Height conversion chart feet to inches pdf
Visit the post for more. Convert cm to inches chart human height conversion table feet convert cm to inches chart 4 best images of conversion table human weight chart height conversion table inches to feet
Convert to cm from ft and in. Convert height measurements from US units of feet and inches to metric units of centimeters. Enter feet and/or inches to convert to height in centimeters. Enter feet and/or inches to convert to height in centimeters.
height conversion chart feet inches to chart cms and printable cm,height conversion table feet inches to meters chart centimeters cm printable and,height conversion chart cms to feet and inches pdf from m table,height conversion chart cms to feet and inches yard into image titled convert meters yards step 4 centimeters cm,height feet to inches conversion chart converting 7 and weight
Height Conversion Table Feet Inches To Meters masuzi January 7, 2018 Uncategorized Leave a comment 55 Views 46 height conversion table necessary calculator charts suitable likewise feet inches chart with metric conversions org 37 millimeter feet inches converter graceful height centimeter conversion chart 7 and height cm to inches conversion chart tools feet centimeters calculator …
onverlsons voirdupois Height Conversion Chart (Feet & Inches to Centimetres) Metric 112 142 173 203 234 22.7 29.0 35.4 41.7 48.1 54.4 60.8 67.1
Use this calculator to convert between meters, feet and inches (m, ft and in), all of which are units of length or height. A chart and explanation for how to convert between meters and feet is further down.
Height conversion chart You can use this table to find any value in feet, in inches or in feet plus inches when you know the value in centimeters. It is an alternative to the Centimeters to Feet and Inches Converter .
Human Height Conversion Table Inches To Feet masuzi January 16, 2018 Uncategorized Leave a comment 126 Views Feet inches conversion chart height conversions feet inches and cm s feet to metres imperial metric height conversions andre joseph feet to centimeters conversion …
1 metre is equal to 39.370078740157 inches, or 3.2808398950131 feet. Note that rounding errors may occur, so always check the results. Use this page to learn how to convert between inches and feet.
converting height feet to inches chart conversion printable cms and cm,convert meters to feet inches or reversion ft in m height conversion chart cm printable and,height feet to inches conversion chart full chihuahua puppy growth and weight centimeters printable cm,printable height conversion chart cm to feet and inches cms weight 7 free documents download,best conversion charts images on
Height Feet To Inches Conversion Chart. Home〉Chart〉 Height Feet To Inches Conversion Chart. Recent Update » Standard Poodle Weight Chart » Drink Equivalency Chart
For instance, to convert U centimeters to feet, you would divide your figure by 30.48, but to convert 147 centimeters to inches, you would divide your figure by 2.54. Rest assured that we have you covered from a mathematical standpoint.
convert foot inch to centimeters centimeters to foot inch
Chart Height Chart Feet To Inches Conversion
Convert 1.82 meters to feet and in. Meter (m) or centimeters (cm) to feet (ft ′) and inches (in ″). Here is the answer to questions like: what is 1.82 meters in feet and inches. 1.82 meters equals 5.97 feet.
Every height between 4’11” and 6’5″ is converted to inches and centimeters with this printable size chart.
Feet And Inches To Inches Calculator It is designed to convert an entry in feet and inches, or, in feet alone or in inches alone, into inches. The results are the total of the feet and inches entered, converted into inches.
Quickly convert height from feet/inches to centimetres using the height converter below. Select Metric to Imperial or Imperial to Metric ; Enter height measurements; The height converter will convert as you type; Height Converter. Convert. Yards Feet Inches. Height Conversion Results. What is a Height converter? A height converter is a simple calculator that converts imperial measurements …
Height Conversion © Occupational Health Solutions Ltd 2011 m inches feet and inches 1.37 54 4 6 1.38 54 1/2 4 6 1/2 1.40 55 4 7 1.41 55 1/2 4 7 1/2
How tall is 156 cm in feet and inches? How high is 156 cm? Use this easy calculator to convert centimeters to feet and inches. How high is 156 cm? Use this easy calculator to convert centimeters to feet and inches.
Use the above calculator to calculate height. Convert meters to feet and inches and centimeters. How much is 2 meters in feet and inches and centimeters? How tall is 2 meters? How far? How long? How wide? How big? How short? How narrow? Convert 2 meters to centimeters 2 = 200 cm Convert 2 meters to feet and inches 2 meters = 6 feet and 6.74 inches Convert 2 meters to inches 2 = 78.74 inches
The following height conversion chart shows height in inches as height in feet and inches, including two different ways to record the height. For additional height ranges, see all of my conversion charts or visit the StudentSurvive 2 Thrive site map.
16/08/2011 · The weight and Height Converter Feet to Inches consists with the diverse weight and height m easuring units like stones, pounds, kilograms (kg), utilized to measure the weight of a human body and feet, inches, meters (m), centimeters (cm) that are utilized to measure the height …
To convert foot-inch lengths into centimeters, enter feet into “ft” box and inches into “in/cm” box. Figure 1 uses 5 foot 6 inch (5′ 6″) as an example. Figure 1 uses 5 foot 6 inch (5′ 6″) as an example.
standard measurement height conversion chart feet inches to cm. printable height conversion chart feet to meters bike and weight uk 7 templates free sample,height and weight conversion chart pdf metric 7 free documents download inches to feet,weight and height conversion chart stones how many steps are in a mile to calculate the blog for inches
Download and create your own document with Height Conversion Chart From Feet To Cm (107KB 1 Page(s)) for free.
Height conversion formula We use the following conversion identities to convert height between metric and imperial units: 1 meter = 100 centimeters 1 foot = 12 inches 1 meter = 3.28084 feet and, 1 ft = 30.48 cm 1 in = 2.54 cm
Height conversions – feet, inches and cm’s . Visit. Discover ideas about Nursing Conversions “metric conversion table METRIC CONVERSION CHART – PDF Printable” Roman Numeral Conversion Numeral Numbers Scar Tattoo Piercing Tattoo Piercings Roman Numerals Chart Roman Numeral Font Roman Numeral Tattoos Roman Numbers Tattoo. Convert standard numbers into …
Rack Units to Inches – Quick Reference Guide What is a Rack Unit. A rack unit, abbreviated “U” or “RU”, is a unit of measure defined as 1.75 inches. It is most frequently used as a measurement of the usable space of 19-inch rack frames, as well as the height of equipment that mounts in these frames, where the height of the equip-ment is expressed as multiples of rack units. The rack
To convert 162 centimeters to feet you need to divide your figure by 30.48, and 162 centimeters to inches divide your figure by 2.54. One of the best aspects of the Free Height Converter is that you can move between feet and inches and centimeters and meters with ease.
The table allows you to fast and easily convert most common human heights between values given in feet and inches, inches and centimeters. There is no column for hight given in meters because conversion from centimeters to meters is extremely easy (1m is equal to 100cm.
Feet inches conversion chart medical assisting meters to feet and inches conversion m ft in height and weight conversion chart 7 free pdf doents meter to feet chart mendi charlasmotivacionales co Share this: Click to share on Twitter (Opens in new window)
Height Inches To Feet Conversion Chart Printable. Home〉Chart〉 Height Inches To Feet Conversion Chart Printable. Recent Update » Standard Poodle Weight Chart » Drink Equivalency Chart
Height Conversion Public holidays in Australia & New Zealand Handy Links NewsLetter Site map. Event Planning Tips. Tips to help you plan your event. For Entertainers & Performing Artists. List your act New Performer tips. OUR SERVICES. Adult Party Themes Entertainers and bands Casino Equipment Entertainers booking Casino tables booking Bands booking Woodfire Pizza Catering …
The converter above allows you to quickly convert between feet and inches and metres and centimetres when you need to find out your height in metres and centimetres. Just type your height into the feet and inches boxes to convert to metres or into the metres box to convert to feet and inches.
Converts height to feet-inches and weight to pounds.
Height Conversion Chart printable pdf download – FormsBank Formsbank.com View, download and print Height Conversion Charts pdf template or form online. 2 Height Conversion Charts are collected for any of your needs.
Height Converter ft to cm cm to ft inches to cm
This conversion Chart Templates is used to measure height against corresponding weight as against the standard units of metric measurement such as from feet to inches …
What’s the conversion? Use the above calculator to calculate height. Convert feet and inches to meters and centimeters. How much is 5’8 in cm and meters?
Height conversion chart You can use this table to find any value in feet, in inches or in feet plus inches when you know the value in centimeters. It is an alternative to the converter above.
height and weight charts conversion chart pdf. metric to standard height conversion chart download weight loss for free cm inches converter feet,7 height and weight conversion chart templates free sample nz metric to standard printable feet meters,conversion chart height inches to cm pediatric and weight evaluation of dental age in protein
Feet to Inches printable conversion chart for length measurement . Visit. Discover ideas about Gram Conversion Chart Every height between. Karen Hall. self help & children goals. See more What others are saying “Measurement Conversions in .” “Height conversions – feet, inches and cm’s” Metric Conversion Chart Kitchen Conversion Chart Weight Conversion Chart Measurement Conversions
For example, if the height is 165 centimeters, the nearest equivalent in inches is 65 inches (5 feet 5 inches) which is 165.1 centimeters. If you don’t have a chart, you can convert height to inches by multiplying the value in centimeters by 0.3937.
Height Chart Feet To Inches Conversion. Home〉Chart〉 Height Chart Feet To Inches Conversion. Recent Update » Standard Poodle Weight Chart » Drink Equivalency Chart » L Oreal Professional Hair Color Chart » Integer Rules Chart » Giants Stadium Virtual Seating Chart » Dmc Mini Cross Stitch Charts » Erik Erikson Developmental Stages Chart » Metric System Chart Steps » 1970 Chevy …
Human Height Conversion Table Inches To Feet
Height Conversion Chart Inches To Centimetres (ft to m
Convert 2 meters to feet and inches Saving
Rack Units to Inches Quick Reference Guide
Chart Height Inches To Feet Conversion Chart Printable
Download Height Conversion Chart From Feet To Cm
Convert 1.82 meters to feet and in coolconversion.com
Student Survive 2 Thrive Height Conversion Chart to Feet
Feet to Inches (ft to in) conversion calculator RapidTables


We analyze a Coxian stochastic queueing model with three phases. The Kolmogorov equations of this model are constructed, and limit probabilities and the stationary probabilities of customer numbers in the system are found. The performance measures of this model are obtained and in addition the optimal order of service parameters is given with a theorem by obtaining the loss probabilities of customers in the system. That is, putting the greatest service parameter at first phase and the second greatest service parameter at second phase and the smallest service parameter at third phase makes the loss probability and means waiting time minimum. We also give the loss probability in terms of mean waiting time in the system. is the transition probability from j-th phase to phase . In this manner while and this system turns into queueing model and while the system turns into Cox(2) queueing model. In addition, loss probabilities are graphically given in a 3D graph for corresponding system parameters and phase transient probabilities. Finally it is shown with a numeric example that this theorem holds.


