Unit Conversions in Science and Math
348 Questions
0 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the formula to calculate the kinetic energy of an object?

  • K.E. = μN
  • K.E. = ½mv² (correct)
  • K.E. = mgh
  • K.E. = Fx

    • What is the unit of gravitational acceleration on the surface of the earth?

  • N/kg
  • kg/m
  • m/s² (correct)
  • m/s

    • What is the formula to calculate the elastic potential energy stored in a spring?

  • P.E. = ½kx² (correct)
  • P.E. = kx²
  • P.E. = k/x
  • P.E. = ½kx

    • What type of force is required to pull an object, opposite of compression?

    <p>Tension force</p> Signup and view all the answers

    What is the coefficient of friction in the given problem, if a 40-kg block of wood is sitting on a cement floor?

    <p>0.6</p> Signup and view all the answers

    What is the formula to calculate the frictional force that must be overcome to move an object?

    <p>F = μN</p> Signup and view all the answers

    If 1 mile is equal to 1609 meters, how many meters are in 5 miles?

    <p>8045 meters</p> Signup and view all the answers

    What is the equivalent of 1 kilometer in meters?

    <p>1000 meters</p> Signup and view all the answers

    If 1 inch is equal to 2.54 centimeters, how many centimeters are in 10 inches?

    <p>25.4 centimeters</p> Signup and view all the answers

    What is the equivalent of 1 foot in centimeters?

    <p>30.48 centimeters</p> Signup and view all the answers

    If 1 mile per hour is equal to 1.47 feet per second, how many feet per second are in 5 miles per hour?

    <p>7.55 feet per second</p> Signup and view all the answers

    What is the equivalent of 1 meter per second in miles per hour?

    <p>2.237 miles per hour</p> Signup and view all the answers

    If 1 cubic foot is equal to 0.02832 cubic meters, how many cubic meters are in 5 cubic feet?

    <p>0.1416 cubic meters</p> Signup and view all the answers

    What is the equivalent of 1 pound per cubic foot in grams per cubic centimeter?

    <p>0.06242 grams per cubic centimeter</p> Signup and view all the answers

    What is the value of 1 kilogram-force in newton?

    <p>9.80665 newton</p> Signup and view all the answers

    What is the unit of energy in which 1 BTU (British thermal unit) is equal to?

    <p>1055 Joule</p> Signup and view all the answers

    What is the formula for the area of a triangle?

    <p>Area = (1/2) b * h</p> Signup and view all the answers

    What is the value of the acceleration of gravity in ft/sec^2?

    <p>32.2 ft/sec^2</p> Signup and view all the answers

    What is the formula for the volume of a sphere?

    <p>V = (4/3)πr^3</p> Signup and view all the answers

    What is the value of 1 candela in lumens per steradian?

    <p>1 lumen/steradian</p> Signup and view all the answers

    What is the formula for kinetic energy?

    <p>K.E. = ½ mv^2</p> Signup and view all the answers

    What is the value of 1 rad in gray?

    <p>10^-2 gray</p> Signup and view all the answers

    What is the formula for the area of a circle?

    <p>Area = πr^2</p> Signup and view all the answers

    What is the value of the velocity of light in m/sec?

    <p>3.0 x 10^8 m/sec</p> Signup and view all the answers

    What is the characteristic of a left skewed distribution?

    <p>Mean &lt; Median &lt; Mode</p> Signup and view all the answers

    What is the percentage of the data set that lies within 2 standard deviations from the mean?

    <p>95.45%</p> Signup and view all the answers

    What is the term for a measure of the average distance of all observations from the mean?

    <p>Standard Deviation</p> Signup and view all the answers

    Which of the following is a characteristic of a symmetrical distribution?

    <p>Mean = Median = Mode</p> Signup and view all the answers

    What is the term for a numerical value that describes data taken from a sample?

    <p>Statistic</p> Signup and view all the answers

    What is the percentage of the data set that lies within 1 standard deviation from the mean?

    <p>68%</p> Signup and view all the answers

    What is the primary purpose of a parameter in statistics?

    <p>To describe the characteristic of a population</p> Signup and view all the answers

    What is the null hypothesis in hypothesis testing?

    <p>A hypothesis that there is no significant difference between populations</p> Signup and view all the answers

    What is the consequence of a Type I error?

    <p>Rejecting a true null hypothesis</p> Signup and view all the answers

    What is the coefficient of variation (CV) in statistics?

    <p>The ratio of the standard deviation to the mean</p> Signup and view all the answers

    What is the purpose of calculating the cumulative error in air sampling?

    <p>To calculate the upper confidence limit and lower confidence limit</p> Signup and view all the answers

    What is the difference between precision and accuracy?

    <p>Precision is the value of the standard deviation, while accuracy is how close the measurement is to the actual value</p> Signup and view all the answers

    What is the purpose of the lower confidence limit (LCL) in OSHA regulations?

    <p>To determine if the measured value exceeds the PEL</p> Signup and view all the answers

    What is the consequence of a Type II error?

    <p>Accepting a false null hypothesis</p> Signup and view all the answers

    What is the physical quantity that is measured in units of N/m?

    <p>Spring constant</p> Signup and view all the answers

    A 2-kg block is moving at a velocity of 5 m/s. What is its kinetic energy?

    <p>25 J</p> Signup and view all the answers

    A spring is stretched by 0.2 m and has a spring constant of 100 N/m. What is its elastic potential energy?

    <p>2 J</p> Signup and view all the answers

    A 30-kg box is being pulled up a slope with a force of 100 N. If the coefficient of friction is 0.4, what is the normal force acting on the box?

    <p>140 N</p> Signup and view all the answers

    A 50-kg block is resting on a horizontal surface with a coefficient of friction of 0.2. What is the minimum force required to overcome the frictional force?

    <p>98 N</p> Signup and view all the answers

    A spring is compressed by 0.1 m and has a spring constant of 50 N/m. What is the force exerted by the spring?

    <p>10 N</p> Signup and view all the answers

    What is the equivalent of 1 kilopascal in pounds per square inch?

    <p>6.89</p> Signup and view all the answers

    If 1 gallon of water is equal to 8.34 pounds, how many pounds are in 5 gallons of water?

    <p>41.7</p> Signup and view all the answers

    What is the equivalent of 1 British Thermal Unit (Btu) in joules?

    <p>1055</p> Signup and view all the answers

    If 1 foot-candle is equal to 10.76 lux, how many lux are in 5 foot-candles?

    <p>53.8</p> Signup and view all the answers

    What is the equivalent of 1 tesla in gauss?

    <p>10,000</p> Signup and view all the answers

    If 1 curie is equal to 3.7 × 10^10 becquerel, how many becquerel are in 2 curies?

    <p>7.4 × 10^10</p> Signup and view all the answers

    What is the equivalent of 1 atmosphere in millimeters of mercury?

    <p>760</p> Signup and view all the answers

    If 1 rad is equal to 10^-2 gray, how many gray are in 5 rad?

    <p>0.05</p> Signup and view all the answers

    What is the equivalent of 1 rem in sievert?

    <p>0.01</p> Signup and view all the answers

    If 1 liter is equal to 1000 cubic centimeters, how many cubic centimeters are in 5 liters?

    <p>5000</p> Signup and view all the answers

    What is the characteristic of a distribution where the Mean is less than the Median and the Mode?

    <p>Left skewed distribution</p> Signup and view all the answers

    What percentage of the data set lies within 3 standard deviations from the mean?

    <p>99.73%</p> Signup and view all the answers

    What is the term for a measure of the spread of a distribution?

    <p>Standard deviation</p> Signup and view all the answers

    What is the characteristic of a right skewed distribution?

    <p>Mode is less than the Median and the Mean</p> Signup and view all the answers

    What is the purpose of a statistic in statistics?

    <p>To describe a sample of the population</p> Signup and view all the answers

    What is the term for a measure of the central tendency of a distribution?

    <p>Mean</p> Signup and view all the answers

    What is the force acting on an object that is displaced 3 m along the horizontal direction, given a normal force of 400 N and a coefficient of friction of 0.35?

    <p>363.7 N</p> Signup and view all the answers

    A force of 40 N is acting on an object at an angle of 30° with the horizontal. What is the modified work done by the force, given a displacement of 3 m?

    <p>363.7 N</p> Signup and view all the answers

    What is the momentum of an object with a mass of 2 kg and a velocity of 5 m/s?

    <p>20 kg m/s</p> Signup and view all the answers

    What is the velocity of an object after 5 seconds, given an initial velocity of 2 m/s and an acceleration of 3 m/s²?

    <p>13 m/s</p> Signup and view all the answers

    What is the work done by a force of 20 N on an object displaced 4 m, given a coefficient of friction of 0.2?

    <p>80 J</p> Signup and view all the answers

    What is the median of a data set with the following values: 2, 4, 6, 8, 10?

    <p>6</p> Signup and view all the answers

    What is the force acting on an object with a mass of 3 kg, given an acceleration of 2 m/s²?

    <p>6.9 N</p> Signup and view all the answers

    What is the distance traveled by an object with an initial velocity of 3 m/s, an acceleration of 2 m/s², and a time of 5 seconds?

    <p>30.5 m</p> Signup and view all the answers

    What is the primary purpose of a parameter in statistics?

    <p>To describe the characteristic of a population</p> Signup and view all the answers

    What is the consequence of a Type I error in hypothesis testing?

    <p>Rejecting the null hypothesis when it is true</p> Signup and view all the answers

    What does the coefficient of variation (CV) measure in statistics?

    <p>The ratio of the standard deviation to the mean</p> Signup and view all the answers

    What is the purpose of calculating the cumulative error in air sampling?

    <p>To calculate the upper and lower confidence limits</p> Signup and view all the answers

    What is the difference between precision and accuracy?

    <p>Precision is the repeatability of the measurement, while accuracy is the closeness to the actual value</p> Signup and view all the answers

    What is the purpose of the lower confidence limit (LCL) in OSHA regulations?

    <p>To determine if the measured value exceeds the PEL</p> Signup and view all the answers

    What is the consequence of a Type II error in hypothesis testing?

    <p>Accepting the null hypothesis when it is false</p> Signup and view all the answers

    What is the purpose of a null hypothesis in hypothesis testing?

    <p>To provide a basis for testing a statistical hypothesis</p> Signup and view all the answers

    If 1 mile is equal to 1609 meters, how many meters are in 3 miles?

    <p>4827 meters</p> Signup and view all the answers

    What is the equivalent of 1 yard in meters?

    <p>0.9144 meters</p> Signup and view all the answers

    If 1 foot is equal to 12 inches, how many inches are in 2 feet?

    <p>24 inches</p> Signup and view all the answers

    What is the equivalent of 1 km/h in ft/s?

    <p>3.281 ft/s</p> Signup and view all the answers

    If 1 inch is equal to 2.54 cm, how many cm are in 5 inches?

