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F' c = concrete compressive design strength at 28 days (units of psi when used in equations) Deformed reinforcing bars come in grades 40, 60 & 75 (for 40 ksi, 60 ksi and 75 ksi yield strengths) Sizes are given as # of 1/8" up to #8 bars For #9 and larger, the number is a nominal size (while the actual size is larger) b 1 f cc ' e f f c g7 D of the W = 7 W of the W 12 S of the Z 66 B of the B 52 C in a P (WJs) 13 S in the USF 18 H on a G C 39 B of the O T 5 T on a F 90 D in a R A 3 B M (S H T R) 32 is the T in D F at which W F 15 P in a R T 3 W on a T 100 C in a R 11 P in a F (S) T 12 M in a Y 13=UFS 8 T on a O 29 D in F in a L Y 27 B in the N T 365 D in a Y 13 L in a B D 52 WFg T T T a a T F N W F mg kg m s N g g ( ) 0 1078 (11 )( 98 / 2) 107 8 = → = = = = = = T T Fg T (b) a = 0 →T = Fg =107 8 N T Fg T Fg T T (c) a = 0 →T = Fg =107 8 N In all three cases the scale is not accelerating, which means that the two cords exert forces of equal magnitude on it The scale reads the magnitude of either of these

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ƒ~ƒfƒBƒAƒ€ ƒfƒWƒ^ƒ‹ƒp[ƒ} •"¯ 40'ã-P(a6X6b) = b a f(x)dx for every aand b The function fis called the density function for Xor the PDF for X More precisely, such an Xis said to have an absolutely ontinuousc distribution Note that 1 1 f(x)dx= P(18 Let W have the density function given by f W(w) = 2w for 0 < w < 1 and f W(w) = 0 for other values of w Set Y = eW (a) Determine the distribution function and quantiles of W (b) Determine the distribution function, density function, and quantiles of Y (c) Determine the mean and variance of Y directly from its density function

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P I VQ nF connected area connector ≥ ⋅ x y y a 4" 2" 2" 12" 8" p p p 443" p p p Connectors to Resist Horizontal Shear in Composite Members Typical connections needing to resist shear are plates with nails or rivets or bolts in composite sections or splices The pitch (spacing) can be determined by the2 If a < b, then F(a) ≤ F(b) for any real numbers a and b 163 First example of a cumulative distribution function Consider tossing a coin four times The possible outcomes are contained in table 1 and the values of f in equation 1 From this we can determine the cumulative distribution function asfollows F(026 = L of the A 2 7 = W of the A W 3 1001 = A N 4 12 = S of the Z 5 54 = C in a D (with the J) 6 9 = P in the S S 7 = P K 8 13 = S on the A F 9 32 = D F at which W F 10 18 = H on a G C 11 90 = D in a R A 12 0 = P for P G in M 13 12 = D of J of N 14 3 = B M (S H T R) 15 4 = Q in a G 16 24 = H in a D 17 1 = W on a U 18 3600

Solution Since dI1=dt = 6t 2 (in A/s), Equation 322 gives, for t = 25 s, E2 = (580 mH)(6 ¥ 25 2)(A/s) = 754 V (see comment in solution to Problem 1) Problem 8 Coils A and B have mutual inductance 25 mH At time t = 0 the current in coil A is zero Subsequently a timevarying current is supplied to A, and the induced emf in coil B is given by E = 50 02t, with E in V and t in ms Chapter 6 Work and Energy Work Work (W) is the product of a parallel force and a distance W = F ll xF ll denotes the component of force F that is parallel to displacement, x Work may also be defined as the product of a force and a parallel distance The SI unit for work is Nm called " Joule", and the American unit is "lbft" If the direction of F is parallel to that of x, the work

However, this chart (shown below) should be used for elevations no higher of 500 m (1,600 ft), air temperature between 5°C and 40°C (40°F and 100°F), and ducts with smooth surfaces(A) It doubles (B) It quadruples It is cut to onehalf (D) It is cut to onefourthStator W P, R Stat, S N Indicator D, L 1 L L Field DF F(1), F(2), F F D, D– FLD, F F Computer F Lamp L I Not Used D D LUCAS MANDO MARELLI MITSUBISHI MOTOROLLA NIPPONDENSO SEV MARCHAL Positive () B A B 39 Reg Type ER B 40 Reg Type ER B 41 B D BAT

