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2. Given the function f(x) = x³ + x² - 8, answer the following: a. Is f(x) even, odd, or neither? Explain your reasoning. b. Over which open interval(s) is the function increasing? c. Over which open interval(s) is f(x) decreasing? d. What is the estimated x intercept of the function?

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Why do you think the majority of study participants conformed and went with the confederates incorrect response?

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Definition: The term __criterion__ means standard or rule for judging, and its plural form is __criteria__. Multiple Choice criterion; criteria critical, criticalities cryptogram; cryptograms criteria, criterias critic; critices

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Reagent Table MW BP MP Structure Diethyl ether 74.12 34.6°C -116.3°C C$_2$H$_5$OC$_2$H$_5$ Density 0.713 g/cm³ MSDS g/mol Sodium hydroxide 39.99 1388°C 318°C NaOH 2.13 g/cm³ g/mol Benzoic acid 122.12 249.2°C 122.2°C C$_6$H$_5$COOH 1.27 g/cm³ g/mol o-toluic acid 136.2 259°C 104-105°C CH$_3$C$_6$H$_4$COOH 1.06 g/cm³ g/mol Naphthalene 128.17 218°C 80.26°C C$_{10}$H$_8$ 1.14 g/cm³ g/mol Benzil 210.23 346-348°C 94.8°C (C$_6$H$_5$CO)$_2$ 1.23 g/cm³ g/mol

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The Boo company produces two different Halloween costumes, using the same assembly line. The skeleton requires 1 hour of assembly line time and $2 of material. The ghost costume requires one-half hour of assembly line time and $3 of material. Assembly line time costs $10/hour. The Novelty Company is run by a former microeconomics student, so it is run according to the best economic principles. If the company is producing both costumes on the line this holiday season, what does that tell you about the price of ghost versus skeleton costumes? I don't understand why ghosts would cost more?? Wouldn't that cost more because it takes half the time and not double?? FYI, apparently the ghosts cost more. I just do not know why.

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ENGR& 214 Statics Howie F18 <HW 04: Section 2.5-2.9 Part 2 3D Vectors and Dot Product Problem 2.126 Figure Part A Determine the magnitude of the projected component of the $F = 100 \text{ lb}$ force acting along the axis BC of the pipe. Suppose that $a = 7 \text{ ft}$ and $h = 1.5 \text{ ft}$. (Figure 1) Express your answer to three significant figures and include the appropriate units. $|F_{BC}| = \text{ Value} \qquad \text{Units}$

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1) 20 pts. The blocks shown move on the planes where the coefficient of friction is 0.20. Determine the acceleration of the system and the tension in the string. 20 kg -50kg 20° 40°

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(2) [1 point] As x approaches infinity, for which of the following functions does f(x) also approach infinity? f(x) = $-6x^4$ f(x) = 18x^3 + 2 f(x) = -4x^5 + 16x^3 + 10 f(x) = 6x^3 + 4x^2 - 18x f(x) = 7x^4 + 19x^2 + 18x - 11 f(x) = -2x^6 - 3x^5 + 18x^3 + 12x + 5

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5. (30 points) A vortex cooler is a real device that, on first glance, seems like it would be impossible. The device doesn't require any work input, but it can take in a stream of gas, and separate it into a hot outlet and a cold outlet. See the image below from www.vortec.com. For this problem, consider a vortex tube that operates on air, which you should treat as an ideal gas with constant specific heats. Air enters the tube at 1,000 kPa and 300 K. The hot exit temperature is 325 K and the cold exit temperature is 250 K. The device is adiabatic, and has no moving parts (so there is no work). a. (25 points) Assuming both exits have the same pressure and the process is reversible (best- case scenario), what is the maximum exit pressure? Hint: you will need to use the 1$^{st}$ law, 2$^{nd}$ law, and mass conservation law. b. (5 points) When introducing the concept of reversibility, I originally said that it was impossible to \"unmix\" hot and cold gases, but this device does exactly that. How is it possible for this device to \"unmix\" gases without violating the 2$^{nd}$ law?

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4. a) Expand $3n^2(5n + n^2)$

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cristian f.