratio in the form a:b or a to b, and a total population amount, this calculator will determine the expected value of A and B from the ratio.

Rebound Ratio

Free Rebound Ratio Calculator - Calculates a total downward distance traveled given an initial height of a drop and a rebound ratio percentage

Receivables Ratios

Free Receivables Ratios Calculator - Given Net Sales, Beginning Accounts Receivable, and Ending Accounts Receivable, this determines Average Accounts Receivable, Receivables turnover ratio, and Average Collection Period.

Right Triangles

Free Right Triangles Calculator - This solves for all the pieces of a right triangle based on given inputs using items like the sin ratio, cosine ratio, tangent ratio, and the Pythagorean Theorem as well as the inradius.

Scientific Notation

Free Scientific Notation Calculator - * Converts a number into scientific notation and determines order of magnitude

* converts scientific notation to a number (standard notation). Also handles scientific notation operations.

* converts scientific notation to a number (standard notation). Also handles scientific notation operations.

Sean is helping his dad build a tiled walkway in their backyard. The walkway will be 606060 feet lon

Sean is helping his dad build a tiled walkway in their backyard. The walkway will be 60 feet long and 2 feet wide. The local hardware store sells tiles which are 2 by 2 feet and come in boxes of 6.
There isn't a calculator for Rational Word Problems.

Security Market Line and Treynor Ratio

Free Security Market Line and Treynor Ratio Calculator - Solves for any of the 4 items in the Security Market Line equation, Risk free rate, market return, Β, and expected return as well as calculate the Treynor Ratio.

Sergeant U has 360 rounds of ammunition to distribute to Lance Corporal (LCpl) F, Lance Corporal (LC

Sergeant U has 360 rounds of ammunition to distribute to Lance Corporal (LCpl) F, Lance Corporal (LCpl) M and Lance Corporal (LCpl) Z in the ratio 3:5:7. How many rounds did Lance Corporal (LCpl) M receive?
Our ratio denominator is:
3 + 5 + 7 = 15
Lance Corporal (LCpl) M gets 5:15 of the ammunition. [URL='https://www.mathcelebrity.com/fraction.php?frac1=5%2F15&frac2=3%2F8&pl=Simplify']Using our fraction simplifier[/URL], we see that 5/15 = 1/3
So we take 360 rounds of ammunition times 1/3:
360/3 = [B]120[/B]

Sharpe Ratio

Free Sharpe Ratio Calculator - Calculates the Sharpe ratio given return on assets, risk free rate, and standard deviation

Signed Integer Operations

Free Signed Integer Operations Calculator - This performs a string of signed integer operations, either all addition and subtraction, or all multiplication and division.

Simplify 2/sqrt(5)

To do this, we need rationalize the denominator. This means get rid of the radical:
Multiply top and bottom by sqrt(5)
2sqrt(5)/sqrt(5) * sqrt(5)
sqrt(5) * sqrt(5) = sqrt(25) so we have:
2sqrt(5)/sqrt(25)
sqrt(25) = 5, so we have:
[B]2sqrt(5)/5[/B]
[MEDIA=youtube]jearVN9LhBE[/MEDIA]

Square Roots and Exponents

Free Square Roots and Exponents Calculator - 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

Synthetic Division

Free Synthetic Division Calculator - Using Ruffinis Rule, this performs synthetic division by dividing a polynomial with a maximum degree of 6 by a term (x ± c) where c is a constant root using the factor theorem. The calculator returns a quotient answer that includes a remainder if applicable. Also known as the Rational Zero Theorem

The ratio between the sum of a and b and the difference of a and b is equal to 5.

The ratio between the sum of a and b and the difference of a and b is equal to 5.
The sum of a and b:
a + b
The difference of a and b:
a - b
The ratio between the sum of a and b and the difference of a and b
(a + b)/(a - b)
The ratio between the sum of a and b and the difference of a and b is equal to 5.
[B](a + b)/(a - b) = 5[/B]

the ratio of 50 and a number added to the quotient of a number and 10

the ratio of 50 and a number added to the quotient of a number and 10
Take this algebraic expression in parts.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The ratio of 50 and x means we divide by 50 by x
50/x
The quotient of a number and 10 means we have a fraction:
x/10
The phrase [I]added to[/I] means we add 50/x to x/10
[B]50/x + x/10[/B]

the ratio of a number x and 4 added to 2

the ratio of a number x and 4 added to 2
Take this algebraic expression in parts.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The ratio of this number and 4 means we have a fraction:
x/4
The phrase [I]added to[/I] means we add 2 to x/4
[B]x/4 + 2[/B]

