Numerade

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Assume that the readings at freezing on a bundle of thermometers are normally distributed with a mean of $0^\circ C$ and a standard deviation of $1.00^\circ C$. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading less than $-1.171^\circ C$. $P(Z < -1.171) = 0.1209$

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Solve the exponential equation for $x$. $4^x = 38$ 1) Exact Solution: $x = 3$ 2) Approximation (Round to 4 decimals): $x = 3.0000$

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The following information is given for iron at 1 atm: boiling point = 2750°C, ΔHvap(2750°C) = 354 kJ/mol melting point = 1535°C, ΔHfus(1535°C) = 16.2 kJ/mol specific heat solid = 0.452 J/g°C, specific heat liquid = 0.824 J/g°C What is ΔH in kJ for the process of freezing a 29.2 g sample of liquid iron at its normal melting point of 1535°C? The following information is given for iron at 1 atm: boiling point = 2750°C, ΔHvap(2750°C) = 354 kJ/mol melting point = 1535°C, ΔHfus(1535°C) = 16.2 kJ/mol specific heat solid = 0.52 J/g°C, specific heat liquid = 0.82 J/g°C What is H in kJ for the process of freezing a 29.2 g sample of liquid iron at its normal melting point of 1535°C.

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\frac{dx}{dt} = \gamma_1 x \frac{k - x}{k + \mu x} - \frac{\beta_1 xy}{1 + \alpha x} \frac{dy}{dt} = \gamma_2 \left( 1 - \frac{\alpha_2 y}{x + k_2} \right) y

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Problem 3 (10 points). The marginal product of labor (i.e., the increase in total output if one more worker is employed) is equal to $\frac{5000}{x+2000}$, where x is the number or employees. Currently the firm employes 500 people and produces 1200 units of product. a) (3 points) Using integrals, find the production function Q(x), i.e., find how much the firm will produce (Q) as a function of how many people it employs (x). b) (3 points) If the wage is equal to $100 per worker and the firm is able to sell its product for $70 per unit, how many people the firm needs to employ to maximize its profit? Note that the profit is equal to $\pi = 70Q - 100x$. Note also that you will have to use the knowledge from previous chapters. c) (1 point) Without performing any calculations, state how your answer to part (b) will change (increase, decrease, or stay the same) if the firm with 500 employees would have produced 1300 units of product instead of 1200. Assume all other information remains the same. d) (3 points) A competitor firm has access to a better technology and has a larger marginal product of labor of ($\frac{5000}{x+2000} + e^{-0.001x}$). By how much the total output of this firm will increase if it increases its current staff from 700 to 1000 employees? Round your answer to the nearest integer number.

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Solve for each anti-derivative. Show all work for full credit. 1. \int 3x^2 + 2x - 5 \, dx 2. \int \sqrt{x^2} \, dx 3. \int sec^3x tanx \, dx 4. Find the function y = f(x) if y' = 2x - 1 and f(1) = 3. 5. \int cos(4x) \, dx 6. \int (x^2 + 1)^2 \, dx 7. \int \frac{1}{x^2+9} \, dx 8. \int x\sqrt{1-x} \, dx 9. \int \frac{x}{\sqrt{x^2-9}} \, dx 10. Find the function y = f(x) if y' = \frac{x}{\sqrt{x^2+4}} + \frac{x}{4} and f(4) = \frac{4}{4}.

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A loan of $30,000 is to be paid off with equal monthly payments over a period of 7½ years. If the first payment is made one month after the loan being accepted and the fixed interest rate is 6%p.a. compound monthly, calculate the amount of the monthly payment. Then calculate how much interest in total is paid? Choose the best available answer below Total Interest= $414.76 Total Interest= $30,000.00 Total Interest= $12,373.50 Total Interest= $7,328.40

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c. 2.5 and 13% x d. 0.42 and 5% Waskowski Company sells three products (A, B, and C) with a sales mix of 3:2:1. Unit sales price are shown. Product A $7 Product B $4 Product C $6 What is the sales price per composite unit? a. $25.00 b. $35.00 c. $17.00 d. $20.00 A company sells two products, Model 101 and Model 202. For every one unit of Model 101, they sell two units of products is shown. Sales Price Variable Cost Model 101 $25 $11 Model 202 $28 $7

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(d) Suppose the sound from the engine of a car is modelled by the function x(t) = cos[\omega(t + \tau) + \theta] where \tau is a time delay, and \theta is a phase. Find the frequency (in Hz) and period (in seconds) of the signal x(t) when: (i) [\omega, \tau, \theta] = [\pi/3, 1/2, \pi/2] (ii) [\omega, \tau, \theta] = [3\pi/4, 1/2, \pi/4]. [2 marks] [2 marks] (e) Suppose the signal from the braking activities of a car is modelled as: x(t) = 3e^{-2t}u(t). [5 marks] Sketch this signal and find the energy and power of the signal. (f) The relationship between the input and output of a discrete time system is given by the expression: y[n]+2y[n-1] = x[n]+2x[n-2], where x[n] is the input and y[n] is the output of the system. (i) Sketch the block diagram representation of the system. [2 marks]

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3. Force and Vector Components A sledge is being pulled by two horses on a flat terrain. The net force on the sledge can be expressed in the Cartesian coordinate system as vector F = (-2980.0 N)\hat{i} + (8200.0 N)\hat{j}, where \hat{i} and \hat{j} denote directions to the east and north, respectively. a. Sketch the vector, ensuring you keep it to scale. Include the unit vector directions in your sketch. b. Calculate the magnitude and direction of the pull with respect to the east direction. Explain your work. c. Without doing a calculation predict the direction of the acceleration of the sledge assuming the horses are the only forces action. Explain your conclusion. d. Suppose the sledge is unmoved as a result of the action of the two horses. What is the direction and magnitude of the third force which must be present. Express this force as vector using \hat{i} and \hat{j} unit vectors. Explain your work.

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yvonne b.