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40 'ã "¯Œ^ ƒƒ"ƒY ƒc[ ƒuƒƒbƒN-Let A, B,andC be sets in a universal setUWearegivenn(U)=66,n(A)=32,n(B)=33, n=33,n(A\B)=16,n(A\C)=10,n(B\C)=18,n(A\B\Cc) = 9 Find the following values (a) n((AB C)c) (b) n(Ac \ \C) 10 Fall 17, Maya Johnson 6 Use the following information to determine the number of people in each region of the VennVenn Diagrams We can visual subsets of a universal set, and how they interact/overlap, using Venn diagrams, as shown below On the left, the brown shaded region is A\B

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From the NATIONAL INSTITUTE of MENTAL HEALTH G e t E x c i t e d A b o u t t h e B r a i n!64 = S on a C B Squares on a Chess Board 24 40 = D and N of the G F Days and Nights of the Great Flood 25 76 = T in the B P Trombones in the Big Parade 26 50 = W to L Y L Ways to Leave Your Lover 27 99 = B of B on the W Bottles of Beer onPursuant to 21 USC §§ 841(b)(1) and 960(b)(3), a statutory range of 0 to years applies to offenses involving lesser quantities of drugs A statutory maximum of five years is provided for offenses involving less than 50 kilograms of marijuana and for certain other lesser offenses See 21 USC §§ 841(b)(1)(D) and 960(b)(4)

CO V I D 1 9 Va c c i n e A l l o c a t i o n B y C o u n t y ( 1 s t d o s e s ) N OTE Vaccine allocation is for 1st doses only and does not include the federal Pharmacy Partnership for LongTerm Care and the federal Retail Pharmacy Only the massvaccination doses reserved for county are included in the county totalsIn t r o D u C t o n Facts and figures simply underscore the relative importance of deer to Californians To most big game hunters, however, the opportunity to harvest a deer is not measured in monetary terms Deer hunting is a very basic experience;26 = 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 18 3600 = S in an H 19 57 = H V 11 = P in a C T 21 1000 = W that a P is W 22 29 = D in F in a L Y 23 64 = S on a C B 24 40 = D and N of the G F More Questions

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C H U R C H A V CA N Y O N C R E E K C R V I L L A G E D R A B B A T E R D D E X T E R D R S R O S E M A R Y L N RB O L E D D W E S T R I D G E D R WOODWAY DR P A P B E A R D R Q U A I L N R U N C A I N D A N G U S V E A C O N D R O R R S T S U F F O K A V W IN D I N Route 40SP C entu ry T 1 MSC 2 Kl eb rg 3 Park West 4 Th eCo tag s 5C L E A N E N E R G Y F U E L S C O R P (E xa c t na m e of re gi s t ra nt a s s pe c i fi e d i n i t s c ha rt e r) 4675 M ac Ar thur Cour t, Sui te 800, Ne wpor t B e ac h, CA (Addre s s of pri nc i pa l e xe c ut i ve offi c e s , i nc l udi ng z i p c ode ) (949)B) current account,a US good import C) financial account, a US asset import D) financial account, a US asset export E) a current account as a US good import and a financial account, a US asset export Answer E The United States issues a $10,000 debt forgiveness to Argentina How is this accounted for in the balance of payments?

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(a) Determine the distribution function of Y (b) Let U be uniformly distributed on (0,1) Determine an increasing function g on (0,1) such that g(U) has the same distribution as Y (c) Determine constants a and b > 0 such that the random variable a bY has lower quartile 0 and upper quartile 15 (Logan, 24 # 1) Solve the problem ut =kuxx, x >0, t >0, ux(0,t)=0, t >0, u(x,0)=φ(x), x >0, with an insulated boundary condition by extending φ to all of the real axis as an even function The solution is u(x,t)= Z ∞ 0 G(x −y,t)G(x y,t)φ(y)dy First note that the solution to the IVP ut = kuxx, −∞ < x < ∞, t > 0, u(x,0) = f(x), −∞These solutions are known as Pythagorean triples (with the simplest example 3,4,5) Around 1637, Fermat wrote in the margin of a book that the more general equation a n b n = c n had no solutions in positive integers if n is an integer greater than 2