The ratio of adults to children at the beach is 4:3. If there are a total of 56 people how many are

The ratio of adults to children at the beach is 4:3. If there are a total of 56 people how many are adults? How many are children?
Using our [URL='http://www.mathcelebrity.com/ratio.php?simpratio=100%3A350&rs=4%3A3&rtot=56&pl=Calculate+Ratio']ratio calculator[/URL], we get:
[LIST]
[*][B]32 adults[/B]
[*][B]24 children[/B]
[/LIST]

The ratio of girls to boys is 14 girls to 12 boys. If there are 6 boys, how many girls are there?

The ratio of girls to boys is 14 girls to 12 boys. If there are 6 boys, how many girls are there?
Set up a proportion of girls to boys:
14/12 = g/6
Using our [URL='http://www.mathcelebrity.com/prop.php?num1=14&num2=g&den1=12&den2=6&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL]:
[B]g = 7[/B]

The ratio of men to women working for a company is 5 to 3 . If there are 75 men working for the

The ratio of men to women working for a company is 5 to 3 . If there are 75 men working for the company, what is the total number of employees?
We read this as a proportion, of men to women.
5/3 = 75/w where w is the number of women for 75 men.
Entering this expression into our [URL='http://www.mathcelebrity.com/prop.php?num1=5&num2=75&propsign=%3D&den1=3&den2=w&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get [B]w = 45[/B].

The ratio of men to women working for a company is 3 to 4. If there are 81 men working for the compa

The ratio of men to women working for a company is 3 to 4. If there are 81 men working for the company, what is the total number of employees?
Men to women is 3:4. Set up a proportion where w is the number of women:
3/4 = 81/w
Using our [URL='http://www.mathcelebrity.com/prop.php?num1=3&num2=81&den1=4&den2=w&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get w = 108.
The problem asks for total employees, so we add men and women:
Total Employees = Men + Women
Total Employees = 81 + 108
Total Employees = [B]189[/B]

The ratio of men to women working for a company is 4 to 7. If there are 319 employees total, how man

The ratio of men to women working for a company is 4 to 7. If there are 319 employees total, how many men work for the company?
[B]116[/B] using our [URL='http://www.mathcelebrity.com/ratio.php?simpratio=100%3A350&rs=4%3A7&rtot=319&pl=Calculate+Ratio']ratio calculator[/URL]

the ratio of ten to a number

the ratio of ten to a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The ratio of 10 and this number x is written as:
[B]10/x[/B]

The ratio of the measures of the 3 angles of a triangle is 1:2:3. What is the measure of the largest

The ratio of the measures of the 3 angles of a triangle is 1:2:3. What is the measure of the largest angle in degrees?
Let the smallest angle be x.
Then we have 3 angles based on the ratio: x, 2x, 3x
We know the sum of the angles of a triangle equals 180. So we have:
x + 2x + 3x = 180
6x = 180
Divide each side by 6:
6x/6 = 180/6
x = 30
The largest angle is 3(30) = [B]90
[MEDIA=youtube]l8Lc6YtK9dg[/MEDIA][/B]

The ratio of the number of carabaos, goats, and cows in a farm is 5:1:2. If there are 48 animals of

The ratio of the number of carabaos, goats, and cows in a farm is 5:1:2. If there are 48 animals of these kinds in his backyard how many of them are goats
Calculate total ratio:
5 + 1 + 2 = 8
Multiply fractional portion of goats by total animals in the backyard.
1/8 * 48 = [B]6 goats[/B]

the ratio of twice c to d

the ratio of twice c to d
Twice c means we multiply c by 2:
2c
The ratio is formed by the quotient:
[B]2c/d[/B]

the ratio of yellow to red balloons is 2:1 respectively. if there are 7 red balloons, how many yello

the ratio of yellow to red balloons is 2:1 respectively. if there are 7 red balloons, how many yellow balloons are there?
7 red balloons means we have twice as many yellow balloons. So 7 * 2 = [B]14[/B].
Written as a proportion, of yellow to red, we have:
2/1 = y/7 where y is the number of yellow balloons.
[URL='https://www.mathcelebrity.com/prop.php?num1=2&num2=y&den1=1&den2=7&propsign=%3D&pl=Calculate+missing+proportion+value']Run this proportion through our search engine[/URL] to get [B]y = 14[/B].

