FE Exam Flashcards: Engineering Equations, Units & Handbook Skills

Tarjetas de este mazo

1. Tarjeta 1

   Pregunta

   SI base unit of length?

   Respuesta

   The metre, symbol $m$.

2. Tarjeta 2

   Pregunta

   Slope between two points?

   Respuesta

   $$m=\frac{y_2-y_1}{x_2-x_1}$$

   This requires $x_2\ne x_1$; slope is the change in the dependent variable per unit change in the independent variable.

3. Tarjeta 3

   Pregunta

   Net force relationship for constant mass in an inertial frame?

   Respuesta

   $$\sum\mathbf{F}=m\mathbf{a}$$

   Use a coherent unit system and include only external forces on the chosen body.

4. Tarjeta 4

   Pregunta

   Cash-flow sign convention from the decision maker's viewpoint?

   Respuesta

   Receipts are positive and disbursements are negative. Choose one viewpoint and keep it consistent across the cash-flow diagram and equations.

5. Tarjeta 5

   Pregunta

   Where should an FE candidate get the current reference handbook for practice?

   Respuesta

   From the candidate's MyNCEES account. Use the current supplied file rather than an old indexed copy or a third-party mirror.

6. Tarjeta 6

   Pregunta

   Probability of the complement of event $A$?

   Respuesta

   $$P(A^c)=1-P(A)$$

7. Tarjeta 7

   Pregunta

   An engineering judgment conflicts with pressure to protect schedule or cost. First duty?

   Respuesta

   Protect public health, safety, and welfare. Document the technical concern and escalate through appropriate channels.

8. Tarjeta 8

   Pregunta

   SI base unit of mass?

   Respuesta

   The kilogram, symbol $kg$. It is a mass unit, not a force unit.

9. Tarjeta 9

   Pregunta

   Linear equation from slope and intercept?

   Respuesta

   $$y=mx+b$$

   Here $m$ is slope and $b$ is the value of $y$ where $x=0$.

10. Tarjeta 10

    Pregunta

    Velocity after time $t$ under constant acceleration?

    Respuesta

    $$v=v_0+at$$

    This one-dimensional form requires constant $a$ and a consistent positive direction.

11. Tarjeta 11

    Pregunta

    Where is an end-of-period cash flow placed?

    Respuesta

    At the boundary marking the end of that period. Interest factors assume consistent period lengths and cash-flow timing.

12. Tarjeta 12

    Pregunta

    How is the FE reference handbook available during the exam?

    Respuesta

    It is supplied onscreen as a searchable PDF. Practice locating information in the same current reference rather than relying on memory of a printed layout.

13. Tarjeta 13

    Pregunta

    Probability of $A$ or $B$ for possibly overlapping events?

    Respuesta

    $$P(A\cup B)=P(A)+P(B)-P(A\cap B)$$

14. Tarjeta 14

    Pregunta

    SI base unit of time?

    Respuesta

    The second, symbol $s$.

15. Tarjeta 15

    Pregunta

    Linear equation from one point and a slope?

    Respuesta

    $$y-y_1=m(x-x_1)$$

    Use it when the line passes through $(x_1,y_1)$ and has slope $m$.

16. Tarjeta 16

    Pregunta

    Position after time $t$ under constant acceleration?

    Respuesta

    $$x=x_0+v_0t+\frac{1}{2}at^2$$

    The acceleration is constant and all signed components use one coordinate direction.

17. Tarjeta 17

    Pregunta

    A project assignment lies outside your competence. Proper response?

    Respuesta

    Accept only the parts you are qualified to perform, or obtain qualified supervision or support. Do not present unfamiliar work as your own competent judgment.

18. Tarjeta 18

    Pregunta

    SI base unit of electric current?

    Respuesta

    The ampere, symbol $A$.

19. Tarjeta 19

    Pregunta

    Future amount under simple interest?

    Respuesta

    $$F=P(1+in)$$

    Here $P$ is principal, $i$ is interest per period, and $n$ is the number of periods; interest is earned only on principal.

20. Tarjeta 20

    Pregunta

    Distance between two Cartesian points?

    Respuesta

    $$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$$

    The coordinate components must use the same length unit.

21. Tarjeta 21

    Pregunta

    Constant-acceleration relation without elapsed time?

    Respuesta

    $$v^2=v_0^2+2a(x-x_0)$$

    Use signed one-dimensional components and constant $a$.

22. Tarjeta 22

    Pregunta

    Where do you search the supplied reference material in the exam interface?

    Respuesta

    Use the exam software's search box beside the supplied reference material.

23. Tarjeta 23

    Pregunta

    Conditional probability of $A$ given $B$?

    Respuesta

    $$P(A\mid B)=\frac{P(A\cap B)}{P(B)}$$

    This requires $P(B)>0$.

24. Tarjeta 24

    Pregunta

    SI base unit of thermodynamic temperature?

    Respuesta

    The kelvin, symbol $K$. Kelvin is written without a degree sign.

25. Tarjeta 25

    Pregunta

    A client asks you to remove an unfavorable test result from a report. Proper response?

    Respuesta

    Keep the material result and explain it accurately. Engineering statements should be objective, complete enough to avoid deception, and supported by evidence.

26. Tarjeta 26

    Pregunta

    Midpoint of two Cartesian points?

    Respuesta

    $$\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$$

    Average corresponding coordinates.

27. Tarjeta 27

    Pregunta

    Linear momentum of a particle?

    Respuesta

    $$\mathbf{p}=m\mathbf{v}$$

    For constant mass, SI units are $kg\cdot m/s$.

28. Tarjeta 28

    Pregunta

    Future amount under compound interest?

    Respuesta

    $$F=P(1+i)^n$$

    The rate period must match the period used for $n$.

29. Tarjeta 29

    Pregunta

    Should an FE search workflow depend on Ctrl+F?

    Respuesta

    No. The May 2026 NCEES Examinee Guide says Ctrl+F isn't available; practice with the exam interface's own search box.

30. Tarjeta 30

    Pregunta

    SI base unit of amount of substance?

    Respuesta

    The mole, symbol $mol$.

31. Tarjeta 31

    Pregunta

    Joint probability expressed with a conditional probability?

    Respuesta

    $$P(A\cap B)=P(A\mid B)P(B)$$

    This elementary formula requires $P(B)>0$.

32. Tarjeta 32

    Pregunta

    Standard equation of a circle centered at $(h,k)$?

    Respuesta

    $$(x-h)^2+(y-k)^2=r^2$$

    The coordinate units and radius unit must match.

33. Tarjeta 33

    Pregunta

    Impulse-momentum relationship?

    Respuesta

    $$\int_{t_1}^{t_2}\sum\mathbf{F}\,dt=\mathbf{p}_2-\mathbf{p}_1$$

    The force is the net external force on the chosen system.

34. Tarjeta 34

    Pregunta

    You discover a financial interest that could affect your recommendation. Proper response?

    Respuesta

    Disclose the conflict promptly to affected parties and obtain appropriate consent or withdraw. Hidden personal interests undermine independent judgment.

35. Tarjeta 35

    Pregunta

    SI base unit of luminous intensity?

    Respuesta

    The candela, symbol $cd$.

36. Tarjeta 36

    Pregunta

    Present worth of one future amount?

    Respuesta

    $$P=\frac{F}{(1+i)^n}$$

    Use an effective rate $i$ per period consistent with $n$.

37. Tarjeta 37

    Pregunta

    Roots of $ax^2+bx+c=0$?

    Respuesta

    $$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$

    This form requires $a\ne0$.