During World War II a Japanese Zero fighter plane crashed onto Aboriginal land in Northern Australia. That started me thinking about the mathematical concept of zero.
Historically, the concept of zero as a number did not exist in western mathematics until it was introduced from the east via Spain, I believe around the 11th century. I wondered if the concept had originated way, way back in a culture like that of traditional Indigenous Australians.
It's worth remembering that modern technology is made possible only by 1 and 0, on and off, west and east, coming together.


New ProSens manual
ProSens in distributed systems
Prosens as a process controller
Prosens – input signals
General Algorithm for sum of digits in a given number: Get the number; Declare a variable to store the sum and set it to 0; Repeat the next two steps till the number is not 0; Get the rightmost digit of the number with help of remainder ‘%’ operator by dividing it with 10 and add it to sum. Print … If two parameters are given, number will be formatted with decimals decimals with a dot (".") Share a link to this answer. PHP | Sum of digits of a number Last Updated: 09-03-2018. The sum of the first and last digits is equal to third digit. Other versions get the string from start. I need to pull just the last four digits (2009). For example, and so on.


Methods of Teaching Mathematics in Secondary Schools
Course: Certificate Programme in Methods of Teaching Mathematics in Secondary Schools
Duration: 24 Hours
Description: Provide students with knowledge and experience to enable them to become effective secondary mathematics teachers. Emphasis will be on modes of instruction, unit planning and lesson planning to maximize student engagement and student learning. Problem solving, effective assessment, classroom management, use of technology, and national curriculum and process standards will be focal points.
Price: 300 TL
Certification: A “Certificate of Participation” will be issued following completion.


Pat/Mike/Kevin vs. Jeff/Aaron/Mark which ended in a 13/3 victory for Pat's team.
The question arose, did the 2nd game count towards the rankings. After careful reflection... Yes... it does. So long as you have 4 players minimum participating, and the score is at least played to 7 points (on games subsequent to the 1st game). The idea is to avoid the situation where only 2 players show (for whatever reasons) and they play a series of six games (because 1 vs 1 are quicker games) - racking up points.
Looking at the results, I see that I still rank highest, but Pat is closing in on the top rank. The player averages are all across the board - with Hatesh (and his 2 games played) ranking in highest at 2.5
By the way, as the highest amount of points a player can collect in a game is 3 (13/0 score) - the highest average you can attain is... yes... 3 and the lowest... 1 (because all of the members of the losing team always get 1 point).


Vector<> is templated by scalar type contained in the vector and its dimension.
Following vector types are used:
typedef Vector<PIX, 2> PIX2D;
typedef Vector<MEX, 2> MEX2D;
typedef Vector<ANGLE, 3> ANGLE3D; // Euclidean angles (h,p,b)
typedef Vector<FLOAT, 2> FLOAT2D;
typedef Vector<FLOAT, 3> FLOAT3D;
typedef Vector<DOUBLE, 2> DOUBLE2D;
typedef Vector<DOUBLE, 3> DOUBLE3D;
Vector<> has standard operators overloaded:
Three norms are defined: Euclidean (Length()), Manhattan (ManhattanNorm()) and Max-norm (MaxNorm).
Normalization works on the vector object itself, and returns its reference (quite like +=).
Elements of the vector are accessed using overloaded operator(), and one-based indices. This is similar to mathematical notations, unlike C-styled arrays. Constructors from elements are given for up to 4 dimensions.
FLOAT3D v(10, 20, 30);
FLOAT x = v(1);
FLOAT y = v(2);
FLOAT z = v(3);
Matrix<> is templated by the scalar type contained in the matrix and its two dimensions.
Following matrix types are used:
typedef Matrix<FLOAT, 3, 3> FLOATmatrix3D;
typedef Matrix<DOUBLE, 3, 3> DOUBLEmatrix3D;
Elements of the matrix are accessed using overloaded operator(), and one-based indices. First index denotes row and the second one column. This is similar to mathematical notations, unlike C-styled arrays. There are no constructors except default one (which trashes the contents in debug version) and constructor for clearing entire matrix to one given value.
Diagonal matrix can be made with diagonal set to a scalar value or filled with a vector using two overloaded versions of Diagonal().
Multiplication/division with scalar is defined by *, /, *= and /=. Matrix is transposed in-place using ! and from another matrix using !=.
Matrix addition substraction is done by +, -, +=, -=. Matrix multiplication is * or *=.
Quaternion<> is templated by the scalar type contained. It defines construction from 4 scalars, conversion from euler angles (FromEuler()) and into a rotation matrix (ToMatrix()).
Standar operations are defined: flipping (-), congjugation (~), inversion (Inv()), multiplication and division by a scalar (*, *=, /, /=), addition and substraction (+, -, +=, -=), multiplication (*, *=) and dot product (%).
Norm() gives Euclidean lenght of the quaternion. For interpolation, Exp(), Log(), Slerp(), and Squad() are defined.
AABBox<> is templated by contained scalar type and dimension.
Following box types are used:
typedef AABBox<MEX, 2> MEXaabbox2D;
typedef AABBox<PIX, 2> PIXaabbox2D;
typedef AABBox<FLOAT, 2> FLOATaabbox2D;
typedef AABBox<FLOAT, 3> FLOATaabbox3D;
typedef AABBox<DOUBLE, 2> DOUBLEaabbox2D;
typedef AABBox<DOUBLE, 3> DOUBLEaabbox3D;
By default, and aabbox is initialized to a normalized empty bounding box. That is a box whose min vector has maximum values and max vector has minimum values allowed for the type.
It can be constructed to contain only one point, a sphere, or two points (for diagonal construction).
Defined operations are: union (|=), intersection (&, &=), translation by a vector (+=, -=), stretching and expanding (Expand(), StretchByFactor(), StretchByVector()).
Bounding box checking is done with == and != for (in)equality, >= and <= for containment, HasContactWith() and TouchesSphere() for adjacency/contact checking.
To get properties of bounding box, you can use: Size(), Center(), Min(), Max() and IsEmpty().
OBBox<> is templated by the contained scalar type and is always a 3D box.
Following box types are used:
typedef OBBox<FLOAT> FLOATobbox3D;
typedef OBBox<DOUBLE> DOUBLEobbox3D;
Oriented bounding box is defined by its center, 3 axis direction vectors and box size along each of the axes.
It can be constructed as empty, from its components, or from an aabbox and given position and orientation in 3D.
It can be tested only against a 3D plane for now.
Plane<> is templated by the contained scalar type and dimension. Currently, only 3D planes are supported.
Following box types are used:
typedef Plane<FLOAT, 3> FLOATplane3D;
typedef Plane<DOUBLE, 3> DOUBLEplane3D;
A plane is defined by the plane normal vector (always normalized) and distance from the origin along the normal vector.
It can be constructed from its components, from normal vector and a point on the plane, and from 3 points on the plane (in ccw order).
You can access the distance parameter by Distance(), and take advantage of the fact that Plane<> inherites from Vector<> to access its normal vector.
Plane can be flipped (-), translated by a vector (+, -, +=, -=), rotated by multiplication with a matrix (*) and offset forward (Offset()).
PointDistance() finds distance of a point from the plane, GetCoordinate() fills in a missing coordinate of a point on the plane, PlaneDistance() finds distance of a plane from the plane (assuming they are parallel or anti-parallel).
ProjectPoint() and ProjectDirection() project a point or a direction vector to the plane.
DeprojectPoint() and DeprojectDirection() project a point or a direction vector to the plane, but not along this planes normal, but rather along another plane's normal (used in projected mapping).
Euler angles (ANGLE3D) used in Serious Engine are Heading, Pitch and Banking (HPB). Heading is rotation around Y axis, Pitch around X axis and Banking around Z axis. All rotations are mathematically positive (counter-clockwise if viewed from the tip of the imaginary plus vector of the rotation axis, along the axis down towards negative direction).
Simplified: increasing Heading rotates left, increasing Pitch rotates up, increasing Banking tilts to the left. Order of rotations is Banking-Pitch-Heading making Heading most influencing one.
To convert between Euler angles and rotation matrices, use following functions:
The first versions perform snapping, while the latter are faster and smooth.
CPlacement3D is a class consisting simply of a 3D vector (FLOAT3D) and a set of 3 Euler angles (ANGLE3D).
It defines position and orientation of an object in a reference system. The reference can be the absolute coordinate system, or some relative system, depending on the meaning in any given context. The class itself does not retain that information.
For various rotations and translations of a placement use:
To transform between different reference systems use:
The base function (non-'Smooth') snap the coordinates of the placement after transformation, and are useful only in GUI editing, or CSG operations. Use 'Smooth' variants if snapping is not required.
CProjection3D is an abstract base class for all projections. Projections are generally used for transforming coordinates from one 3D space to another 3D or 2D space.
CSimpleProjection3D implements simple transformation from 3D to 3D, including translation, rotation, uniform stretch and mirroring.
CIsometricProjection3D implements 3D to 2D orthografic projection along an axis parallel to the viewing plane.
CPerspectiveProjection3D implements 3D to 2D perspective projection.
CParallelProjection3D implements 3D to 2D orthografic projection along an axis that is generally not parallel to the viewing plane.
They are mostly used inside engine when rendering or performing some other calculations. From the outside, you will only need to set them up by adjusting viewer placement and viewing parameters (FOV, zoom etc.). You will seldom need to manually project points using projections.
You can transform Euclidean angles to direction vectors and vice versa using:
To mirror a vector or rotation matrix by a give plane use:
Misc. management with vectors and matrices (useful in AI and physics):


