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The table below depicts the relationship between the price level and aggregate demand and aggregate supply. Aggregate Demand and Aggregate Supply Short-Run Aggregate Price Level Aggregate Demand (in Supply (in millions) Long-Run Aggregate Supply (in millions) millions) 80 $500 $20 $100 90 400 40 100 100 300 60 100 110 200 80 100 120 100 100 100 What is the market equilibrium? Multiple Choice

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4. [0/1 Points] DETAILS MY NOTES ZILLDIFFEQMODAP12 7.2.020. Theorem 7.2.1 - Some Inverse Transforms a. $1 = \mathcal{L}^{-1}\left\{ \frac{1}{s} \right\}$ b. $t^n = \mathcal{L}^{-1} \left\{ \frac{n!}{s^{n+1}} \right\}$, $n = 1, 2, 3, \dots$ c. $e^{at} = \mathcal{L}^{-1} \left\{ \frac{1}{s-a} \right\}$ d. $\sin(kt) = \mathcal{L}^{-1} \left\{ \frac{k}{s^2 + k^2} \right\}$ e. $\cos(kt) = \mathcal{L}^{-1} \left\{ \frac{s}{s^2 + k^2} \right\}$ f. $\sinh(kt) = \mathcal{L}^{-1} \left\{ \frac{k}{s^2 - k^2} \right\}$ g. $\cosh(kt) = \mathcal{L}^{-1} \left\{ \frac{s}{s^2 - k^2} \right\}$ Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your answer as a function of t.) $\mathcal{L}^{-1} \left\{ \frac{1}{s^2 + s - 30} \right\}$

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Question 9 What is the IUPAC name for the molecule with the line structure: SH sulfanyl butanoate 2-methylpentane-2-thiol 1,1-dimethylbutane-1-thiol 1,1-dimethylsulfanyl-1-butanoate hexane-2-thiol

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Clue: inflammation of the tonsils

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Simplify completely: \[ i^{9287}+i^{6943} \]

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(II) (a) Show that each plate of a parallel-plate capacitor exerts a force on the other, by calculating dW/dx where dW is the work needed to increase the separation by dx. (b) Why does using , with E being the electric field between the plates, give the wrong answer?

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Question 1 1 pts The system x' = 2x + 2y + 3 y'= -x + y + 1 is homogeneous. O True O False Question 2 1 pts The system x' = cos(x)x + sin(y)y y' = cos(y)x + sin(x)y is linear. O True O False

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(b) Find the area of the region.

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- Definitions of Perfect Competition, Monopoly, Monopolistic Competition, and Oligopoly - Current event article about Amazon - Title, date, and source - Outline of key points - Summary statement about which Market Structure Amazon belongs to and why - Opinion on whether Amazon is too big and should be broken up - Based on readings about Standard Oil and Anti-Trust laws

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please solve all questions in clear paper Problem#1[25marks] Web crawlers need to estimate the frequency of changes to Web sites to maintain a current index for Web searches Assume that the changes to a Web site follow a Poisson process with a mean of 3.5 days. a) [6 pts] What is the probability that the next change occurs in less than 2.0 days? b) [6 pts] What is the probability that the time until the next change is greater 7.0 days? c) [6 pts] What is the time of the next change that is exceeded with probability 90%? d [7 pts] What is the probability that the next change occurs in less than 10.0 days,given that it has not yet occurred after 3.0 days? Problem#2[25marks] Assume that the weights of individuals are independent and normally distributed with a mean of 76Kg and a standard deviation of 16 Kg. Suppose that 25 people squeeze into an elevator that is designed to hold 1950 Kg. (a [8 pts] What is the average and standard deviation of the total weight inside the elevator? (b) [8 pts] What is the probability that the load (total weight exceeds the design limit? person getting into the elevator after the first 10 persons. Find the mean of the total electricity cost and its variance for the total number of people who squeezed inside the elevator. Problem #3 [25marks] Suppose the time it takes a data collection operator to fill out an electronic form for a database is uniformly between 1.5 and 2.2 minutes [6 pts] What is the mean and variance of the time it takes an operator to fill out the form? b) [6 pts] What is the probability that it will take less than two minutes to fill out the form? [6pts]Determine the value forx such that PX<x=0.9. d [7 pts] Determine the cumulative distribution function of the time it takes to fill out the form. Problem#4[25marks] QNB branch at QU has two cashier lines, one is known to be faster than the other. Let I denote the number of customers in the first line and X2 denote the number of customers in the second (fast) line at the same time of the day.Suppose that the joint p.m.f. of XI and X2 is given by the shown table. a [4 pts] What is the probability that both lines are empty? (b [4 pts] What is the probability that both lines have the same X1 length (i.e.same number of customers)? c [4 pts] What is the probability that the total number of 0 1 2 3 customers in the two lines is exactly four? 0 0.05 0 0 0 (d [4 pts] What is the probability that the faster line has more than I customer given that the first line is empty? 1 0.15 0.05 0 0 (e[5 pts]Find the correlation between X andXand comment on the existence and strength of linear relation between X X2 2 0.1 0.15 0 0 andX2. 3 0.05 0.05 0.1 0 (f[4 pts] Are Xand Xindependent?Why 4 0.05 0.05 0.15 0.05

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brittany c.