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And Louise 10% Let B be the event that Bob is at the grill, T Tina and L Louise Let F be the event the grill catches fire (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 notB 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 universal118 Show that for a surjective function f A !

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A so that f g = idB Solution For each b 2 B we can set g(b) to be any element a 2 A such that f(a) = b Since f is surjective, there is such an a 2 A for each b 2 B Then f g(b) = f(g(b)) = f(a) = b, ie f g = idB 119 Show that for an injective function fIt is much easier to draw pictures of small sets and indicate your functions on the pictures (a) f is onetoone but not onto, and g is onto but not onetoone1 Fractions Let a,b,c, and d be numbers (a) You can break up a fraction from a sum in the numerator, but not in the denominator ab c = a c b c but a bc 6= a b a c (b) Cancellation of the c here requires that it appears in each additive term of the numerator and denominator cacb cd = c(ab) cd = ab d but cab cd 6= ab d

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URGENT F(A,B,C,D,E) = 60 (mod 32) 65 (mod 32) 70 (mod 32) if nn = 34 then nn (mod 32) = A value of 2 means the function is 1 and F = A'B'C'DE'Mean Value Theorem Let f f be continuous over the closed interval a,b a, b and differentiable over the open interval (a,b) ( a, b) Then, there exists at least one point c ∈ (a,b) c ∈ ( a, b) such that f ′ (c) = f(b)−f(a) b−a f ′ ( c) = f ( b) − f ( a) b − aF A → B and g B → C which satisfy the given conditions NOTE you do not need to give formulas on Z or R;

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Academic grading in the United States commonly takes on the form of five, six or seven letter grades Traditionally, the grades are A, A, A−, B, B, B−, C, C, C−, D, D, D− and F, A being the highest and F being lowest In some cases, grades can also be numerical Numerictolettergrade conversions generally vary from system to Both f (1) and f (2)=2 There is c in (0,2) such that f' (c)=f (b)f (a)/ba By the MVT, there is a number c in (0, 1) such that f' (c) = f (1) f (0)/ (1 0) = 2/1 = 2 You can use the same idea to show that for another number c in (1, 2), f' (c) = 0 If you knew that f' was continuous, you could use the Intermediate Value Theorem to show2 days ago 

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Tuesday 21 September Wednesday 22 September Thursday 23 September Friday 24 SeptemberCalculate the volume 1 lbmole of ideal gas will occupy at a) 147 psia and 60°F b) 141 psia and 32°F c) 147 plus 10 oz and 80°F d) psia and 60°FSOLUTION The following information can be deduced from the above information D (female) is a doctor and A (female) is a housewife E is the son of B and A That means C and F are grandchildren of A The gender of C and F cannot be determined But in all cases, A is the grandmother of C

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 Answers 26 L of the A 26 Letters of the Alphabet 7 D of the W 7 days of the Week 7 W of the W 7 wonders of the world 12 S of the Z 12 signs of the zodiac 66 B of the B 66 books of the bible 52 C in a P (W J) 52 cards in a pack (without jokers) 13 S in the U S F 13 stripes in the United States flagB Scale 100 kgf A Scale 60 kgf F Scale 60 kgf 15T Scale 15 kgf 30T Scale 30 kgf 45T Scale 45 kgf 3000 kgf Hardness 10 kgf 500 gf & over Equiv 1000 lb sq in 100 62 93 73 240 240 251 116 99 61 93 72 234 234 246 112 98 60 93 71 228 228 241 109 97 60 92 81 70 222 222 236 106(b) Suppose that Fo = 2 kHz and Fs = 50 kHz Plot the signal yn created by taking the evennumbered samples of xn OF N ON MATLAB

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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 U50 °C = 122 °F 60 °C = 140 °F 70 °C = 158 °F 80 °C = 176 °F 90 °C = 194 °F 100 °C = 212 °F The temperature scale is named after the German physicist Daniel Gabriel Fahrenheit (1686 1736), who proposed it in 1724 In Fahrenheit scale, the freezing point of water is 32 degrees F (written "32 °F"), and the boiling point is 212 The Grade Point Average calculator computes a student's GPA for Letter Grades grade point average between 00 and 40 based on averages of up to ten grades The grades are in the alphabet range of A, A, B, B, B, C, C, C, D, D and F Some people use E instead of F INSTRUCTIONS Enter the number of A's through F's

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CIVL 4135 158 TBeam Code allows the following maximum effective widths 1 Symmetrical Beam ACI318, Section 8102 bw hf b 1) b ≤ span 4 2) b−b w 2 ≤8h f 3) b−bPOSTorder A, C, E, D, B, H, I, G, F Important Point lexicographical order (dictionary order) is a generalization of the way words are alphabetically ordered based on the alphabetical order of their component lettersTranslates into the following assembly code add t0, g, h add f, g, h add t1, i, j or sub f, f, i sub f, t0, t1 sub f, f, j • Each version may produce a different result because floatingpoint operations are not necessarily associative and commutative

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