Law of Large Numbers
When you are playing Ladder on Peergame, how do you decide which side to bet? Did you ever make a decision based on the statistics? Which side are you most likely to bet on if the statistics showed the results below?
You probably would want to bet on Left, am I right?
This prediction of your behavior is made based on the law of large numbers. Even if you aren’t familiar with this law, you are most likely aware of it subconsciously, and you subconsciously apply this law to make all kinds of decisions and predictions in life.
What is the Law of Large Numbers?
The law of large numbers states that as the number of trials and their outcomes increases, the average of the results gets closer to the expected value. This law is important because it guarantees that the average of random outcomes will eventually be close to the number based on theoretical or expected probability if a large number of trials have been observed.
To give you an example, let’s consider a coinflip. We all know that the expected probability of flipping heads is 50%. This, however, does not guarantee that if you flip the coin 10 times, you will get 5 heads. You might only get 2 heads, or you could even get 10 heads, which is far from the expected probability. But if you flip the coin a million times, the results would most likely be close to 50%. If you flip the coin indefinitely, the cumulative results would be 50%, if not, extremely close to it.
Since the law pretty much guarantees that with a large enough number of trials, the overall average approaches the expected probability, it is often used in gambling, which leads to a common misconception.
This misconception, called gambler’s fallacy, refers to people’s tendency to believe that the next outcome will be affected by previous outcomes due to the law of large numbers.
If 10 coinflips resulted in 10 heads, you probably would bet the next flip to be tails, because you believe the proportion of heads to tails is supposed to even out to 50%. You are guessing what the next random outcome would be based on previous outcomes. However, it does not work this way, as each coin flip is an independent event, not affected by any of the previous events. So starting out with 10 heads does not mean you are more likely to get tails next. The law of large numbers simply means that those 10 heads will eventually be evened out with more tails at some point in a large number of flips, causing the proportion to become closer to 50%.
Applying the Law of Large Numbers in Peergame
In some ways, the law of large numbers can be used as a guide to navigating through randomness. Even though you can never be certain of what the next coin flip would result in, you can always be certain that over time, you will end up having about half heads and half tails. You can apply this principle to many different strategies to win more and lose less over time. At Peergame, we provide statistics for all games. Use this wisely to your advantage, and always remember to play responsibly. Good luck!


Do you have any idea about how to ascertain the chances of scoring that sweepstakes, including the Florida Lottery? You can work out each set of chances for each unique lottery game you play. With the help of a little hand held mini-computer or with the free adding machine on your PC, you simply increase the numbers together and add one division process when “the request” of your picked numbers isn’t needed for a specific lottery game.
What you “really want to know” is the quantity of all out balls that the triumphant numbers are drawn from…..is it 59, 56, 42, 49, or 39? Assuming that there is an optional drawing for the single additional ball, for example, the “red ball” with Powerball or the Mega Millions’ “gold ball” you really want to realize the number of balls are in this gathering too. Are there 49 or 39?
It doesn’t make any difference in the event that it is the Florida, Ohio, Texas, PA or NJ Lottery. This methodology or recipe gives you the genuine chances. Florida Lottery is 6/53. New York Lottery is 6/59. The Ohio Lottery, Massachusetts Lottery, Wisconsin Lottery, and the State of Washington Lottery convey a 6/49 lottery numbers proportion. Illinois Lottery conveys a 6/52.
When you have this data accurately before you and your number cruncher close by, you can begin working the equations. You really want to pick five standard balls and an additional one ball accurately matched to the triumphant attracted numbers to win the multi-million dollar bonanza that a large portion of us long for winning sometime in the not so distant future.
In the principal model there are 56 balls in the main gathering and 46 balls in the auxiliary gathering. To win the Jackpot you really want to match this large number of balls (5 + 1) precisely, yet not really all together. The California Lottery’s Super Lotto Plus is 47/27. The enormous drum is turning with the underlying piece of the drawing. You have a 1/56 opportunity to match your number to this first ball.
With one ball eliminated after the main number has been drawn, you presently have a 1/55 possibility matching another of your numbers to the subsequent ball drawn. With each drawn number a ball is taken out bringing down the quantity of residual balls by a sum of one.
The chances of you accurately matching the number on the third ball to be drawn is presently 1/54 from the all out number of balls staying in the drum. With the third ball eliminated from the drum and sitting with the other two winning numbers, your chances of accurately matching the fourth ball is decreased to 1/53.
As you can see each time a ball is let out of the drum the chances are decreased by one. You began with a 1/56 possibility, then, at that point, with each new winning number it is decreased to 1/55, 1/54, 1/53, and with the fifth ball you have the chances of 1/52 accurately matching this fifth winning number. This is the initial segment of the equation of how to work out your chances of walking away with that sweepstakes, including the Florida Lottery.
Presently take these five chances addressing the five winning numbers (1/56, 1/55, 1/54, 1/53, and 1/52). The “1” on top of the division addresses your solitary opportunity to accurately match the drawn number.
Presently you take your adding machine and increase every top number (1x1x1x1x1) equivalent one (1). Next you increase every one of the base numbers (56x55x54x53x52). Accurately entered and increased you find the all out is 458,377,920. The new portion becomes 1/458,377,920. This is a 458 million to a single opportunity to win. Assuming you were expected to pick the numbers all together very much like they are drawn, then, at that point, these eventual the chances against you to win this Pick 5/56 ball lottery game.
Luckily or sadly, you are not expected to pick the numbers in the specific request they are drawn. The second step of the equation will decrease the chances, which permits you to match these five winning numbers in any request. In this progression you will increase the quantity of balls drawn – – five (1x2x3x4x5). With number cruncher close by you see that the absolute equivalents 120.
To give you the option to pick your five matching numbers in any request, you make these chances by isolating 120/417,451,320. You most certainly need a mini-computer for this one. 120/458,377,920 lessens your chances of walking away with this sweepstakes to 1/3,819,816. These are over 3.5 million to one chances against you of winning this Pick 5/56 ball lottery game.
On the off chance that this were the Mega Millions Lottery, you really want to add the “gold ball” to these five winning attracted balls request to win the Multi-Million 토토사이트 Dollar Jackpot. The single gold ball is determined as a 1/46 possibility matching it accurately, and since you are drawing only one number it must be a careful match. Once more, you just have that “1” opportunity to do it right. Presently you want to duplicate 3,819,816 by 46.
Snatch your number cruncher and do the increase. Your last chances against you winning the Mega Millions Jackpot are determined to be 175,711,536 or obviously expressed 175 million, 711 thousand, 5 hundred 36 36 to one (175,711,536 to 1). Presently you know how to ascertain the chances of walking away with the Mega Millions Sweepstakes.
The Powerball Lottery estimations depend on a 1/59 for the initial five white balls and 1/39 for the “red” power ball. The originally set of multipliers is 59x58x57x56x55. This gathering sums 600,766,320. Presently partition 600,766,360 by 120 (1x2x3x4x5). Your new complete is 5,006,386. There is a 1/39 opportunity to get the “red” ball. 39 x 5,006,386 provides you with the genuine chances of winning the Powerball Jackpot, in particular 195,249,054 to 1.
Another 5 +1 Lottery that is by all accounts wherever in the United States is the “Hot Lotto” which has a 39/19 count. It is played in 15 distinct States. DC Lottery, Delaware Lottery, Idaho Lottery, Iowa Lottery, Kansas Lottery, Maine Lottery, Minnesota Lottery, Montana Lottery, New Hampshire Lottery, New Mexico Lottery, North Dakota Lottery, Oklahoma Lottery, South Dakota Lottery, Vermont Lottery, and the West Virginia Lottery. The last chances of winning the base $1 Million Jackpot is 10,939,383 to 1.
A Pick 6/52 ball Lottery game equation resembles this: (1/52, 1/51, 1/50, 1/49, 1/48, 1/47) for a sum of 14,658,134,400 isolated by 720 (1x2x3x4x5x6) for the chances of 1/20,358,520. Your opportunity to win the 6/52 Lottery is over 14.5 million to one to win, like the Illinois Lotto.
The Hoosier Lottery that utilizes Indiana State’s moniker, conveys a 6/48. Michigan Lottery is 6/47, Arizona Lottery and Missouri Lottery are 6/44, Maryland Lottery is 6/43, and Colorado Lottery is 6/42. Contrast this with the Florida Lottery.
A Pick 5/39 ball Lottery game equation resembles this: (1/39, 1/38, 1/37, 1/36, 1/35) for an aggregate of 69,090,840 partitioned by 120 (1x2x3x4x5) for the chances of 1/575,757 of winning the Jackpot like the Illinois Little Lotto. Different States with a similar 5/39 lottery numbers incorporate the NC Lottery, Georgia and Florida Lottery Fantasy 5, and Tennessee Lottery’s Pick 5. Virginia Lottery’s Cash 5 conveys a 5/34 territory.


