Engineering

Q: The detailed shape of a normal-distribution curve is determined by its mean and standard deviation values. An experiment with a small standard deviation will produce a tall, narrow curve; whereas a large standard deviation will result in a short, wide curve. a. True b. False

Q: The probability distribution for many engineering experiments is approximated by a. the average (mean) value of the data. b. a normal distribution. c. the standard deviation. d. none of the above.

Q: For any probability distribution, the sum of probabilities is always a. 0 b. 0.5 c. 1 d. equal to the standard deviation.

Q: A probability distribution shows the probability values for the occurrence of the outcomes of an experiment. A probability distribution that has a bell-shaped curve is called a normal distribution. a. True b. False

Q: A list of temperature readings (in degrees Fahrenheit) is shown below. Calculate the standard deviation for these data: 72, 76, 81, 69, 73, 76, 75, 82, 83, 68, 69, 76, 74, 65, 62

Q: A list of temperature readings (in degrees Fahrenheit) is shown below. Calculate the variance for these data: 72, 76, 81, 69, 73, 76, 75, 82, 83, 68, 69, 76, 74, 65, 62

Q: The standard deviation is a. the square root of the variance. b. the square of the variance. c. the root mean squared of the variance. d. the absolute value of the variance.

Q: A common way of measuring the dispersion of data is by calculating the a. spread b. scattering c. mode d. variance

Q: A list of temperature readings (in degrees Fahrenheit) is shown below. Calculate the median temperature: 72, 76, 81, 69, 73, 76, 75, 82, 83, 68, 69, 76, 74, 65, 62

Q: Median is the value in the middle of a data. It is that value that separates the higher half of the data from its lower half. a. True b. False

Q: A list of temperature readings (in degrees Fahrenheit) is shown below. Calculate the mean temperature: 72, 76, 81, 69, 73, 76, 75, 82, 83, 68, 69, 76, 74, 65, 62

Q: The arithmetic average of a list of numbers is known as the a. median b. mode c. mean d. root mean squared

Q: Random errors a. can be detected and avoided by properly calibrating instruments. b. are generated by a number of unpredictable variations. c. rarely occur in a properly designed experiment. d. can be removed from the data set through proper statistical analysis.

Q: Systemic errors are errors a. that occur throughout the entire system. b. that occur on a frequent basis. c. associated with using an inaccurate instrument. d. associated with the design and setup of the experiment.

Q: There are basically two types of observation errors: a. personal and professional. b. systemic and random. c. partial and complete. d. visual and measured.

Q: The cumulative frequency does not show the cumulative number of data with values up to and including those in the given range. a. True b. False

Q: A histogram is a way to show the range of data and their frequency. The height of the bars shows the frequency of the data within the given ranges. a. True b. False

Q: In statistics, one way of showing the range of values and their frequency is by showing a mean value. a. True b. False

Q: One simple way of organizing the data better would be to identify the lowest and the highest values, and then group the data into equal intervals or ranges: a. True b. False

Q: In statistics, smaller portion of the entire data or population is commonly called a a. subset b. group c. data set d. sample

Q: In statistics, something with a large number of data points is commonly called a a. population b. group c. data set d. sample

Q: Statistics deals with methods and techniques that can be used to draw conclusions about the characteristics of something with a large number of data points sing a smaller portion of the entire data. a. True b. False

Q: That area of science that deals with collection, organization, analysis, and interpretation of data is known as a. probability b. statics c. statistics d. mathematics

Q: There are 20 red marbles and 10 blue marbles mixed together in a cloth bag. If you reach in and pull out a marble, without looking, what are the odds of selecting a blue marble? a. 1:2 b. 1:3 c. 1:4 d. 1:5

Q: There are 20 red marbles and 10 blue marbles mixed together in a cloth bag. If you reach in and pull out a marble, without looking, what is the probability of selecting a blue marble? a. 0.75 b. 0.50 c. 0.25 d. 0.33

Q: This question has four possible answers listed below and only one of them is correct. If you select one at random, what are the odds that you pick the correct answer? a. 1:2 b. 1:3 c. 1:4 d. 1:5

Q: This question has four possible answers listed below and only one of them is correct. If you select one at random, what is the probability that you pick the correct answer? a. 0.75 b. 0.50 c. 0.25 d. 0.10

Q: In probability, a random experiment is one that has random outcomes that cannot be predicted exactly. a. True b. False

Q: In probability, the result of an experiment is called a. the end product b. an outcome c. the answer d. the product

Q: In probability, each time you repeat an experiment is called a a. trial b. test run c. measurement d. guess

Q: Manufacturing engineers use statistics for quality control assurance of the products they produce. a. True b. False

Q: Civil engineers use statistical models to study the reliability of construction materials and structures and to design for flood control and water supply management. a. True b. False

Q: The term rate of change always refers to how a physical quantity varies with time. a. True b. False

Q: Calculate the average rate of change for the following functions: between and

Q: Calculate the average rate of change for the following function: between and

Q: The rate of change refers to how a dependent variable changes with respect to an independent variable. a. True b. False, that's the definition of slope.

Q: Calculus is commonly divided into two broad areas: a. single variable and multivariable calculus. b. differential and integral calculus. c. vector and matrix calculus. d. linear and nonlinear calculus.

Q: A company advertises a gadget at the regular price of $8, with a coupon for a second gadget at half price. The company sold 50 gadgets for a total of $364. How many coupons were redeemed?