    <p>45.72 cm</p> Signup and view all the answers

    What is the equivalent of 1 ft^3 in cu.m?

    <p>0.02832 cu.m</p> Signup and view all the answers

    If 1 cal is equal to 4.187 J, how many J are in 5 cal?

    <p>10.935 J</p> Signup and view all the answers

    What is the equivalent of 1 lb/cu.ft in g/cu.cm?

    <p>62.42 g/cu.cm</p> Signup and view all the answers

    What is the characteristic of a left skewed distribution?

    <p>Mean &lt; Median &lt; Mode</p> Signup and view all the answers

    What percentage of the data set lies within 2 standard deviations from the mean?

    <p>95.45%</p> Signup and view all the answers

    What is the unit of force equivalent to 1 kilogram?

    <p>Newton</p> Signup and view all the answers

    What is the conversion factor to convert Celsius to Kelvin?

    <p>Add 273</p> Signup and view all the answers

    Which of the following is a characteristic of a symmetrical distribution?

    <p>Mean = Median = Mode</p> Signup and view all the answers

    What is the term for a measure of the average distance of all observations from the mean?

    <p>Standard Deviation</p> Signup and view all the answers

    What is the formula to find the area of a rectangle?

    <p>Length * Width</p> Signup and view all the answers

    What percentage of the data set lies within 1 standard deviation from the mean?

    <p>68%</p> Signup and view all the answers

    What is the unit of energy equivalent to 4.186 Joules?

    <p>Calorie</p> Signup and view all the answers

    What is the term for a numerical value that describes data taken from a sample?

    <p>Statistic</p> Signup and view all the answers

    What is the formula to find the volume of a cylinder?

    <p>πr²h</p> Signup and view all the answers

    What is the value of acceleration of gravity on the surface of the earth?

    <p>9.8 m/s²</p> Signup and view all the answers

    What is the unit of light equivalent to 1 lumen per steradian?

    <p>Candela</p> Signup and view all the answers

    What is the formula to find the area of a triangle?

    <p>(1/2)b*h</p> Signup and view all the answers

    What is the unit of radiation equivalent to 10⁻² gray?

    <p>Rad</p> Signup and view all the answers

    What is the value of the velocity of light in meters per second?

    <p>3.0 x 10⁸ m/s</p> Signup and view all the answers

    What is the unit of force in the formula F = ma?

    <p>N</p> Signup and view all the answers

    What is the formula to calculate the work done by a force?

    <p>W = FS</p> Signup and view all the answers

    What is the definition of momentum?

    <p>Momentum is the product of mass and velocity</p> Signup and view all the answers

    What is the formula to calculate the velocity of an object?

    <p>v = v0 + at</p> Signup and view all the answers

    What is the purpose of a histogram in statistics?

    <p>To display the frequency of a data set</p> Signup and view all the answers

    What is the formula to calculate the normal force on an object?

    <p>N = mg</p> Signup and view all the answers

    What is the coefficient of friction in the problem where a force is acting at 30° with the horizontal on an object?

    <p>0.35</p> Signup and view all the answers

    What is the unit of work done?

    <p>Joules</p> Signup and view all the answers

    What is the purpose of a null hypothesis in hypothesis testing?

    <p>To test if there is no significant difference between the population means</p> Signup and view all the answers

    What is the consequence of a Type I error?

    <p>Rejecting a true null hypothesis</p> Signup and view all the answers

    What is the coefficient of variation (CV) in statistics?

    <p>The ratio of the standard deviation to the mean</p> Signup and view all the answers

    What is the purpose of calculating the cumulative error in air sampling?

    <p>To calculate the upper and lower confidence limits for air sampling</p> Signup and view all the answers

    What is the difference between precision and accuracy?

    <p>Accuracy refers to how close the measurement is to the true value, while precision refers to how close the measurements are to each other</p> Signup and view all the answers

    What is the purpose of the lower confidence limit (LCL) in OSHA regulations?

    <p>To determine if the measured value exceeds the PEL</p> Signup and view all the answers

    What is the consequence of a Type II error?

    <p>Accepting a false null hypothesis when there is an actual difference</p> Signup and view all the answers

    What is the parameter that describes the characteristic of the population?

    <p>Parameter</p> Signup and view all the answers

    What is the force that opposes motion between two surfaces that are in contact?

    <p>Frictional force</p> Signup and view all the answers

    What type of energy is stored in elastic materials as a result of their stretching or compressing?

    <p>Elastic potential energy</p> Signup and view all the answers

    What is the formula for the elastic potential energy stored in a spring?

    <p>P.E. = ½ kx2</p> Signup and view all the answers

    What is the unit of force required to give a 1-kg mass an acceleration of 1 m/s2?

    <p>Newton</p> Signup and view all the answers

    What is the formula for the frictional force that must be overcome to move an object?

    <p>F = μN</p> Signup and view all the answers

    What is the type of force exerted by a compressed or stretched spring?

    <p>Spring force</p> Signup and view all the answers

    What is the formula to calculate the work done by a force?

    <p>W = FS</p> Signup and view all the answers

    What is the formula to calculate the momentum of an object?

    <p>ρ = mv</p> Signup and view all the answers

    What is the coefficient of friction in the given problem, if a force is acting at 30° with the horizontal on an object that is displaced 3 m along the horizontal direction?

    <p>0.35</p> Signup and view all the answers

    What is the formula to calculate the velocity of an object after a certain time, given the initial velocity, acceleration, and time?

    <p>v = v0 + at</p> Signup and view all the answers

    What is the formula to calculate the normal force on a surface, given the mass of the object and the acceleration due to gravity?

    <p>F = mg</p> Signup and view all the answers

    What is the definition of a histogram in statistics?

    <p>A graph used to distribute frequency of the data</p> Signup and view all the answers

    What is the formula to calculate the final velocity of an object, given the initial velocity, acceleration, and time?

    <p>v^2 = v0^2 + 2as</p> Signup and view all the answers

    What is the formula to calculate the distance traveled by an object, given the initial velocity, acceleration, and time?

    <p>s = v0t + ½at^2</p> Signup and view all the answers

    What is the formula for the area of a rectangle?

    <p>length * width</p> Signup and view all the answers

    What is the unit of energy in which 1 BTU is equal to 1055?

    <p>Joule</p> Signup and view all the answers

    What is the trigonometric identity C² = a² + b² - 2ab cos θ?

    <p>Law of Cosines</p> Signup and view all the answers

    What is the formula for kinetic energy?

    <p>K.E. = ½ mv²</p> Signup and view all the answers

    What is the force that opposes motion between two surfaces that are in contact?

    <p>Friction</p> Signup and view all the answers

    What is the formula for the volume of a cylinder?

    <p>V = πr²h</p> Signup and view all the answers

    What is the unit of energy in which 1 calorie is equal to 4.186?

    <p>Joule</p> Signup and view all the answers

    What is the formula for the area of a triangle?

    <p>A = (1/2)bh</p> Signup and view all the answers

    What is the formula for the volume of a prism?

    <p>V = Bh</p> Signup and view all the answers

    What is the formula for the area of a circle?

    <p>A = πr²</p> Signup and view all the answers

    What is the force exerted by a compressed or stretched spring?

    <p>Spring force</p> Signup and view all the answers

    Which type of energy is stored in an object as the result of its stretching or compressing?

    <p>Elastic potential energy</p> Signup and view all the answers

    A block of wood is sitting on a cement floor with a coefficient of friction of 0.6. What is the force required to overcome the frictional force?

    <p>F = μN</p> Signup and view all the answers

    A spring is stretched by 0.3 m and has a spring constant of 200 N/m. What is its elastic potential energy?

    <p>P.E. = ½(200)(0.3)^2</p> Signup and view all the answers

    An object is moving at a velocity of 10 m/s. What is its kinetic energy if its mass is 5 kg?

    <p>K.E. = ½(5)(10)^2</p> Signup and view all the answers

    What is the unit of force in which a 1-kg mass is given an acceleration of 1 m/s^2?

    <p>Newton</p> Signup and view all the answers

    What is the force of friction when the normal force is 400 N and the coefficient of friction is 0.35?

    <p>140 N</p> Signup and view all the answers

    What is the work done by a force of 140 N when it displaces an object by 3 m at an angle of 30° with the horizontal?

    <p>363.7 Nm</p> Signup and view all the answers

    What is the momentum of an object with a mass of 2 kg and a velocity of 5 m/s?

    <p>10 kgm/s</p> Signup and view all the answers

    What is the final velocity of an object that starts with an initial velocity of 3 m/s and accelerates at 2 m/s² for 4 seconds?

    <p>9 m/s</p> Signup and view all the answers

    What is the distance traveled by an object with an initial velocity of 2 m/s, accelerating at 3 m/s² for 5 seconds?

    <p>25 m</p> Signup and view all the answers

    What is the type of graph used to display the frequency of data?

    <p>Histogram</p> Signup and view all the answers

    What is the median of a data set with an even number of values?

    <p>The average of the two middle values</p> Signup and view all the answers

    What is the formula to calculate the force of an object, given its mass and acceleration?

    <p>F = ma</p> Signup and view all the answers

    What is the unit of force in the MKS system?

    <p>Newton</p> Signup and view all the answers

    What is the formula to calculate the area of a rectangle?

    <p>Area = length × width</p> Signup and view all the answers

    What is the unit of energy in the British thermal unit (BTU) system?

    <p>BTU</p> Signup and view all the answers

    What is the formula for the volume of a cylinder?

    <p>V = πr²h</p> Signup and view all the answers

    What is the trigonometric function that relates the lengths of the sides of a right triangle?

    <p>A/SinA = b/SinB = c/SinC</p> Signup and view all the answers

    What is Hooke's Law in relation to springs?

    <p>Force is proportional to the displacement of the spring.</p> Signup and view all the answers

    What is the unit of radiation exposure in the SI system?

    <p>Gray</p> Signup and view all the answers

    What is the formula for the kinetic energy of an object?

    <p>K.E. = ½mv²</p> Signup and view all the answers

    What is the unit of pressure in the SI system?

    <p>Pascal</p> Signup and view all the answers

    What is the formula for the area of a circle?

    <p>Area = πr²</p> Signup and view all the answers

    A 60-kg person is climbing a ladder with a coefficient of friction of 0.5 between the person's shoes and the ladder rungs. If the person is exerting a force of 200 N upwards, what is the normal force exerted by the ladder on the person?

    <p>294 N</p> Signup and view all the answers

    A spring has a spring constant of 200 N/m and is compressed by 0.05 m. What is the elastic potential energy stored in the spring?

    <p>0.25 J</p> Signup and view all the answers

    A 20-kg box is being pulled across a horizontal surface with a coefficient of friction of 0.3. If the force exerted to pull the box is 50 N, what is the acceleration of the box?

