A plant manufacturing nails and screws uses a large pool (volume = 10,000 L) to collect and treat its residual wastewater before discharging it in a nearby stream. The manufacturing process makes use of a strong acid (HCl) and a weaker one (phosphoric acid, H₃PO₄; pK_a1 = 2.148, pK_a2 = 7.20, pK_a3 = 12.15), before discharging them in the pool for treatment (neutralization). Once the pool is filled to its maximum capacity, a technician measures the chlorine and phosphorus concentrations in the wastewater to be 0.5 M and 1.0 M, respectively. Assume (i) that chlorine and phosphorus come only from HCl and phosphoric acid, respectively, and (ii) that no H⁺ was consumed (or neutralized) in the manufacturing process.

Knowing that the technician has to bring the pH of the waste water back to a minimum of 7.2 before discharging it in the stream, what is the minimum amount (in kg) of NaOH_(s) (40 g/mol) that he has to add to the pool before discharging the waste water in the stream?

What will be the pH of the wastewater following the addition of 200 kg of NaOH to the initial wastewater?

What will then be the number of moles of each phosphorus species (H₃PO₄, H₂PO₄^-, HPO₄^2- and PO₄^3-) in the pool after the addition of NaOH?

What will be the pH of the wastewater if the technician adds 10.0 kg of NaOH in excess to what is needed to bring the pH to 7.2?

1. Three materials X, Y, and Z are required to produce two products A and B. The profit function of each product is nonlinear. The total profit function for Product A is 80A - A2 and the total profit function for Product B is 72B - 0.8B2. Thus, the total profit for producing A and B together is 80A - A2

+ 72B - 0.8B2. (These two profit functions are independent.)

a. Use the Nonlinear Solver (GRG Nonlinear) to solve the nonlinear profit function for this problem. (Note: this problem does not have a constraint.) What is the optimal production quantity for each product? What is the total profit? Why is the solution optimal? Is the total profit function a function with decreasing marginal return? Why?

b. Following information about resource requirement and availability is given. Formulate the problem with constraints as a nonlinear programming model on the spreadsheet to maximize the total profit.

C. Solve the problem using the Nonlinear Solver. What is the optimal solution? What is the maximum total profit?

D. Explain why solutions in (a) and (c) are different.

E. Formulate the problem in (b) as an algebraic model.

1) Blue Ram Brewing Company currently has no debt in its capital structure, but it is considering using some debt and reducing its outstanding equity. The firm’s unlevered beta is 1.15, and its cost of equity is 11.55%. Because the firm has no debt in its capital structure, its weighted average cost of capital (WACC) also equals 11.55%. The risk-free rate of interest (rRFrRF) is 3.5%, and the market risk premium (RPMRPM) is 7%. Blue Ram’s marginal tax rate is 25%.

Blue Ram is examining how different levels of debt will affect its costs of debt and equity, as well as its WACC. The firm has collected the financial information that follows to analyze its weighted average cost of capital (WACC). Complete the following table.

1). A star with an absolute magnitude of 4.5 is located 50 pc from Earth. Ignoring the dimming effect of the interstellar medium, its apparent magnitude will be...

Question 38 options:

2). The absolute magnitude of a star is 2.6, but its apparent magnitude viewed from Earth is 8.9. How far away from Earth is the star?

Question 37 options:

3). Two stars have the same radius, but surface temperatures star A is 3,000 K and the surface temperature of star B is 12,000 K. How much more luminous is star B than star A?

4). A star has an absolute magnitude of 2.84. What is its luminosity in solar units?

Question 40 options:

Please help. Thanks

You have been able to get a part-time job in a University laboratory. The group is planning a set of experiments to study the forces between nuclei in order to understand the energy output of the Sun. To do this experiment, you shoot alpha particles from a Van de Graaf accelerator at a sheet of lead. The alpha particle is the nucleus of a helium atom and is made of 2 protons and 2 neutrons. The lead nucleus is made of 82 protons and 125 neutrons. The mass of the neutron is almost the same as the mass of a proton. To assure that you are actually studying the effects of the nuclear force, an alpha particle should come into contact with a lead nucleus. Assume that both the alpha particle and the lead nucleus have the shape of a sphere. The alpha particle has a radius of 1.0 x 10-15 m and the lead nucleus has a radius 4 times larger. Your boss wants you to make two calculations: (a) What is the minimum speed of such an alpha particle if the lead nucleus is fixed at rest? (b) What is the potential difference between the two ends of the Van de Graaf accelerator if the alpha particle starts from rest at one end (from a bottle of helium gas)? ...Note: Asked to use the following equations to solve the problem : F=ma & F=QE

