Consider a 1.0 L solution which is 0.40 M CH₃CO₂H and 0.2 M CH₃CO₂Na (K_a for CH₃CO₂H = 1.8 x 10⁻⁵). Calculate the pH of the original soultion, the pH after 0.10 mol of HCl is added to the original solution, and the pH after 0.20 mol of NaOH is added to the original solution. Calculate all the pH values to two decimal places. Assume no volume change on addition. Please explain and /or show work please.

A particle of diameter 0.2 μmand density 1 g cm-3is being carried by an airstream at 1 atm and 298 K in they direction with a velocity of 100 cm s-1. The particle enters a charging device and acquires a charge of two electrons (the charge of a single electron is 1.6 x 10-19C) and moves into an electric filed of constant potential gradient Ex= 1000 V cm-1perpendicular to the direction of flow. (Hint: The effect of gravity and drag force can be ignored.) (a)Determine the characteristic relaxation time of the particle. (b) Plot the particle trajectory assuming that it starts at the origin at time zero. (Please show detailed steps and equations used to plot the trajectory as marks will be given for that.)

1. Given events A and B from the same sample space and:

P(A) = 0.2, P(B) = 0.6, P(A and B) = 0.1. Find the probability: P(A or B).

2. The scores of the class have a normal distribution with a mean of 77 and a standard deviation of 8. Find the 80^th percentile score.

   a) 85                b) 0.375                 c) 83.7                 d) 84.8

Flextronchip, an OEM manufacturer, has a fifth-generation chip for cell phones, with chip specification of 0.2 ± 0.0002 mm for the distance between two adjacent pins. The loss due to a defective chip has been estimated as $36.

Required:

1. Compute the value of k, the cost coefficient in the Taguchi quality loss function (QLF), L(x) = k(x − T)².

2. Assume that the quality control manager takes a sample of 100 chips from the production process. The results are as follows:

a. & b. Use the appropriate Taguchi quality loss function, L(x), to calculate the estimated quality loss for each of the observed measurements. Additionally, calculate the expected (i.e., average) loss per unit for the production process as a whole.

Complete this question by entering your answers in the tabs below.

Assume that the quality control manager takes a sample of 100 chips from the production process.

a. & b. Use the appropriate Taguchi quality loss function, L(x), to calculate the estimated quality loss for each of the observed measurements. Additionally, calculate the expected (i.e., average) loss per unit for the production process as a whole. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

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Giving this situation in 1980: Real GDP growth rate = -0.2% Inflation rate = 13.5% Unemployment rate = 7.1% Federal Funds Rate = 13.35%

1. Explain which monetary policy tool could be used in this situation.

2. What are some potential concerns if this action is implemented?

3. What is the economic term for this type of situation?

Giving this situation in 1968: Real GDP growth rate = 4.8% Inflation rate = 4.2% Unemployment rate = 3.6%

1. Given that this was during the Vietnam War, explain which type of policy could be used in this situation.

2. What are some potential concerns if this action is implemented?

3. Is it possible to have monetary policy and fiscal policy working in opposite directions? Explain.

Part 1

The probability of observing a certain event is 0.2. Suppose we make repeated observations until we have observed the desired event three times. What is the probability that we make five observations in order to have observed the desired event three times.? (Round your answer to four decimal places.)

Part 2

A probability of failure on any given trial is given as 0.01.

Use the Poisson approximation to the binomial to find the (approximate) probability of at least five failures in 200 trials? (Round your answer to three decimal places.)

2. Suppose a hurricane hits south Florida in any given year with probability 0.2. Describe the distribution of the following random variables, including both the name of the distribution and the parameters (such as X~Bernoulli(0.4)). (2 points each)

a.Let X be the number of years until the next hurricane hits South Florida.

b.Let X be the number of hurricanes that will hit south Florida in the next 10 years.

c.Let X indicate whether a hurricane will hit south Florida in 2020.

d.Let X indicate whether south Florida will avoid getting a hurricane in 2020.

A radio tube inserted into a system has probability 0.2 of lasting 500 hours. 20 tubes are tested.

1. Find probability that exactly that 'k' of these tubes will last more than 500 hours.

2. Find probability that number of tubes that last more than 500 hours will fall between 12 and 17.

3. Sketch the CDF of the random variable that describes the random phenomenon

Also: a die is rolled 120 times. Find probability that 35 or more sixes will be rolled.

Show all steps, thank you.

1. Suppose that the Canadian stock market return, denoted by a random variable X, varies within {−0.2, −0.1, 0, 0.1, 0.2, 0.4, 0.9}, and suppose that P (X = x) = (1 − x)/10 for x < 0.5 and P (X = 0.9) = 0. Determine each of the following:

   (a) The pdf of X. (b) The cdf of X.

   (c) The expected value of X. (d) The variance of X.

   (e) The standard deviation of X.
   (f) Calculate the sample median of X.

   (g) Let Y denote another random variable such that Y = X2, determine the variance of Y .

2. Let Φ(z) represent the cdf of a N(0,1) random variable at some cut-off point, z. Let X denote

   a N(0.5,1.5) random variable.

   1. (a) Calculate P (−1 ≤ X ≤ 2).

   2. (b) Let Y be a N(0,2) random variable that is independent of X defined above. Calculate P(−0.5≤X+Y ≤3).

3. At the points, x = 0,1,...,6, the cdf for the discrete random variable, X, has the value F(x) = x(x + 1)/42. Find the pdf for X.