    <p>1 m/s^2</p> Signup and view all the answers

    A 40-kg block is attached to a spring with a spring constant of 100 N/m. If the block is displaced by 0.1 m from its equilibrium position, what is the force exerted by the spring on the block?

    <p>20 N</p> Signup and view all the answers

    A 30-kg block is moving at a velocity of 5 m/s. What is its kinetic energy?

    <p>175 J</p> Signup and view all the answers

    A 10-kg block is being lifted up a frictionless inclined plane with an angle of 30° to the horizontal. If the force exerted to lift the block is 50 N, what is the normal force exerted by the plane on the block?

    <p>35 N</p> Signup and view all the answers

    What is the work done by the force if a force of 140 N is acting at an angle of 30° with the horizontal on an object that is displaced 3 m along the horizontal direction?

    <p>363.7 N</p> Signup and view all the answers

    A force of 400 N is acting on an object at an angle of 30° with the horizontal. If the coefficient of friction is 0.35, what is the frictional force?

    <p>140 N</p> Signup and view all the answers

    What is the formula for the velocity of an object under constant acceleration?

    <p>v = v0 + at</p> Signup and view all the answers

    What is the unit of force in which 1 kilogram-force is equal to?

    <p>9.8 N</p> Signup and view all the answers

    What is the formula for the distance traveled by an object under constant acceleration?

    <p>s = v0t + ½ at2</p> Signup and view all the answers

    What is the formula for the momentum of an object?

    <p>ρ = mv</p> Signup and view all the answers

    What is the formula for the force exerted by a spring?

    <p>F = kx</p> Signup and view all the answers

    What is the formula for the velocity of an object under constant acceleration in terms of its initial and final velocities?

    <p>v2 = v02 + 2as</p> Signup and view all the answers

    What is the formula to calculate the area of a triangle with a base 'b' and height 'h'?

    <p>Area = (1/2) b * h</p> Signup and view all the answers

    What is the formula to calculate the volume of a cylinder with radius 'r' and height 'h'?

    <p>V = πr2h</p> Signup and view all the answers

    What is the formula to calculate the kinetic energy of an object with mass 'm' and velocity 'v'?

    <p>K.E. = (1/2)mv^2</p> Signup and view all the answers

    What is the formula to calculate the force of friction 'F' when the normal force 'N' and coefficient of friction 'μ' are given?

    <p>F = μN</p> Signup and view all the answers

    What is the formula to calculate the elastic potential energy 'U' of a spring with spring constant 'k' and displacement 'x'?

    <p>U = (1/2)kx^2</p> Signup and view all the answers

    What is the formula to calculate the trigonometric identity 'C' using sides 'a', 'b', and angle 'θ'?

    <p>C = a^2 + b^2 - 2ab cos θ</p> Signup and view all the answers

    What is the unit of energy in which 1 British Thermal Unit (Btu) is equal to?

    <p>1055 Joule</p> Signup and view all the answers

    What is the value of the acceleration of gravity in ft/sec^2?

    <p>32.2 ft/sec^2</p> Signup and view all the answers

    What is the formula to calculate the volume of a sphere with radius 'r'?

    <p>V = (4/3)πr^3</p> Signup and view all the answers

    What is the value of 1 kilogram-force in newton?

    <p>9.80665 N</p> Signup and view all the answers

    What is the unit of force equivalent to 1 kilogram-force?

    <p>9.80665 N</p> Signup and view all the answers

    What is the formula to find the area of a rectangle?

    <p>Area = length * width</p> Signup and view all the answers

    What is the unit of energy equivalent to 1 calorie?

    <p>4.186 J</p> Signup and view all the answers

    What is the equivalent of 1 yard in meters?

    <p>0.9144 m</p> Signup and view all the answers

    What is the formula to find the volume of a cylinder?

    <p>V = πr²h</p> Signup and view all the answers

    What is the unit of radiation equivalent to 1 rad?

    <p>10⁻² gray</p> Signup and view all the answers

    If 1 mile is equal to 1609 meters, how many meters are in 3.5 miles?

    <p>5635.5 m</p> Signup and view all the answers

    What is the equivalent of 1 cubic meter in liters?

    <p>1000 L</p> Signup and view all the answers

    What is the formula to find the area of a triangle?

    <p>Area = (1/2)b×h</p> Signup and view all the answers

    What is the unit of luminous intensity equivalent to 1 candela?

    <p>1 lumen/steradian</p> Signup and view all the answers

    If 1 inch is equal to 2.54 centimeters, how many centimeters are in 12.5 inches?

    <p>31.75 cm</p> Signup and view all the answers

    What is the equivalent of 1 foot per second in kilometers per hour?

    <p>1.0973 km/h</p> Signup and view all the answers

    What is the unit of energy equivalent to 1 BTU?

    <p>1055 J</p> Signup and view all the answers

    If 1 calorie is equal to 4.187 joules, how many joules are in 250 calories?

    <p>1046.75 J</p> Signup and view all the answers

    What is the equivalent of 1 pound per cubic foot in kilograms per cubic meter?

    <p>16.02 kg/m^3</p> Signup and view all the answers

    If 1 mile per hour is equal to 1.47 feet per second, how many feet per second are in 2.5 miles per hour?

    <p>3.675 ft/s</p> Signup and view all the answers

    In a left-skewed distribution, which of the following is true?

    <p>Mean &lt; Median &lt; Mode</p> Signup and view all the answers

    What percentage of a dataset lies within 3 standard deviations from the mean?

    <p>99.99%</p> Signup and view all the answers

    What is the term for a measure of the average distance of all observations from the mean?

    <p>Standard Deviation</p> Signup and view all the answers

    In a symmetrical distribution, what is the relationship between the mean, median, and mode?

    <p>Mean = Median = Mode</p> Signup and view all the answers

    What is the term for a numerical value that describes data taken from a population?

    <p>Parameter</p> Signup and view all the answers

    What is the formula for variance?

    <p>Σ(X-Xav)2/N</p> Signup and view all the answers

    What is the percentage of a dataset that lies within 1 standard deviation from the mean in a normal distribution?

    <p>68%</p> Signup and view all the answers

    What is the relationship between the mean, median, and mode in a right-skewed distribution?

    <p>Mode &lt; Median &lt; Mean</p> Signup and view all the answers

    What is the force acting on the surface in a direction perpendicular to the surface in the formula F = μN?

    <p>Normal force</p> Signup and view all the answers

    A 60-kg person is standing on a scale on the surface of the earth. What is the force exerted on the scale?

    <p>600 N</p> Signup and view all the answers

    A spring is compressed by 0.4 m and has a spring constant of 200 N/m. What is the elastic potential energy stored in the spring?

    <p>32 J</p> Signup and view all the answers

    A 30-kg block is being pushed up a slope with a force of 120 N. If the coefficient of friction is 0.3, what is the normal force acting on the block?

    <p>110 N</p> Signup and view all the answers

    A 50-kg block is resting on a horizontal surface with a coefficient of friction of 0.3. What is the minimum force required to overcome the frictional force?

    <p>45 N</p> Signup and view all the answers

    A spring is stretched by 0.5 m and has a spring constant of 150 N/m. What is the force exerted by the spring?

    <p>75 N</p> Signup and view all the answers

    A 20-kg block is moving at a velocity of 8 m/s. What is its kinetic energy?

    <p>160 J</p> Signup and view all the answers

    A 40-kg block is sitting on a cement floor with a coefficient of friction of 0.6. What is the frictional force that must be overcome to move the block?

    <p>168 N</p> Signup and view all the answers

    What is the purpose of calculating the coefficient of variation in statistics?

    <p>To measure the dispersion of a probability distribution or frequency distribution</p> Signup and view all the answers

    What is the consequence of a Type I error in hypothesis testing?

    <p>Rejecting the null hypothesis when it's true</p> Signup and view all the answers

    What is the purpose of the lower confidence limit in OSHA regulations?

    <p>To determine if the measured value exceeds the PEL</p> Signup and view all the answers

    What is the difference between precision and accuracy in statistics?

    <p>Accuracy is how close the measurement is to the actual value, while precision is the value of SD of repeated measurements</p> Signup and view all the answers

    What is the null hypothesis in hypothesis testing?

    <p>There is no significant difference between the population</p> Signup and view all the answers

    What is the consequence of a Type II error in hypothesis testing?

    <p>Accepting the null hypothesis when it's false</p> Signup and view all the answers

    What is the purpose of using a 95% confidence interval in hypothesis testing?

    <p>To ensure that there is a 95% chance of the true result</p> Signup and view all the answers

    What is the cumulative error used for in air sampling?

    <p>To calculate the upper and lower confidence limits</p> Signup and view all the answers

    How many millimeters are in 1 inch?

    <p>25.4</p> Signup and view all the answers

    What is the equivalent of 1 kilometer in meters?

    <p>1000</p> Signup and view all the answers

    How many centimeters are in 1 foot?

    <p>30.48</p> Signup and view all the answers

    What is the equivalent of 1 mile per hour in feet per second?

    <p>1.47</p> Signup and view all the answers

    How many cubic meters are in 5 cubic feet?

    <p>0.14216</p> Signup and view all the answers

    What is the equivalent of 1 pound per cubic foot in grams per cubic centimeter?

    <p>0.01602</p> Signup and view all the answers

    How many kilometers are in 1 mile?

    <p>1.60</p> Signup and view all the answers

    What is the equivalent of 1 nautical mile in miles?

    <p>0.868</p> Signup and view all the answers

    What is the equivalent of 1 kilogram-force in newton?

    <p>9.80665 N</p> Signup and view all the answers

    What is the formula for the area of a rectangle?

    <p>Area = l × w</p> Signup and view all the answers

    What is the unit of energy in which 1 BTU is equal to 1055?

    <p>Joule</p> Signup and view all the answers

    What is the value of 1 rad in gray?

    <p>10-2 gray</p> Signup and view all the answers

    What is the formula for the volume of a cylinder?

    <p>V = π × r2 × h</p> Signup and view all the answers

    What is the value of 1 candela in lumens per steradian?

    <p>1 lumen/steradian</p> Signup and view all the answers

    What is the formula for the trigonometric function cosine?

    <p>C = a2 + b2 - 2ab cos θ</p> Signup and view all the answers

    What is the equivalent of 1 foot-candle in lux?

    <p>10.76 lux</p> Signup and view all the answers

    What is the unit of force required to give a 1-kg mass an acceleration of 1 m/s2?

    <p>Newton</p> Signup and view all the answers

    What is the type of energy stored in an object due to its position or state?

    <p>Potential energy</p> Signup and view all the answers

    What is the force that opposes motion between two surfaces in contact?

    <p>Frictional force</p> Signup and view all the answers

    What is the amount of compression or stretching of a spring when it is at its equilibrium position?

    <p>Zero</p> Signup and view all the answers

    What is the normal force acting on the surface of an object in contact with another surface?