38. Tarjeta 38

    Pregunta

    When is total linear momentum conserved?

    Respuesta

    When net external impulse on the system is zero. Internal forces can redistribute momentum but do not change the system total.

39. Tarjeta 39

    Pregunta

    Why avoid memorizing FE handbook page numbers?

    Respuesta

    Pagination and layout can change. Remember section names, concepts, and strong search terms instead.

40. Tarjeta 40

    Pregunta

    Probability condition that defines independence of $A$ and $B$?

    Respuesta

    $$P(A\cap B)=P(A)P(B)$$

    Independence is not the same as mutual exclusivity.

41. Tarjeta 41

    Pregunta

    SI unit of frequency in base-unit form?

    Respuesta

    The hertz, $Hz=s^{-1}$, applies to periodic phenomena. One hertz is one cycle per second.

42. Tarjeta 42

    Pregunta

    Present worth of an end-of-period uniform series $A$?

    Respuesta

    $$P=A\frac{(1+i)^n-1}{i(1+i)^n}$$

    This requires $i\ne0$; at $i=0$, $P=An$.

43. Tarjeta 43

    Pregunta

    What does $b^2-4ac$ reveal for a real-coefficient quadratic?

    Respuesta

    It determines the root type: positive gives two distinct real roots, zero gives one repeated real root, and negative gives a complex-conjugate pair.

44. Tarjeta 44

    Pregunta

    Work done by a constant force through displacement?

    Respuesta

    $$W=\mathbf{F}\cdot\mathbf{s}=Fs\cos\theta$$

    Use the angle between force and displacement; SI units are joules.

45. Tarjeta 45

    Pregunta

    A vendor offers a valuable gift while you evaluate bids. Proper response?

    Respuesta

    Decline it and follow the organization's disclosure policy. Even an intended courtesy can create an actual or apparent conflict.

46. Tarjeta 46

    Pregunta

    SI unit of force in base-unit form?

    Respuesta

    The newton, $N=kg\cdot m/s^2$.

47. Tarjeta 47

    Pregunta

    First search cue for a named quantity such as coefficient of thermal expansion?

    Respuesta

    Search the exact technical noun phrase. Distinctive nouns usually narrow results better than a whole question sentence.

48. Tarjeta 48

    Pregunta

    Bayes' rule for $P(A\mid B)$?

    Respuesta

    $$P(A\mid B)=\frac{P(B\mid A)P(A)}{P(B)}$$

    This requires $P(B)>0$.

49. Tarjeta 49

    Pregunta

    Product of powers with the same positive base and real exponents?

    Respuesta

    $$a^m a^n=a^{m+n}$$

    This form assumes $a>0$ and real exponents $m$ and $n$.

50. Tarjeta 50

    Pregunta

    Translational kinetic energy of a particle?

    Respuesta

    $$K=\frac{1}{2}mv^2$$

    Mass and speed must use a coherent unit system.

51. Tarjeta 51

    Pregunta

    SI unit of pressure in force-area form?

    Respuesta

    The pascal, $Pa=N/m^2$. It is the SI derived unit for pressure and stress.

52. Tarjeta 52

    Pregunta

    Equivalent annual amount for present worth $P$?

    Respuesta

    $$A=P\frac{i(1+i)^n}{(1+i)^n-1}$$

    For the displayed formula, $i\ne0$; at $i=0$, $A=P/n$. Payments occur at period ends and $i$ matches that period.

53. Tarjeta 53

    Pregunta

    May confidential client information be shared for personal benefit?

    Respuesta

    No. Protect it unless the client authorizes disclosure or law, safety, or professional duty requires it.

54. Tarjeta 54

    Pregunta

    A handbook search term returns too many results. Best refinement?

    Respuesta

    Add one meaningful qualifier, such as the phenomenon, geometry, distribution, or material property you need.

55. Tarjeta 55

    Pregunta

    Quotient of powers with the same positive base and real exponents?

    Respuesta

    $$\frac{a^m}{a^n}=a^{m-n}$$

    This form assumes $a>0$ and real exponents $m$ and $n$.

56. Tarjeta 56

    Pregunta

    Net work-energy relationship for a particle?

    Respuesta

    $$W_{net}=K_2-K_1$$

    The net work includes the work of all forces represented in the particle model.

57. Tarjeta 57

    Pregunta

    Ordered selections of $r$ objects from $n$ distinct objects?

    Respuesta

    $$P(n,r)=\frac{n!}{(n-r)!}$$

    Use this when order matters and selection is without replacement.

58. Tarjeta 58

    Pregunta

    Future worth of an end-of-period uniform series $A$?

    Respuesta

    $$F=A\frac{(1+i)^n-1}{i}$$

    This requires $i\ne0$; at $i=0$, $F=An$.

59. Tarjeta 59

    Pregunta

    Power of a power for a positive base and real exponents?

    Respuesta

    $$(a^m)^n=a^{mn}$$

    This form assumes $a>0$ and real exponents $m$ and $n$.

60. Tarjeta 60

    Pregunta

    SI unit of energy in force-distance form?

    Respuesta

    The joule, $J=N\cdot m$.

61. Tarjeta 61

    Pregunta

    A problem gives only an unfamiliar symbol. Best search preparation?

    Respuesta

    Translate the symbol into its likely quantity name and discipline context before searching; symbol-only searches are often ambiguous.

62. Tarjeta 62

    Pregunta

    Confidential information reveals an imminent public-safety risk. What comes first?

    Respuesta

    Take steps required to protect people, using appropriate legal and organizational channels. Share only what is necessary and document the basis for escalation.

63. Tarjeta 63

    Pregunta

    Unordered selections of $r$ objects from $n$ distinct objects?

    Respuesta

    $$C(n,r)=\frac{n!}{r!(n-r)!}$$

    Use this when order does not matter and selection is without replacement.

64. Tarjeta 64

    Pregunta

    Change in gravitational potential energy near Earth's surface?

    Respuesta

    $$\Delta U_g=mg\Delta h$$

    Use approximately constant $g$ and a clearly chosen height datum.

65. Tarjeta 65

    Pregunta

    Negative-exponent rule for a positive base and real exponent?

    Respuesta

    $$a^{-n}=\frac{1}{a^n}$$

    This form assumes $a>0$ and real exponent $n$.

66. Tarjeta 66

    Pregunta

    Uniform end-of-period deposit needed for future amount $F$?

    Respuesta

    $$A=F\frac{i}{(1+i)^n-1}$$

    For the displayed formula, $i\ne0$; at $i=0$, $A=F/n$. The first deposit is one period from now and the last occurs at period $n$.

67. Tarjeta 67

    Pregunta

    A handbook search for an acronym fails. Next move?

    Respuesta

    Try the expanded term and a common alternate name. Acronyms vary by section and discipline.

68. Tarjeta 68

    Pregunta

    SI unit of power in energy-time form?

    Respuesta

    The watt, $W=J/s$.

69. Tarjeta 69

    Pregunta

    Logarithm of a product?

    Respuesta

    $$\log_b(xy)=\log_b x+\log_b y$$

    For real logarithms, $b>0$, $b\ne1$, and both arguments are positive.

70. Tarjeta 70

    Pregunta

    Conditions for a binomial model?

    Respuesta

    A fixed number of independent trials, two outcomes per trial, and the same success probability on every trial.

71. Tarjeta 71

    Pregunta

    Using another engineer's analysis in your deliverable?

    Respuesta

    Credit the source and verify the analysis before relying on it. Do not present someone else's work as your own.

72. Tarjeta 72

    Pregunta

    SI unit of electric charge in current-time form?