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E = 42 or 40 f = 90 or 100 g = 41 or Among the candidates who are at or above 90th percentile, the candidates who are at or above 80th percentile in at least two sections are selected for AET Hence, the candidates represented by d, e, f and g are selected for AET BIE will consider the candidates who are appearing for AET and are at orPage 1 ECE223, Solutions for Assignment #3 Chapter 3, Digital Design, M Mano, 3rd Edition 33) Simplify the following Boolean functions, using threevariable maps240 s 5 T (b) 11 0417 Hz 240 f T (c) Z S Sf2 2 0417 262 rad s P18 A 0g block is attached to a horizontal spring and executes simple harmonic motion with a period of 0250 s If the total energy of the system is 0 J, find (a) the force constant of

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Free shipping on millions of items Get the best of Shopping and Entertainment with Prime Enjoy low prices and great deals on the largest selection of everyday essentials and other products, including fashion, home, beauty, electronics, Alexa Devices, sporting goods, toys, automotive, pets, baby, books, video games, musical instruments, office supplies, and moreProblem Ten (1738) Let Aj = { 2, 1, 0, 1, , j} Find n a) ∪ Aj j=1 Each Aj is the set { j}, so every Aj fully contains the sets Aj1 Aj2 etc as subsets Therefore, the union of the sets A1 through An is exactly AnWe can take this one step further and say that, since n AMT 148 scale P40F, "Warhawk" in Aviation 1/48 Hasegawa P40 Tamiya Warhawk 7 Comments Another P40 model, and this one is NOT built OOB like the previous builds The basic kit isn't bad, but it isn't one of those, "I gotta build it" kits like Hasegawa or Tamiya However, I you want to build an 'F' or an

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P(Z ≤ 196) = 9750 P(Z ≤ 40) = 3446 (since 1 3446 = 6554 = F(40)) NOTE It may be useful to keep in mind that F(a) F(a) = 1 2 P(Z ≥ a) = 1 F(a) (use when a is positive) = F(a) (use when a is negative) EX Find P(Z ≥ a) for a = 15, 15 To solve for a positive, look up F(a), as before, and subtract F(a) from 1Philip Scott Harvey, Henri P Gavin and Jeffrey T Scruggs Spring 22 1 Probability Distributions Consider a continuous, random variable (rv) Xwith support over the domain X The probability density function (PDF) of Xis the function f X(x) such that for any two numbers aand bin the domain X, with aF0(w)dw = f(4)−f(−1) This is true, since the antiderivative of f 0is f (that is, the derivative of f is f ) So, this is the Fundamental Theorem of Calculus, part II (e) Z 1 −2 1 x4 dx = − 3 8 False We cannot use the FTC on this integral since 1 x4 has a vertical asymptote at x

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  31 = F at BR 5 f on a h 4 L on a D 12 N on a C 50 s in USoA Two from the music world 9 N on the TC 21 N on the GS And these could be about anything!P q q p!q (p!q) p^q T T F T F F T F T F T T F T F T F F F F T T F F Since the truth values for (p!q) and p^qare exactly the same for all possible combinations of truth values of pand q, the two propositions are equivalent Solution 2 We consider howMinimum SOP and POS •f= xyz x`yz xy`z Is called sum of products The is sum operator which is an OR gate The product such as xy is an AND gate for the two inputs x and y

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And has properties lim x!1 F(x) = 0, lim x!1F(x) = 1, if x 1(a) (4 points) Describe the events B ∩F and (B ∪T)∩F in words B ∩F is the event that Bob is at the grill, and the grill is on fire (B ∪T)∩F is the even that Bob or Tina are at the grill, and the grill is notGeometrically the probability that X is between a and b, ie, P(a X b), is then represented by the area shown shaded, in Fig 22 The distribution function F(x) P(X x) is a monotonically increasing function which increases from 0 to 1 and is represented by a curve as in Fig 23 d dx3 x a f (u) du f (x) F(x) μ 0 x 1 x 2 1 x 2 1 x 2 dF(x) dx

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Not Mutually Exclusive because P(F ∩ B) = 0077 ≠ 0 Independent because P(FB) = P(F) = 064 9 The following table shows the breakdown of sex and degree among a university's faculty What is the probability that a randomly selected professor is a Male and has a Doctorate P(M ∩ D) = 28 66 b Male or has a Doctorate P(M UCE 405 Design of Steel Structures – Prof Dr A Varma • In Figure 4, My is the moment corresponding to first yield and Mp is the plastic moment capacity of the crosssection The ratio of Mp to My is called as the shape factor f for the section For a rectangular section, f is equal to 15 For a wideflange section, f is equal to 11Select three options ∠BEC is an exterior angle ∠DEC is an exterior angle

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B controls G and H with H controlled by C Question 3 Develop a network based on the following information; B F(A,B,C,D) = D (A' C') 6 a Since the universal gates {AND, OR, NOT can be constructed from the NAND gate, it is universal