    <p>Force perpendicular to the surface</p> Signup and view all the answers

    What is the formula to calculate the frictional force that must be overcome to move an object?

    <p>F = μN</p> Signup and view all the answers

    What is the type of energy stored in an object due to its motion?

    <p>Kinetic energy</p> Signup and view all the answers

    What is the force exerted by a compressed or stretched spring?

    <p>Spring force</p> Signup and view all the answers

    What is the characteristic of a distribution where the mean is greater than the median?

    <p>Right skewed distribution</p> Signup and view all the answers

    What is the term for the measure of the average distance of all observations from the mean?

    <p>Standard deviation</p> Signup and view all the answers

    What percentage of the data set lies within 3 standard deviations from the mean?

    <p>99.73%</p> Signup and view all the answers

    What is the term for a numerical value that describes data taken from a sample?

    <p>Statistic</p> Signup and view all the answers

    What is the characteristic of a distribution where the mean, median, and mode are equal?

    <p>Symmetrical distribution</p> Signup and view all the answers

    What is the formula to calculate the variance?

    <p>Σ(X-Xav)^2/N</p> Signup and view all the answers

    What is the term for a measure of the spread of a distribution?

    <p>Standard deviation</p> Signup and view all the answers

    What percentage of the data set lies within 1 standard deviation from the mean?

    <p>68%</p> Signup and view all the answers

    What is the purpose of a null hypothesis in hypothesis testing?

    <p>To test if there is no significant difference between the populations</p> Signup and view all the answers

    What is the consequence of a Type I error?

    <p>Rejecting a true null hypothesis</p> Signup and view all the answers

    What is the coefficient of variation (CV)?

    <p>A relative standard deviation</p> Signup and view all the answers

    What is the purpose of calculating the cumulative error in air sampling?

    <p>To determine the upper and lower confidence limits</p> Signup and view all the answers

    What is the difference between precision and accuracy?

    <p>Precision is a measure of the variation of repeated measurements, while accuracy is a measure of how close to the true value</p> Signup and view all the answers

    What is the purpose of the lower confidence limit (LCL) in OSHA regulations?

    <p>To determine if the measured value is above the PEL</p> Signup and view all the answers

    What is the consequence of a Type II error?

    <p>Failing to reject a false null hypothesis</p> Signup and view all the answers

    What is the coefficient of variation (CV) formula?

    <p>S/Xmean = %</p> Signup and view all the answers

    How many millimeters are in 1 meter?

    <p>1000 mm</p> Signup and view all the answers

    What is the equivalent of 1 yard in feet?

    <p>3 feet</p> Signup and view all the answers

    How many square centimeters are in 1 square inch?

    <p>6.452 sq.cm</p> Signup and view all the answers

    What is the equivalent of 1 mile per hour in feet per second?

    <p>1.47 ft/s</p> Signup and view all the answers

    How many liters are in 1 cubic foot?

    <p>28.32 L</p> Signup and view all the answers

    What is the equivalent of 1 kilometer in meters?

    <p>1000 m</p> Signup and view all the answers

    How many inches are in 1 meter?

    <p>39.37 in</p> Signup and view all the answers

    What is the equivalent of 1 foot in centimeters?

    <p>30.48 cm</p> Signup and view all the answers

    What is the unit of force in the given equation F = ma/g?

    <p>N</p> Signup and view all the answers

    What is the formula to calculate the momentum of an object?

    <p>ρ = mv</p> Signup and view all the answers

    What is the formula to calculate the work done by a force?

    <p>W = FS</p> Signup and view all the answers

    What is the definition of median in statistics?

    <p>The central number of a data set</p> Signup and view all the answers

    What is the formula to calculate the velocity of an object under constant acceleration?

    <p>v = v0 + at</p> Signup and view all the answers

    What is the formula to calculate the distance traveled by an object under constant acceleration?

    <p>S = vt + ½at^2</p> Signup and view all the answers

    What is the force that opposes motion between two surfaces in contact?

    <p>Frictional force</p> Signup and view all the answers

    What is the type of graph used to distribute frequency of the data?

    <p>Histogram</p> Signup and view all the answers

    What is the equivalent of 1 kilogram-force in newtons?

    <p>9.81 N</p> Signup and view all the answers

    What is the equivalent of 1 liter in cubic inches?

    <p>61.02 cu in</p> Signup and view all the answers

    What is the value of 1 atm in mm Hg?

    <p>760 mm Hg</p> Signup and view all the answers

    What is the equivalent of 1 British Thermal Unit (Btu) in joules?

    <p>1055 J</p> Signup and view all the answers

    What is the value of 1 radian in degrees?

    <p>180°/π</p> Signup and view all the answers

    What is the equivalent of 1 tesla in gauss?

    <p>10,000 gauss</p> Signup and view all the answers

    What is the characteristic of a left skewed distribution?

    <p>Mean &lt; Median &lt; Mode</p> Signup and view all the answers

    What percentage of the data set lies within 3 standard deviations from the mean?

    <p>99.99%</p> Signup and view all the answers

    What is the value of 1 foot-candle in lux?

    <p>10.76 lux</p> Signup and view all the answers

    What is the term for a measure of the average distance of all observations from the mean?

    <p>Standard Deviation</p> Signup and view all the answers

    What is the equivalent of 1 kilogram in pounds?

    <p>2.205 lb</p> Signup and view all the answers

    What is the relationship between Mean, Median, and Mode in a symmetrical distribution?

    <p>Mean = Median = Mode</p> Signup and view all the answers

    What is the term for a numerical value that describes data taken from a sample?

    <p>Statistic</p> Signup and view all the answers

    What is the formula to calculate the Variance?

    <p>Σ(X-Xav)2/N</p> Signup and view all the answers

    What percentage of the data set lies within 1 standard deviation from the mean?

    <p>68%</p> Signup and view all the answers

    What is the relationship between Mode, Median, and Mean in a right skewed distribution?

    <p>Mode &lt; Median &lt; Mean</p> Signup and view all the answers

    What is the purpose of the null hypothesis in hypothesis testing?

    <p>To provide a basis for assuming no significant difference between the populations</p> Signup and view all the answers

    What is the consequence of a Type I error?

    <p>Rejecting a true null hypothesis</p> Signup and view all the answers

    What is the coefficient of variation (CV) in statistics?

    <p>The ratio of the standard deviation to the mean</p> Signup and view all the answers

    What is the purpose of calculating the cumulative error in air sampling?

    <p>To calculate the upper and lower confidence limits</p> Signup and view all the answers

    What is the difference between precision and accuracy?

    <p>Accuracy is the closeness of the measurement to the true value, while precision is the closeness of the measurement to the mean</p> Signup and view all the answers

    What is the purpose of the lower confidence limit (LCL) in OSHA regulations?

    <p>To determine if the measured value exceeds the PEL</p> Signup and view all the answers

    What is the consequence of a Type II error?

    <p>Failing to reject a false null hypothesis</p> Signup and view all the answers

    What is the measure of the dispersion of a probability distribution or frequency distribution?

    <p>Relative standard deviation</p> Signup and view all the answers

    What is the equivalent of 1 mile in kilometers?

    <p>1.609 km</p> Signup and view all the answers

    What is the equivalent of 1 inch in centimeters?

    <p>2.54 cm</p> Signup and view all the answers

    What is the equivalent of 1 foot in meters?

    <p>0.3048 m</p> Signup and view all the answers

    What is the equivalent of 1 cubic meter in cubic feet?

    <p>35.28 cu.ft</p> Signup and view all the answers

    What is the equivalent of 1 pound per cubic foot in grams per cubic centimeter?

    <p>0.01602 g/cu.cm</p> Signup and view all the answers

    What is the equivalent of 1 kilometer per hour in miles per hour?

    <p>0.6213 mi/h</p> Signup and view all the answers

    What is the equivalent of 1 mile per hour in feet per second?

    <p>1.4670 ft/s</p> Signup and view all the answers

    What is the equivalent of 1 calorie in joules?

    <p>4.187 J</p> Signup and view all the answers

    What is the unit of force in the formula F = ma?

    <p>N</p> Signup and view all the answers

    What is the formula to calculate the momentum of an object?

    <p>ρ = mv</p> Signup and view all the answers

    What is the unit of work done in the formula W = FS?

    <p>J</p> Signup and view all the answers

    What is the formula to calculate the final velocity of an object under constant acceleration?

    <p>v = v0 + at</p> Signup and view all the answers

    What is the characteristic of a right skewed distribution?

    <p>Mode &lt; Median &lt; Mean</p> Signup and view all the answers

    What is the type of graph used to distribute frequency of the data?

    <p>Histogram</p> Signup and view all the answers

    What is the measure of the average distance of all observations from the mean?

    <p>Standard deviation</p> Signup and view all the answers

    What is the formula to calculate the mean of a data set?

    <p>ΣXn/n</p> Signup and view all the answers

    What is the coefficient of friction in the given problem, if a force is acting at 30° with the horizontal on an object that is displaced 3 m along the horizontal direction?

    <p>0.35</p> Signup and view all the answers

    What percentage of the data set lies within 1 standard deviation from the mean?

    <p>68%</p> Signup and view all the answers

    What is the unit of force required to give a 1-kg mass an acceleration of 1 m/s2?

    <p>N</p> Signup and view all the answers

    What is the formula to calculate the work done by a force at an angle with the horizontal direction?

    <p>W = FS cos θ</p> Signup and view all the answers

    What is the definition of a parameter in statistics?

    <p>A statistical value that describes the entire population</p> Signup and view all the answers

    What is the characteristic of a symmetrical distribution?

    <p>Mean = Median = Mode</p> Signup and view all the answers

    What is the direction of the force acting on the surface in a frictional force calculation?

    <p>Perpendicular to the surface</p> Signup and view all the answers

    What is the percentage of the data set that lies within 3 standard deviations from the mean?

    <p>99.73%</p> Signup and view all the answers

    What type of energy is stored in an object as the result of its stretching or compressing?

    <p>Elastic potential energy</p> Signup and view all the answers

    What is the term for a numerical value that describes data taken from a sample?

    <p>Statistic</p> Signup and view all the answers

    What is the formula for the elastic potential energy stored in a spring?

    <p>½ kx2</p> Signup and view all the answers

    What is the condition required for a spring to have elastic potential energy?

    <p>The spring is stretched or compressed</p> Signup and view all the answers

    What is the formula to calculate the variance?

    <p>Σ(X-Xav)^2/N</p> Signup and view all the answers

    What is the force exerted by a compressed or stretched spring?

    <p>Spring force</p> Signup and view all the answers

    What is the direction of the tension force?

    <p>Opposite to the compression</p> Signup and view all the answers

    What is the formula for the frictional force that must be overcome to move an object?