    Respuesta

    The coulomb, $C=A\cdot s$.

73. Tarjeta 73

    Pregunta

    Average power from work over elapsed time?

    Respuesta

    $$P_{avg}=\frac{W}{\Delta t}$$

    Use consistent energy and time units; watts are joules per second.

74. Tarjeta 74

    Pregunta

    Annual equivalent of cost $P$ with salvage $S$ after $n$ periods?

    Respuesta

    $$A=P\frac{i(1+i)^n}{(1+i)^n-1}-S\frac{i}{(1+i)^n-1}$$

    The first factor converts present cost to an annual amount; the second converts future salvage. Use the same effective rate and period basis. At $i=0$, $A=(P-S)/n$.

75. Tarjeta 75

    Pregunta

    Logarithm of a positive quantity raised to a power?

    Respuesta

    $$\log_b(x^p)=p\log_b x$$

    For real logarithms, $x>0$, $b>0$, and $b\ne1$.

76. Tarjeta 76

    Pregunta

    SI unit of electric potential difference in energy-charge form?

    Respuesta

    The volt, $V=J/C$.

77. Tarjeta 77

    Pregunta

    Instantaneous mechanical power delivered by a force?

    Respuesta

    $$P=\mathbf{F}\cdot\mathbf{v}$$

    Use the velocity of the force's point of application.

78. Tarjeta 78

    Pregunta

    A precise handbook term gives no useful match. Next move?

    Respuesta

    Try a standard synonym or the broader parent concept, then narrow within the relevant section.

79. Tarjeta 79

    Pregunta

    Mean of $X\sim\operatorname{Binomial}(n,p)$?

    Respuesta

    $$E[X]=np$$

80. Tarjeta 80

    Pregunta

    SI unit of electrical resistance in voltage-current form?

    Respuesta

    The ohm, $\Omega=V/A$.

81. Tarjeta 81

    Pregunta

    Moment of a force about a point?

    Respuesta

    $$\mathbf{M}=\mathbf{r}\times\mathbf{F}$$

    Vector $\mathbf{r}$ runs from the moment point to a point on the force's line of action.

82. Tarjeta 82

    Pregunta

    Cash-flow pattern described by an arithmetic gradient $G$?

    Respuesta

    A series that changes by the same amount $G$ each period. In the usual convention, the first gradient increment appears after the first base payment.

83. Tarjeta 83

    Pregunta

    Inverse relationship between the natural log and exponential?

    Respuesta

    $$\ln(e^x)=x,\qquad e^{\ln x}=x$$

    The second identity requires $x>0$.

84. Tarjeta 84

    Pregunta

    SI prefix giga?

    Respuesta

    $G=10^9$.

85. Tarjeta 85

    Pregunta

    Angular velocity after time $t$ under constant angular acceleration?

    Respuesta

    $$\omega=\omega_0+\alpha t$$

    Use consistent angular sign convention and radians for angular measures.

86. Tarjeta 86

    Pregunta

    When should an engineer sign or seal technical work?

    Respuesta

    Only when authorized and when the work was prepared by the engineer or under the level of responsible charge required by the applicable jurisdiction.

87. Tarjeta 87

    Pregunta

    Best memory target for returning to a handbook formula?

    Respuesta

    The section or concept name plus a distinctive search phrase. That survives layout changes better than a page number.

88. Tarjeta 88

    Pregunta

    SI prefix mega?

    Respuesta

    $M=10^6$. Uppercase matters: lowercase $m$ means milli.

89. Tarjeta 89

    Pregunta

    Convert degrees to radians?

    Respuesta

    $$\theta_{rad}=\theta_{deg}\frac{\pi}{180}$$

    Use radians in calculus formulas unless a formula explicitly says otherwise.

90. Tarjeta 90

    Pregunta

    Variance of $X\sim\operatorname{Binomial}(n,p)$?

    Respuesta

    $$\operatorname{Var}(X)=np(1-p)$$

91. Tarjeta 91

    Pregunta

    Cash-flow pattern described by a geometric gradient rate $g$?

    Respuesta

    A series in which each payment is the previous payment multiplied by $1+g$. Keep $g$ on the same period basis as the interest rate.

92. Tarjeta 92

    Pregunta

    Where do licensure and sealing requirements come from?

    Respuesta

    The applicable jurisdiction's current laws and board rules. Confirm local requirements rather than assuming one state's rules apply everywhere.

93. Tarjeta 93

    Pregunta

    Rotational kinetic energy about a fixed axis?

    Respuesta

    $$K_{rot}=\frac{1}{2}I\omega^2$$

    $I$ is the mass moment of inertia about that axis.

94. Tarjeta 94

    Pregunta

    SI prefix kilo?

    Respuesta

    $k=10^3$.

95. Tarjeta 95

    Pregunta

    Right-triangle definition of sine?

    Respuesta

    Sine is opposite over hypotenuse. This definition applies to an acute angle in a right triangle.

96. Tarjeta 96

    Pregunta

    After search lands near a result, what should you scan first?

    Respuesta

    The section heading and nearby subheading. They establish whether the result belongs to the right model and subject.

97. Tarjeta 97

    Pregunta

    Rotational analogue of Newton's second law about a fixed principal axis?

    Respuesta

    $$\sum M=I\alpha$$

    This scalar form assumes the stated fixed-axis model and a consistent sign convention.

98. Tarjeta 98

    Pregunta

    SI prefix milli?

    Respuesta

    $m=10^{-3}$. Context distinguishes the prefix from the metre symbol.

99. Tarjeta 99

    Pregunta

    Meaning of a nominal annual rate compounded $m$ times per year?

    Respuesta

    It is a quoted annual rate equal to $m$ times the periodic rate. It is not itself the effective annual rate unless compounding is annual.

100. Tarjeta 100

     Pregunta

     Standardize an observation $x$ from a distribution with mean $\mu$ and standard deviation $\sigma$?

     Respuesta

     $$z=\frac{x-\mu}{\sigma}$$

     This requires $\sigma>0$; using a normal probability table also assumes an appropriate normal model.

101. Tarjeta 101

     Pregunta

     Right-triangle definition of cosine?

     Respuesta

     Cosine is adjacent over hypotenuse. This definition applies to an acute angle in a right triangle.

102. Tarjeta 102

     Pregunta

     Force-displacement relation for an ideal linear spring?

     Respuesta

     $$F=-kx$$

     The minus sign shows restoring direction; the model applies within the spring's linear range.

103. Tarjeta 103

     Pregunta

     May qualifications or project responsibility be exaggerated in a proposal?

     Respuesta

     No. State education, licensure, experience, and responsibility accurately, including the actual roles of collaborators.

104. Tarjeta 104

     Pregunta

     SI prefix micro?

     Respuesta

     $\mu=10^{-6}$.

105. Tarjeta 105

     Pregunta

     A handbook symbol conflicts with your usual notation. What controls?

     Respuesta

     The definition beside the selected relationship. Symbols can represent different quantities in different sections.

106. Tarjeta 106

     Pregunta

     Periodic rate from nominal annual rate $r$ compounded $m$ times per year?

     Respuesta

     $$i=\frac{r}{m}$$

     Use consistent decimal units, and pair this rate with the number of compounding periods.

107. Tarjeta 107

     Pregunta

     Right-triangle definition of tangent?

     Respuesta

     Tangent is opposite over adjacent, or $\sin\theta/\cos\theta$ where $\cos\theta\ne0$.

108. Tarjeta 108

     Pregunta

     Average normal stress under centered axial load?