I have been playing "school" with the boys occasionally, since both boys love this pretend game. We all get a turn as teacher, and I've been having to up the ante with various skills lately.
Tonight, we were playing "Math Class," and Matthew is getting bored with basic addition. I threw a wrinkle in it and had him guess at what the missing number would be - it takes a little thought, but he eventually gets most of them. This didn't surprise me very much: he's five and addition isn't too far beyond his ken.
Nolan, however, is kind of freaky with his math skills. Not only can he add smaller numbers, but he also had these nailed without even thinking about the answer. If you listen carefully, he gives the answer to the final problem long before Matt comes up with the answer, at about 1:05 in the video (transcript provided below):
Nolan has done this several times. I'm not quite sure how well he can add, but he's been spot-on every time I ask Matt a question. His teacher of the deaf was over the other day, and had him put cheerios next to the numbers. He did fine until he got to the number seven, when he smiled slyly and placed four cheerios by the number. Thinking he had reached the "ceiling" of his counting abilities, the TOD said, "Nolan, is that seven?"
He looked aghast and told her, "No! I need three more to make seven!"
The good news is that he'll be very ready for kindergarten by the time he gets there. The bad news (for me) is that he may surpass my mathematical skills at a very early age!
Me: What do you think the first one is?
Me: You're right! What do you think the next one is?
Matt: A three!
Me: Mmm..Two plus "X" equals four...
Matt: Uh, that's a two.
Me: Yes, a two. What do you think the next one is?
Me: Mmm.. three plus "X" equals five.
Me: If you have three, how many more do you need to get five?
Matt: TWO!... uh, ONE!
Me: You're right... no, two.
Me: And two plus "X" equals seven. How many more do you need... if you have two, how many more do you need to get seven?
Nolan: Um, Mom, Matthew needs five.
Matt: Um, we don't need to get to ten or eleven, so that's a higher number.
Me: No. You're only going to seven. You have seven, and you already have two..
Matt: So I need five more.
Me: You need five more - that's good.
Matt: I couldn't think of the X on that one. Five X.


During the three years project time, the partners commited to develop the idea of mobile math trails further. To create tools which will help teachers to easily create math trails for their students. To create a catalogue of generic tasks which can be found everywhere to support users with good content. To create material and a schedule for curriculum in pre teacher and in-service teacher education.
Two mobile applications, one for navigating along math trails, and one for creating math trails. The mobile apps will be provided for students, teachers and people who want to discover math in their environment or in foreign cities.
An interactive web portal which provides authoring tools to easily and fast create math trails. The web portal should further allow interaction between users in order to create a community in which the users work together and share tasks with other users.
A catalogue of generic tasks, which is a collection of tasks that can be found outside and easily be adapted to the needs of the users. This supports the interactive web portal with lots of ideas for mathematical problems.


Is your child having difficulty with basic maths? Don't know where to start? Then try this handy little game to get your child on track, or to give them a real edge. This game is very effective at making them learn their sums the old fashioned way. From structured to random Flash Cards on the tables you want to focus on to the advanced Time Trial where you can go head-to-head with your child to see who really knows their maths the best.
Check out our site at http://www.forjunior.com for the companion wall charts and worksheets for a really intensive examination in this most fundamental of the maths principles behind addition.
Times Tables is a free trial software application from the Mathematics subcategory, part of the Education category.
The app is currently available in English and it was last updated on 2009-10-15. The program can be installed on Win95, Win98, WinME, WinNT 3.x, WinNT 4.x, Windows2000, WinXP, Windows2003, Windows Vista Starter, Windows Vista Home Basic, Windows Vista Home Premium, Windows Vista Business, Windows Vista Enterprise, Windows Vista Ultimate.
Times Tables (version 2.3) has a file size of 1.84 MB and is available for download from our website.
Just click the green Download button above to start. Until now the program was downloaded 387 times.
We already checked that the download link to be safe, however for your own protection we recommend that you scan the downloaded software with your antivirus.


Find the slope of the line segment.
The slope or gradient of a line describes both the direction and the steepness of a line.
A slope is rise over run, the change in y over the change in x.
Here we can measure this with line segments, but it must be remembered our line can extend in both directions.
How steep is the line? A downwards slope is negative and an upwards slope is positive.
The slope of the line is consistant. In the following program the two points are picked, and from that you can find the slope.
We would keep our answer as a fraction to express the ratio but in this program we'll show the answer in decimal form,
as the ten line units allows us to do. Converting back is easy enough, 0.1 is 1/10.
To see the answer, move your mouse inside the large blue border outline
For new problems, reload the page by clicking on the circle arrow
at the left top of your browser window.


Note that the first box carries the odds to win based on the % of time that the score hit AFC vertically and NFC horizontally. So for instance, the NFC 4 and the AFC 1, happened a total of 2 times in the past 44 super bowls or a percentage of 1.14%. Of those two times since there is 1 asterisk, it was the final score once. The asterisks represent how many times that score hit for the final game ending score. This is updated through Super Bowl XLIV (the 2010 Superbowl).
The second box carries the odds to win straight-up, not taking into account the AFC and NFC. As you can see the percentages are the same regardless if you are looking up, say a 7 horizontally and a 0 vertically versus a 0 horizontally and a 7 vertically.
For great step by step information on creating Superbowl boxes and the formats of 100, 50 and 25 box sheets click on this link:


Free Wolfram Alpha Step-by-Step Solutions
Get free access to step-by-step solutions. Unlock the power of Wolfram|Alpha Pro for free. Wolfree is free and open-source software. Thousands of learners use Wolfree to bypass paywalls.
How To Use Wolfree
Wolfree operates through a network of mirror sites to ensure uninterrupted access to step-by-step solutions. If you can't access this web page, visit one of our mirror sites to continue your learning journey.
Wolfree is free and open-source software. Our inclusive community welcomes individuals from diverse backgrounds to collaborate on our source code. Let's foster diversity, equity, and inclusion on the Internet. ❤
How Wolfree Works
Here's a simplified breakdown of how Wolfree works:
- Programmers distribute the Dockerfile on Fediverse, including platforms compatible with ForgeFed, like Forgejo and Gitea.
- Website operators install and run Docker.
- Docker automatically downloads the Dockerfile from Fediverse and builds a Docker image.
- Web hosting service providers deploy Wolfree mirror sites.
- Internet service providers allow your web browser to connect to Wolfree mirror sites.
- You gain free access to the computational capabilities of Wolfram|Alpha Pro. 🎉
Wolfree leverages a shadow library that shares step-by-step solutions, ensuring you have free access to the learning resources you need.
Here's what our community has to say about Wolfree:
"Wolfree has been a transformative addition to my academic journey. The step-by-step solutions powered by Wolfram|Alpha Pro have profoundly enriched my understanding of complex math concepts. Thanks to Wolfree, my grades have seen remarkable improvement. I now approach math confidently." - Olivia (they/them), Student.
"As a math teacher, I wholeheartedly endorse Wolfree for my students. The step-by-step solutions promote genuine comprehension of math concepts. By incorporating the computational capabilities of Wolfram|Alpha Pro into my classroom, Wolfree has significantly elevated my students' learning experiences." - Mx. Smith (they/them), Educator.
What You'll Get with Wolfree
By using Wolfree, you'll get free access to the full potential of Wolfram|Alpha Pro, including:
- Get answers and hints for your math homework problems.
- Use step-by-step calculators for chemistry, calculus, algebra, trigonometry, and equation solving.
- Develop a deeper understanding of your homework with detailed steps and hints guiding you from problems to answers.
Unleash the full potential of your learning with Wolfree and elevate your studies to a whole new level. 🚀
It's free! Type your math problem and click "Show Steps" now!


How many ways can you tile a (1 x n) board with (1 x 1) squares and (1 x 2) dominoes?
A (1 x 1) board can only be tiled 1 way.
A (1 x 2) board can be tiled 2 ways: either two squares or one domino.
A (1 x 3) board can be tiled 3 ways: three squares, or a domino-square, or a square-domino.
A (1 x 4) board can be tiled 5 ways…
Hey, they are all Fibonacci numbers! These are numbers you get when you start a sequence 0 and 1 and generate the next sequence member by adding the previous two numbers: i.e., 0, 1, 1, 2, 3, 5, 8, …
Draw pictures, and have students count the number of tilings themselves.
The Math Behind the Fact:
The Fibonacci property can be seen by conditioning on whether the first tile is a square or domino: the number of tilings where the first tile is a square is the number of ways to tile the remaining (n-1)-length board, and the number of tilings where the first tile is a domino is the number of ways to tile the remaining (n-2)-length board. A generalization of this idea can be used to develop combinatorial interpretations for many “Gibonacci” identities (recurrences in which the first terms are not necessarily 1 and 1); see the Benjamin-Quinn-Su reference for more on this.
An alternate generalization asks how many ways to tile an (m x n) board with dominoes; note that the (2 x n) case is equivalent to tiling a (1 x n) board with squares and dominoes. See the Graham-Knuth-Patashnik reference.
other generalizations can be found in the Brigham-Caron-Chinn-Grimaldi reference. If you like this Fun Fact, you'll like all the stuff that is in the Benjamin-Quinn book in the references.
How to Cite this Page:
References: Fun Fact suggested by:
Su, Francis E., et al. “Domino and Square Tilings.” Math Fun Facts.
A. Benjamin, J. Quinn, and F. Su, “Phased Tilings and Generalized Fibonacci Identities”, Fibonacci Quarterly, 2000.
Brigham, Caron, Chinn and Grimaldi, “A Tiling Scheme for the Fibonacci Numbers”, J. Recreational Math, 28(1), 1996-7, pp. 10-17.
Graham, Knuth, Patashnik, Concrete Mathematics, Section 7.1. Benjamin and Quinn, Proofs that Really Count
Fun Fact suggested by:


A cowboy rides into town on Friday, stays three days and rides out on Friday. How did he do this.
Here's a long one. Three guys stay at a hotel. They ask how much the room is. "It's $30". So they each pitch in $10. They head to the room. The manager tells the guy at the desk that it's only $25 and he needs to take the five bucks up to them. As he's going along he figures he can't divide $5 between the three guys so he is only gonna give them each a dollar and keep 2 for himself. So they each paid $9. So simple math here. 3 times 9 is 27, he keeps 2 for himself which equals 29. Wait where did the other dollar go?


