A cooler has 6 Gatorades, 2 colas, and 4 waters. You select 3 beverages from the cooler at random. Let B denote the number of Gatorade selected and let C denote the number of colas selected. For example, if you grabbed a cola and two waters, then C = 1 and B = 0.

a) construct a joint probability distribution for B and C.

b) compute E[3B-C^2].

Let V = {P(x) ∈ P10(R) : P'(−4) = 0 and P''(2) = 0}. If V= M_3×n(R), find n.

Case Project 4-2: Configuring Preferences

Users in the Engineering Department need a higher level of access on their local computers than other users do. In addition, you want to set power options on mobile computers that Engineering users use. All Engineering Department user and computer accounts are in the Engineering OU.

What should you configure to meet the following criteria?

• When an Engineering user signs into a computer, the user account is added to the local Administrators group on that computer.

• Enable the hibernation power mode but only if the user’s computer is identified as a portable computer. Set the power scheme to hibernate mode if the laptop’s lid is closed or the power button is pressed.

Thermodynamics of Dissolution of Substance

Reaction Eqn of borax and HCL

B4O5(OH)4 2-(aq) + 2HCl + 3H2O <_> 4H3BO3 (aq) + 2Cl-

calculate

** I understand that for ΔH ΔS, you need to plot ln(Ksp) vs 1/T and determine their value from that graph.

Values for enthalpy and entropy of the dissolution of borax in water are 110 kJ/mol and 380 J/mol*K respectively. Do your values agree? Calculate your percent error.

You assumed that H and S are constant over the temperature range studied. Are they?

4. You own an 8,000 ft^2 (K = 8,000) factory that produces N95 masks and you produce them by combining labor and capital (your factory) as follows: Q = 4K^(1/3)L^(2/3), where Q is the number of masks produced per week. Assume there are many competing factories and all factories are identical. Until two months ago, the price of masks in this perfectly 1 competitive market was $1.50 each. Today the price is $3.00 ea. The rental value of your factory is $.50 per ft^2/week. Answer the following 2 questions: a)How much profit do you expect to make each week if the price remains at $3.00 ea.? b)If a new identical factory costs $1 million and it is operational within one month, should you purchase it today?

Calculate the enthalpy change for the reaction:

4 Fe(s) + 3 O₂(g) → 2 Fe₂O₃(s)            ΔH°_rxn = ?

where:

2 Fe(s) + 6 H₂O(ℓ) → 2 Fe(OH)₃(s) + 3 H₂(g)               ΔH₁° = +321.8 kJ

                    2 H₂O(ℓ) → 2 H₂(g) + O₂(g)                               ΔH₂° = +571.7 kJ

Fe₂O₃(s) + 3 H₂O(ℓ) → 2 Fe(OH)₃(s)                                 ΔH₃° = +288.6 kJ

4.(12 pts) A 20,000 liter tank is initially half full with 10,000 liters of 2% nitric acid. A solution of 5% nitric acid is pumped in at a rate of 30 liters per minute and the well mixed mixture is pumped out at the same rate of 30 liters per minute.

(a)(8 pts) Set up (But Don’t Solve) an IVP whose solution gives the amount of x(t) of pure nitric acid (in liters) in the tank at time t

(b)(4 pts) Use a quick qualitative analysis of the IVP you found in part (a) to predict how much pure nitric acid will be in the tank as t→infinity(Show a phase line or direction field to predict what happens as t→infinity

Sketch images of the folloing, shading the described regions.

(a)|z|<4(b) |z − i| < 2 (c) 1 <|z − i + 2| < 2 (d) Re(z) <|z|

***Given the following***

Balanced Equation: 2 N₂O₅ -> 4 NO₂ + O₂

Rate Constant, k= 4.66 x 10^-4 s^-1

Temperature: 72Degrees Celcius

***How much N₂O₅ remains in the solution after 115 minutes if the initial concentration of N₂O₅ is 0.60 M?

***What % of N₂O₅ has reacted at this point?

If you're able to show your work for me to get a better understanding it would be greatly appreciated! Thank you!