     Respuesta

     $$\sigma=\frac{F}{A}$$

     $F$ is normal to area $A$; the average ignores local stress concentrations.

109. Tarjeta 109

     Pregunta

     Mean, median, and mode of a symmetric normal distribution?

     Respuesta

     They are equal and located at $\mu$. The distribution is symmetric about that center.

110. Tarjeta 110

     Pregunta

     SI prefix nano?

     Respuesta

     $n=10^{-9}$.

111. Tarjeta 111

     Pregunta

     Fundamental Pythagorean trigonometric identity?

     Respuesta

     $$\sin^2\theta+\cos^2\theta=1$$

112. Tarjeta 112

     Pregunta

     Engineering normal strain?

     Respuesta

     $$\varepsilon=\frac{\Delta L}{L_0}$$

     It is dimensionless and uses original gauge length $L_0$.

113. Tarjeta 113

     Pregunta

     A candidate retrieves a formula from the handbook. What must be checked with it?

     Respuesta

     Its applicability assumptions and variable definitions. A familiar equation used under the wrong model is still wrong.

114. Tarjeta 114

     Pregunta

     Technical duty to an employer or client?

     Respuesta

     Act as a faithful professional within lawful, ethical limits, communicate material risks, and preserve independent technical judgment.

115. Tarjeta 115

     Pregunta

     How does a length conversion factor apply to area?

     Respuesta

     Square it. If $1\,u=a\,v$, then $1\,u^2=a^2\,v^2$.

116. Tarjeta 116

     Pregunta

     Effective annual rate from nominal rate $r$ compounded $m$ times per year?

     Respuesta

     $$i_{eff}=\left(1+\frac{r}{m}\right)^m-1$$

117. Tarjeta 117

     Pregunta

     When is a Poisson count model reasonable?

     Respuesta

     For counts in a fixed interval when events occur independently at an approximately constant average rate and simultaneous events are negligible.

118. Tarjeta 118

     Pregunta

     Relationship for the third side of a non-right triangle?

     Respuesta

     $$c^2=a^2+b^2-2ab\cos C$$

     Angle $C$ lies between sides $a$ and $b$, opposite side $c$.

119. Tarjeta 119

     Pregunta

     Linear elastic stress-strain relation in uniaxial loading?

     Respuesta

     $$\sigma=E\varepsilon$$

     Use it in the material's linear elastic range; $E$ has stress units.

120. Tarjeta 120

     Pregunta

     How does a length conversion factor apply to volume?

     Respuesta

     Cube it. If $1\,u=a\,v$, then $1\,u^3=a^3\,v^3$.

121. Tarjeta 121

     Pregunta

     What should you record for every variable in a retrieved equation?

     Respuesta

     Its meaning and expected unit or dimension. This catches swapped symbols and incompatible substitutions.

122. Tarjeta 122

     Pregunta

     Effective annual rate for continuous compounding at nominal rate $r$?

     Respuesta

     $$i_{eff}=e^r-1$$

     Here $r$ is expressed as a decimal per year.

123. Tarjeta 123

     Pregunta

     A supervisor directs an illegal engineering action. Proper response?

     Respuesta

     Refuse the illegal action, document the direction, and escalate through appropriate legal or organizational channels.

124. Tarjeta 124

     Pregunta

     Magnitude of a three-component vector $\mathbf{v}$?

     Respuesta

     $$\lVert\mathbf{v}\rVert=\sqrt{v_x^2+v_y^2+v_z^2}$$

     All components must represent the same physical quantity in compatible units.

125. Tarjeta 125

     Pregunta

     Mass density?

     Respuesta

     $$\rho=\frac{m}{V}$$

     Use mass, not weight, in the numerator.

126. Tarjeta 126

     Pregunta

     Inches in one foot?

     Respuesta

     $12\,in=1\,ft$.

127. Tarjeta 127

     Pregunta

     Mean and variance of $X\sim\operatorname{Poisson}(\lambda)$?

     Respuesta

     Both equal $\lambda$. The standard deviation is $\sqrt{\lambda}$.

128. Tarjeta 128

     Pregunta

     How should subscripts be handled in a retrieved relationship?

     Respuesta

     Read what each subscript identifies—state, direction, phase, location, or reference—before substituting values.

129. Tarjeta 129

     Pregunta

     Dot product from vector magnitudes and included angle?

     Respuesta

     $$\mathbf{a}\cdot\mathbf{b}=\lVert\mathbf{a}\rVert\lVert\mathbf{b}\rVert\cos\theta$$

     The result is a scalar.

130. Tarjeta 130

     Pregunta

     Average normal pressure on an area?

     Respuesta

     $$p=\frac{F_n}{A}$$

     $F_n$ is the normal force; pressure is scalar in a fluid at rest.

131. Tarjeta 131

     Pregunta

     Feet in one yard?

     Respuesta

     $3\,ft=1\,yd$.

132. Tarjeta 132

     Pregunta

     When are two interest rates equivalent?

     Respuesta

     When they produce the same accumulation over the same time interval. Convert both rates to a common effective period before comparing them.

133. Tarjeta 133

     Pregunta

     You discover a material error in issued work. Proper response?

     Respuesta

     Notify responsible parties promptly, assess the safety impact, correct the record, and document the response. Do not hide the error.

134. Tarjeta 134

     Pregunta

     Expected value of a discrete random variable?

     Respuesta

     $$E[X]=\sum_x xP(X=x)$$

     Sum over all possible values with a valid probability mass function.

135. Tarjeta 135

     Pregunta

     Dot-product test for perpendicular nonzero vectors?

     Respuesta

     Their dot product is zero. The zero vector also has zero dot product with every vector, so require both vectors to be nonzero before concluding perpendicularity.

136. Tarjeta 136

     Pregunta

     Hydrostatic pressure change with vertical depth in a constant-density fluid?

     Respuesta

     $$\Delta p=\rho g\Delta h$$

     Depth increases downward and the fluid is at rest.

137. Tarjeta 137

     Pregunta

     Feet in one statute mile?

     Respuesta

     $5280\,ft=1\,mi$.

138. Tarjeta 138

     Pregunta

     Present-worth acceptance rule for an independent investment at the minimum attractive rate of return?

     Respuesta

     Accept it when net present worth is nonnegative. All cash flows must be discounted to the same time using the chosen comparison rate.

     

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139. Tarjeta 139

     Pregunta

     A retrieved formula contains signed quantities. What should you confirm?

     Respuesta

     The stated sign convention and positive direction. Do not mix magnitudes with signed components silently.

140. Tarjeta 140

     Pregunta

     Magnitude of a vector cross product?

     Respuesta

     $$\lVert\mathbf{a}\times\mathbf{b}\rVert=\lVert\mathbf{a}\rVert\lVert\mathbf{b}\rVert\sin\theta$$

     The direction follows the right-hand rule.

141. Tarjeta 141

     Pregunta

     Exact inch-to-metre relationship?

     Respuesta

     $1\,in=0.0254\,m$ exactly.

142. Tarjeta 142

     Pregunta

     Volumetric flow rate through a cross-section?

     Respuesta

     $$Q=Av_{avg}$$

     Velocity is the area-average component normal to the section.

143. Tarjeta 143

     Pregunta

     Variance from the mean $\mu$?

     Respuesta

     $$\operatorname{Var}(X)=E[(X-\mu)^2]$$

     Variance has squared units; standard deviation has the original units.

144. Tarjeta 144

     Pregunta

     Future-worth acceptance rule for an independent investment?

     Respuesta

     Accept it when net future worth at the study horizon is nonnegative, using the minimum attractive rate of return consistently.

