An electrochemical cell is composed of pure copper and pure lead electrodes immersed in solutions of their respective divalent ions. For a 0.7 M concentration of Cu²⁺, the lead electrode is oxidized yielding a cell potential of 0.520 V. Calculate the concentration of Pb²⁺ ions if the temperature is 25˚C. The standard potentials for Cu and Pb are +0.340 V and -0.126 V.

Please show your work!

A production manager at a wall clock company wants to test their new wall clocks. The designer claims they have a mean life of 16 years with a variance of 16. If the claim is true, in a sample of 48 wall clocks, what is the probability that the mean clock life would differ from the population mean by greater than 0.7 years? Round your answer to four decimal places.

The pharmacokinetics of a new drug was studied in a healthy volunteer. It was known that the drug followed a first-order, one compartment model kinetics, had a t_1/2 of 1 hr, and a CL_t of 0.7 L/hr. The drug was administered by intravenous infusion for 8 hrs at a rate of 1.4 mg/hr. Calculate the plasma [drug] (in mg/L) two hours after the start of the infusion.

A particle of mass 0.000117 g and charge 15 mC moves in a region of space where the electric field is uniform and is 4.5 N/C in the x direction and zero in the y and z direction. If the initial velocity of the particle is given by vy = 3.6 × 10^5 m/s, vx = vz = 0, what is the speed of the particle at 0.7 s? Answer in units of m/s.

In the CAPM world, two securities, A and B, are priced efficiently, i.e., they fall on the SML. The expected return of A is 20%, and its beta is 1.6. The expected return of B is 11%, and its beta is 0.7. The expected return of the market portfolio is ___and the risk free rate is ___.

The possible outcomes for the returns on Stock X and the returns on the market portfolio have been estimated as follows:

Calculate the market beta for Stock X. Round your answer to the nearest tenth.

Let X denote a random variable that follows a binomial distribution with parameters n=5, p=0.3, and Y denote a random variable that has a Poisson distribution with parameter λ = 6. Additionally, assume that X and Y are independent random variables.

(a) What are the possible values for (X, Y ) pairs.

(b) Derive the joint probability distribution function for X and Y. Make sure to explain your steps.

(c) Using the joint pdf function of X and Y, form the summation /integration (whichever is relevant) that gives the expected value for X4 + Y + 7.

(d) Using the joint pdf function of X and Y, set up the summation /integration (whichever is relevant) that gives the expected value for X, and COMPUTE its value.

1. You have extracted the following standards for one of your company’s products:

Direct materials: 0.3 metres @ $15 = $4.50

Direct labour: 0.5 hour @ $20 = $10

The following actual results were recorded for the period:

Direct materials: 3500 metres purchased and used; total cost $53,900

Direct labour: 5000 hours; total labour cost $105,000

Production = 12,000 units

         Compute the materials price and usage variances, and the labour rate and      

         efficiency variances, for your company.                                                      

Based on the standard analytical practice during a titration of taking pH-volume measurements every 0.3 pH units, how many measurements should you take between the addition of 5 mL and 7.5 mL of titrant, (a) in the titration of a 10-mL aliquot of standard 0.1500 M TRIS base (pKb = 1.2 X 10-6) (in beaker) with 0.1000 M HCl (in buret). (b) in the titration of a 10-mL aliquot of 0.1500 M NaOH (in buert) with standard 0.1000 M HCl (in buret).

Hints: To solve these questions, it may be helpful to draw a diagram of the titration set up. Before starting, reason out whether the pH will increase or decrease with the addition of titrant. You need to calculate the pH at the 5 and 7.5 mL points in each of the two titrations. Because HCl and NaOH are a strong acid and base respectively, they dissociate completely and the pH of the solution is dependent only on the excess acid or base in the beaker at that point in the titration.