Numerade

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Complex Numbers Consider the circuit which includes the following: • A sinusoidally varying voltage source, V. • An inductor, with an inductance, L. • A capacitor, with a capacitance, C. • A resistor, with a resistance, R. We can find the current, I, in the circuit by using Ohm's law (generalized for alternating currents), $V = IZ_T$ where $Z_T$ is the total impedance in the circuit. (Impedance is the AC corollary to resistance.) Assume that the impedance for each component is as follows: $Z_L = 0 + 5j \text{ ohms}$ $Z_C = 0 - 15j \text{ ohms}$ $R = Z_R = 5 + 0j \text{ ohms}$ $Z_T = Z_C + Z_L + R$ and that the applied voltage is $V = 10 + 0j \text{ volts}$ (Electrical engineers usually use $j$ instead of $i$ for imaginary numbers.) Find the current, I, in the circuit. You should expect a complex number as a result. Enter the complex values of impedance into your calculations using the complex function.

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Assume the random variable X is normally distributed with mean ? = 50 and standard deviation ? = 7. Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded. P(X > 35) Which of the following normal curves corresponds to P(X > 35)? A. B. C.

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The four elements of a compensation plan for salespeople are A. a fixed amount, a variable amount, expenses, and salary B. a fixed amount, a variable amount, expenses, and fringe benefits C. a fixed amount, a variable amount, expenses, and commission D. a fixed amount, a variable amount, stock ownership, and fringe benefits E. a fixed amount, a variable amount, salary, and commission

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5. Firms will borrow to finance an investment project if the ______ interest rate is ______ the project MPK. a. market, above b. market, below c. break-even, above d. break-even, below

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Daily activity 7.1, critical thinking Hypothesize which molecules might easily pass through a phospholipid bilayer and which would not (hint: the nonpolar fatty acids of the interior represent the most significant obstacle) CH$_4$ C$_6$H$_{12}$O$_6$ H$_2$O Na$^+$

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All of the following information about the franchisor is included in the franchise disclosure document (FDD) EXCEPT for which piece of information? a. financial obligations b. selling price c. financial statements d. involvement in litigation

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If $f(x) = (x^2 - 9)(2x - 3)$, find the following. a. $f(2) = -5$ b. $f'(2) = $

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The seeds of tropical trees are dispersed throughout the rainforest by fruit eating birds. These seeds germinate and produce communities which are regulated by intense competition for resources. This association of plant species would best be described by the... intermediate disturbance hypothesis interactive hypothesis stability-diversity hypothesis individualistic hypothesis non-equilibrium hypothesis

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A chemist has a block of aluminum metal (density is 2.7 g/mL). The block weighs 1.3 g. What is the volume, in mL, of the aluminum block?

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1) What is the conversion for KPa to psi ? 2) Normal atmospheric pressure is 14.7 psi. What is this pressure in KPa units ? 3) A car tire is inflated to 30 psi at 45° F. What is the pressure in the tire at 75 psi? (assume tire has constant volume)

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-ngeles s.