145. Tarjeta 145

     Pregunta

     What coordinate detail should be checked before using a vector or mechanics formula?

     Respuesta

     Axis directions and the reference point or origin. Components and moments depend on those choices.

146. Tarjeta 146

     Pregunta

     Exact foot-to-metre relationship?

     Respuesta

     $1\,ft=0.3048\,m$ exactly.

147. Tarjeta 147

     Pregunta

     How should important uncertainty be communicated?

     Respuesta

     State the assumptions, limits, and plausible consequences clearly enough for the decision maker to understand the risk.

148. Tarjeta 148

     Pregunta

     When is the matrix product $AB$ defined?

     Respuesta

     It is defined when the number of columns of $A$ equals the number of rows of $B$. If $A$ is $m\times n$ and $B$ is $n\times p$, then $AB$ is $m\times p$.

149. Tarjeta 149

     Pregunta

     Steady one-inlet, one-outlet mass continuity?

     Respuesta

     $$\rho_1A_1v_1=\rho_2A_2v_2$$

     Here $v_1$ and $v_2$ are cross-sectional average velocity components normal to their sections, with density treated as uniform over each section. For incompressible flow with constant density, this reduces to $A_1v_1=A_2v_2$.

150. Tarjeta 150

     Pregunta

     Sample mean of observations $x_1,\ldots,x_n$?

     Respuesta

     $$\bar{x}=\frac{1}{n}\sum_{i=1}^n x_i$$

151. Tarjeta 151

     Pregunta

     Square feet in one acre?

     Respuesta

     $1\,acre=43{,}560\,ft^2$.

152. Tarjeta 152

     Pregunta

     Determinant of $\begin{bmatrix}a&b\\c&d\end{bmatrix}$?

     Respuesta

     $$ad-bc$$

153. Tarjeta 153

     Pregunta

     Bernoulli relationship along a streamline for ideal steady flow?

     Respuesta

     $$\frac{p}{\rho g}+\frac{v^2}{2g}+z=\text{constant}$$

     This basic form assumes steady, incompressible, negligible-viscosity flow with no shaft work or heat effects between points.

154. Tarjeta 154

     Pregunta

     May inconvenient measurements be discarded without a technical basis?

     Respuesta

     No. Use a documented, technically justified rule for excluding data and preserve the original record.

155. Tarjeta 155

     Pregunta

     Annual-worth acceptance rule for an independent investment?

     Respuesta

     Accept it when equivalent annual worth is nonnegative. Compare alternatives over compatible service assumptions.

156. Tarjeta 156

     Pregunta

     Before using a handbook equation, what unit-system check matters?

     Respuesta

     Confirm that every input and any embedded constant use one compatible unit system. Convert first when necessary.

157. Tarjeta 157

     Pregunta

     Cubic metres in one litre?

     Respuesta

     $1\,L=10^{-3}\,m^3$.

158. Tarjeta 158

     Pregunta

     What does a zero determinant mean for a square matrix?

     Respuesta

     The matrix is singular and has no inverse. A corresponding linear system cannot have one unique solution.

159. Tarjeta 159

     Pregunta

     Reynolds number for internal flow using characteristic length $L$?

     Respuesta

     $$Re=\frac{\rho vL}{\mu}=\frac{vL}{\nu}$$

     It is dimensionless; use consistent properties and the geometry-appropriate characteristic length.

160. Tarjeta 160

     Pregunta

     Unbiased sample variance for an independent sample from one population?

     Respuesta

     $$s^2=\frac{1}{n-1}\sum_{i=1}^n(x_i-\bar{x})^2$$

     This requires at least two observations, so $n\ge2$. The $n-1$ denominator estimates population variance after fitting the sample mean.

161. Tarjeta 161

     Pregunta

     How should mutually exclusive alternatives be compared?

     Respuesta

     Use one consistent economic measure over a common study period and select the economically preferred feasible alternative; do not accept every alternative with a positive individual worth.

162. Tarjeta 162

     Pregunta

     Cubic centimetres in one millilitre?

     Respuesta

     $1\,mL=1\,cm^3$.

163. Tarjeta 163

     Pregunta

     Why keep contemporaneous engineering records?

     Respuesta

     They preserve assumptions, decisions, calculations, approvals, and changes so the work can be checked and responsibilities understood.

164. Tarjeta 164

     Pregunta

     Fast check after substituting into a handbook formula?

     Respuesta

     Verify that the resulting dimensions match the requested quantity and that additive terms share dimensions.

165. Tarjeta 165

     Pregunta

     Matrix solution of $A\mathbf{x}=\mathbf{b}$ when $A$ is invertible?

     Respuesta

     $$\mathbf{x}=A^{-1}\mathbf{b}$$

     In numerical work, direct factorization is usually preferable to explicitly forming the inverse.

166. Tarjeta 166

     Pregunta

     Sensible heat for constant specific heat and no phase change?

     Respuesta

     $$Q=mc\Delta T$$

     $c$ must match the material, temperature range, mass unit, and temperature-difference unit.

167. Tarjeta 167

     Pregunta

     Standard error of the mean for an i.i.d. sample with population standard deviation $\sigma$?

     Respuesta

     $$SE(\bar{x})=\frac{\sigma}{\sqrt{n}}$$

     The observations are independent and identically distributed with common variance $\sigma^2$. Use $s$ for unknown $\sigma$ only when the selected inference method allows it.

168. Tarjeta 168

     Pregunta

     Safe setup for converting $25\,ft^2$ to square metres?

     Respuesta

     $$25\,ft^2\left(\frac{0.3048\,m}{1\,ft}\right)^2$$

     The squared length factor cancels $ft^2$ and leaves $m^2$.

169. Tarjeta 169

     Pregunta

     Purpose of incremental analysis for mutually exclusive alternatives?

     Respuesta

     It tests whether the additional investment in the higher-cost option earns the required return compared with the lower-cost option.

170. Tarjeta 170

     Pregunta

     Physical meaning of $dy/dx$?

     Respuesta

     It is the instantaneous rate of change of $y$ with respect to $x$, with units of the $y$ unit divided by the $x$ unit.

171. Tarjeta 171

     Pregunta

     One-dimensional steady conduction through a plane wall?

     Respuesta

     $$\dot Q=-kA\frac{dT}{dx}$$

     The minus sign indicates heat flows toward lower temperature; $k$ is thermal conductivity.

172. Tarjeta 172

     Pregunta

     When should you algebraically rearrange a handbook relationship?

     Respuesta

     After confirming the correct equation, definitions, assumptions, and sign convention. Then isolate the requested variable without changing its domain restrictions.

173. Tarjeta 173

     Pregunta

     Safe setup for converting $2\,in^3$ to cubic metres?

     Respuesta

     $$2\,in^3\left(\frac{0.0254\,m}{1\,in}\right)^3$$

     Cube the exact length conversion because the original quantity is volume.

174. Tarjeta 174

     Pregunta

     A client changes a safety-critical design requirement verbally. Proper response?

     Respuesta

     Confirm the change in writing, analyze its consequences, and obtain the required approvals before relying on it.

175. Tarjeta 175

     Pregunta

     Derivative of $x^n$ for constant $n$?

     Respuesta

     $$\frac{d}{dx}x^n=nx^{n-1}$$

     Apply domain restrictions when $n$ is non-integer or negative.

176. Tarjeta 176

     Pregunta

     Convective heat-transfer rate at a surface?

     Respuesta

     $$\dot Q=hA(T_s-T_\infty)$$

     $h$ depends on the flow and geometry; the sign follows the chosen temperature difference.