Places I like to hang out on the internet
Project Euler - Programming problems intersect math problems! It's fun, I swear! I use it to sharpen my algorithm programming, and my optimization skills. After you solve a problem, there are discussion boards for how to solve it faster and better. New problems come out regularly, and there is an archive of problems from their initial launch.
Jackbox Games - The party game people. Jackbox has a host of games that you can play online or in person, so there's something for everyone, any way you want to play. Check them out! Better yet, come play them with me on Mondays and Wednesday at 10 pm Eastern.
IMDb: Collaborations Search - When you just can't come up with who "that guy, that starred with those other two guys, in those movies" is! You can search for actors common to two works, or works common to two actors. VERY useful.


Hitori can be a bit daunting for beginner players. There are several starting positions and patterns to
that will help you solve a hitori puzzle.
-If there are 3 identical digits in a sequence in a row or column, the middle cell must be white so can be
circled and the
outer two cells must be black. This is because if the center cell were black, one of the other two cells
to it would also have to be black to ensure there's only one of that digit in the row or column which is
as no adjacent black cells are allowed.
-When 1 digit is sandwiched by 2 different, but identical to each other digits, the middle digit must be
Since one of the outside 2 numbers must be black, the inside number must be white or there would be
-If 2 identical numbers are adjacent and the row or column contains another identical digit, the digit by
must be black. If not, then both the adjacent cells would have to be black.


Please use this identifier to cite or link to this item:
|Title:||The Minimum Vacation Cost Problem: A Novel Generalization of the Traveling Salesman Problem with Vertex Costs and Flexible Time Windows|
|Department:||Operations Research and Financial Engineering|
|Abstract:||This thesis presents and explores the Minimum Vacation Cost Problem (MVCP), a novel combinatorial optimization problem and generalization of the classical Traveling Salesman Problem (TSP). The MVCP models the realistic problem of a traveler planning a vacation itinerary through multiple cities with a fixed constraint on trip length but flexibility in the time windows to spend in each city. While previous scholars have explored variations of the TSP with similar characteristics to the MVCP, the MVCP is novel in introducing: (1) the use of a flexible time window (with upper and lower bound constraints [a, b]) to optimize over price variations in time, and (2) the consideration of time-dependent vertex costs (i.e. hotel costs) in optimizing overall itineraries. In this work, we present an integer programming formulation for representing and solving the MVCP. Additionally, we present two computational algorithms, a brute-force search algorithm and shortest-path algorithm with subgradient optimization, that are able to find optimal solutions to the problem. We also introduce newly developed problem instances using commercial flight and hotel price data to test our algorithms’ performance, and provide a comprehensive analysis of performance in response to various parameters (including number of cities, trip length, and time window constraints). Finally, we analyze MVCP solutions across hundreds of itineraries in the US and find that solving the MVCP results in a 27.09% reduction in travel costs on average. We thus conclude that optimization of multi-city travel itineraries using the MVCP can create substantial cost savings for travelers.|
|Type of Material:||Princeton University Senior Theses|
|Appears in Collections:||Operations Research and Financial Engineering, 2000-2016|
Files in This Item:
This content is embargoed until 2017-07-01. For more information contact the Mudd Manuscript Library.
Items in Dataspace are protected by copyright, with all rights reserved, unless otherwise indicated.


You don't want "teaspoons", your answer is a weight (or volume of a solution).
Get formula weight of HCO3- = 61.02 grams/mol
Figure out how many moles you need;
M (molarity) = n (moles)/ L (volume)
0.03303 = n / 1L
n = 0.03303 moles
Convert moles to grams via formula weight;
0.03303 moles * 61.02 g/mol = 2.02 grams of HCO3- (which is not NaHCO3)
So then, 2.02 grams of HCO3- in 1 liter of water gives you a 33.03 mM solution (millimolar).
Edit: this just illustrates the math using HCO3-, which you can't do as Matt points out. They must use other salts to get different molarities of sodium (Na) and bicarbonate (HCO3-) ions. At the very least, you should have the whole paper before proceeding, which will include specific Materials & Methods. If you wanted to follow the paper, you really should follow it directly, as in an exact duplication of the study. However, these things tend to balance out over time and this paper is from 1990. If baking soda was the cure for hypertension, I think word would be out (I'm not a physician, and never stay at Holiday Inn Express).
Sodium bicarbonate NaHCO3 has a molar mass of 84 mg per mmol. Sodium bicarbonate is a 1:1 ratio of sodium cations to bicarbonate anions, thus you can't get 6.2 mM sodium with 33 mM HCO3 without some other cation balancing the bicarbonate.
Is the result from that paper really that significant that you want to try it?


Round the Clock is an easy game for young children as soon as they can recognise the number of spots on dice and can count to twelve. It is a useful game to help children as they learn these skills.
Age: All ages
No. of players: 2 to 4
Equipment: Two dice
Time: 5 minutes+
Aim: To be the first player to throw all the numbers from 1 to 12 in order.
1. Players throw the dice, the player with the lowest total going first.
2. Player One throws both dice, hoping to throw a '1'. Players take it in turns (in a clockwise direction) looking to throw a '1'.
3. On the next round, any player who did not throw a '1' in the first round will try again this round, while those players who did throw a '1' will try to throw a '2'. They can either throw a '2' or they could throw two '1s'.
4. Play continues round by round with players trying to throw all the numbers from 1 to 12 in sequence. They can count the spots on just one die or on both dice added together. For example, throwing a '2' and a '5' could be counted as '2', '5' or '7'.
5. The first player to go Round the Clock (throw all the numbers from 1 to 12 in order) wins the game.
Variation: A player can keep throwing the dice during their turn until they fail to get the number they are trying for.
|Click on the links below for more Dice Games such as ...|
Do you have a favourite Dice game that you want to share with all our readers? You can share YOUR Dice game and/or check out other readers' favourite Dice games. It's easy! Just click on this share YOUR Dice game link and follow the instructions.
Thank you for visiting our website!


2+2=5, but only for large quantities of "2"...
The History of 2 + 2 = 5
by Houston Euler
"First and above all he was a logician. At least thirty-five years of the half-century or so of his existence had been devoted exclusively to proving that two and two always equal four, except in unusual cases, where they equal three or five, as the case may be."
-- Jacques Futrelle, "The Problem of Cell 13"Most mathematicians are familiar with -- or have at least seen references in the literature to -- the equation 2 + 2 = 4. However, the less well known equation 2 + 2 = 5 also has a rich, complex history behind it. Like any other complex quantity, this history has a real part and an imaginary part; we shall deal exclusively with the latter here.
Many cultures, in their early mathematical development, discovered the equation 2 + 2 = 5. For example, consider the Bolb tribe, descended from the Incas of South America. The Bolbs counted by tying knots in ropes. They quickly realized that when a 2-knot rope is put together with another 2-knot rope, a 5-knot rope results.
Recent findings indicate that the Pythagorean Brotherhood discovered a proof that 2 + 2 = 5, but the proof never got written up. Contrary to what one might expect, the proof's nonappearance was not caused by a cover-up such as the Pythagoreans attempted with the irrationality of the square root of two. Rather, they simply could not pay for the necessary scribe service. They had lost their grant money due to the protests of an oxen-rights activist who objected to the Brotherhood's method of celebrating the discovery of theorems. Thus it was that only the equation 2 + 2 = 4 was used in Euclid's "Elements," and nothing more was heard of 2 + 2 = 5 for several centuries.
Around A.D. 1200 Leonardo of Pisa (Fibonacci) discovered that a few weeks after putting 2 male rabbits plus 2 female rabbits in the same cage, he ended up with considerably more than 4 rabbits. Fearing that too strong a challenge to the value 4 given in Euclid would meet with opposition, Leonardo conservatively stated, "2 + 2 is more like 5 than 4." Even this cautious rendition of his data was roundly condemned and earned Leonardo the nickname "Blockhead." By the way, his practice of underestimating the number of rabbits persisted; his celebrated model of rabbit populations had each birth consisting of only two babies, a gross underestimate if ever there was one.
Some 400 years later, the thread was picked up once more, this time by the French mathematicians. Descartes announced, "I think 2 + 2 = 5; therefore it does." However, others objected that his argument was somewhat less than totally rigorous. Apparently, Fermat had a more rigorous proof which was to appear as part of a book, but it and other material were cut by the editor so that the book could be printed with wider margins.
Between the fact that no definitive proof of 2 + 2 = 5 was available and the excitement of the development of calculus, by 1700 mathematicians had again lost interest in the equation. In fact, the only known 18th-century reference to 2 + 2 = 5 is due to the philosopher Bishop Berkeley who, upon discovering it in an old manuscript, wryly commented, "Well, now I know where all the departed quantities went to -- the right-hand side of this equation." That witticism so impressed California intellectuals that they named a university town after him.
But in the early to middle 1800's, 2 + 2 began to take on great significance. Riemann developed an arithmetic in which 2 + 2 = 5, paralleling the Euclidean 2 + 2 = 4 arithmetic. Moreover, during this period Gauss produced an arithmetic in which 2 + 2 = 3. Naturally, there ensued decades of great confusion as to the actual value of 2 + 2. Because of changing opinions on this topic, Kempe's proof in 1880 of the 4-color theorem was deemed 11 years later to yield, instead, the 5-color theorem. Dedekind entered the debate with an article entitled "Was ist und was soll 2 + 2?"
Frege thought he had settled the question while preparing a condensed version of his "Begriffsschrift." This condensation, entitled "Die Kleine Begriffsschrift (The Short Schrift)," contained what he considered to be a definitive proof of 2 + 2 = 5. But then Frege received a letter from Bertrand Russell, reminding him that in "Grundbeefen der Mathematik" Frege had proved that 2 + 2 = 4. This contradiction so discouraged Frege that he abandoned mathematics altogether and went into university administration.
Faced with this profound and bewildering foundational question of the value of 2 + 2, mathematicians followed the reasonable course of action: they just ignored the whole thing. And so everyone reverted to 2 + 2 = 4 with nothing being done with its rival equation during the 20th century. There had been rumors that Bourbaki was planning to devote a volume to 2 + 2 = 5 (the first forty pages taken up by the symbolic expression for the number five), but those rumor remained unconfirmed. Recently, though, there have been reported computer-assisted proofs that 2 + 2 = 5, typically involving computers belonging to utility companies. Perhaps the 21st century will see yet another revival of this historic equation.
From: Mathematics Magazine, December 1990.
© 1990 Houston Euler. Last update: Sunday, November 16, 1997


