Numerade

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Question 1 [10 Points] Use the Pumping Lemma to demonstrate that the following languages are not regular. a) L1 = {w ∈ {0, 1}*: 0i1j where i ≤ j} b) L2 = {w ∈ {a, b, c}*: aibjck+2 where i = k and i, j, k ≥ 0} c) L3 = {w1#w2 such that |w1| = 2.|w2|, where Σ = {0, 1} } d) L4 = {w ∈ {a}*: a2n where n ≥ 0}

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John Snow, in Snow on Cholera: ? a. was the father of modern bio-statistics. b. established postulates for transmission of infectious disease. ?c. was an English anesthesiologist who used natural experiments. ?d. argued that the environment was associated with diseases such as malaria ?e. was a London surgeon who identified an environmental cause of cancer.

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1. For each of the following IR spectra: (i) label all major peaks (for example, sp³ C - H, acid O - H, ketone C=O, etc) using the labels given on the "color IR band handout." (1.5 pts per spectrum) (ii) give the name of each functional group present in the space provided. (0.5 pt per spectrum) Note: The table given below the spectrum indicates the frequency (cm?¹) of each peak followed by the intensity (%T). Spectrum 1: 100 4000 3000 2000 1500 1000 500 WAVENUMBER (cm?¹) cm?¹ %T 2959 12 1468 48 1123 74 2929 8 1460 50 1074 84 2874 19 1419 30 969 31 2659 16 1379 60 938 44 2672 47 1290 29 727 77 1711 4 1223 36 680 79 1666 42 1173 62 625 81 Name(s) of functional group(s): fingerprint region

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During the 1945-1946 Hungarian hyperinflation, when the rate of inflation reached 41.9 quadrillion percent per month, the Hungarian government discovered that the real value of its tax receipts was falling dramatically. To keep real tax revenues more stable, it created a good called a "tax pengö", in which all bank deposits were denominated for purposes of taxation. Nevertheless, payments for goods and services were made only in terms of the regular Hungarian currency, whose value tended to fall rapidly even though the value of a tax pengö remained stable. Prices were also quoted only in terms of the regular currency. Lenders, however, began denominating loan payments in terms of tax pengös. The tax pengö functioned as money in Hungary in 1945 and 1946 ◻ A. as a barter exchange. B. as a medium of exchange. C. as a unit of accounting During the 1945-1946 Hungarian hyperinflation, when the rate of inflation reached 41.9 quadrillion percent per month, the Hungarian government discovered that the real value of its tax receipts was falling dramatically. To keep real tax revenues more stable, it created a good called a "tax pengö", in which all bank deposits were denominated for purposes of taxation. Nevertheless, payments for goods and services were made only in terms of the regular Hungarian currency, whose value tended to fall rapidly even though the value of a tax pengö remained stable. Prices were also quoted only in terms of the regular currency. Lenders, however, began denominating loan payments in terms of tax pengös. The tax pengö functioned as money in Hungary in 1945 and 1946 A. as a barter exchange. B. as a medium of exchange. C. as a unit of accounting

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2. Solve the following differential equation using Laplace transform \frac{d^2y}{dt^2} - 2\frac{dy}{dt} = te^{-2t}, y(0) = 0, y'(0) = 1.

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Express 2 less than or equal to x < 8 in interval notation

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Simplify $\cos\theta + \sin\theta \cdot \tan\theta$

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Which of the following statements is true about the semicircular canals of the inner ear?

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Contractionary monetary policy involves: Select one: Odecreasing the money supply, increasing interest rates and decreasing aggregate demand. ? increasing the money supply, interest rates, and aggregate demand. O increasing the money supply, decreasing interest rates and aggregate demand. O decreasing the money supply, interest rates, and aggregate demand.

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Find a such that int_1^a 2dx=7 a Find a such that 2dx=7. J1

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gerald r.