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Math 160, Finite Mathematics for Business Section 51 and 52 – Discussion Notes Brian Powers – TA – Fall 11 A set is a collection of things The things in a set are its elementsWe tend to use capital letters for setsTo m a n a g e th e C O V I D 1 9 p a n d em i c , w e m u st b a l a n c e N ew Yor k C i ty ' s op er a ti n g b u d g et F a c i n g a d ec l i n e i n r ev en u e of a p p r ox i m a tel y $ 9 b i l l i on f or F Y2 0 a n d F Y2 1 , th a t w i l l r eq u i r e p a i n f u l c h oi c esA chance to pit your brain and muscle against the challenges

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 How about 40 Channels on a Citizens' Band Radio?2122 B ay C i t y H S B e l l Sc he dul e Dut y / Tut ori al s 700 – 725 First Bell 7 25 1s t 7 30 – 8 15 2nd 8 19 – 9 04 HOMEROOM/ GOAL Time 9 08 – 9 36 3rd 9 40 – 10 25 4t h 10 29 – 11 14 A l u n c h 5t h 1114 – 1144Overview Pythagorean origins The Pythagorean equation, x 2 y 2 = z 2, has an infinite number of positive integer solutions for x, y, and z;

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E n d o r s e d b y t h e c o m m a n d e r o r s e n i o r leader of the requesting activity and forwarded through their higher headquarters to the policy proponent Refer to AR 2530 for specific guidance Army management control process This regulation contains management conT h e Ja s o n ville 40 is a 40 a c r e p r o p e r t y lo c a t e d in s o u t h e r n Cla y Co u n t y ju s t n o r t h o f Ja s o n ville , IN T h is p r o p e r t y h a s a s m a ll 396 S qA Coloring & Activity Book For Kids Ages 8–12 The National Institute of Mental Health (NIMH) is the lead federal agency for research

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 n(B ∪ C )=36 Firstly there are 3 overlapping circles, A,B and C The cap sign means intersection, which is where things overlap The cup sign U means union, which includes everything that is mentioned So where they all overlap is 6, put that in firstC U(x, y) = x2/3 y1/3 Since the indifference curves are bowed towards the origin, they do obey the assumption of diminishing MRS y x 8 8 1 1 512 512 Economics 3070 d U(x, y) =min(2X, 3Y) This is an example of perfect complements The MRS is undefined at the vertex where 2X=3Y But lets graph the indifference curve, remember they L shapedC Bad Let V equal the volume of the tank and let a, b and c represent the flow

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B) P(jX=Y 1j 025);Yc(t) = c xc(t) If we can write c = Aej', then A is the amplitude and ' is the phase of the output relative to the amplitude and phase of the input 32A = the set of all even numbers B = {2, 4, 6} C = {2, 3, 4, 6} Here B ⊂ A since every element of B is also an even number, so is an element of A More formally, we could say B ⊂ A since if x ∈ B, then x ∈ A It is also true that B ⊂ C C is not a subset of A, since

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Superior Court of California C O U N T Y O F A L A M E DA POLICY NO 08 01 01 TITLE Travel Expense Reimbursement for Judicial Officers and Court Employees EFFECTIVE DATE Revised policy effective CONTACT Laura Stine, Senior Accountant POLICY STATEMENT See Section 10, Page 1 GOVERNING STATUTES AND RULES JUDIC IAL COU NCIL OF CAL FOR2 29 if a ib=0 wherei= p −1, then a= b=0 30 if a ib= x iy,wherei= p −1, then a= xand b= y 31 The roots of the quadratic equationax2bxc=0;a6= 0 are −b p b2 −4ac 2a The solution set of the equation is (−b p 2a −b− p 2a where = discriminant = b2 −4ac 32P(AC ∩ AC ∩ AC ∩ AC ∩ A) = (076)4(024) = 8 In the parking lot of the a large mall 64% of cars are foreign made, 12% are the color blue and 77% are blue and foreign made cars a Draw a Venn Diagram 077 b What is the probability that a randomly selected car was i A foreign car or a blue car?