177. Tarjeta 177

     Pregunta

     What does the central limit theorem say about a sample mean?

     Respuesta

     For sufficiently large independent, identically distributed samples with finite variance, the sampling distribution of the properly standardized mean approaches normality. It does not make the raw data normal.

178. Tarjeta 178

     Pregunta

     Internal rate of return?

     Respuesta

     The discount rate that makes net present worth zero. Multiple sign changes in cash flow can produce multiple or no meaningful real rates.

179. Tarjeta 179

     Pregunta

     Several similar handbook equations appear together. How do you choose?

     Respuesta

     Match each equation's stated geometry, boundary conditions, material model, and variable definitions to the problem.

180. Tarjeta 180

     Pregunta

     Convert Celsius temperature to kelvin?

     Respuesta

     $$T_K=T_{^\circ C}+273.15$$

     This conversion is for absolute temperature, not temperature difference.

181. Tarjeta 181

     Pregunta

     Derivative of a product $u(x)v(x)$?

     Respuesta

     $$(uv)'=u'v+uv'$$

182. Tarjeta 182

     Pregunta

     Internal escalation does not resolve a serious public-safety threat. Next step?

     Respuesta

     Use the next appropriate authority or reporting channel, consistent with law and the urgency of the hazard. Keep a factual record.

183. Tarjeta 183

     Pregunta

     Two-sided confidence interval for a population mean with known $\sigma$?

     Respuesta

     $$\bar{x}\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$$

     Use the normal-model conditions and the critical value for confidence level $1-\alpha$.

184. Tarjeta 184

     Pregunta

     Net thermal radiation from a small gray surface to large surroundings?

     Respuesta

     $$\dot Q=\varepsilon\sigma A(T_s^4-T_{sur}^4)$$

     Use absolute temperatures; the model assumes the stated gray-surface surroundings.

185. Tarjeta 185

     Pregunta

     Basic benefit-cost acceptance rule for an independent public project?

     Respuesta

     Accept when the consistently defined benefit-cost ratio is at least one. For mutually exclusive choices, use an incremental comparison rather than ranking by individual ratios alone.

186. Tarjeta 186

     Pregunta

     Derivative of a composite function $f(g(x))$?

     Respuesta

     $$\frac{d}{dx}f(g(x))=f'(g(x))g'(x)$$

187. Tarjeta 187

     Pregunta

     Why inspect boundary or initial conditions near a formula?

     Respuesta

     They determine which solution form applies and can eliminate constants or terms. A formula without its conditions may be unusable.

188. Tarjeta 188

     Pregunta

     Convert Celsius temperature to Fahrenheit?

     Respuesta

     $$T_{^\circ F}=\frac{9}{5}T_{^\circ C}+32$$

189. Tarjeta 189

     Pregunta

     Ethical basis for expert technical testimony?

     Respuesta

     Offer opinions only within your competence, disclose important assumptions and limitations, and distinguish facts from professional judgment.

190. Tarjeta 190

     Pregunta

     Meaning of a breakeven value?

     Respuesta

     The value of a selected variable that makes two alternatives economically equivalent or makes net worth zero. Other assumptions are held fixed.

191. Tarjeta 191

     Pregunta

     Derivative of $e^x$?

     Respuesta

     $$\frac{d}{dx}e^x=e^x$$

192. Tarjeta 192

     Pregunta

     First-law energy balance for a closed system with work positive out?

     Respuesta

     $$\Delta E=Q-W$$

     $Q$ is heat into the system and $W$ is work done by the system; state a different sign convention before using it.

193. Tarjeta 193

     Pregunta

     Frequentist meaning of a 95% confidence procedure?

     Respuesta

     Across repeated samples, about 95% of intervals built by the procedure would contain the fixed population parameter. It is not a 95% probability assigned to this already-computed interval.

194. Tarjeta 194

     Pregunta

     A needed value falls between handbook table entries. What is the cue?

     Respuesta

     Check whether interpolation is appropriate, keep both axes and units straight, and avoid extrapolating unless the source supports it.

195. Tarjeta 195

     Pregunta

     Derivative of $\ln x$ over the real domain?

     Respuesta

     $$\frac{d}{dx}\ln x=\frac{1}{x}$$

     This real-valued form requires $x>0$.

196. Tarjeta 196

     Pregunta

     Relationship between Celsius and kelvin temperature differences?

     Respuesta

     $1\,K$ of temperature difference equals $1\,^{\circ}C$ of temperature difference. Do not add $273.15$ to a difference.

197. Tarjeta 197

     Pregunta

     How should credit for team engineering work be assigned?

     Respuesta

     Accurately recognize each contributor's work and responsibility. Do not claim sole credit for a collaborative result.

198. Tarjeta 198

     Pregunta

     Main limitation of simple payback period?

     Respuesta

     It ignores the time value of money and usually ignores cash flows after payback. Discounted payback fixes the first issue, not the second.

199. Tarjeta 199

     Pregunta

     Roles of the null and alternative hypotheses?

     Respuesta

     The null states the baseline parameter claim tested; the alternative states the competing direction or difference supported when evidence is strong enough.

200. Tarjeta 200

     Pregunta

     Ideal-gas equation of state?

     Respuesta

     $$pV=nRT$$

     Use absolute temperature and a gas constant consistent with pressure, volume, amount, and energy units.

201. Tarjeta 201

     Pregunta

     First check when reading a handbook table?

     Respuesta

     Read the title, column headings, units, notes, and basis conditions before selecting a value.

202. Tarjeta 202

     Pregunta

     Candidates for absolute extrema of a continuous function on a closed interval?

     Respuesta

     The endpoints and every interior point where the first derivative is zero or does not exist. Evaluate the function at each candidate; the largest and smallest values are the absolute extrema.

203. Tarjeta 203

     Pregunta

     How should a sunk cost affect a current engineering-economy decision?

     Respuesta

     It should not affect the choice because it cannot be changed by the decision. Use future incremental cash flows instead.

204. Tarjeta 204

     Pregunta

     Convert Fahrenheit absolute temperature to Rankine?

     Respuesta

     $$T_{^\circ R}=T_{^\circ F}+459.67$$

     Rankine uses the Fahrenheit-sized degree from absolute zero.

205. Tarjeta 205

     Pregunta

     Ohm's law for an ideal resistor?

     Respuesta

     $$V=IR$$

     Use a consistent passive sign convention; $R$ is constant only over the assumed operating range.

206. Tarjeta 206

     Pregunta

     You have confidential details about a competitor's bid. Proper response?

     Respuesta

     Do not use or disclose improperly obtained information. Notify the appropriate procurement or ethics contact.

207. Tarjeta 207

     Pregunta

     Physical meaning of a definite integral $\int_a^b f(x)\,dx$?

     Respuesta

     It is signed accumulation of $f$ from $a$ to $b$. Its units are the units of $f$ multiplied by the units of $x$.

208. Tarjeta 208

     Pregunta

     Is a radian dimensionless?

     Respuesta

     Yes. It is the ratio of arc length to radius, so the length units cancel; keep $rad$ when it clarifies angular meaning.

209. Tarjeta 209

     Pregunta

     Electrical power absorbed under the passive sign convention?

     Respuesta

     $$P=VI$$

     For a resistor, this also gives $P=I^2R=V^2/R$ when Ohm's law applies.

210. Tarjeta 210

     Pregunta

     Meaning of a p-value?

     Respuesta

     Assuming the null hypothesis and model are correct, it is the probability of a result at least as extreme as the observed result. It is not the probability that the null is true.

211. Tarjeta 211

     Pregunta

     First check when reading a handbook graph?