The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes

The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 6 to 5. If there were 4570 no votes, what was the total number of votes?
Set up a proportion where y is the number of yes votes to 4570 no votes
6/5 = y/4570
Using our [URL='http://www.mathcelebrity.com/prop.php?num1=6&num2=y&den1=5&den2=4570&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator,[/URL] we get:
[B]y = 5484[/B]

The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes

The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 4 to 3 . If there were 2958 no votes, what was the total number of votes?
Set up a ratio of yes to no votes
4/3 = x/2958
Using our [URL='http://www.mathcelebrity.com/prop.php?num1=4&num2=x&den1=3&den2=2958&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get x = 3,944 for yes votes.
Adding yes votes and no votes together to get total votes, we get:
Total Votes = Yes Votes + No Votes
Total Votes = 3,944 + 2,958
Total Votes = [B]6,902[/B]

The Waist to Hip Ratio (WHR) is commonly expressed as a decimal. WHR has been shown to be a good pre

The Waist to Hip Ratio (WHR) is commonly expressed as a decimal. WHR has been shown to be a good predictor of possible cardiovascular problems in both men and women. If Jonia has a WHR greater than 1, she is at “high risk” for cardiovascular problems. Jonia’s waist measurement is 42 inches and her hip measurement 2 inches less.
Jonia's WHR:
WHR = W/H
WHR = 42/(42 - 2)
WHR =4 2/40
WHR = [B]1.5 which is high risk[/B]

There are 100 teachers in a school of 3300 students find the ratio of number of teachers to the numb

There are 100 teachers in a school of 3300 students find the ratio of number of teachers to the number of students.
The Ratio is 100/3300.
Divide top and bottom by 100:
1/330 or [B]1:33
[/B]
You can also this into the search engine: [URL='https://www.mathcelebrity.com/ratio.php?simpratio=100%3A3300&rs=+7%3A5&rtot=+36&ab=+7%3A3&bc=+2%3A5&pl=Simplify+Ratio']Ratio of 100 to 3300[/URL].

There are 144 people in an audience. The ratio of adults to children is 5 to 3. How many are adults?

There are 144 people in an audience. The ratio of adults to children is 5 to 3. How many are adults?
We set up an equation to represent this:
5x + 3x = 144
[URL='https://www.mathcelebrity.com/1unk.php?num=5x%2B3x%3D144&pl=Solve']Typing this equation into our search engine[/URL], we get:
x = 18
This means we have:
Adults = 5(18)
[B]Adults = 90[/B]
Children = 3(18)
[B]Children = 54[/B]

There are 144 people in the audience. The ratio of adults to children is 5 to 3. How many adults are

[SIZE=6]There are 144 people in the audience. The ratio of adults to children is 5 to 3. How many adults are there?
Let x be the number of people, we have:
5x + 3x = 144
[/SIZE]
[URL='https://www.mathcelebrity.com/1unk.php?num=5x%2B3x%3D144&pl=Solve'][SIZE=6]Typing this problem in our search[/SIZE][/URL][SIZE=6][URL='https://www.mathcelebrity.com/1unk.php?num=5x%2B3x%3D144&pl=Solve'] engine[/URL], we get x = 18.
Which means we have 5(18) = [B]90 adults[/B][/SIZE]

There are 32 female performers in a dance recital. The ratio of men to women is 3:8. How many men ar

There are 32 female performers in a dance recital. The ratio of men to women is 3:8. How many men are in the dance recital?
3:8 = x:32
3/8 = x/32
Cross multiply:
8x = 96
Divide each side by 8
x = 12
Check our work:
12:32
Divide each part by 4
12/4 = 3 and 32/4 = 8 so we have 3:8 :)

there are some red counters and some yellow counters in the ratio 1:5. There are 20 yellow counters

There are some red counters and some yellow counters in the ratio 1:5. There are 20 yellow counters in the bag.
Set up a proportion where x is the amount of red counters to 20 yellow counters
1/5 = x/20
Enter that in the search engine and our [URL='http://www.mathcelebrity.com/prop.php?num1=1&num2=x&den1=5&den2=20&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL] gives us:
[B]x = 4[/B]