    <p>F = μN</p> Signup and view all the answers

    What is the purpose of the null hypothesis in hypothesis testing?

    <p>To assume no significant difference between the populations</p> Signup and view all the answers

    What is the consequence of a Type I error?

    <p>Rejecting the null hypothesis when it's true</p> Signup and view all the answers

    What is the coefficient of variation (CV) in statistics?

    <p>A measure of the dispersion of a probability distribution</p> Signup and view all the answers

    What is the purpose of calculating the cumulative error in air sampling?

    <p>To calculate the upper and lower confidence limits</p> Signup and view all the answers

    What is the difference between precision and accuracy?

    <p>Precision is a measure of the closeness of repeated measurements, while accuracy is a measure of the closeness to the true value</p> Signup and view all the answers

    What is the purpose of the lower confidence limit (LCL) in OSHA regulations?

    <p>To determine if the measured value exceeds the permissible exposure limit (PEL)</p> Signup and view all the answers

    What is the consequence of a Type II error?

    <p>Accepting the null hypothesis when it's false</p> Signup and view all the answers

    What is the formula for the coefficient of variation (CV)?

    <p>CV = S / Xmean</p> Signup and view all the answers

    Study Notes

    Conversions

    • 1 m = 100 cm = 1000 mm
    • 1 km = 1000 m
    • 1 mile = 5280 feet = 1609 meters
    • 1 mile/hour = 1.47 ft/second
    • 1 inch = 2.54 cm
    • 1 foot = 30.48 cm = 12 inches
    • 1 meter = 3.2 feet
    • 1 foot = 12 inches

    Energy

    • 1 calorie = 4.187 J = 0.003968 Btu
    • 1 Btu = 252 cal = 1055 J
    • 1 joule = 1 kg · m/s²

    Length

    • 1 micron = 0.001 mm
    • 1 inch = 2.54 cm = 25.4 mm
    • 1 foot = 30.48 cm = 12 inches
    • 1 yard = 3 feet
    • 1 mile = 5280 feet = 1609 meters
    • 1 nautical mile = 0.868 US miles

    Area

    • 1 square inch = 6.452 square cm
    • 1 square foot = 144 square inches = 0.09290 square meters
    • 1 square yard = 9 square feet

    Volume

    • 1 cubic centimeter = 1 milliliter
    • 1 cubic inch = 16.39 cubic centimeters
    • 1 cubic foot = 1728 cubic inches = 0.02832 cubic meters
    • 1 liter = 1.057 quarts (US)

    Temperature

    • To convert to absolute temperature scales: oR = oF + 460, oK = oC + 273
    • Tc = Tf - 32/1.8, Tk = Tc + 273, F = 460 + R

    Force

    • 1 kilogram-force = 9.80665 newton [N]

    Radiation

    • 1 rad = 10⁻² gray, 1 rem = 10⁻² sievert, 1 curie = 3.7 × 10¹⁰ becquerel
    • 1 becquerel = 1 disintegration/second

    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 lux

    Physical Constants

    • acceleration of gravity = 32.2 ft/sec² = 9.8 m/sec²
    • velocity of light = 3.0 × 10⁸ m/sec
    • Planck's constant = 6.626 × 10⁻³⁴ J·sec
    • Avogadro's number = 6.024 × 10²³/gram-mole

    Boolean Postulates

    • Area of a rectangle: Area = length × width
    • Area of a square: Area = s², where s = side
    • Area of a triangle: Area = (1/2) b × h, where b = base and h = height
    • Area of a circle: Area = π × r², where r = radius

    Volume of Shapes

    • Rectangular solid: V = l × w × h
    • Cube: V = a³
    • Cylinder: V = πr²h
    • Prism: V = B × h
    • Sphere: V = (4/3)πr³
    • Pyramid: V = (1/3) × B × h

    Trigonometric Functions

    • C² = a² + b² - 2ab cos C
    • A/SinA = b/SinB = c/SinC

    Energy and Work

    • Kinetic energy: K.E. = ½ mv²
    • Potential energy: P.E. = mgh
    • Elastic potential energy: P.E. = ½ kx², where k = spring constant and x = amount of compression

    Force and Friction

    • 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: F = μN, where μ = coefficient of friction and N = force acting on the surface

    Statistics

    • Mean, median, mode, and standard deviation are measures of central tendency
    • Standard deviation (S): a measure of the average distance of all observations from the mean
    • Variance: Σ(X-Xav)²/N
    • Standard deviation (S) = √(X-Xav)²/N
    • 1 standard deviation = 68% of the data set
    • 2 standard deviations = 95.45% of the data set
    • 3 standard deviations = 99.73% of the data set

    Hypothesis Testing

    • Null hypothesis (H0): no significant difference between the population
    • Alternative hypothesis (H1): significant difference between the population
    • Type I error: rejecting the null hypothesis when it is true (α)
    • Type II error: failing to reject the null hypothesis when it is false (β)

    Unit Conversions

    • 1 quart = 0.9463 L
    • 1 US gallon = 3.785 L
    • 1 ft³ = 28.317 L
    • 1 psia = 6.895 kN/m²
    • 1 atm = 760 mm Hg = 14.7 psi
    • 1 bar = 14.5 psi = 0.98 atm = 105 N/m²
    • 1 mm Hg = 0.01934 psia

    Mass and Weight

    • 16 ounces = 1 lb
    • 1 g = 1000 mg
    • 2.205 lb = 1 kg
    • 1 ton (US) = 2000 lb
    • 1 tonne (Metric ton) = 1000 kg
    • 1 dram = 1771.85 mg

    Heat Capacity

    • 1 Btu/lb/°F = 1 cal/g/°C
    • 1 cal/g/°C = 4187 J/kg·K

    Force, Pressure, or Stress

    • 1 pound-force = 4.45 Newtons
    • 1 pound-force/square inch = 6.89 Kilopascals

    Illumination

    • 1 foot-candle = 10.76 lux
    • 1 foot-lambert = 3.426 candela/square meter

    Length

    • 1 inch = 25.4 millimeters
    • 1 foot = 0.305 meters
    • 1 yard = 0.914 meters
    • 1 mile = 1.61 kilometers

    Area

    • 1 square inch = 645.2 square millimeters
    • 1 square foot = 0.093 square meters
    • 1 square yard = 0.836 square meters
    • 1 acre = 0.405 hectares
    • 1 square mile = 2.59 square kilometers

    Volume

    • 1 fluid ounce = 29.57 milliliters
    • 1 gallon = 3.785 liters
    • 1 cubic foot = 0.028 cubic meters
    • 1 cubic yard = 0.765 cubic meters

    Temperature

    • Fahrenheit to Celsius: (°F - 32) / 9
    • Celsius to Fahrenheit: (°C × 9) / 5 + 32
    • Celsius to Kelvin: °C + 273
    • Fahrenheit to Rankine: °F + 460

    Energy

    • 1 British Thermal Unit (Btu) = 1055 J
    • 1 faraday = 9.65 × 10⁴ coulombs
    • 1 g-cal = 4.19 J
    • 1 ampere-hour = 3600 coulombs
    • 1 kwh = 3.6 × 10⁶ J

    Standards

    • STP (physical science) = 0°C and 1 atm
    • STP (ventilation) = 70°F and 1 atm
    • STP (industrial hygiene) = 25°C and 1 atm
    • Air density = 0.075 lb/ft³ at 70°F and 1 atm

    Density of Water

    • 1 g/cm³ = 1.94 slugs/ft³
    • Weight density = 62.4 lb/ft³
    • 1 US gallon of H₂O = 8.345 lb

    Angles

    • 1 radian = 180°/π

    Light

    • 1 candela = 1 lumen/steradian
    • 1 foot-candle = 10.76 candela/m² = 10.76 lux

    Magnetic Fields

    • 1 tesla = 10,000 gauss

    Physical Constants

    • Acceleration of gravity = 32.2 ft/s² = 9.8 m/s²
    • Velocity of light = 3.0 × 10⁸ m/s
    • Planck’s constant = 6.626 × 10⁻³⁴ J·s
    • Avogadro’s number = 6.024 × 10²³/g-mol

    Radiation

    • 1 rad = 10⁻² gray
    • 1 rem = 10⁻² sievert
    • 1 curie = 3.7 × 10¹⁰ becquerel
    • 1 becquerel = 1 disintegration/s

    Mechanics

    • Potential Energy (P.E.) = mgh, where m is the mass of the object, g is the gravitational acceleration, and h is the height above the earth's surface
    • Elastic Potential Energy (P.E.) = ½kx², where k is the spring constant and x is the amount of compression
    • Force (F) = ma, where m is the mass of the object and a is the acceleration
    • Frictional Force (F) = μN, where μ is the coefficient of friction and N is the force acting on the surface in a direction perpendicular to the surface

    Statistics

    • Histogram: a graph used to display the frequency distribution of the data
    • Mean: the average value of a data set, calculated using ΣXn/n
    • Median: the central number of a data set, where if there are two numbers in the middle, the median is the average of those two numbers
    • Mode: the number in a data set that occurs most frequently
    • Left Skewed: Mean < Median < Mode, where the majority of values are at the right of the Mean
    • Right Skewed: Mode < Median < Mean, where the majority of values are at the left of the Mean
    • No Skew: Mean = Median = Mode, where the distribution is symmetrical

    Standard Deviation

    • Standard Deviation (S) = √(Σ(X-Xav)²/N)
    • Variance = Σ(X-Xav)²/N
    • Coefficient of Variation (CV) = S/Xmean
    • Relative Standard Deviation (RSD) = S/Xmean

    Hypothesis Testing

    • Null Hypothesis (H₀): no significant difference between the populations, where if any observed difference is due to sampling or experimental error
    • Type I Error: rejecting the null hypothesis when it is true, where there is no actual difference between the means
    • Type II Error: failing to reject the null hypothesis when it is false, where there is an actual difference between the means

    Conversions

    • 1 meter (m) = 100 centimeters (cm) = 1000 millimeters (mm) = 1,000,000 microns
    • 1 kilometer (km) = 1000 m
    • 1 mile = 5280 feet = 1609 m
    • 1 mile per hour = 1.47 feet per second

    Length

    • 1 inch = 2.54 cm
    • 1 foot = 30.48 cm = 12 inches
    • 1 meter = 3.2 feet

    Area

    • 1 square inch (sq.in.) = 6.452 square centimeters (sq.cm) = 6452 square millimeters (sq.mm)
    • 1 square foot (sq.ft) = 144 sq.in. = 0.09290 square meters (sq.m)
    • 1 square yard (sq.yd.) = 9 sq.ft

    Volume

    • 1 cubic centimeter (cm³) = 1 milliliter (mL)
    • 1 cubic inch (in³) = 16.39 cm³
    • 1 cubic foot (ft³) = 1728 in³ = 0.02832 cubic meters (cu.m)
    • 1 liter (L) = 1.057 quarts (US)