     Respuesta

     Identify both axes, scales, units, curve labels, and any log scale before estimating a value.

212. Tarjeta 212

     Pregunta

     Difference between mass and weight?

     Respuesta

     Mass measures inertia; weight is gravitational force on that mass. Their dimensions and units are different.

213. Tarjeta 213

     Pregunta

     Kirchhoff's current law at a node?

     Respuesta

     The algebraic sum of currents at a node is zero. Choose one sign convention, such as currents entering positive, and apply it consistently.

214. Tarjeta 214

     Pregunta

     Evaluate $\int_a^b f(x)\,dx$ from an antiderivative $F$?

     Respuesta

     $$\int_a^b f(x)\,dx=F(b)-F(a)$$

     This applies when $F'=f$ on the interval under the usual continuity conditions.

215. Tarjeta 215

     Pregunta

     Opportunity cost?

     Respuesta

     The value of the best forgone alternative. Include it when choosing one use of a scarce resource prevents another valuable use.

216. Tarjeta 216

     Pregunta

     Weight from mass in a gravitational field?

     Respuesta

     $$W=mg$$

     Use compatible units; $g$ is local gravitational acceleration, not a universal constant for every location.

217. Tarjeta 217

     Pregunta

     Kirchhoff's voltage law around a closed loop?

     Respuesta

     The algebraic sum of voltage rises and drops around the loop is zero. Traverse the loop once with a consistent polarity convention.

218. Tarjeta 218

     Pregunta

     Decision rule using significance level $\alpha$?

     Respuesta

     Reject the null when the p-value is at most $\alpha$; otherwise fail to reject it. Failing to reject does not prove the null.

219. Tarjeta 219

     Pregunta

     Can proprietary methods from a former employer be reused freely?

     Respuesta

     Only if you have the legal right or permission to use them. General skill and experience may transfer; confidential proprietary material does not.

220. Tarjeta 220

     Pregunta

     Pound-force to newtons?

     Respuesta

     $1\,lbf\approx4.44822\,N$. Use more digits only when the required precision justifies them.

221. Tarjeta 221

     Pregunta

     When does a definite integral equal ordinary geometric area?

     Respuesta

     When the integrand is nonnegative over the interval. If it changes sign, the integral is signed area; integrate the absolute value or split the interval for total area.

222. Tarjeta 222

     Pregunta

     Charge-voltage relation for an ideal capacitor?

     Respuesta

     $$q=CV$$

     $C$ is capacitance in farads; $V$ is the voltage across the capacitor under the chosen polarity.

223. Tarjeta 223

     Pregunta

     Searching for a material or fluid property: what qualifiers often matter?

     Respuesta

     Material identity, phase, temperature, pressure, and composition. Use only the qualifiers relevant to that property source.

224. Tarjeta 224

     Pregunta

     Force produced when one slug accelerates at $1\,ft/s^2$?

     Respuesta

     $1\,lbf$. Equivalently, $1\,lbf=1\,slug\cdot ft/s^2$.

225. Tarjeta 225

     Pregunta

     Relationship among nominal rate $i$, real rate $r$, and inflation $f$?

     Respuesta

     $$1+i=(1+r)(1+f)$$

     Keep cash-flow dollars and discount rates on the same real-or-nominal basis.

226. Tarjeta 226

     Pregunta

     Antiderivative of $x^n$ for $n\ne-1$?

     Respuesta

     $$\int x^n\,dx=\frac{x^{n+1}}{n+1}+C$$

227. Tarjeta 227

     Pregunta

     Time constant of a first-order resistor-capacitor circuit?

     Respuesta

     $$\tau=RC$$

     Use the resistance seen by the capacitor in the applicable first-order linear circuit.

228. Tarjeta 228

     Pregunta

     What physical quantity does pound-mass measure?

     Respuesta

     Mass. Do not substitute $lbm$ directly where a force unit such as $lbf$ is required.

229. Tarjeta 229

     Pregunta

     Type I error?

     Respuesta

     Rejecting a true null hypothesis. Its probability is controlled by the chosen significance level under the test assumptions.

230. Tarjeta 230

     Pregunta

     A search hit contains the right words. Is that enough?

     Respuesta

     No. Read the surrounding definition, equation label, units, and notes to confirm the hit answers the actual question.

231. Tarjeta 231

     Pregunta

     Annual straight-line depreciation from basis $B$ to salvage $S$ over $n$ years?

     Respuesta

     $$D=\frac{B-S}{n}$$

     This is an accounting allocation, not a market-value forecast.

232. Tarjeta 232

     Pregunta

     Purpose of $g_c$ in some US customary force-mass equations?

     Respuesta

     It reconciles chosen $lbm$, $lbf$, foot, and second units. Include it only when the equation and unit convention require it; coherent SI equations do not use it.

233. Tarjeta 233

     Pregunta

     Recognizable form of a separable first-order differential equation?

     Respuesta

     $$\frac{dy}{dx}=g(x)h(y)$$

     Rearrange to place the $y$ terms with $dy$ and the $x$ terms with $dx$, while checking for solutions lost by division.

234. Tarjeta 234

     Pregunta

     Using unverified software output in a safety-relevant calculation?

     Respuesta

     Check inputs, assumptions, units, and results with an independent method appropriate to the risk. The engineer remains responsible for professional judgment.

235. Tarjeta 235

     Pregunta

     Equivalent resistance of ideal resistors in series?

     Respuesta

     $$R_{eq}=\sum_i R_i$$

     Series elements carry the same current with no branching node between them.

236. Tarjeta 236

     Pregunta

     Pressure conversion from psi to pascals?

     Respuesta

     $1\,psi\approx6894.76\,Pa$. Keep enough significant figures for the problem's data.

237. Tarjeta 237

     Pregunta

     Type II error?

     Respuesta

     Failing to reject a false null hypothesis. Its probability is $\beta$ for a specified alternative.

238. Tarjeta 238

     Pregunta

     Useful flashcard to make after a failed handbook search?

     Respuesta

     A short scenario-to-search-cue card recording the section name and terms that eventually worked—not a copied problem or page number.

239. Tarjeta 239

     Pregunta

     Standard form of a first-order linear differential equation?

     Respuesta

     $$\frac{dy}{dx}+P(x)y=Q(x)$$

     An integrating factor is $e^{\int P(x)\,dx}$.

240. Tarjeta 240

     Pregunta

     Equivalent resistance of ideal resistors in parallel?

     Respuesta

     $$\frac{1}{R_{eq}}=\sum_i\frac{1}{R_i}$$

     Parallel elements share the same two nodes and therefore the same voltage.

241. Tarjeta 241

     Pregunta

     Book value after $k$ years of straight-line depreciation?

     Respuesta

     $$BV_k=B-kD$$

     Apply it within the depreciable life and do not depreciate below the assumed salvage value.

242. Tarjeta 242

     Pregunta

     Standard atmosphere in pascals?

     Respuesta

     $1\,atm=101{,}325\,Pa$ exactly.

243. Tarjeta 243

     Pregunta

     Using AI-generated technical content in engineering work?

     Respuesta

     Treat it as unverified input: protect confidential data, check sources and calculations, disclose use when required, and keep accountable human review.

244. Tarjeta 244

     Pregunta

     Trial form for a homogeneous linear ODE with constant coefficients?

     Respuesta

     Use $y=e^{rx}$ to obtain the characteristic polynomial in $r$. Repeated or complex roots require the corresponding standard solution forms.

245. Tarjeta 245

     Pregunta

     Wave-speed relationship among frequency and wavelength?