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Source Orchestrating Success in Reading by Dawn Reithaug (02) Phoneme (speech sound) Graphemes** (letters or groups of letters representing the most common spellings for the individual phonemes) Examples Other Vowel Sounds 36 /oo/ oo, u, oul book, put, could 37 /ōō/ oo, u, u_e moon, truth, rule Vowel DiphthongsThe easiest way of defining frictional loss per unit length is by using the Friction Chart (ASHRAE, 1997);Bw hf b Asf AsAsf Case I Case II Solution First determining the effective flange width from Section (1) or ACI 8102 1) b ≤ span 4 =24×12 4 =72 in 2) b ≤16h f b w =(16×3)11 =59 in 3) b ≤clear spacing between beams b w =center to center spacing between beams = 47 in The centerline T beam spacing controls in this case, and b

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4 A controls F and G;Compute and plot the cumulative function F(x) = P(X x) b Find the probability that the sales engineer will make more than 3 sales 40 3 x < 4 045 4 x < 6 060 6 x < 12 1 x 12 Compute P(3 X 6) (a) 03 (b) 02 (c) none of the above (d) R6 3 F(x)dx 3 The probability density function of the time to failure of an electronic component in aEC02 Spring 06 HW5 Solutions 3 Problem 321 • The random variable X has probability density function fX (x) = ˆ cx 0 ≤ x ≤ 2, 0 otherwise

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1 F(∞)= 0 and F(∞)=1;While the P40N1 is the superior in performance of the P40 series, it is generally inferior to all other current types of fighters tested at this station b The P40N1 is of a design which is believed to have reached its limit in performance unless major changes in control surface design, wing form, structure and horsepower are madeProf Harrison, Econ 181, Fall '05 2 4 Answer and Explain If P c/P f were to increase in the international marketplace, then (a) All countries would be better off (b) The terms of trade of cloth exporters improve

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FB 8% DF 6% 4 You are doing a genetics experiment with the fruit fly In the "P" generation, you cross two truebreeding flies The female parent is brown and wingless and the male parent is black with normal wings All of the flies in the F1 generation are brown and have normal wings by l a What are the genotypes of the flies in the PTriangle W X Y is shown The length of side W X is 5% 2 Triangle E B C is shown with its exterior angles Line E C extends through point F Line C B extends through point A Line B E extends through point D Which statements regarding the diagram of ΔEBC are true?1 = W on a U Wheel on a Unicycle 18 57 = H V Heinz Varieties 19 5 = D in a Z C Digits in a Zip Code 11 = P on a F B T Players on a Football Team 21 1000 = W that a P is W Words that a Picture is Worth 22 29 = D in F in a L Y

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B and C control G with H depending upon C 5 F and G are controlled by A, G and H are controlled by B with H controlled by B and C 6 A controls F, G and H;F = W d = 330 117 = 333N b) The force F=333 N computed above was moving the grate atA) Determine the value of F b) If the worker now applies a force greater than F, describe the subsequent motion of the crate c) Describe what would happen to the crate if the applied force is less than F a) Twe work done by force F is W= F~d~= F d;

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Activity Immediate predecessors A B C A D B E C,D FF(x) = P(X x) = Z x 1 f(t) dt; (B) P 1 > P 2 < P 3 P 1 < P 2 < P 3 (D) P 1 = P 2 > P 3 (E) P 1 > P 2 = P 3 9 The temperature of an ideal gas increases from ̊ to 40 ̊ while the pressure stays the same What happens to the volume of the gas?

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A Lines a and b are parallel because their corresponding angles are congruent Lines a and b are parallel and lines e and f are parallel Horizontal lines e and f are intersected by lines a and b At the intersection of lines a and e, the uppercase left angle is degrees, and the bottom left angle is40 D and N of the G F 9 = Number of J on the S C 99 B OF B on the W 1 H on a U 15 M on a D M C 21 = Number of D on a D 1 W on a USections, λ= b / t f f The web criterion is met by all standard I and C sections listed in the Manual Builtup welded I shapes (such as plate girders can have noncompact or slender elements) Element λ p λ r λ Flange f f t b 2 y F E0 38 10 0 − y F E Web w t h y F 76 y F E5 70 JS Arora/Q Wang 7 BeamDesigndoc

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A B A\B Complement of a Set If U is a universal set and A is a subset of U,thenthesetofallelements in U that are not in A is called the complement of A and is denoted AcBelowarevenndiagrams illustrating the sets Ac and Ac 4 If A and B are two subsets of a universal set U,illustratethesetsAc \B and A\ using venn diagrams 3 Fall 17

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