Moda Geometry Euclid Graph Dark Blue Fabric
- Buy 6 or more for £3.09 each and save 5%
- Buy 12 or more for £2.93 each and save 10%
- Buy 40 or more for £2.76 each and save 15%
The Moda Geometry Euclid Dark Blue Fabric is a 100% cotton quilting fabric, sold and priced as a 1/4m Long Length. It can be used for patchwork and quilting, home decor, light to medium weight curtains, cushions, craft projects and for making beautiful clothes
The Moda Geometry fabric collection, by Janet Clare, celebrates here love of maths equipment; from rulers, protractors, compasses to the best of them all - the graph paper. Give Janet Clare some indigo ink and a piece of squared paper and she's a very happy quilter!. The Geometry Fabric range features isosceles triangles, right angles, quadrants and cubes all painted by hand on graph paper, in co-ordinating colours with the addition of a nice sharp green for added flair. Why not use Geometry for your next quilting masterpiece....
Priced Per 1/4m Long Length, with multiple lengths supplied in a continuous length. (e.g. a quantity of 5 meaning 5 x 1/4m = 1.25 metres, which would be cut and sent as a 1.25 metre piece.
This Cotton patchwork fabric material is 44 Inch Wide Wide.
Please note, that this product cannot be returned once cut from the roll. Thank you.
|Manufacturer Code||1495 21|
|Theme of Fabric||Geometric|
|Type of Fabric||100% Cotton|
|Available in the Future?||No|
|Width of Fabric||44 Inches Wide (112cm)|
|Sold as||Cut as a 1/4m Length x the width of the fabric. When you buy 5, we will supply 1.25m of fabric in one piece|


How to do a permutation. Each such matrix say p represents a permutation of m elements and when used to multiply another matrix say a results in permuting the rows when pre multiplying ie pa or columns when post multiplying ap of the. Just make one table per list wih respective values and then do a cross join between them. Rearranges the elements in the range firstlast into the next lexicographically greater permutation. The permutation function allows you to get permutation of n values within a list where order mattersfor instance selecting n2 values with 123 is done as follows.
Rearranges the elements in the range firstlast into the previous lexicographically ordered permutation. The first such sorted possible permutation the one that would. Possible arrangements the elements can take where n is the number of elements in the range. Because factorials grow very quickly the formula above only works for n10.
Lets start with permutations or all possible ways of doing something. A few things to note. An introduction to permutations and combinations. Possible arrangements the elements can take where n is the number of elements in the range.
Other descendants of mutare in english include commute. A permutation is each one of the n. Permutations suppose we want to find the number of ways to arrange the three letters in the word cat in different two letter groups where ca is different from ac and. Different permutations can be ordered according to how they compare lexicographicaly to each other.
However this isnt really a limitation because 10. Permutation has not changed all that much since it was borrowed into middle english from anglo french in the 14th century as permutacioun meaning exchange transformationpermutacioun traces back to the latin verb permutare meaning to change thoroughly exchange and ultimately derives from the latin mutare to change. In mathematics particularly in matrix theory a permutation matrix is a square binary matrix that has exactly one entry of 1 in each row and each column and 0s elsewhere. And see fast food combinations.
This is the one that associates to σ the matrix m whose entry m ij is 1 if i σj and 0 otherwisethe resulting matrix has exactly one entry 1 in each column and in each. The first such sorted possible permutation the one that. For anyone who needs permutations it is much easier using sql if you can. Different permutations can be ordered according to how they compare lexicographicaly to each other.
3628800 which is a number that exceeds the maximum number of rows in excel 2010 which is 1048576. Were using the fancy pants term permutation so were going to care about every last detail including the order of each item.


Numbers - Number Games. Number games online help kids improve their understanding of numbers in a fun, educational way. We have plenty of free number games for you to try from our online learning program, Brainzy, including number recognition games, counting games, and comparing numbers games.. We're sorry. We don't support your browser! The California Lottery wants you to have the very best possible experience at calottery.com. We suggest you use one of the supported browsers listed below to enjoy all the features on this site.. The most familiar numbers are the natural numbers (sometimes called whole numbers or counting numbers): 1, 2, 3, and so on. Traditionally, the sequence of natural numbers started with 1 (0 was not even considered a number for the Ancient Greeks.)However, in the 19th century, set theorists and other mathematicians started including 0 (cardinality of the empty set, i.e. 0 elements, where 0 is.
Nov 08, 2008 · Numbers has 21,038 ratings and 2,466 reviews. Tatiana said: Numbers is yet another victim of misleading marketing. Everything about this book's packaging. Numbers printatable activities: worksheets, flash cards, coloring pages suitable for toddlers, preschool and kindergarten to help children learn numerals and early math concepts.. Rockalingua’s number games in Spanish offer a fun and educational way to help kids and adults to learn how to count and spell the numbers in Spanish..
Opening NUMBERS files. Did your computer fail to open a NUMBERS file? We explain what NUMBERS files are and recommend software that we know can open or convert your NUMBERS files.. This is a number learning game for preschoolers. In this number game, kids learn to identify numbers from 1 to 10.. c.1300, "sum, aggregate of a collection," from Anglo-French noumbre, Old French nombre and directly from Latin numerus "a number, quantity," from PIE root *nem-"to divide, distribute, allot" (related to Greek nemein "to deal out;" see nemesis).Meaning "symbol or figure of arithmatic value" is from late 14c. Meaning "single (numbered) issue of a magazine" is from 1795..
You can find your routing/transit number on the bottom of each of your checks — next to the number of your checking account and the check number.. "Numbers" is the seventh campaign mission in Call of Duty: Black Ops. The setting of this map is also featured in the First Strike map pack. A thunderstorm and heavy rain set the tone for this level.. Older and wiser The Numbers Game is the oldest game still offered by the Massachusetts Lottery. The first drawing was on April 10, 1976. Originally designed to compete with the illegal numbers game, the Lottery’s Numbers Game gives players an opportunity to select their numbers, the type of bet, the length of time and dollar amount (beginning at $.25) they would like to play..
Writing Numbers. Except for a few basic rules, spelling out numbers vs. using figures (also called numerals) is largely a matter of writers' preference.. The consonants at the end of the French numbers cinq, six, huit, and dix are pronounced when at the end of a sentence or in front of a vowel.However, they drop the final sound when followed by a word beginning with a consonant (such as cent, fois, mois, or livres).For example, dix is normally pronounced [dees] and dix élèves is [dee zay lehv], but dix livres is pronounced [dee leevr(eu)]..