     Respuesta

     $$v=f\lambda$$

     Use frequency in cycles per second and wavelength in compatible length units.

246. Tarjeta 246

     Pregunta

     Statistical power?

     Respuesta

     The probability of rejecting the null when a specified alternative is true: $1-\beta$. Larger effects, larger samples, or lower variability commonly increase power.

247. Tarjeta 247

     Pregunta

     Bar in pascals?

     Respuesta

     $1\,bar=100{,}000\,Pa$ exactly.

248. Tarjeta 248

     Pregunta

     How should handbook navigation be practiced before the FE exam?

     Respuesta

     Use the current handbook from MyNCEES while solving original or properly licensed practice problems, and rehearse the exact search terms that find definitions and assumptions.

249. Tarjeta 249

     Pregunta

     Is depreciation itself a cash outflow?

     Respuesta

     No. It is a noncash accounting expense, though it can affect taxes and therefore after-tax cash flow.

250. Tarjeta 250

     Pregunta

     First-order linear approximation of $f(x)$ near $x=a$?

     Respuesta

     $$f(x)\approx f(a)+f'(a)(x-a)$$

     It is most accurate for $x$ close to $a$ when higher derivatives stay bounded.

251. Tarjeta 251

     Pregunta

     Relationship between period and frequency?

     Respuesta

     $$T=\frac{1}{f}$$

     This requires $f>0$; $T$ has time units.

252. Tarjeta 252

     Pregunta

     How should foreseeable environmental harm enter an engineering decision?

     Respuesta

     Identify and communicate it, follow applicable requirements, and consider practicable ways to reduce harm without compromising public safety.

253. Tarjeta 253

     Pregunta

     Foot-pound-force in joules?

     Respuesta

     $1\,ft\cdot lbf\approx1.35582\,J$. This is a work or energy conversion; keep torque labeled as force times distance even though its dimensions match energy.

254. Tarjeta 254

     Pregunta

     Allowed range and sign meaning of Pearson correlation $r$?

     Respuesta

     $-1\le r\le1$. The sign gives the direction of linear association, and magnitude measures its linear strength.

255. Tarjeta 255

     Pregunta

     When should you search instead of relying on recall?

     Respuesta

     Search when a constant, coefficient, convention, specialized relationship, or applicability detail could change the result. Recall can start the route; the reference should confirm details.

256. Tarjeta 256

     Pregunta

     After-tax effect of a deductible expense $E$ at marginal tax rate $t$?

     Respuesta

     The net cost is $E(1-t)$ under the simplified assumption that the deduction can be used fully in that period.

257. Tarjeta 257

     Pregunta

     Centered finite-difference approximation to $f'(x)$?

     Respuesta

     $$f'(x)\approx\frac{f(x+h)-f(x-h)}{2h}$$

     For smooth $f$, truncation error is proportional to $h^2$ before roundoff dominates.

258. Tarjeta 258

     Pregunta

     General material balance on a control volume?

     Respuesta

     $$\text{accumulation}=\text{in}-\text{out}+\text{generation}-\text{consumption}$$

     At steady state, accumulation is zero; generation and consumption depend on reactions or sources.

259. Tarjeta 259

     Pregunta

     Approximate joules in one International Table Btu?

     Respuesta

     $1\,Btu_{IT}\approx1055.06\,J$. Identify the Btu convention when precision matters.

260. Tarjeta 260

     Pregunta

     What is the defender in a replacement analysis?

     Respuesta

     The currently owned asset being compared with a proposed replacement. Its current market value is an opportunity cost; its original purchase price is sunk.

261. Tarjeta 261

     Pregunta

     Speaking publicly about a technical matter outside your expertise?

     Respuesta

     Limit claims to what you can support, identify the boundary of your expertise, and avoid implying qualifications you do not have.

262. Tarjeta 262

     Pregunta

     Single-interval trapezoidal approximation to an integral?

     Respuesta

     $$\int_a^b f(x)\,dx\approx\frac{b-a}{2}[f(a)+f(b)]$$

     It is exact for linear $f$.

263. Tarjeta 263

     Pregunta

     Energy efficiency of a device?

     Respuesta

     $$\eta=\frac{\text{useful output energy}}{\text{input energy}}$$

     Use the same energy basis in numerator and denominator; a real passive device has $0\le\eta\le1$.

264. Tarjeta 264

     Pregunta

     Purpose of sensitivity analysis in engineering economics?

     Respuesta

     It shows how the decision changes when an uncertain input changes. Vary inputs over plausible ranges while preserving units and model relationships.

265. Tarjeta 265

     Pregunta

     Can a strong correlation establish causation?

     Respuesta

     No. Correlation alone cannot rule out confounding, reverse direction, selection effects, or coincidence.

266. Tarjeta 266

     Pregunta

     Where should you confirm the tested topics for your FE discipline?

     Respuesta

     Use the discipline specification linked from the official NCEES FE exam hub. This common deck does not replace that discipline-specific boundary.

267. Tarjeta 267

     Pregunta

     Mechanical horsepower in watts?

     Respuesta

     $1\,hp\approx745.7\,W$, based on $550\,ft\cdot lbf/s$. Distinguish it from metric horsepower.

268. Tarjeta 268

     Pregunta

     Combine independent standard uncertainties $u_1,\ldots,u_n$ in a sum or difference?

     Respuesta

     $$u_c=\sqrt{u_1^2+u_2^2+\cdots+u_n^2}$$

     This root-sum-square form assumes uncorrelated inputs and coefficients of magnitude one; otherwise include sensitivities and covariance.

269. Tarjeta 269

     Pregunta

     Newton iteration for a root of $f(x)=0$?

     Respuesta

     $$x_{k+1}=x_k-\frac{f(x_k)}{f'(x_k)}$$

     It requires $f'(x_k)\ne0$ and a suitable starting value; convergence is not guaranteed.

270. Tarjeta 270

     Pregunta

     Meaning of slope in simple linear regression of $y$ on $x$?

     Respuesta

     It is the estimated change in mean response $y$ for a one-unit increase in $x$, under the fitted linear model. Its units are $y$ units per $x$ unit.

271. Tarjeta 271

     Pregunta

     Kilowatt-hour in joules?

     Respuesta

     $1\,kW\cdot h=3.6\times10^6\,J$. It is energy, not power.

272. Tarjeta 272

     Pregunta

     Percent error relative to an accepted nonzero value?

     Respuesta

     $$\%\,error=\left|\frac{x_{measured}-x_{accepted}}{x_{accepted}}\right|100\%$$

     The accepted value must be nonzero and both values must use compatible units.

273. Tarjeta 273

     Pregunta

     Does legal compliance alone settle an engineering ethics question?

     Respuesta

     No. Law sets mandatory boundaries, while professional duties can require stronger action, especially when safety, honesty, or conflicts are involved.

274. Tarjeta 274

     Pregunta

     Does handbook fluency replace discipline-specific problem practice?

     Respuesta

     No. Pair navigation and common recall with the current discipline specification and timed, rights-safe problems that match your selected FE discipline.

275. Tarjeta 275

     Pregunta

     Linear interpolation between $(x_1,y_1)$ and $(x_2,y_2)$?

     Respuesta

     $$y\approx y_1+(y_2-y_1)\frac{x-x_1}{x_2-x_1}$$

     Use it between distinct $x$ values when local linear behavior is reasonable.

276. Tarjeta 276

     Pregunta

     Dimensional requirement for a physically meaningful additive equation?

     Respuesta

     Every term being added or equated must have the same dimensions. A dimensionally consistent equation can still be physically wrong, but an inconsistent one is wrong.