Q: Solve the following set of equations using the Gaussian method:

Q: Solve the following set of equations using matrices:

Q: Given the following matrix: calculate the determinant of .

Q: Given the following matrix: find .

Q: Perform the following operations on the given matrices:

Q: The gravitational force between two masses is modeled using the following function: where gravitational force (Newtons) mass number 1 (kilograms) mass number 2 (kilograms) distance between centers of masses (meters) Which type of mathematical model is used here to describe the gravitational force? a. Linear model b. Nonlinear model c. Exponential model d. Trigonometric model

Q: The position of an object subjected to constant acceleration can be described by the following function: where position (m) initial position (m) initial velocity (m/s) acceleration (m/s^2) time (sec) Which type of mathematical model is used here to describe the object's position? a. Linear model b. Nonlinear model c. Exponential model d. Trigonometric model

Q: The path of flight (trajectory) of a football thrown by a quarterback is described by the following function: where y = vertical position of football relative to the ground (ft) x = horizontal position of football relative to launch position (ft) How high above the ground is the football when it is 30 yards downfield from the quarterback? a. 26.2 ft b. 29.8 ft c. 13.8 ft d. 53.8 ft

Q: The path of flight (trajectory) of a football thrown by a quarterback is described by the following function: where y = vertical position of football relative to the ground (ft) x = horizontal position of football relative to launch position (ft) How high above the ground is the football as it leaves the quarterback's hand? a. 0.002 ft b. 0.7 ft c. 7 ft d. 7.7 ft

Q: The path of flight (trajectory) of a football thrown by a quarterback is described by the following function: where y = vertical position of football relative to the ground y0 = vertical launch position of football relative to the ground x = horizontal position of football relative to launch position g = magnitude of gravitational acceleration v0 = launch speed Î¸ = launch angle relative to horizontal Which type of mathematical model is used here to describe the football's trajectory? a. Linear model b. Nonlinear model c. Exponential model d. Trigonometric model

Q: The velocity of an object under constant acceleration can be modeled using the following function: v(t) = v0 + at where v = velocity v0 = initial velocity a = acceleration t = time Which type of mathematical model is used to describe velocity in this application? a. Linear model b. Nonlinear model c. Exponential model d. Logarithmic model

Q: Hooke's Law describes the relationship between force F and deflection x in a spring according to the following equation: . Which type of mathematical model is used in Hooke's Law? a. Linear model b. Nonlinear model c. Exponential model d. Logarithmic model

Q: For nonlinear models (equations) the slope is constant. a. True b. False

Q: For many engineering situations, exponential and logarithmic models are used to describe the relationships between dependent and independent variables because they predict the actual relationships more accurately than linear models do. a. True b. False

Q: For many engineering situations, nonlinear models are used to describe the relationships between dependent and independent variables because they predict the actual relationships more accurately than linear models do. a. True b. False

Q: Find an equation of the line through (5,2) that is perpendicular to the line .

Q: Find an equation of the line through (5,2) that is parallel to the line .

Q: Find an equation of the line that passes through the points (-1,2) and (3,-4).

Q: Find an equation of the line through (1,-3) with a slope of .

Q: The pitch of a roof refers to its "steepness" and is expressed in terms of the number of inches the roof rises for each 12 inches of run. For example, an 8-12 pitch means that the roof rises 8 inches vertically for each 12 inches of horizontal run. What is the slope of a roof with an 8-12 pitch?

Q: Find the slope of the line that passes thru the points (2,1) and (8,5).

Q: The quantity or numerical value within a linear model that shows by how much the dependent variable changes each time a change in the independent variable is introduced is known as a. the x-intercept. b. the y-intercept. c. the dependent intercept. d. the slope.

Q: In the spring equation F = k x, the deformation of the spring, x is called a. a dependent variable b. an independent variable c. none of the above

Q: In the spring equation F = k x, the spring force, F is called a. a dependent variable b. an independent variable c. none of the above

Q: The simplest form of models commonly used to describe a wide range of engineering situations is a. linear equations. b. nonlinear equations. c. exponential equations. d. logarithmic equations.

Q: What is the name of the following Greek alphabetic character? a. Omega b. Mu c. Gamma d. Lambda

Q: What is the name of the following Greek alphabetic character? a. Epsilon b. Zeta c. Gamma d. Lambda

Q: Greek alphabetic characters quite commonly are used to express angles, dimensions, and physical variables in drawings and in mathematical equations and expressions. It is therefore very important to be familiar with these characters in order to communicate with other engineers. a. True b. False

Q: Mathematics is a language that has its own symbols and terminology. As an engineering student, you need to learn mathematical symbols and their meanings. a. True b. False

Q: In general, engineering problems are mathematical models of physical situations. a. True b. False

Q: Initial conditions tell us about the initial conditions of a system (at time t = 0), before a disturbance or a change is introduced.a. Trueb. False

Q: Boundary conditions provide information about what is happening physically at the boundaries of a problem. a. True b. False

Q: What kind of mathematical model contains derivatives of functions? a. nonlinear equation b. differential equation c. exponential equation d. logarithmic equation

Q: Many engineering problems are modeled using differential equations with a set of corresponding boundary and/or initial conditions. a. True b. False

Q: Evaluate:

Q: Find the derivative of .

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