Domain 1 - Math and Science.docx

**Domain: 1 Advanced Science and Math** +-----------------------------------+-----------------------------------+ | **Conversions:** | 1 m = 100 cm | | | | | **[Length]** | 1 m = 1000...

**Domain: 1 Advanced Science and Math** +-----------------------------------+-----------------------------------+ | **Conversions:** | 1 m = 100 cm | | | | | **[Length]** | 1 m = 1000 mm | | | | | | 1 m = 1,000,000 microns | | | | | | 1 km = 1000 m | | | | | | 1 mile = **5280** feet | | | | | | 1 mile =1609 meter | | | | | | **1 mile/hour = 1.47 ft/second** | | | | | | **1 inch =2.54 cm** | | | | | | **1foot = 30.48 cm** | | | | | | **1meter= 3.2 foot** | | | | | | **1foot = 12 inch** | +===================================+===================================+ | | +---------+---------+---------+ | | | | **Lengt | **Energ | | | | | | h** | y** | | | | | +---------+---------+---------+ | | | | 2.54 cm | 1 cal = | | | | | | = 1 | 0.00396 | | | | | | inch | 8 | | | | | | | Btu | | | | | +---------+---------+---------+ | | | | 25.4 mm | 1 cal = | | | | | | = 1 | 4.187 J | | | | | | inch | | | | | | +---------+---------+---------+ | | | | **12 | **1 Btu | | | | | | inches | = 252 | | | | | | = 1 | cal** | | | | | | foot** | | | | | | +---------+---------+---------+ | | | | 3 feet | | | | | | | = 1 | | | | | | | yard | | | | | | +---------+---------+---------+ | | | | 5280 | **Veloc | | | | | | feet = | ity** | | | | | | 1 mile | | | | | | +---------+---------+---------+ | | | | 1760 | 1 ft/s | | | | | | yards = | = | | | | | | 1 mile | 0.3048 | | | | | | | m/s | | | | | +---------+---------+---------+ | | | | **1.6 | 1 ft/s | | | | | | Km = 1 | = | | | | | | mile** | 0.8618 | | | | | | | mi/h | | | | | +---------+---------+---------+ | | | | 0.868 | 1 ft/s | | | | | | nautica | = | | | | | | l | 0.5921 | | | | | | miles = | knots | | | | | | 1 US | | | | | | | mile | | | | | | +---------+---------+---------+ | | | | **Area* | 1 m/s = | | | | | | * | 3.281 | | | | | | | ft/s | | | | | +---------+---------+---------+ | | | | **1 sq. | 1 m/s = | | | | | | in. = | 2.237 | | | | | | 6.452 | mi/h | | | | | | sq. | | | | | | | cm** | | | | | | +---------+---------+---------+ | | | | 1 sq. | 1 mi/h | | | | | | in. = | = | | | | | | 6452 | 0.4470 | | | | | | sq. mm | m/s | | | | | +---------+---------+---------+ | | | | **1 sq. | 1 mi/h | | | | | | ft = | = 1.467 | | | | | | 144 sq. | ft/s | | | | | | in.** | | | | | | +---------+---------+---------+ | | | | 1 sq. | 1 knot | | | | | | ft = | = | | | | | | 0.09290 | 0.5148 | | | | | | sq. m | m/s | | | | | +---------+---------+---------+ | | | | 1 sq. | 1 knot | | | | | | yd. = 9 | = 1.151 | | | | | | sq. ft | mi/h | | | | | +---------+---------+---------+ | | | | **Volum | 1 knot | | | | | | e** | = 1.689 | | | | | | | ft/s | | | | | +---------+---------+---------+ | | | | **1 | **Densi | | | | | | cm^3^ = | ty** | | | | | | 1 mL** | | | | | | +---------+---------+---------+ | | | | **1 | 1 | | | | | | in^3^ = | lb/cu. | | | | | | 16.39 | ft = | | | | | | cm^3^** | 0.01602 | | | | | | | cu. cm | | | | | +---------+---------+---------+ | | | | **1 | 1 g/cu. | | | | | | ft^3^ = | cm = | | | | | | 1728 | 62.42 | | | | | | in^3^** | lb/cu. | | | | | | | ft | | | | | +---------+---------+---------+ | | | | 1 cu. | 1 g/cu. | | | | | | ft = | cm = | | | | | | 0.02832 | 1000 | | | | | | cu. m | kg/cu. | | | | | | | m | | | | | +---------+---------+---------+ | | | | 1 L = | 1 | | | | | | 1.057 | kg/cu. | | | | | | quarts | m = | | | | | | (US) | 0.001 | | | | | | | g/cu. | | | | | | | cm | | | | | +---------+---------+---------+ | | | | 0.9463 | **Press | | | | | | L = 1 | ure** | | | | | | quart | | | | | | +---------+---------+---------+ | | | | **7.4 | 1 psia | | | | | | US | = 6.895 | | | | | | gallon | kN/m2 | | | | | | = 1 | | | | | | | ft^3^** | | | | | | +---------+---------+---------+ | | | | 1 US | **1 | | | | | | gallon | psia = | | | | | | = | 0.0680 | | | | | | 0.8327 | atm** | | | | | | Imperia | | | | | | | l | | | | | | | gallons | | | | | | +---------+---------+---------+ | | | | | **1 | | | | | | | psia = | | | | | | | 27.67 | | | | | | | in. | | | | | | | H2O** | | | | | | | | | | | | | | **1 bar | | | | | | | = 14.5 | | | | | | | PSI= | | | | | | | 0.98 | | | | | | | atm=760 | | | | | | | mm Hg= | | | | | | | 10^5^ | | | | | | | N/m^2^* | | | | | | | * | | | | | +---------+---------+---------+ | | | | | **1 | | | | | | | psia = | | | | | | | 51.72 | | | | | | | mm Hg** | | | | | +---------+---------+---------+ | | | | | **1 | | | | | | | psig = | | | | | | | ADD | | | | | | | 14.7 | | | | | | | psia** | | | | | +---------+---------+---------+ | | | | | 1 mm Hg | | | | | | | (Torr) | | | | | | | = | | | | | | | 0.01934 | | | | | | | psia | | | | | +---------+---------+---------+ | | | | | | | | | | +---------+---------+---------+ | | | | **Mass | | | | | | | and | | | | | | | Weight* | | | | | | | * | | | | | | +---------+---------+---------+ | | | | **16 | | | | | | | ounces( | | | | | | | oz) | | | | | | | = 1 | | | | | | | lb** | | | | | | +---------+---------+---------+ | | | | 1 g = | | | | | | | 1000 mg | | | | | | +---------+---------+---------+ | | | | **2.205 | | | | | | | lb = | | | | | | | 1kg** | | | | | | +---------+---------+---------+ | | | | **1 ton | | | | | | | (US) = | | | | | | | 2000 | | | | | | | lb** | | | | | | +---------+---------+---------+ | | | | 1 tonne | | | | | | | (Metric | | | | | | | ton) = | | | | | | | 1000 kg | | | | | | +---------+---------+---------+ | | | | 1 dram | | | | | | | = | | | | | | | 1771.85 | | | | | | | mg | | | | | | +---------+---------+---------+ | | | | 1 bar = | 1 | | | | | | 100 | cal/g/° | | | | | | kN/m^2^ | C | | | | | | | = 1 | | | | | | | Btu/lb/ | | | | | | | °F | | | | | +---------+---------+---------+ | | | | 1 kN/m2 | **Conce | | | | | | = | ntratio | | | | | | 0.1450 | n** | | | | | | psia | | | | | | +---------+---------+---------+ | | | | 1 bar = | **1 ppm | | | | | | 0.9869 | = 1 | | | | | | atm | mg/L** | | | | | +---------+---------+---------+ | | | | 1 kN/m2 | | | | | | | = | | | | | | | 0.00986 | | | | | | | 9 | | | | | | | atm | | | | | | +---------+---------+---------+ | | | | 1 bar = | 1 mg/m3 | | | | | | 1.020 | = 1 × | | | | | | kg/cm2 | 10−9 | | | | | | | g/cm3 | | | | | +---------+---------+---------+ | | | | **Heat | 1 g/cm3 | | | | | | Capacit | = 1 × | | | | | | y** | 109 | | | | | | | mg/m3 | | | | | +---------+---------+---------+ | | | | 1 | 1 g/m3 | | | | | | Btu/lb/ | = 62.42 | | | | | | °F | lb/ft3 | | | | | | = 1 | | | | | | | cal/g/° | | | | | | | C | | | | | | +---------+---------+---------+ | | | | 1 | 1 | | | | | | Btu/lb/ | lb/ft3 | | | | | | °F | = | | | | | | = 4187 | 0.01602 | | | | | | J/kg·K | g/cm3 | | | | | +---------+---------+---------+ | | | | **Force | | | | | | | , | | | | | | | Pressur | | | | | | | e, | | | | | | | or | | | | | | | Stress* | | | | | | | * | | | | | | +---------+---------+---------+ | | | | **Pound | **4.45* | **Newto | | | | | -force* | * | ns** | | | | | * | | | | | | +---------+---------+---------+ | | | | Pound-f | 6.89 | Kilopas | | | | | orce/sq | | cals | | | | | uare | | | | | | | inch | | | | | | +---------+---------+---------+ | | | | **Illum | | | | | | | ination | | | | | | | ** | | | | | | +---------+---------+---------+ | | | | **Foot- | **10.76 | **Lux** | | | | | candle* | ** | | | | | | * | | | | | | +---------+---------+---------+ | | | | Foot-la | 3.426 | Candela | | | | | mbert | | /square | | | | | | | meter | | | | +---------+---------+---------+ | | | | | | ----------------- ------------- | | | ----- -------------------- | | | **Length** | | | | | | Inches 25.4 | | | Millimeters | | | Feet 0.305 | | | Meters | | | Yards 0.914 | | | Meters | | | Miles 1.61 | | | Kilometers | | | **Area** | | | | | | Square inches 645.2 | | | Square millimeters | | | Square feet 0.093 | | | Square meters | | | Square yards 0.836 | | | Square meters | | | Acres 0.405 | | | Hectares | | | Square miles 2.59 | | | Square kilometers | | | **Volume** | | | | | | Fluid ounce 29.57 | | | Milliliters | | | **Gallons** **3.785** | | | **Liters** | | | Cubic feet 0.028 | | | Cubic meters | | | Cubic yards 0.765 | | | Cubic meters | | | **Mass** | | | | | | Ounce 28.35 | | | Grams | | | Pounds 0.454 | | | Kilograms | | | **Temperature** | | | | | | **Fahrenheit** **5(°F − 32)/ | | | 9** **Celsius** | | | Celsius 9(°C + 32)/5 | | | Fahrenheit | | | **Celsius** **°C + 273** | | | **Kelvin** | | | **Fahrenheit** **°F + 460** | | | **Rankine** | | | ----------------- ------------- | | | ----- -------------------- | | | | | | **STP (industrial hygiene) = 25°C | | | and 1 atm** | | | | | | 1 tesla = 10,000 gauss | | | | | | 1 becquerel = 1 disintegration/s | +-----------------------------------+-----------------------------------+ | **Volume** | 1 liter = 1000 cm3 | | | | | | 1 liter = 1000 ml | | | | | | 1 m3 = 1000 liter | | | | | | 1 liter = 1.06 qt = 61.02 in^3^ = | | | 0.03531 ft^3^ | | | | | | 1 ml = 1 cm3 | | | | | | 1% by volume = 10,000 part per | | | million (ppm) | | | 1,000,000/100=10,000 | | | | | | **1 ft^3^ = 7.5 gallons** | | | | | | **1 gallon of water = 8.34 lb** | | | | | | **1 gallon = 3.78 liters** | | | | | | 1 liter = 61.02 cu in | | | | | | 1 hour = 3600 seconds | +-----------------------------------+-----------------------------------+ | **Mass** | 1 kg = 2.2 lb | | | | | | 1 lb = 454 gram | | | | | | 1 ton (US) =2000 lb | +-----------------------------------+-----------------------------------+ | **Pressure** | 1 atm = 14.7 psi = 760 mm Hg = | | | 33.90 ft. H20 = 760 torr = 101.3 | | **Temperature** | kPa | | | | | | Tc=Tf-32/1.8 , Tk=Tc+273 , F=460 | | | + R | | | | | | To convert to absolute | | | temperature scales use: | | | | | | o*R* = o*F* + 460 | | | | | | o*K* = o*C* + 273 | +-----------------------------------+-----------------------------------+ | **Force** | 1 kilogram- = 9.80665 newton | | | \[N\] | +-----------------------------------+-----------------------------------+ | **Energy Unit Conversion** | 1 calorie = 4.186 Joule | | | | | | 1 BTU (British thermal unit) = | | | 1055 Joule | | | | | | 1 foot-pound=1.356 Joule | | | | | | 1 joule = 1 kg · m/s2. | +-----------------------------------+-----------------------------------+ | **Radiation** | 1 rad = 10‐2 gray , 1 rem = 10‐2 | | | sievert , 1 curie = 3.7x1010 | | | becquerel , | | | | | | 1 becquerel = 1 | | | disintegration/sec | +-----------------------------------+-----------------------------------+ | **Density of Water** | 1 gm/cm3 = 1.94 slugs/ft3 (weight | | | density = 62.4 lb/ft3) | +-----------------------------------+-----------------------------------+ | **Light** | 1 candela = 1 lumen/steradian | | | | | | 1 footcandle = 10.76 candela/m2 = | | | 10.76 lux | +-----------------------------------+-----------------------------------+ | **PHYSICAL CONSTANTS** | acceleration of gravity = 32.2 | | | ft/sec^2^ = 9.8 m/sec2 | | | | | | velocity of light = 3.0 x 10^8^ | | | m/sec | | | | | | Planck's constant = 6.626 x | | | 