    Temperature

    • To convert to absolute temperature scales: oR = oF + 460, oK = oC + 273
    • Temperature conversion formulas: Tc = Tf - 32/1.8, Tk = Tc + 273, F = 460 + R

    Energy

    • 1 calorie = 4.186 Joules
    • 1 British thermal unit (BTU) = 1055 Joules
    • 1 foot-pound = 1.356 Joules
    • 1 Joule = 1 kilogram· meter per second square

    Radiation

    • 1 rad = 10⁻² gray, 1 rem = 10⁻² sievert, 1 curie = 3.7 × 10¹⁰ becquerel
    • 1 becquerel = 1 disintegration per second

    Density of Water

    • 1 gram per cubic centimeter (gm/cm³) = 1.94 slugs per cubic foot (weight density = 62.4 pounds per cubic foot)

    Light

    • 1 candela = 1 lumen per steradian
    • 1 footcandle = 10.76 candela per square meter = 10.76 lux

    Physical Constants

    • Acceleration of gravity = 32.2 feet per second square = 9.8 meters per second square
    • Velocity of light = 3.0 × 10⁸ meters per second
    • Planck's constant = 6.626 × 10⁻³⁴ Joule-seconds
    • Avogadro's number = 6.024 × 10²³ per gram-mole

    Boolean Postulates

    • No notes provided for this section

    Area Formulas

    • Rectangle: Area = length × width
    • Square: Area = s², where s = side
    • Triangle: Area = (1/2) × b × h, where b = base and h = height
    • Circle: Area = π × r², where r = radius

    Volume Formulas

    • Rectangular solid or cuboid: V = l × w × h
    • Cube: V = a³, where a = length of edge or side
    • Cylinder: V = π × r² × h
    • Prism: V = B × h, where B = area of base and h = height
    • Sphere: V = (4/3) × π × r³
    • Pyramid: V = (1/3) × B × h

    Trigonometric Functions

    • C² = a² + b² - 2ab × cosC
    • A/SinA = b/SinB = c/SinC

    Kinetic Energy

    • K.E. = ½ × m × v²
    • 1 Newton (N) = 1 kilogram × meter per second square
    • 1 kilogram = 2.2 pounds

    Force and Distance

    • F₁ × D₁ = F₂ × D₂

    Momentum

    • ρ = m × v, where ρ = momentum, m = mass, and v = velocity

    Force

    • F = m × a, where F = force, m = mass, and a = acceleration
    • F = 40 × 9.8 = 392 N, F = μ × N = 0.6 × 392 = 235.2 N

    Work Done

    • W = F × S, where W = work done, F = force, and S = distance
    • W = FS, where W = work done, F = force, and S = distance

    Newton's Second Law

    • F = m × a, where F = force, m = mass, and a = acceleration
    • F = m × a / g, where F = force, m = mass, a = acceleration, and g = acceleration due to gravity

    Statistics

    • Histogram: a graph used to distribute frequency of data
    • Mean: the average value of a data set, found using the formula ΣXn/n
    • Median: the central value of a data set
    • Mode: the value that occurs most frequently in a data set
    • Left skewed distribution: Mean < Median < Mode
    • Right skewed distribution: Mode < Median < Mean
    • No skew: Mean = Median = Mode

    Standard Deviation

    • Central tendency: the measure of four Mean, Median, Mode, and Standard Deviation
    • Variance: the average of the squared differences from the mean, Σ(X-Xav)²/N
    • Standard Deviation S = √(X-Xav)²/N
    • 1 standard deviation = 68% of the data set
    • 2 standard deviations = 95.45% of the data set
    • 3 standard deviations = 99.73% of the data set

    Statistic and Parameter

    • Statistic: a numerical value that describes data taken from a sample
    • Parameter: a characteristic of the population, summarizes data, and entire population
    • F-test: used to measure the accuracy of a statistic

    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 means

    Type I and Type II Errors

    • Type I error: reject the null hypothesis when it is true (α)
    • Type II error: fail to reject the null hypothesis when it is false (β)

    Coefficient of Variation

    • Relative standard deviation RSD, measures the dispersion of a probability distribution or frequency distribution
    • Coefficient of variation CV = S/Xmean = %
    • Cumulative error: used to calculate the upper confidence limit and lower confidence limit for air sampling

    Energy

    • Kinetic Energy (K.E.) = ½ mv², where m is the mass of the object and v is the speed of the object
    • Potential Energy (P.E.) = mgh, where m is the mass of the object, g is the gravitational acceleration of the earth (9.8 m/s²), and h is the height above the earth's surface
    • Elastic Potential Energy (P.E. elastic) = ½ kx², where k is the spring constant and x is the amount of compression

    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 is exerted by a compressed or stretched spring
    • Frictional Force (F) = μN, where μ is the coefficient of friction and N is the force acting on the surface in a direction that is normal (perpendicular) to the surface

    Force and Distance

    • F₁D₁ = F₂D₂, where F₁ and F₂ are forces and D₁ and D₂ are distances

    Momentum

    • ρ = mv, where ρ is the momentum, m is the mass, and v is the velocity

    Velocity

    • v = v₀ + at, where v is the final velocity, v₀ is the original velocity, a is the acceleration, and t is the time
    • S = v₀t + ½ at², where S is the distance from the original position, v₀ is the initial velocity, a is the acceleration, and t is the time

    Work Done

    • W = FS, where W is the work done, F is the force, and S is the distance from the original position

    Newton's Second Law

    • F = ma/g, where F is the force, m is the mass, a is the acceleration, and g is the gravitational acceleration of the earth (9.8 m/s²)

    Statistics

    • Histogram is a graph used to distribute frequency of the data
    • Mean is the average value of a data set and is found using the calculation ΣXn/n
    • Median is the central number of a data set
    • Mode is the number in a data set that occurs most frequently

    Temperature

    • Tc = Tf - 32/1.8, where Tc is the temperature in Celsius and Tf is the temperature in Fahrenheit
    • Tk = Tc + 273, where Tk is the temperature in Kelvin
    • F = 460 + R, where F is the temperature in Fahrenheit and R is the temperature in Rankine

    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 = 3.7 x 10¹⁰ 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/sec² = 9.8 m/sec²
    • velocity of light = 3.0 x 10⁸ m/sec
    • Planck's constant = 6.626 x 10⁻³⁴ J-sec
    • Avogadro's number = 6.024 x 10²³/gram-mole

    Area and Volume

    • Area of a rectangle = length * width
    • Area of a square = s², where s is the side
    • Area of a triangle = (1/2) b * h, where b is the base and h is the height
    • Area of a circle = π * r², where r is the radius
    • Volume of a rectangular solid = l * w * h
    • Volume of a cube = a³
    • Volume of a cylinder = πr²h
    • Volume of a prism = B * h
    • Volume of a sphere = (4/3)πr³
    • Volume of a pyramid = (1/3) * B * h

    Trigonometric Functions

    • C² = a² + b² - 2ab cos 0C
    • A/SinA = b/SinB = c/SinC

    Energy

    • Kinetic Energy (K.E.) = ½ mv², where m is the mass of the object and v is the speed of the object
    • Potential Energy (P.E.) = mgh, where m is the mass of the object, g is the gravitational acceleration of the earth (9.8 m/s²), and h is the height above the earth's surface
    • Elastic Potential Energy (P.E. elastic) = ½ kx², where k is the spring constant and x is the amount of compression

    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 is exerted by a compressed or stretched spring
    • Frictional Force (F) = μN, where μ is the coefficient of friction and N is the force acting on the surface in a direction that is normal (perpendicular) to the surface

    Force and Distance

    • F₁D₁ = F₂D₂, where F₁ and F₂ are forces and D₁ and D₂ are distances

    Momentum

    • ρ = mv, where ρ is the momentum, m is the mass, and v is the velocity

    Velocity

    • v = v₀ + at, where v is the final velocity, v₀ is the original velocity, a is the acceleration, and t is the time
    • S = v₀t + ½ at², where S is the distance from the original position, v₀ is the initial velocity, a is the acceleration, and t is the time

    Work Done

    • W = FS, where W is the work done, F is the force, and S is the distance from the original position

    Newton's Second Law

    • F = ma/g, where F is the force, m is the mass, a is the acceleration, and g is the gravitational acceleration of the earth (9.8 m/s²)

    Statistics

    • Histogram is a graph used to distribute frequency of the data
    • Mean is the average value of a data set and is found using the calculation ΣXn/n
    • Median is the central number of a data set
    • Mode is the number in a data set that occurs most frequently

    Temperature

    • Tc = Tf - 32/1.8, where Tc is the temperature in Celsius and Tf is the temperature in Fahrenheit
    • Tk = Tc + 273, where Tk is the temperature in Kelvin
    • F = 460 + R, where F is the temperature in Fahrenheit and R is the temperature in Rankine

    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 = 3.7 x 10¹⁰ 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/sec² = 9.8 m/sec²
    • velocity of light = 3.0 x 10⁸ m/sec
    • Planck's constant = 6.626 x 10⁻³⁴ J-sec
    • Avogadro's number = 6.024 x 10²³/gram-mole

    Area and Volume

    • Area of a rectangle = length * width
    • Area of a square = s², where s is the side
    • Area of a triangle = (1/2) b * h, where b is the base and h is the height
    • Area of a circle = π * r², where r is the radius
    • Volume of a rectangular solid = l * w * h
    • Volume of a cube = a³
    • Volume of a cylinder = πr²h
    • Volume of a prism = B * h
    • Volume of a sphere = (4/3)πr³
    • Volume of a pyramid = (1/3) * B * h

    Trigonometric Functions

    • C² = a² + b² - 2ab cos 0C
    • A/SinA = b/SinB = c/SinC

    Energy

    • Kinetic Energy (K.E.) = ½ mv², where m is the mass of the object and v is the speed of the object
    • Potential Energy (P.E.) = mgh, where m is the mass of the object, g is the gravitational acceleration of the earth (9.8 m/s²), and h is the height above the earth's surface
    • Elastic Potential Energy (P.E. elastic) = ½ kx², where k is the spring constant and x is the amount of compression

    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 is exerted by a compressed or stretched spring
    • Frictional Force (F) = μN, where μ is the coefficient of friction and N is the force acting on the surface in a direction that is normal (perpendicular) to the surface

    Force and Distance

    • F₁D₁ = F₂D₂, where F₁ and F₂ are forces and D₁ and D₂ are distances

    Momentum

    • ρ = mv, where ρ is the momentum, m is the mass, and v is the velocity

    Velocity

    • v = v₀ + at, where v is the final velocity, v₀ is the original velocity, a is the acceleration, and t is the time
    • S = v₀t + ½ at², where S is the distance from the original position, v₀ is the initial velocity, a is the acceleration, and t is the time

    Work Done

    • W = FS, where W is the work done, F is the force, and S is the distance from the original position

