Numerade

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Where would you look for the mantle of a freshwater mussel? inside the visceral mass lining the inside of the shell freshwater mussels do not have a mantle lining the outside of the shell

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6. In Fig. 6.37 , if $ \triangle A B E \cong \triangle A C D $, show that $ \triangle \mathrm{ADE} \sim \triangle \mathrm{ABC} $. 7. In Fig. 6.38, altitudes AD and CE of $ \triangle \mathrm{ABC} $ intersect each other at the point $ P $. Show that: (i) $ \triangle \mathrm{AEP} \sim \triangle \mathrm{CDP} $ (ii) $ \triangle \mathrm{ABD} \sim \triangle \mathrm{CBE} $ (iii) $ \triangle \mathrm{AEP} \sim \triangle \mathrm{ADB} $ (iv) $ \triangle \mathrm{PDC} \sim \triangle \mathrm{BEC} $ Fig. 6.37

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Price Level LRAS AS AD AD$_1$ Real GDP (billions of dollars) Instructions: Enter your answers as a whole number. a. How much does aggregate demand need to increase to restore the economy to its long-run equilibrium? \$ 100 billion b. If the MPC is 0.9, how much does government purchases need to increase to shift aggregate demand by the amount you found in part a? \$ 10 billion Suppose instead that the MPC is 0.8.

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The first diagnostic examination usually performed to evaluate a clinical suspicion of lung cancer is _____________. Question 11 options: Biopsy Bronchoscopy Chest x-ray CT chest

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Tools Fill \& 6| Pahina Basahin mo ang mga pangungusap mula sa binasang teksto. Ito ay mga uri ng pangungusap na ginamit upang isalaysay ang mga pangyayari o karanasan sa teksto. 1. Naku! Tila uulan. 2. Lumalakas ang buhos ng ulan. 3. Huwag kayong lumabss, balca matamaan kayo ng mga nagliliparang yero. 4. Sino ang mga sumisigaw? 5. Tulong! Ang bubong namin nailipad. 6. Kung maaari, dumito muna kayo sa aming bahay. Ligtas kayo dito. 7. Ferdie, pakikuha mo ang tuwalya sa ating silid. 8. Punasan mo ang iyong katawan. 9. Anak, pakisara mo ang pinto. 10.Tuwang-tuwa si Ferdie sa ginawa ng kanyang mga magulang. Tandaan: May apat na uri ng pangungusap ayon sa gamit. Maaaring ito ay nagsasalaysay, nagtatanong, nag-uutos - nalikiusap at maaaring nagsasaad ng matinding damdamin. Ang mga ito ay masari mong gamitin upang isalaysay ang iyong karanasan. Ang pagsasalaysay ay pagpapahayag na may layuning magkuwento ng mga pangyayari. Ito ay isang pamamaraan upang ipabatid ang mga mahahalagang pangyayaring may kaugnayan sa ating karanasan. Ang karanasan at nakikita sa kapaligiran ay maaring pagmulan ng pagsasalaysay ng isang tao. 7 | Pahina

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If in that same function L = f(t), where t represents the number of years after 2010 and L represents the liters of water in a backyard pond, then what would f(3) = 38.95 represent in the context of the situation? - In 2013, the pond had 38.95 liters of water in it. - In 2010, 3 ponds had 38.95 liters of water in them. - 3 Liters were added in 2010, making a total of 38.95 liters. - In 2013, there were 38.95 ponds.

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An intoxicated clockmaker produces a grandfather clock whose pendulum has a period of 1.4 s. What is the length of the pendulum?

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1) Let G3 = ({S}, {a,b}, ?, S) be a grammar, where the set of rules I is defined as follows: S? aSbSa S? bSbSa S ? aSbSb S? ? a) Does there exist a regular expression R such that L(R) = L(G3)? If it exists, provide such R; otherwise, simply put 0. Let L = {c^{2n-1}a^m c^3 b^{2m+1} a^n | n, m > 0}. b) Complete the following context-free grammar G such such L(G) = L. S ? ccSa | < missing string > A ? aAbbb | aBbb B ? ccc Provide the missing string as a single line in the given text file (e.g., if your response is xSSy, submit a file with a single line containing string "xSSy" (of course, without the quotes)). c) Does there exist a regular expression, DFA, regular grammar or PDA over the alphabet ? = {a, b, c} which is equivalent to the language L? (Answer the following question as a string of bits that translate to 1 for yes and 0 for no. For example, if your answer is "no, no, yes, no" give your response as 0010).

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Problem 9. Prove that there exist regular expressions \gamma and express them in terms of regular expressions \alpha, \beta such that (1) $L(\gamma) = (L(\alpha))^R$. (2) $L(\gamma) = L(\alpha) \setminus L(\beta)$. Prove the existence of such \gamma using NFAs. (3) $L(\gamma) = L(\alpha) \cap L(\beta)$. Prove the existence of such \gamma using NFAs.

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5. (6 points) Given the following vector in cylindrical coordinates: $A = \rho z \sin \phi \hat{\rho} + 3\rho \cos \phi \hat{\phi} + \rho \cos \phi \sin \phi \hat{z}$. (a) Transform this vector to spherical coordinates (b) Evaluate both the cylindrical form and the spherical form of this vector at the point $P(6, 120^\circ, 200^\circ)$ in spherical coordinates. Verify that your answers give the same magnitude for the vector, regardless of whether it is expressed in cylindrical or spherical coordinates.

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guillermo d.