10^‐34^ J‐sec | | | | | | Avogadro's number = 6.024 x | | | 10^23^/ gram‐mole | +-----------------------------------+-----------------------------------+ | **BOOLEAN POSTULATES** | | +-----------------------------------+-----------------------------------+ | **Area** | To find the area of a | | | **rectangle**, you use this | | | formula: | | | | | | *Area = length \* width* | | | | | | The area of a **square** is found | | | with this formula: | | | | | | *Area = s^2^, where s = side* | | | | | | The formula for the area of a | | | triangle is: | | | | | | *Area = (1/2) b \* h, where b = | | | base and h = height* | | | | | | To find the area of a circle, use | | | this formula: | | | | | | *Area = π \* r^2^, where r = | | | radius* | +-----------------------------------+-----------------------------------+ | **Volume** | +---------+---------+---------+ | | | | **Shape | **Volum | **Varia | | | | | s** | e | bles** | | | | | | Formula | | | | | | | ** | | | | | +=========+=========+=========+ | | | | Rectang | V = l × | l = | | | | | ular | w × h | Length | | | | | Solid | | | | | | | or | | w = | | | | | Cuboid | | Width | | | | | | | | | | | | | | h = | | | | | | | Height | | | | +---------+---------+---------+ | | | | Cube | V = | a = | | | | | | a^3^ | Length | | | | | | | of edge | | | | | | | or side | | | | +---------+---------+---------+ | | | | Cylinde | V = | r = | | | | | r | πr^2^h | Radius | | | | | | | of the | | | | | | | circula | | | | | | | r | | | | | | | base | | | | | | | | | | | | | | h = | | | | | | | Height | | | | +---------+---------+---------+ | | | | Prism | V = B × | B = | | | | | | h | Area of | | | | | | | base, | | | | | | | (B = | | | | | | | side^2^ | | | | | | |  or | | | | | | | length. | | | | | | | breadth | | | | | | | ) | | | | | | | | | | | | | | h = | | | | | | | Height | | | | +---------+---------+---------+ | | | | Sphere | V = | r = | | | | | | (4⁄3)πr | Radius | | | | | | ^3^ | of the | | | | | | | sphere | | | | +---------+---------+---------+ | | | | Pyramid | V = | B = | | | | | | (1⁄3) × | Area of | | | | | | B × h | the | | | | | | | base, | | | | | | | | | | | | | | h = | | | | | | | Height | | | | | | | of the | | | | | | | pyramid | | | | +---------+---------+---------+ | +-----------------------------------+-----------------------------------+ | | | +-----------------------------------+-----------------------------------+ | **TRIGONOMETRIC FUNCTIONS** | Right Triangle Definitions for | | | Trigonometry Functions - dummies | | | | | | **C^2^= a^2^ + b^2^ -- 2ab cos | | | ^0^C** | | | | | | **A/SinA=b/Sinb=c/Sinc** | +-----------------------------------+-----------------------------------+ | **Kinetic Energy** | *v* = speed of the object | | | (velocity) | +-----------------------------------+-----------------------------------+ | **Potential Energy** | | +-----------------------------------+-----------------------------------+ | **Elastic Potential Energy** | energy stored in elastic | | | materi­als as the result of their | | | stretching or compressing | | | | | | **Hooke's law**, states that if a | | | spring is not stretched or | | | compressed, then there is no | | | elastic potential energy stored | | | in it, The spring is said to be | | | at its **equilibrium position.** | +-----------------------------------+-----------------------------------+ | **Force** | **A newton N***:* is the amount | | | of force required to give a 1-kg | | | mass an acceleration of 1 m/s2. | | | | | | **Tension forces** are required | | | to pull an object (opposite of | | | compression). | | | | | | **Spring force** exerted by a | | | compressed or stretched spring | +-----------------------------------+-----------------------------------+ | **Frictional Force** | *N* = force acting on the surface | | | in a direction that is normal | | | (perpendicu­lar) to the surface | | | (N) | | | | | | 1 Newton (N) = 1 Kg\*m/s2. 