For the reaction

2Co3+(aq)+2Cl−(aq)→2Co2+(aq)+Cl2(g).  E∘=0.71 V

what is the cell potential at 25 ∘C if the concentrations are [Co3+]= 0.634 M , [Co2+]= 0.385 M , and [Cl−]= 0.491 M and the pressure of Cl2 is PCl2= 6.10 atm ?

For the reaction 2Co3+(aq)+2Cl−(aq)→2Co2+(aq)+Cl2(g). E∘=0.483 V what is the cell potential at 25 ∘C if the concentrations are [Co3+]= 0.222 M , [Co2+]= 0.275 M , and [Cl−]= 0.309 M and the pressure of Cl2 is PCl2= 3.80 atm ?

(a) Compute the derivative of the speed of sound in air with respect to the absolute temperature, and show that the differentials dv and dT obey dv/v=1/2 dT/T. (b) Use this result to estimate the percentage change in the speed of sound when the temperature changes from 0

Problem 2: Consider a representative consumer whose preferences over consumption and leisure are given by the following utility function: U˜(C, l) = U(C) + V (l) (2) where U(.) and V (.) are twice differentiable functions (that is, their first and second derivatives exist). Suppose that this consumer faces lump-sum taxes, T, and receives dividend income, Π, from the 100% ownership of shares of the representative firm.

A) Write down the consumer’s optimization problem and the first-order conditions determining optimal consumption and leisure. B) Carefully explain the effect of a sudden boom in the stock market, which increases dividend income, on the optimal choice of consumption and leisure? Use the ABCDEF of Cramer’s rule to answer this question. Clearly state any assumptions you make. C) Using a carefully labeled diagram, describe the effects of this positive stock market shock characterized in (b).

A company sells two types of life insurance policies (P and Q) and one type of health insurance policy. A survey of potential customers revealed the following:

i) No survey participant wanted to purchase both life policies.

ii) Twice as many survey participants wanted to purchase life policy P as life policy Q.

iii) 45% of survey participants wanted to purchase the health policy.

iv) 18% of survey participants wanted to purchase only the health policy.

v) The event that a survey participant wanted to purchase the health policy was independent of the event that a survey participant wanted to purchase a life policy. Calculate the probability that a randomly selected survey participant wanted to purchase exactly one policy.

The answer is 0.51. If someone could show the process to solve and explain more about how to handle the last fact (v), it would be very helpful!

1. Beatrice Bainson runs a business altering and repairing clothes. When she started business on 1 January 2012, she bought a Scoopatitch II sewing machine for GH₵2,500. She depreciates sewing machines using the straight-line method at a rate of 20% pa, and she charges a full year depreciation in the year of acquisition and none in the year of disposal.

The business has now grown such that she needs a faster machine, and she will upgrade to Scoopatitch V during December 2015. The Scoopatitch salesman has offered her a part exchange deal as follows:

Part exchange allowance for Scoopatitch II GH₵750

Balance to be paid in cash for Scoopatitch V GH₵4,850

Required

1. Show the ledger entries for the year ended 31 December 2015 to reflect this transaction.                                                                                                   7 Marks

Show the relevant extracts in the appropriate financial statements

The cost in dollars of operating a jet-powered commercial airplane Co is given by the following equation
Co = k*n*v^(3/2)
where
n is the trip length in miles,
v is the velocity in miles per hour, and
k is a constant of proportionality.
It is known that at 590 miles per hour the cost of operation is $300 per mile. The cost of passengers' time in dollars equals $226,000 times the number of hours of travel. The airline company wants to minimize the total cost of a trip which is equal to the cost of operating plus the cost of passengers' time.
At what velocity should the trip be planned to minimize the total cost?
HINT: If you are finding this difficult to solve, arbitrarily choose a number of miles for the trip length, but as you solve it, you should be able to see that the optimal velocity does not depend on the value of n​

You push a box of mass 19.1 kg with your car up to an icy hill slope of irregular shape to a height 5.9 m. The box has a speed 12.9 m/s when it starts up the hill, the same time that you brake. It then rises up to the top (with no friction) to a flat area before sliding into a box larger box of mass 13 kg. The boxes then fall off a sheer cliff together to the ground (with no drag).

a) What is the velocity of the pair just before hitting the ground? {coordinate form}

   V = ________y, ________z

b) What is the velocity of the pair just before hitting the ground? {vector form}

   V = ________ (_________y, __________z)

c) What is the path basis just before impact?

   t = _________x + _________y + _________z

n = _________x + __________y + _________z

b = _________x + __________y + _________z