Beyond the Boundaries
Prof. Damiano Brigo
Imperial College London
Professor Damiano Brigo holds the Chair in Mathematical Finance at Imperial College, London. He is the former Director of the cosultancy group Capco Institute and the former Head of Credit Models of the Investment Bank Banca IMI's front office. His research interests include mathematical finance, systems theory, probability and statistics. Prof. Brigo is the author of much-acclaimed books on stochastic interest rates and credit risk modelling.
Dr. Katia Colaneri
University of Rome-Tor Vergata
Katia is currently Assistant Professor at the Department of Economics and Finance,
University of Rome - Tor Vergata. Perviously, she was lecturer at the University of Leeds. Her research interests include filtering and stochastic control problems under full and partial information with applications to finance.
Prof. Rama Cont
University of Oxford
Prof. Rama Cont is the Head of the Oxford Mathematical and Computational Finance Group. He is also the Director of the EPSRC Centre for Doctoral Training in Mathematics of Random Systems, Senior Research Fellow at the Institute for New Economic Thinking and Principal Investigator at Oxford Suzhou Centre for Advanced Research.
His research evolves around stochastic analysis (pathwise methods in stochastic analysis, functional Itô calculus) and applications to finance, systemic risk and financial stability, and mathematical foundations of Data Science and Data-driven decision systems. Rama is also Scientific Advisor for the International Monetary Fund and the recipient of the APEX Award of the Royal Society for Excellence in Interdisciplinary Research.
Prof. Alexander Cox
University of Bath
Alex Cox is a Reader in Probability at the University of Bath. His research focuses on questions arising in Probability and its applications in Mathematical Finance. He is particularly interested in questions which relate to robustness and model-independence when considering the pricing and hedging of financial derivative contracts.
Prof. Stéphane Crépey
Université d'Evry-Paris Saclay
Stéphane Crépey is professor at the Mathematics department of Université d'Evry-Paris Saclay, in charge of the probability and finance group. His research interests are in financial modelling; counterparty credit risk, XVA analysis; risk measures, central counterparties; simulation methods; calibration; machine learning techniques; uncertainty quantification and model risk. Stéphane is a member of the scientific council of the French financial markets authority. He is
the author of two successful books on financial modelling and counterparty risk.
Prof. Christa Cuchiero
Christa is a professor at Vienna University. Her research interests evolve around Mathematical finance, Stochastic Analysis, and Quantitative Risk Management, in particular multivariate stochastic and rough volatility modelling, stochastic portfolio theory, data driven risk inference and machine learning in Finance. Christa has received the Bruti-Liberati Visiting Fellowship in Sydney and, in 2019, she was awarded the highly prestigious START award of the Austrian Science Fund (FWF).
Prof. Griselda Deelstra
Université Libre de Bruxelles
Griselda Deelstra is Professor in Stochastic Finance and Actuarial Sciences. She is an expert in Stochastic Modelling in Finance and Insurance, in particular: Pricing and Hedging of financial instruments and insurance products in stochastic models, Interest Rate Models and Interest Rate Derivatives, Asset-Liability management, Risk modelling and risk measures in finance and insurance. She is the author of Risk Theory and Reinsurance (with G. Plantin).
The online talk by Griselda has been cancelled.
Prof. Giulia Di Nunno
University of Oslo
Giulia di Nunno is professor of Risk and Stochastics at the University of Oslo. Her research interests include stochastic analysis, stochastic calculus and control, with focus on mathematical finance. In particular, modelling, pricing, hedging and other optimal portfolio problems under full, partial, and inside information; sensitivity and robustness; markets with memory and energy finance. Giulia is the chair of the European Mathematical Society's Committee for Developing Countries and the recipient of the Su Buchin Prize of the International Council for Industrial and Applied Mathematics for her activity in promoting top-level mathematical research and education in African countries.
Prof. Monique Jeanblanc
Université d'Evry-Paris Saclay
Monique Jeanblanc is now Emeritus Professor at University Evry-Paris Saclay. She is the author of more than 100 papers in probability theory and mathematical finance and of four highly acclaimed books. Monique's recent research focuses on credit risk modelling and the rôle of information in financial markets. Monique is a member of the executive board of Institut Louis Bachelier. She is also Chevalier of the Ordre National de la Légion d'Honneur (the highest decoration in France).
The online talk by Monique has been cancelled.
Prof. Alexander McNeil
University of York
Alexander McNeil is Professor of Actuarial Science at the University of York. He is the founder of the Scottish Financial Risk Academy (SFRA). His research interests are in financial risk management, models for market, credit and insurance risks, financial time series analysis, models for extreme risks and correlated risks, and enterprise-wide models for solvency and capital adequacy. He is the author, together with R. Frey and P. Embrechts, of the reference book "Quantitative Risk Management: Concepts, Techniques and Tools". Alex is also an Honorary Fellow of the Institute and Faculty of Actuaries and a Corresponding Member of the Swiss Association of Actuaries.
Prof. Nicolas Perkowski
Free University Berlin
Nicolas is Professor at the Free University-Berlin. Previously, he was Junior Professor for Stochastic Analysis at Humboldt-Universität zu Berlin and DFG Heisenberg Researcher at Max Planck Institute for Mathematics in the Sciences, Leipzig. His research focuses on singular stochastic partial differential equations and robust methods in financial mathematics. He is the recipient of prestigious awards, such as the Rollo Davidson Prize (2018) and of the Heinz Maier-Leibnitz Prize (2019).
Prof. Frank Riedel
Frank Riedel is Professor for Mathematics and Economics and the Director of the Center for Mathematical Economics at Bielefeld University. His main research interests are: microeconomic and mathematical foundations of financial markets, strategic interactions of rational agents, stochastic games and singular control problems in finance under Knightian uncertainty. Frank is a principal investigator at the Collaborative Research Centre "Taming uncertainty and profiting from randomness and low regularity in analysis, stochastics and their applications".
Prof. Mete Soner
Prof. Mete Soner (Princeton and until recently ETH Zurich) is a leading researcher in the field of probability and financial mathematics. He has led the Bachelier Finance Society for a number of years. He works on stochastic optimal control, nonlinear partial differential equations and mathematical finance. In 2008, he was awarded a European Research Council Advanced Project entitled Mathematical Methods for Financial Risk Management. In 2014, he received an Alexander von Humboldt Foundation Research Award, and was elected as a SIAM Fellow on 2015. Mete has authored several books among which the much-acclaimed “Controlled Markov Processes and Viscosity Solutions”(with W.H. Fleming).
Dr. Lukasz Szpruch
University of Edinburgh
Lukasz is Reader at the School of Mathematics, University of Edinburgh and the Scientific Director of the Finance and Economics Programme at the Alan Turing Institute, London. Formerly, he held a Nomura Junior Research Fellowship at the Institute of Mathematics, University of Oxford. His research interests include probability theory, stochastic analysis and machine learning. Lukasz has run joint projects with the financial services industry on topics such as model calibration and risk computation.
Prof. Josef Teichmann
Josef Teichmann has been Full Professor at ETH Zürich since June 2009. He is currently also the Executive Secretary of the Bachelier Finance Society. His research interests evolve around stochastic processes, filtering and control, as well as artificial intelligence. He is associate editor of several journals in probability and financial mathematics among which “Stochastic Processes and Applications” and “Finance and Stochastics”.
Josef is the recipient of prestigious accolades, such as the Prize of the Austrian Mathematical Society (2005), the Start-Preis of the Austrian Science Fund (2006), and the Louis Bachelier Prize (2014).
Prof. Nizar Touzi
Ecole Polytechnique-Paris Saclay
Nizar Touzi is Professor of Applied Mathematics at École Polytechnique (since 2006). Nizar specializes in the fields of financial mathematics, applied probability, and control theory. He was an invited session speaker at the International Congress of Mathematicians in Hyderabad (2010). He received a number of distinctions, such as the Louis Bachelier prize (2012), and the Paris Europlace Institute prize for Best Young Researcher in Finance (2007). In 2010, Nizar held the University of Toronto Dean's Distinguished Chair position. He is also recipient of an Advanced Grant of the ERC. Nizar is also Scientific Director of The Chair Financial Risks of Louis Bachelier Group.
Prof. Alexander Veretennikov
University of Leeds
Alexander Veretennikov is Professor of probability at the University of Leeds and Chief Research Fellow at the Laboratory of Stochastic Analysis and its Applications at Higher School of Economics (Moscow). He has made significant contributions in several areas of probability, among which stochastic differential equations and approximations; Markov processes and stochastic control; mixing rates, averaging, diffusion approximation; large deviations; parameter estimations and mean-field models.


Power at the Nozzle
Regardless of the size or type of pump or the size of its drive motor, the real measure of power output is the power at the waterjet nozzle. This is a direct function of the nozzle pressure and the volume flow rate through the nozzle, which can be expressed by the following formula:
HP = 0.58PQ
HP equals the hydraulic power actually delivered through the nozzle in units of horsepower
- P is the water pressure at the nozzle in units of thousands of pounds per square inch (for example, use 55 for 55,000 psi). This can usually be closely approximated by the pump output pressure, but watch out for systems that try to operate relatively large nozzle orifices (say greater that 0.014”) using relatively long runs of ¼” ultra-high pressure tubing with many fittings. The pressure drop between the pump and the nozzle for such systems can be several thousand psi.
- Q is the volume flow rate through the nozzle, in units of gallons per minute
- The constant of 0.58 accounts for the units of measure being used in the equation.
This simple equation makes two things very clear:
- The size of pump motor and the exact design and brand of pump are not in the equation. All that really matters in determining true nozzle power are the nozzle pressure and the volume flow rate
- Both pressure and volume flow rate are in the equation and have equal effect. Power at the nozzle can be increased by increasing pressure or increasing volume flow rate or a combination of both.
So the next time you are trying to compare ultra-high pressure pumps, ignore the size of the drive motor shown on the manufacturer’s spec sheet. Go further down the spec sheet and find the values of the recommended continuous operating pressure and the corresponding output volume flow rate. Then grab your calculator and determine for yourself the actual effective output power.


Natomas USD: Teacher of the Year 2018 – Derek D. Dykstra
Representing the Natomas Unified School District for 2018 Teacher of the Year is Derek D. Dykstra. Derek teaches Calculus, Trigonometry, IB Mathematics, Link Crew Coordinator at Inderkum HS.
The Sacramento County Teachers of the Year program recognizes excellence in teaching within the county’s schools. Participating districts nominate individual teachers to receive this special recognition.
Derek spoke at the Teachers of the Year awards recognition dinner.
For additional information about the Sacramento Teacher of the Year program, please visit: https://www.scoe.net/News/Pages/2017/august/28toy.aspx


These are the sources and citations used to research Ethnomathematics. This bibliography was generated on Cite This For Me on
In-text: (Dickenson-Jones, 2008)
Your Bibliography: Dickenson-Jones, A., 2008. Transforming ethnomathematical ideas in western mathematics curriculum texts. Mathematics Education Research Journal, 20(3), pp.32-53.
In-text: (Ju, Moon and Song, 2015)
Your Bibliography: Ju, M., Moon, J. and Song, R., 2015. History of Mathematics in Korean Mathematics Textbooks: Implication for Using Ethnomathematics in Culturally Diverse School. International Journal of Science and Mathematics Education, 14(7), pp.1321-1338.
In-text: (Knijnik, 2012)
Your Bibliography: Knijnik, G., 2012. Differentially positioned language games: ethnomathematics from a philosophical perspective. Educational Studies in Mathematics, 80(1-2), pp.87-100.
In-text: (Rahman, 2013)
Your Bibliography: Rahman, K., 2013. Belonging and learning to belong in school: the implications of the hidden curriculum for indigenous students. Discourse: Studies in the Cultural Politics of Education, 34(5), pp.660-672.
In-text: (Rosa et al., 2016)
Your Bibliography: Rosa, M., D’Ambrosio, U., Orey, D., Shirley, L., Alangui, W., Palhares, P. and Gavarrete, M., 2016. Current and Future Perspectives of Ethnomathematics as a Program. 1st ed. Cham: Springer International Publishing.
10,587 students joined last month!