1 kg = | | | 2.2 lb | | | | | | F= 40 \* 9.8 = 392 N | | | | | | **F = μN = 0.6 x 392 =** 235.2 N | | | | | | If there angle = **Nsin angle + μ | | | \*N cos angle)** | +-----------------------------------+-----------------------------------+ | **Force and Distance** | **F1D1 = F2D2,** | +-----------------------------------+-----------------------------------+ | **Momentum** | | +-----------------------------------+-----------------------------------+ | **Velocity** | **v = v~0~ + at , v** = final | | | velocity, meters per second, m/s | | | | | | **vo** = original velocity at the | | | start of the acceleration, m/s , | | | | | | **a** = acceleration m/s2 , **t** | | | = time, seconds, | +-----------------------------------+-----------------------------------+ | | **S = 𝐯~𝟎~𝐭 + ½ 𝐚𝐭^𝟐^, 𝐯^𝟐^ | | | =𝐯~𝟎~^𝟐^ + 𝟐𝐚𝐬** | | | | | | **s** = distance from its | | | original position, m | | | | | | **vo** = initial velocity before | | | the start of the acceleration, | | | m/s | | | | | | **a** = acceleration m/s^2^ , | | | **t** = time, seconds, s | +-----------------------------------+-----------------------------------+ | **Work done** | **W = FS , W** = work done, J, | | | **F** = force, Newton, N | | | | | | **S** = distance from its | | | original position in m | +-----------------------------------+-----------------------------------+ | **Newton second Law** | **F = ma/g** , m is the mass , a | | | : acceleration, g = 9.8 or | | | 32.2(us) | +-----------------------------------+-----------------------------------+ | | A force is acting at 30° with the | | | horizontal on an object that is | | | displaced 3 m along the | | | horizontal direction. The normal | | | force on the surface is 400 N and | | | the coefficient of friction is | | | 0.35. Calculate the work done by | | | the force. | | | | | | *F*~fric~ = 400 N(0.35) | | | | | | W~modified~ = (140 N)(3 m)(cos | | | 30°) , *W*~modified~ = 363.7 N. | +-----------------------------------+-----------------------------------+ | **Statistics** | | +-----------------------------------+-----------------------------------+ | **Definition** | **histogram** is a graph used to | | | distribute frequency of the data | | | (incident) | | | | | | **mean** is the same as the | | | average value of a data set and | | | is found using a calculation | | | **ΣXn/n ** | | | | | | **Median** is the **central | | | number** of a data set.( If there | | | are 2 numbers in the middle, the | | | median is the average of those 2 | | | numbers.) | | | | | | **Mode** is the number in a data | | | set that occurs most frequently. | +-----------------------------------+-----------------------------------+ | **Left skewed** | Mean \< Median \< Mode | | | | | | -ve skewed, longer tails at lower | | | values , most of values are at | | | the right of Mean | | | | | |  | +-----------------------------------+-----------------------------------+ | **Right skewed** | Mode \< Median \< Mean , most of | | | values are at the left of mean | | | | | | +ve skewed, longer tails at | | | Higher values | | | | | | Mean vs. median vs. mode in right | | | skewed distribution | | | | | | **No Skew -[symmetrical | | | distribution](https://www.statolo | | | gy.org/symmetric-distribution/):* | | | * Mean | | | = Median = Mode | +-----------------------------------+-----------------------------------+ | **Standard deviation** | **Central tendency** is the | | | measure of **four** Mean, Median, | | | Mode and Standard deviation | | | | | | a **measure** of the **average** | | | **distance** of all | | | **observations** from the | | | **mean**. | | | | | | Variance = **Σ(X-X~av~)^2^/N.