There is a ratio of 5 girls to 3 boys in the chorus. There are 24 boys in the chorus.How many girls

There is a ratio of 5 girls to 3 boys in the chorus. There are 24 boys in the chorus.How many girls are in the chorus?
Set up a proportion of girls to boys:
5/3 = g/24 where g is the number of girls for 24 boys.
Typing 5/3 = g/24 into the [URL='http://www.mathcelebrity.com/prop.php?num1=5&num2=g&den1=3&den2=24&propsign=%3D&pl=Calculate+missing+proportion+value']math tutoring calculator[/URL] gives us [B]g = 40[/B].
[MEDIA=youtube]c-xshqvfvig[/MEDIA]

Use number 7,6,5 and 3 only one time to get 75

Use number 7,6,5 and 3 only one time to get 75
We do it using this order of operations:
[B](7 + 5) * 6 + 3[/B]
Simplifying, we get:
12*6 + 3
72 + 3
75

Utility and Cost Utility Ratio

Free Utility and Cost Utility Ratio Calculator - Given 2 methods with a set of utilities and weights/probabilities, this will calculate the utility for each method, as well as the total utility using the additive method, as well as the Cost Utility Ratio

Vectors

Free Vectors Calculator - 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.

What can we conclude if the coefficient of determination is 0.94?

What can we conclude if the coefficient of determination is 0.94?
[LIST]
[*]Strength of relationship is 0.94
[*]Direction of relationship is positive
[*]94% of total variation of one variable(y) is explained by variation in the other variable(x).
[*]All of the above are correct
[/LIST]
[B]94% of total variation of one variable(y) is explained by variation in the other variable(x)[/B]. The coefficient of determination explains ratio of explained variation to the total variation.

What is the inverse of dividing by 3

What is the inverse of dividing by 3
[B]Multiplying by 3[/B]
Suppose we have 2 divided by 3:
2/3
To undo this operation to get to 2 again, we'd multiply by 3:
2/3 * 3 = 2

What is the ratio 18b^2 to 45b written in simplest for

What is the ratio 18b^2 to 45b written in simplest for
Using our [URL='https://www.mathcelebrity.com/monomial.php?num1=+%286xy%5E3%29%5E4&num2=+%283y%5E4%29%5E5%288x%5E6y%5E3%29&num3=18b%5E2%2F45b&pl=Divide']monomial calculator[/URL], we see that 18b^2/45b is
[B]2b/5[/B]

What is the ratio of the area of a circle to the area of a square drawn around that circle? Express

What is the ratio of the area of a circle to the area of a square drawn around that circle? Express your answer in terms of pi.
Area of a circle = pir^2
area of a square = (2r)^2 = 4r^2
Ratio = pir^2/4r^2
Ratio = [B]pi/4[/B]

What is the ratio of vowels to consonants in the word RAINBOW

What is the ratio of vowels to consonants in the word RAINBOW
Vowels (3):
A, I, O
Consonants (4):
R, N, B, W
Ratio of vowels to consonants:
[B]3:4[/B]

You are making identical gift bags using 24 candles and 36 bottles of lotion. What is the greatest n

You are making identical gift bags using 24 candles and 36 bottles of lotion. What is the greatest number of gift bags you can make with no items left over?
We take the greatest common factor [URL='https://www.mathcelebrity.com/gcflcm.php?num1=24&num2=36&num3=&pl=GCF+and+LCM']GCF (24, 36) = 12[/URL]
So we have a ratio of 24/12 = 2 candles and 36/12 = 3 bottles of lotion per bag giving us [B]12 bags[/B].

You collect a total of 75 in donations from three people. The three donations are in the ratio 4:4:7

You collect a total of 75 in donations from three people. The three donations are in the ratio 4:4:7. How much is each of the smaller donations?
4 + 4 + 7 = 15
Each person's donation ratio is:
[LIST=1]
[*]Donation 1 is 4/15 of 75
[*]Donation 2 is 4/15 of 75
[*]Donation 3 is 7/15 of 75
[/LIST]
4/15(75) = 5 * 4 = 20
7/15(75) = 5 * 7 = 35
Each person's donation amount is:
[LIST=1]
[*][B]$20[/B]
[*][B]$20[/B]
[*][B]$35[/B]
[/LIST]
Check out work:
20 + 20 + 35 = 75!