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2. A student club with 12 members wants to select a governing committee of 4 different members. The governing committee consists of a president, a vice president, and 2 other members (who have no specific titles). How many different ways are there to choose a governing committee? Your answer may be a number or an expression involving binomial coefficients. 3. How many solutions are there to the following equations with the given conditions? In each part, every variable must be a nonnegative integer (0 or greater). Your answer may be a number or an expression involving terms that look like $\binom{n}{k}$ or $\left( \begin{array}{c} n \ k \end{array} \right)$. (a) $x + y + z = 20$. (b) $x + y + z = 20$, all variables are $\ge 1$. (c) $x + y + z = 20$, $x \ge 3$, $y \ge 1$, $z \ge 2$. (d) $x + y + z = 20$, all variables are even.

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1. You are given the following Cobb-Douglass production function: \[ Y=K^{l / 4} H^{1 / 3}(A L)^{1 / 2} \text {, } \] Where, $ K= $ Physical capital; $ H= $ Human capital; $ L= $ Labour; $ A= $ Effectiveness of labour. Given the following growth rates: Growth rate of $ Y=2,7 \% $; Growth rate of $ K=5.8 \% $; Growth rate of $ H=7.2 \% $; Growth rate of $ L=2.8 \% $. It can be concluded that joint contribution of Physical and Human capital contribution to the growth rate of output is $ 50 \% $.

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Find $\frac{dy}{dx}$ for $y = \sqrt{u}$ and $u = x^2 + 4$.

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Which of the following parameters affect how well an analyte extracts into an organic solvent

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Note: You may need to assume the fact that $\lim_{M \to \infty} M^n e^{-M} = 0$ for all $n$. Decide whether or not the given integral converges. $\int_{-1}^2 \frac{5}{x^{1/3}} dx$ The integral converges. The integral diverges. If the integral converges, compute its value. (If the integral diverges, enter DNE.) Need Help? Read It Submit Answer 10. [1/2 Points] DETAILS PREVIOUS ANSWERS WANEFMAC7 14.5.020. Note: You may need to assume the fact that $\lim_{M \to \infty} M^n e^{-M} = 0$ for all $n$. Decide whether or not the given integral converges. $\int_{-1}^3 \frac{2x}{x^2 - 1} dx$ The integral converges. The integral diverges. If the integral converges, compute its value. (If the integral diverges, enter DNE.)

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16. You are designing a rectangular steel vat with a square base, an open top, and a volume of 32 ft$^3$. (a) What dimensions will minimize the square footage of steel needed? (b) If the thicker steel for the bottom costs $4/ft$^2$ and the thinner steel for the sides costs only $2/ft$^2$, what dimensions will minimize the cost of the tank?

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Sales mix and break-even sales. Rosenberg Sports Inc. manufactures and sells two products, baseball bats and baseball gloves. The fixed costs are $296,800, and the sales mix is 40% bats and 60% gloves. The unit selling price and the unit variable cost for each product are as follows: Products Bats Gloves Unit Salling Price $40 100 Unit Variable Cost $30 60 a. Compute the break-even sales (units) for the overall company's mix of product, M. units b. How many units of each product, baseball bats and baseball gloves, would be sold at the break-even point? Baseball bats Baseball gloves units units

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QUESTION 3a - (12 marks) Consider the system shown with open-loop transfer function of $G H(s) = \frac{K(s+2)}{(s^2-1)(s+5)}$ (a) Using Root-Locus design, determine K and a such that the closed-loop system has dominant poles with $\zeta = 0.5$ and $\omega_n = 2$ rad/sec.

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Problem #5 [4] The following state table describes a sequential circuit with one synchronous input X and one mealy output Z. The initial state is 000. Q2Q1Q0 X=0 X=1 000 000/0 011/0 001 110/1 000/1 010 000/0 011/0 011 010/1 001/1 110 001/1 111/1 111 001/0 111/1 Q2*Q1*Q0*/Z Using the state assignments (Q2Q1Q0) defined above, determine the simplified equation for the next state of each state variable and the output Z. Use a minimum cost strategy (use don't care for any unused state assignments). (a) [1 pt] Q2* = (b) [1 pt] Q1* = (c) [1 pt] Q0* = (d) [1 pt] Z =

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Question 32 Privett Company Accounts payable $ 30,000 Accounts receivable 35,000 Accrued liabilities 7,000 Cash 25,000 Intangible assets 40,000 Inventory 72,000 Long-term investments 100,000 Long-term liabilities 80,000 Marketable securities 38,000 Notes payable (short-term) 20,000 Property, plant, and equipment 500,000 Prepaid expenses 3,000 Based on the data for Privett Company, complete the following. a. What is the current ratio? (Round to the nearest whole number. No decimals.) b. What is the amount of working capital? (Round answer to the nearest dollar. Use a comma, as applicable. Dollar sign is provided.) $

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terri f.