** | | | | | | **Standard Deviation S = Square | | | Root** **(X-X~av~)^2^/N** | | | | | | 1 std dev = 68% of the data set | | | | | | 2 std dev = 95.45% of the data | | | set | | | | | | 3 std dev = 99.73% of the data | | | set | | | | | | **Sx** = standard deviation, | | | **r** = correlation coefficient | +-----------------------------------+-----------------------------------+ | **Statistic and parameter** | **Statistic**: **Numerical** | | | value that **describes** data | | | taken from a **sample** (a | | | **subset** of the | | | **population**), we use | | | **F**-**test** to **measure** the | | | **accuracy**. | | | | | | **Parameter**: is to describe the | | | **characteristic** of the | | | **population**, it summaries | | | **data** and the entire | | | **population** | +-----------------------------------+-----------------------------------+ | **Null Hypothesis** | No **significant** **difference** | | | between the **population**, if | | | any observed **difference** is | | | due to **sampling** or | | | experimental error H0= M1=M2 no | | | difference between **population** | | | | | | Used in **conjunction** with | | | **95**% **confidence** means that | | | there **95**% chance of **true** | +-----------------------------------+-----------------------------------+ | **Type I error-False +ve- Alfa** | **reject** the **null** | | | **hypothesis** when its **true** | | | (you **should** **accept** it), | | | that there's a **difference** | | | between the **means** when there | | | is **no** actual **difference** | +-----------------------------------+-----------------------------------+ | **Type II error-False --ve-Beta** | **Reject false null Hypothesis, | | | no difference in mean,** where | | | there **is actual difference** | | | | | | **accept the null hypothesis when | | | its false (you should reject | | | it)** | +-----------------------------------+-----------------------------------+ | **Coefficient variation CV** | Relative standard deviation RSD, | | | measure of the dispersion of | | | probability distribution or | | | frequency distribution and define | | | the ration of SD to the mean | +-----------------------------------+-----------------------------------+ | **Coefficient of variation-CV** | **S/X~mean~** = % | +-----------------------------------+-----------------------------------+ | **Cumulative error** | Is used to **calculate** the | | | **upper confidence limit** and | | | **lower confidence limit** for | | | air sampling, due to common | | | **errors**: **calibration**, | | | **lab**, **instrument** | | | measurement, and **correction** | | | errors during sampling | | | calculation as sample size | | | **increases** the **result** and | | | **assessment** of mean | | | **enhanced** | +-----------------------------------+-----------------------------------+ | **Precision and accuracy** | **Accuracy**: how close the | | | **measurement** is to the | | | **actual** or **accepted** | | | value-**F-test** | | | | | | **Precision**: the value of | | | **SD** of **repeated** | | | **measurement** of the same | | | **true** or **accepted** | | | **value** with **same** | | | **measurement** method | +-----------------------------------+-----------------------------------+ | **Lower confidence limit-LCL** | Used by the OSHA officer to | | | determine if the measured is | | | exceed the PEL | | | | | | If LCL \> PEL **Noncompliance** , | | | PEL \> LCL **compliance**, | | | | | | **Overexposure** TWA or PEL \>1 | | | and LCL \