Fall is officially upon us. It’s the season of candy corn and corn mazes! So why not get some number practice in with this preschool corn counting activity?
This simple preschool activity allows your child to practice their counting by adding the correct number of ears of corn to corn stalks.
You can either use the paper ears of corn on the printable provided or add a little extra fun (and sugar) to the activity by using candy corn!
Corn Counting Preschool Activity
- Corn counting printable (download below)
- Cardstock paper (optional)
- Candy corn (optional)
Print out the corn counting activity printable available below. I like to print the corn stalk pages (pages 1 and 2) on cardstock paper so that they are a little sturdier.
Using the paper ears of corn
If you want to use the paper ears of corn provided, print page 3 of the printable and cut out the ears of corn.
Glue the correct number of ears of corn to each stalk depending on the number below.
Using candy corn or manipulatives
You can also choose to use candy corn, corn kernels, or another manipulative instead. Just place the correct number on each stalk of corn.
This preschool counting activity kept my son entertained for a long time while he carefully cut out each piece of corn and glued it in its place.
And if your child is like mine, they will be so pleased with their efforts when they finish and see their full field of corn!
Other posts you might be interested in:


Slowly realizing how unbelievably ignorant I am about grading and related issues, I went on a short trip and discovered these two articles that discuss grading on a bell curve. The second one is particularly interesting, as it uses this quote from Einstein (or rather a sign he had in his office) :
Not everything that counts can be counted, and not everything that can be counted counts
and includes a discussion of summative versus formative assessments.
For the mathematically challenged like me there are these two articles that explain how grading on a bell curve is done. The first gives the general idea, the second is a tutorial on how to calculate standard deviation using Microsoft Excel.
2 thoughts on “I’m grading on a bell curve, don’t know when I’ll be back again”
Fortunately at my school all I do is plug in what I have decided the grades should be and the university server curves them for me.


For a metric like conversion rate, a simple average over multiple days provides a misleading picture. For example, activity on the weekends is often much different than the weekdays. Here's how to do weighted averages in DoubleLoop so you can get an accurate sense of metric performance over time.
Instead of sending a metric like conversion rate to DoubleLoop, send the numerator and the denominator as separate metrics. For example, create two separate metrics for transactions and sessions.
Create a metric source in DoubleLoop I set "Calculated" as the source. This will allow you to select the numerator and denominator.
Attach a metric to your calculated metric source.
For the roll-up calculation for the metric, choose "Weighted average." When this option is selected, the map stats will divide the sum of the numerator values by the sum of the denominator values.


This is a rant about trig. I wouldn’t suggest reading this unless you’re really bored.
Ha, so I remember signing up for the 4 math classes at the beginning of the year, my mom ‘helping’… She thought that Adv. Algebra and Algebra 2 were the same class. And, when I told her it would be 4 math classes and I promised I’d be able to do it, I was sure I would be.
Trigonometry. Calculator this, calculator that. I’m in Adv. Algebra the so-called ‘hard’ math class before pre-cal. My lowest grade in Adv. Algebra is a 95, that I got on a quiz. I got a 99 on a test, a 100 on another quiz, etc.
But trig? Not so good, not at all. My high grade in trig is an 89 (Wait, thinking about it, I got a 95 on something, but that wasn’t a quiz… It might count the same, though… But still). Yeah. Not good. The only reason I’m typing this out is because I need to vent, because I’m worried. I shouldn’t be, there’s more than enough time to pull up my trig grade, but I’m having trouble understanding it…
And that poses a problem. I know very well I’ll pass Trig with an A average, but at what cost? What I’m worried about is not actually learning anything, just cramming and hoping to get lucky… Which isn’t good. Unlike Algebra 2, where I started the same way, I don’t have enough time to get lucky towards the end. There’s no second quarter to trig… I have to get my grade up NOW.
And, there is only about 4 or 5 weeks left in the class. This shorter quarter thing is hurting very, very bad.
I thought about staying after school… But it’s Mr. Jones. I don’t understand half of what he says, and he doesn’t do the explaining thing very well. My mom was good at trig, she says, so I have to get her to help me.
It’s funny, this seems to happen a lot. I’ve just underestimated trig, I think. It reminds me of Geometry. I hated Geometry, and I did a lot worse in Geometry at the beginning.
Typing this out makes me feel a lot better, which is good. Whoever invented Trig/Geometry deserves to die.
It’s too bad Trig is required for like… Everything in this school, or I would probably drop it.
If you made it all the way down to here (I feel sorry for you), post a comment that says, “The blue fish catches the red pineapple if the green stream is willing.”
Okay, I’m done boring you with my pitiful problems.
Now that you’ve skipped that mess, I remind you that the Super Bowl is today.
Anyone who likes football or even cares in the least bit, check my next post…


It’s been known for years that the way manufactures tally up hard drive capacity and the way computers tally up capacity are slightly different. We, as people, use the decimal system to count, as do the manufactures of hard drives. Computers, on the other hand, use the binary system.
Binary is base 2. Two states—on or off. Our regular decimal number system is base 10 (I’m guessing the significance of this has something to do with the number of fingers we have). Manufacturers count off in base 10 for the sake of simplicity and consistency. Computers count off in base 2 because of the nature of electricity and how it’s used in all things electronic.
So, when computers calculate the capacity of a hard drive, they count up all the available bytes. There are 8 bits to a byte. Bits are either a 1 or a 0. A byte is the smallest unit of storage available to a computer system, which can store a single ASCII character.
So, the next unit of measurement up from a byte is a kilobyte. The prefix “kilo” means “1,000”, so when counting in the decimal system, about 1,000 bytes equals 1 kilobyte. However, since computers run on the binary system, this number is actually 1,024 bytes.
Since the decimal system is in base 10, when you work with exponents in calculations, you must use 10 as a base (in other words, there are 10 different possible states of any one unit—0 to 9). So, to get a figure of 1,000 bytes, you take 10 and raise it by 3 (10^3).
Since the binary system is base 2, you must use a base of 2 (because there are two possible states of any one unit—0 to 1). In order to reach the approximate same value as the base 10 decimal system using whole numbers, the base will be raised to the power of 10 (2^10), which will result in 1,024 bytes.
Hopefully this is starting to become clear as to why the discrepancy exists. When a number system is referred to a base “x” system, the “x” stands for the number of different possible states a digit can be. In base 10, you can use digits 0,1,2,3,4,5,6,7,8, or 9. In base 2, you can use digits 0 or 1. So, in base 10, you are using powers of 10, while in base 2, you are using powers of 2.
In terms of capacity, in order to move up to the next unit of measurement (for example, from byte to kilobyte), powers of 1024 (rather than 1000) are used to calculate capacity.
So, 1,024 bytes = 1 kilobyte. 1,024 kilobytes = 1 megabyte. 1,024 megabytes = 1 gigabyte. 1,024 gigabytes = 1 terabyte.
Referring back to earlier when saying that hard drives determine capacity by counting the number of bytes, this means that the computer recognized a byte as the smallest measurable unit for data storage. So, since each unit of measurement in increasing magnitude is 1,024 more than the previous measurement of magnitude, you get this:
1 B = 1 byte
1 KB = 2^10 bytes = 1,024 bytes
1 MB = 2^20 bytes = 10,485,76 bytes
1GB = 2^30 bytes = 1,073,741,824 bytes
…and so on.
Who can remember that 1,073,741,824 bytes is 1GB? I surely can’t. This is why manufactures find it easier to work with a base 10 system—all the numbers are nice and even! This is how manufacturers see capacity:
1 B = 1 byte
1 KB = 10^3 bytes = 1,000 bytes
1 MB = 10^6 bytes = 1,000,000 bytes
1GB = 10^9 bytes = 1,000,000,000 bytes
…and so on.
Notice the difference?
So, when a manufacturer advertises an 80GB drive, what they say you’re getting in terms of bytes is 80,000,000,000 bytes. This, of course, is capacity in terms of the base 10 system.
So, here’s the part you’ve been waiting for…
How to get the real capacity of your hard drive
There are three calculations to perform on the advertised capacity of 80GB. There are 3 calculations because unit of GB is three orders of magnitude above the unit of B (byte).
So, take the advertised capacity and divide it by 1.024 three times. If you do this correctly, an advertised capacity of 80GB will yield an actual capacity of 74.5GB (74,505,805,970 bytes)—the total capacity that is usable under a binary number system.
Try this method with large capacity drives, such as 300GB or 320GB. As you’ll be able to see, you won’t get exactly the capacity advertised. For reference, here’s a list of common drive capacities matched with their actual data capacities (rounded to the nearest hundredths place):
- 10 GB = 9.31 GB
- 20 GB = 18.63 GB
- 30 GB = 27.94 GB
- 36 GB = 33.53 GB
- 40 GB = 37.25 GB
- 60 GB = 55.88 GB
- 74 GB = 68.91 GB
- 80 GB = 74.51 GB
- 100 GB = 93.13 GB
- 120 GB = 111.76 GB
- 160 GB = 149.01 GB
- 180 GB = 167.64 GB
- 200 GB = 186.26 GB
- 250 GB = 232.83 GB
- 300 GB = 279.40 GB
- 320 GB = 298.02 GB
Yes, this is a little misleading, hence the recent lawsuit against Western Digital for advertising one capacity for a hard drive, and having it show up as a slightly different capacity when used in a computer. However, this is not the fault of WD, but the fault of the conversion process between the two number systems; similar to the conversion process between the Fahrenheit and Celsius temperature scales.