    Newton's Second Law

    • F = ma/g, where F is the force, m is the mass, a is the acceleration, and g is the gravitational acceleration of the earth (9.8 m/s²)

    Statistics

    • Histogram is a graph used to distribute frequency of the data
    • Mean is the average value of a data set and is found using the calculation ΣXn/n
    • Median is the central number of a data set
    • Mode is the number in a data set that occurs most frequently

    Temperature

    • Tc = Tf - 32/1.8, where Tc is the temperature in Celsius and Tf is the temperature in Fahrenheit
    • Tk = Tc + 273, where Tk is the temperature in Kelvin
    • F = 460 + R, where F is the temperature in Fahrenheit and R is the temperature in Rankine

    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 = 3.7 x 10¹⁰ 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/sec² = 9.8 m/sec²
    • velocity of light = 3.0 x 10⁸ m/sec
    • Planck's constant = 6.626 x 10⁻³⁴ J-sec
    • Avogadro's number = 6.024 x 10²³/gram-mole

    Area and Volume

    • Area of a rectangle = length * width
    • Area of a square = s², where s is the side
    • Area of a triangle = (1/2) b * h, where b is the base and h is the height
    • Area of a circle = π * r², where r is the radius
    • Volume of a rectangular solid = l * w * h
    • Volume of a cube = a³
    • Volume of a cylinder = πr²h
    • Volume of a prism = B * h
    • Volume of a sphere = (4/3)πr³
    • Volume of a pyramid = (1/3) * B * h

    Trigonometric Functions

    • C² = a² + b² - 2ab cos 0C
    • A/SinA = b/SinB = c/SinC

    Conversions

    • 1 meter (m) equals 100 centimeters (cm), 1000 millimeters (mm), and 1,000,000 microns
    • 1 kilometer (km) equals 1000 meters
    • 1 mile equals 5280 feet, 1609 meters, and 1.47 feet per second
    • 1 inch equals 2.54 cm, and 1 foot equals 30.48 cm and 12 inches
    • 1 meter equals 3.2 feet
    • 1 foot equals 12 inches
    • 1 mile per hour equals 1.47 feet per second, 0.4470 meters per second, and 0.8618 miles per hour
    • 1 foot per second equals 0.3048 meters per second, 0.5921 knots, and 0.8618 miles per hour

    Length

    • 2.54 cm equals 1 inch
    • 25.4 mm equals 1 inch
    • 12 inches equals 1 foot
    • 3 feet equals 1 yard
    • 5280 feet equals 1 mile
    • 1760 yards equals 1 mile
    • 1.6 kilometers equals 1 mile
    • 0.868 nautical miles equals 1 US mile

    Area

    • 1 square inch (sq.in.) equals 6.452 square centimeters (sq.cm) and 6452 square millimeters (sq.mm)
    • 1 square foot (sq.ft) equals 144 square inches and 0.09290 square meters
    • 1 square yard (sq.yd) equals 9 square feet

    Volume

    • 1 cubic centimeter (cm3) equals 1 milliliter (mL)
    • 1 cubic inch (in3) equals 16.39 cubic centimeters
    • 1 cubic foot (ft3) equals 1728 cubic inches and 0.02832 cubic meters
    • 1 liter (L) equals 1.057 quarts (US)

    Temperature

    • To convert to absolute temperature scales, use: oR = oF + 460, and oK = oC + 273
    • Temperature conversion formulas: Tc=Tf-32/1.8, Tk=Tc+273, F=460 + R

    Energy

    • 1 calorie equals 4.186 Joules
    • 1 British thermal unit (BTU) equals 1055 Joules
    • 1 foot-pound equals 1.356 Joules
    • 1 Joule equals 1 kg · m/s2

    Radiation

    • 1 rad equals 10^-2 gray
    • 1 rem equals 10^-2 sievert
    • 1 curie equals 3.7x10^10 becquerel
    • 1 becquerel equals 1 disintegration/second

    Density of Water

    • 1 gram per cubic centimeter (gm/cm3) equals 1.94 slugs per cubic foot (weight density equals 62.4 pounds per cubic foot)

    Light

    • 1 candela equals 1 lumen per steradian
    • 1 footcandle equals 10.76 candela per square meter equals 10.76 lux

    Physical Constants

    • Acceleration of gravity equals 32.2 feet per second squared equals 9.8 meters per second squared
    • Velocity of light equals 3.0 x 10^8 meters per second
    • Planck's constant equals 6.626 x 10^-34 J-sec
    • Avogadro's number equals 6.024 x 10^23 per gram-mole

    Boolean Postulates

    • Not applicable

    Area Formulas

    • Rectangle: Area equals length times width
    • Square: Area equals side squared
    • Triangle: Area equals half times base times height
    • Circle: Area equals pi times radius squared

    Volume Formulas

    • Rectangular solid or cuboid: Volume equals length times width times height
    • Cube: Volume equals edge cubed
    • Cylinder: Volume equals pi times radius squared times height
    • Prism: Volume equals base area times height
    • Sphere: Volume equals four-thirds times pi times radius cubed
    • Pyramid: Volume equals one-third times base area times height

    Trigonometric Functions

    • C2 equals a2 plus b2 minus 2ab times cosine C
    • A divided by sine A equals b divided by sine B equals c divided by sine C

    Kinetic Energy

    • Kinetic energy equals half times mass times velocity squared

    Potential Energy

    • Potential energy equals mass times gravitational acceleration times height
    • Elastic potential energy equals half times spring constant times compression squared

    Force

    • One newton equals the amount of force required to give a 1-kilogram mass an acceleration of 1 meter per second squared
    • Tension forces are required to pull an object (opposite of compression)
    • Spring force exerted by a compressed or stretched spring
    • Frictional force equals coefficient of friction times normal force

    Statistics

    • Left-skewed distribution: Mean less than Median less than Mode
    • Right-skewed distribution: Mode less than Median less than Mean
    • No skew-symmetrical distribution: Mean equals Median equals Mode
    • Standard deviation: average distance of all observations from the mean
    • Variance equals summation of X minus X average squared divided by N
    • Standard deviation S equals square root of summation of X minus X average squared divided by N
    • One standard deviation equals 68% of the data set
    • Two standard deviations equal 95.45% of the data set
    • Three standard deviations equal 99.73% of the data set

    Statistic and Parameter

    • Statistic: numerical value that describes data taken from a sample
    • Parameter: describes the characteristic of the population

    Null Hypothesis

    • No significant difference between the population
    • If any observed difference is due to sampling or experimental error
    • H0 equals M1 equals M2, no difference between population
    • Used in conjunction with 95% confidence means that there is a 95% chance of true

    Type I and Type II Errors

    • Type I error: reject the null hypothesis when it is true
    • Type II error: fail to reject the null hypothesis when it is false

    Coefficient of Variation

    • Relative standard deviation RSD, measure of the dispersion of probability distribution or frequency distribution
    • Coefficient of variation CV equals standard deviation divided by mean times 100%

    Cumulative Error

    • 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

    Conversions

    • 1 meter (m) equals 100 centimeters (cm), 1000 millimeters (mm), and 1,000,000 microns
    • 1 kilometer (km) equals 1000 meters
    • 1 mile equals 5280 feet, 1609 meters, and 1.47 feet per second
    • 1 inch equals 2.54 cm, and 1 foot equals 30.48 cm and 12 inches
    • 1 meter equals 3.2 feet
    • 1 foot equals 12 inches
    • 1 mile per hour equals 1.47 feet per second, 0.4470 meters per second, and 0.8618 miles per hour
    • 1 foot per second equals 0.3048 meters per second, 0.5921 knots, and 0.8618 miles per hour

    Length

    • 2.54 cm equals 1 inch
    • 25.4 mm equals 1 inch
    • 12 inches equals 1 foot
    • 3 feet equals 1 yard
    • 5280 feet equals 1 mile
    • 1760 yards equals 1 mile
    • 1.6 kilometers equals 1 mile
    • 0.868 nautical miles equals 1 US mile

    Area

    • 1 square inch (sq.in.) equals 6.452 square centimeters (sq.cm) and 6452 square millimeters (sq.mm)
    • 1 square foot (sq.ft) equals 144 square inches and 0.09290 square meters
    • 1 square yard (sq.yd) equals 9 square feet

    Volume

    • 1 cubic centimeter (cm3) equals 1 milliliter (mL)
    • 1 cubic inch (in3) equals 16.39 cubic centimeters
    • 1 cubic foot (ft3) equals 1728 cubic inches and 0.02832 cubic meters
    • 1 liter (L) equals 1.057 quarts (US)

    Temperature

    • To convert to absolute temperature scales, use: oR = oF + 460, and oK = oC + 273
    • Temperature conversion formulas: Tc=Tf-32/1.8, Tk=Tc+273, F=460 + R

    Energy

    • 1 calorie equals 4.186 Joules
    • 1 British thermal unit (BTU) equals 1055 Joules
    • 1 foot-pound equals 1.356 Joules
    • 1 Joule equals 1 kg · m/s2

    Radiation

    • 1 rad equals 10^-2 gray
    • 1 rem equals 10^-2 sievert
    • 1 curie equals 3.7x10^10 becquerel
    • 1 becquerel equals 1 disintegration/second

    Density of Water

    • 1 gram per cubic centimeter (gm/cm3) equals 1.94 slugs per cubic foot (weight density equals 62.4 pounds per cubic foot)

    Light

    • 1 candela equals 1 lumen per steradian
    • 1 footcandle equals 10.76 candela per square meter equals 10.76 lux

    Physical Constants

    • Acceleration of gravity equals 32.2 feet per second squared equals 9.8 meters per second squared
    • Velocity of light equals 3.0 x 10^8 meters per second
    • Planck's constant equals 6.626 x 10^-34 J-sec
    • Avogadro's number equals 6.024 x 10^23 per gram-mole

    Boolean Postulates

    • Not applicable

    Area Formulas

    • Rectangle: Area equals length times width
    • Square: Area equals side squared
    • Triangle: Area equals half times base times height
    • Circle: Area equals pi times radius squared

    Volume Formulas

    • Rectangular solid or cuboid: Volume equals length times width times height
    • Cube: Volume equals edge cubed
    • Cylinder: Volume equals pi times radius squared times height
    • Prism: Volume equals base area times height
    • Sphere: Volume equals four-thirds times pi times radius cubed
    • Pyramid: Volume equals one-third times base area times height

    Trigonometric Functions

    • C2 equals a2 plus b2 minus 2ab times cosine C
    • A divided by sine A equals b divided by sine B equals c divided by sine C

    Kinetic Energy

    • Kinetic energy equals half times mass times velocity squared

    Potential Energy

    • Potential energy equals mass times gravitational acceleration times height
    • Elastic potential energy equals half times spring constant times compression squared