Novell Networks manufactures five different models of network interface cards for desktop and laptop computers. As summarized in the following table, each of these network devices require differing amounts of printed circuit (PC) board, resistors, memory chips, and assembly time. Per Unit Requirements HyperLink FastLink SpeedLink MicroLink EtherLink PC Board, sq. in. 20 15 10 8 5 Resistors 28 24 18 12 16 Memory Chips 8 8 4 4 6 Labor (in hours) .75 .60 .50 .65 1.0 The unit wholesale price and manufacturing cost for each model are as follows: Per Unit Revenue and Costs HyperLink FastLink SpeedLink MicroLink EtherLink Wholesale Price $189 $149 $129 $169 $139 Manufacture Cost $136 $101 $96 $137 $101 In the next production period, Novell Networks has 80,000 square inches of PC board, 100,000 resistors, 30,000 memory chips, and 5,000 hours of assembly time available. The company can sell all the product it can manufacture, but the marketing department wants to be sure that it produces at least 500 units of each network interface card. Determine the product mix that maximizes profit.

Please use Excel

QUESTION 5

The variable Z has a standard normal distribution. The probability P(- 0.5 < Z < 1.0) is:

QUESTION 6

If a random variable X is normally distributed with a mean of 30 and a standard deviation of 10, then P(X=20) =

QUESTION 7

If P( -z < Z < +z) = 0.8812, then the z-score is:

QUESTION 8

If the mean of a normal distribution is negative,

QUESTION 9

The starting salaries of individuals with an MBA degree are normally distributed with a mean of $90,000 and a standard deviation of $20,000. What is the probability that a randomly selected individual with an MBA degree will have a starting salary of at least $78,500?

1. 0.2810
2. 0.8840
3. 0.7190
4. 0.8210

QUESTION 10

The starting salaries of individuals with an MBA degree are normally distributed with a mean of $90,000 and a standard deviation of $20,000. What is the lowest salary for those individuals with an MBA degree whose starting salary is in the top 25 percent?

1. $104,500
2. $103,600
3. $83,750
4. $106,400

A random sample of n = 15 heat pumps of a certain type yielded the following observations on lifetime (in years):

(a) Assume that the lifetime distribution is exponential and use an argument parallel to that of this example to obtain a 95% CI for expected (true average) lifetime. (Round your answers to two decimal places.)

  ,

years

(b) How should the interval of part (a) be altered to achieve a confidence level of 99%?

A 99% confidence level requires using a new value of n to capture an area of 0.005 in each tail of the chi-squared distribution.A 99% confidence level requires using a new value of n to capture an area of 0.1 in each tail of the chi-squared distribution.    A 99% confidence level requires using critical values that capture an area of 0.1 in each tail of the chi-squared distribution.A 99% confidence level requires using critical values that capture an area of 0.005 in each tail of the chi-squared distribution.

(c) What is a 95% CI for the standard deviation of the lifetime distribution? [Hint: What is the standard deviation of an exponential random variable?] (Round your answers to two decimal places.)

  ,

years

A base dissociation (hydrolysis) takes the following reaction pattern:

Base    +   H₂O    = OH^-     +    Conjugate acid     

For example the dissociation reaction of CH3COO- is presented as

CH₃COO^- +    H₂O   =     OH^-    +      CH₃COOH           

If you write down the dissociation (hydrolysis) reaction of CN^-, it is presented as [Q1].

Do not try to make subscriptization or superscriptization. Just type numbers, and + and - signs in the same way as you type words. Examples: H3O+, Cl-, HPO42-, etc.

In order to give a space, hit the space bar once after typing each compound formula or ion formula or + sign or equal sign.

Write down the expression of the equilibrium constant of the combined reaction of the following two dissociation reactions:

HCN + H₂O = H₃O⁺ + CN^-   K_a

CN^- + H₂O =   HCN + OH^- K_b

Do not try to make subscriptization or superscriptization. Just type numbers, and + and - signs in the same way as you type words. Examples: H3O+, Cl-, HPO42-, etc.

The equilibrium constant for the following reaction at 500 K is assumed to be 100.

             3H₂      +     N₂      =     2NH₃

Concentrations of H₂, N₂, and NH₃ are observed to be 1.0 M, 2.0 M, and 10.0 M, respectively, at the same temperature of 500 K.

An equilibrium has______________reached. The reaction should proceed to the __________________.

Type the word left or right for the second question.