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The 40/40 Club is named after one of baseball's most prestigious achievements A benchmark for power and speed, The 40/40 Club includes players who hit 40 home runs and steal 40 bases in one season Only Barry Bonds (1996), Alex Rodriguez (1998),  The latest sales tax rates for cities in California (CA) state Rates include state, county and city taxes rates included for24 c JFessler,May27,04,1310(studentversion) 212 Classication of discretetime signals The energy of a discretetime signal is dened as Ex 4= X1 n=1 jxnj2 The average power of a signal is dened as Px 4= lim N!1 1 2N 1 XN n= N jxnj2 If E is nite (E < 1) then xn is called an energy signal and P = 0 If E is innite, then P can be either nite or innite

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C) P(Y XjY 025) SOLUTION These problems are most easily solved by drawing pictures and computing the areas of the triangular regions that you see For part (a) the answer is 1 12(2)(3 4)(3 4) = 7 16 (we did this as an example in class) For part (b) the answer is 1 1 2 (1)(4 5) 1 2 (1)(3 4) = 9 40 For part (c), P(Y X;Y 0Tough as nails themeless #40 ccccc o m b o p e a k p e r v ooooo r i o n s l u r e l o i mmmmm i n a u d i e r e e s m e mmmmm o u s s e c a m b r i a n aaaaa l i tO f f i c e o f Management and Budget Circular A–123, and DODI This regulation increases the involvement and accountability of commanders and managers It does n o t c o n t a i n i n s t r u c t i o n s f o r e v a l u a t i

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U˘B(n;p) (3) Find the distributions of the random variables that have the MGFs (a) m X(t) = (1=3)et (2=3) 5 (b) m Y (t) = et 2 et (c) m Z(t) = e2(e t 1) (d) m U(t) = e 2 t2 2 (e) m V (t) = e2 t e t (f) m W(t) = 1 (1 3t)5 Solution (a) m X(t) = (1=3)et (2=3) 5 = (1=3)et (1 1=3)5, so X˘B(5;1 3) (b) m Y (t) = et 2 te = 1 2Ub 14 Utility Y Income 2 U1 U2 U = f(Y) 15 Von NeumannMorganstern Utility • N states of the world, with incomes defined as Y1 Y2 Yn • The probabilities for each of these states is P 1 P2Pn • A valid utility function is the expected utility of the gamble • E(U) = P1U(Y1) P2U(Y2) PnU(Yn) 16 • E(U) is the sum of theS E C U R I T I E S A N D E X C H A N G E C O M M I S S I O N Washington, DC 549 F O R M 8K CURRENT REPORT Pursuant to Section 13 or 15(d) of the Securities Exchange Act of 1934 Date of Report (Date of earliest event reported) C E N T E R P O I N T E N E R G Y, I N C

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M e n d e d C h a n g e s t o P u b l i c a t i o n s a n d Blank Forms) directly to the Office of the P r o v o s t M a r s h a l G e n e r a l ( D A P M – M P O – L E ) , 2 8 0 0 A r m y P e n t a gon, Washington, DC 310–2800 Committee management AR 15–1 reAbout Business Programs The Business Programs Division, the largest division of the Secretary of State's office, supports California Businesses by registering business entities and trademarks and enabling secured creditors to protect their financial interestsG 025 N 4 007 / 025 602 10 / ( 4 ) ( 252 10 ) 865 / 252 10 073 / / ( 602 10 ) 3 4 G 025 N 4 23 92 9 23 2 2 3 2 ' ' u u u u u u u u u u u u y u y u ' ' u u u u J V J S S S J V J S We think this is a reasonable approach, but the value seems high

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(X ∪ Y)' = {9} Example Given U = {x 1 ≤ x ≤10, x is an integer}, A = The set of odd numbers, B = The set of factors of 24 and C = {3, 10} a) Draw a Venn diagram to show the relationship b) Using the Venn diagram or otherwise, find i) (A ∪ B ) ' ii) (A ∪ C ) '41 Chapter 4 Discretetime Fourier Transform (DTFT) 41 DTFT and its Inverse Forward DTFT The DTFT is a transformation that maps Discretetime (DT) signal xn into a complex valued function of the real variable w, namely −= ∑ ∈ℜ ∞ =−∞U = x·y3 FInd her utility maximizing x and y as well as the value of λ 2 A consumer has the following utility function U(x,y)=x(y 1),wherex and y are quantities of two consumption goods whose prices are p x and p y respectively The consumer also has a budget of B Therefore the consumer's maximization problem is x(y 1)λ(B −p xx−p

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