    Force

    • One newton equals the amount of force required to give a 1-kilogram mass an acceleration of 1 meter per second squared
    • Tension forces are required to pull an object (opposite of compression)
    • Spring force exerted by a compressed or stretched spring
    • Frictional force equals coefficient of friction times normal force

    Statistics

    • Left-skewed distribution: Mean less than Median less than Mode
    • Right-skewed distribution: Mode less than Median less than Mean
    • No skew-symmetrical distribution: Mean equals Median equals Mode
    • Standard deviation: average distance of all observations from the mean
    • Variance equals summation of X minus X average squared divided by N
    • Standard deviation S equals square root of summation of X minus X average squared divided by N
    • One standard deviation equals 68% of the data set
    • Two standard deviations equal 95.45% of the data set
    • Three standard deviations equal 99.73% of the data set

    Statistic and Parameter

    • Statistic: numerical value that describes data taken from a sample
    • Parameter: describes the characteristic of the population

    Null Hypothesis

    • No significant difference between the population
    • If any observed difference is due to sampling or experimental error
    • H0 equals M1 equals M2, no difference between population
    • Used in conjunction with 95% confidence means that there is a 95% chance of true

    Type I and Type II Errors

    • Type I error: reject the null hypothesis when it is true
    • Type II error: fail to reject the null hypothesis when it is false

    Coefficient of Variation

    • Relative standard deviation RSD, measure of the dispersion of probability distribution or frequency distribution
    • Coefficient of variation CV equals standard deviation divided by mean times 100%

    Cumulative Error

    • 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

    Conversions

    • 1 meter (m) = 100 centimeters (cm) = 1000 millimeters (mm) = 1,000,000 microns
    • 1 kilometer (km) = 1000 meters (m)
    • 1 mile = 5280 feet = 1609 meters
    • 1 mile per hour = 1.47 feet per second
    • 1 inch = 2.54 centimeters = 25.4 millimeters
    • 1 foot = 30.48 centimeters = 12 inches
    • 1 meter = 3.2 feet

    Energy

    • 1 calorie (cal) = 0.003968 British Thermal Units (Btu) = 4.187 Joules (J)
    • 1 Btu = 252 calories
    • 1 joule (J) = 0.239 calories

    Velocity

    • 1 foot per second (ft/s) = 0.3048 meters per second (m/s) = 0.8618 miles per hour (mi/h) = 0.5921 knots
    • 1 meter per second (m/s) = 3.281 feet per second = 2.237 miles per hour
    • 1 mile per hour = 0.4470 meters per second = 1.467 feet per second
    • 1 knot = 0.5148 meters per second = 1.151 miles per hour = 1.689 feet per second

    Area

    • 1 square inch (sq.in.) = 6.452 square centimeters = 6452 square millimeters
    • 1 square foot (sq.ft) = 144 square inches = 0.09290 square meters
    • 1 square yard (sq.yd) = 9 square feet

    Volume

    • 1 cubic centimeter (cm³) = 1 milliliter (mL)
    • 1 cubic inch (in³) = 16.39 cubic centimeters
    • 1 cubic foot (ft³) = 1728 cubic inches = 0.02832 cubic meters
    • 1 liter (L) = 1.057 quarts (US) = 0.9463 quarts (Imperial)
    • 1 US gallon = 0.8327 Imperial gallons

    Mass and Weight

    • 1 ounce (oz) = 28.35 grams
    • 1 pound (lb) = 0.454 kilograms
    • 1 ton (US) = 2000 pounds = 1000 kilograms
    • 1 dram = 1771.85 milligrams

    Force, Pressure, or Stress

    • 1 pound-force (lbf) = 4.45 Newtons
    • 1 pound-force per square inch (psi) = 6.89 kilopascals

    Illumination

    • 1 foot-candle = 10.76 lux
    • 1 foot-lambert = 3.426 candelas per square meter

    Other Conversions

    • 1 radian = 180°/π
    • 1 candela = 1 lumen per steradian
    • 1 foot-candle = 10.76 lux
    • 1 tesla = 10,000 gauss

    Physical Constants

    • Acceleration of gravity = 32.2 feet per second squared = 9.8 meters per second squared
    • Velocity of light = 3.0 × 10^8 meters per second
    • Planck's constant = 6.626 × 10^−34 Joule-seconds
    • Avogadro's number = 6.024 × 10^23 per gram-mole

    Radiation

    • 1 rad = 10^−2 gray
    • 1 rem = 10^−2 sievert
    • 1 curie = 3.7 × 10^10 becquerels
    • 1 becquerel = 1 disintegration per second

    Statistics

    • Histogram: a graph used to distribute frequency of data
    • Mean: the average value of a data set, calculated using ΣXn/n
    • Median: the central number of a data set
    • Mode: the number in a data set that occurs most frequently
    • Skewed distributions: left-skewed (mean < median < mode), right-skewed (mode < median < mean), and no skew (symmetrical distribution: mean = median = mode)

    Standard Deviation

    • A measure of the average distance of all observations from the mean
    • Variance = Σ(X-Xav)^2/N
    • Standard deviation = square root of variance

    Statistics and Parameters

    • Statistic: a numerical value that describes data taken from a sample
    • Parameter: a characteristic of the population, summarizing data from the entire population

    Hypothesis Testing

    • Null hypothesis: no significant difference between populations
    • Type I error: rejecting the null hypothesis when it's true (false positive)
    • Type II error: failing to reject the null hypothesis when it's false (false negative)
    • Alpha (α): the probability of a Type I error
    • Beta (β): the probability of a Type II error

    Conversions

    • 1 meter (m) is equal to 100 centimeters (cm) and 1000 millimeters (mm)
    • 1 kilometer (km) is equal to 1000 meters (m)
    • 1 mile is equal to 5280 feet and 1609 meters
    • 1 mile per hour is equal to 1.47 feet per second
    • 1 inch is equal to 2.54 centimeters and 25.4 millimeters
    • 1 foot is equal to 30.48 centimeters and 12 inches
    • 1 meter is equal to 3.2 feet

    Energy

    • 1 calorie (cal) is equal to 0.003968 British thermal units (Btu) and 4.187 joules (J)
    • 1 Btu is equal to 252 calories
    • 1 cal is equal to 4.187 J

    Velocity

    • 1 foot per second (ft/s) is equal to 0.3048 meters per second (m/s) and 0.8618 miles per hour (mi/h)
    • 1 foot per second is equal to 0.5921 knots
    • 1 meter per second is equal to 3.281 feet per second and 2.237 miles per hour
    • 1 mile per hour is equal to 0.4470 meters per second and 1.467 feet per second
    • 1 knot is equal to 0.5148 meters per second and 1.151 miles per hour

    Area

    • 1 square inch (sq in) is equal to 6.452 square centimeters (sq cm) and 6452 square millimeters (sq mm)
    • 1 square foot (sq ft) is equal to 144 square inches and 0.09290 square meters
    • 1 square yard (sq yd) is equal to 9 square feet

    Volume

    • 1 cubic centimeter (cm³) is equal to 1 milliliter (mL)
    • 1 cubic inch (in³) is equal to 16.39 cubic centimeters
    • 1 cubic foot (ft³) is equal to 1728 cubic inches
    • 1 cubic foot is equal to 0.02832 cubic meters
    • 1 liter (L) is equal to 1.057 quarts (US)

    Density

    • 1 pound per cubic foot (lb/cu ft) is equal to 0.01602 grams per cubic centimeter (g/cm³)
    • 1 gram per cubic centimeter is equal to 62.42 pounds per cubic foot
    • 1 gram per cubic centimeter is equal to 1000 kilograms per cubic meter (kg/m³)

    Potential Energy

    • Potential energy (PE) is equal to mgh, where m is the mass of the object, g is the gravitational acceleration, and h is the height above the earth's surface
    • Elastic potential energy is equal to ½kx², where k is the spring constant and x is the amount of compression

    Force

    • A newton (N) is the amount of force required to give a 1-kilogram mass an acceleration of 1 meter per second squared
    • Tension forces are required to pull an object, opposite of compression
    • Spring force is exerted by a compressed or stretched spring
    • Frictional force (F) is equal to μN, where μ is the coefficient of friction and N is the normal force

    Force and Distance

    • F₁D₁ = F₂D₂, where F is the force and D is the distance

    Momentum

    • Momentum (ρ) is equal to mv, where m is the mass and v is the velocity

    Velocity

    • Velocity (v) is equal to v₀ + at, where v₀ is the initial velocity, a is the acceleration, and t is the time
    • v² = v₀² + 2as, where v is the final velocity, v₀ is the initial velocity, a is the acceleration, and s is the distance
    • s = v₀t + ½at², where s is the distance, v₀ is the initial velocity, t is the time, and a is the acceleration

    Work Done

    • Work done (W) is equal to FS, where F is the force and S is the distance
    • W = ∫F dl, where F is the force and dl is the infinitesimal displacement

    Newton's Second Law

    • F = ma/g, where F is the force, m is the mass, a is the acceleration, and g is the gravitational acceleration

    Statistics

    • Definition: A histogram is a graph used to distribute the frequency of the data
    • Mean is the average value of a data set and is found using the calculation ΣXn/n
    • Median is the central number of a data set
    • Mode is the number in a data set that occurs most frequently
    • Left skewed: Mean < Median < Mode
    • Right skewed: Mode < Median < Mean
    • No skew: Mean = Median = Mode

    Standard Deviation

    • Central tendency is the measure of the mean, median, mode, and standard deviation
    • Standard deviation (S) is the square root of (X-X̄)²/N
    • Variance is the average of the squared differences from the mean
    • 1 standard deviation (1σ) is equal to 68% of the data set
    • 2 standard deviations (2σ) are equal to 95.45% of the data set
    • 3 standard deviations (3σ) are equal to 99.73% of the data set

    Statistic and Parameter

    • Statistic: A numerical value that describes data taken from a sample
    • Parameter: A characteristic of the population
    • F-test is used to measure the accuracy of the sample

    Null Hypothesis

    • H₀: M₁ = M₂, no significant difference between the populations
    • Used in conjunction with 95% confidence means that there is a 95% chance of the true hypothesis

    Type I and Type II Errors

    • Type I error: Rejecting the null hypothesis when it is true
    • Type II error: Failing to reject the null hypothesis when it is false

    Coefficient of Variation

    • Coefficient of variation (CV) is a measure of the dispersion of a probability distribution or frequency distribution
    • CV is equal to the ratio of the standard deviation to the mean

    Cumulative Error

    • 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

    Studying That Suits You

    Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

    Quiz Team

    Related Documents

    Domain 1 - Math and Science PDF

    Description

    Test your knowledge of unit conversions in length, energy, and more with this advanced science and math quiz. Review common conversions and practice applying them to real-world problems.

    More Like This

    Use Quizgecko on...
    Browser
    Open
    Browser
    Browser