Using the definition of Ka and the Debeye-Huckel expression for the mean ionic activity
coefficient, calculate the pH of a 0.10 M acetic acid solution in (a) pure water (b) 0.1 M
NaCl and (c) in 0.2 M MgSO4. Assume consistent results after 3 iterations in each case

The linear regression equation for predicting poverty (%) from the high school graduation rate (%) is as follows: ˆ y = 29 -0.2*x High school graduation rate for North Carolina is 22% and the poverty rate is 29.5%. Find the residual for this observation (round your answer to one decimal place)

Assume that the monetary base (B) is $600 billion, money supply is $3300 billion, the reserve deposit ratio (rr) is 0.1.

1) What is the currency deposit ratio (cr)? (5 points)

2) If cr changes to 0.2, but rr and B are unchanged, what is the money supply? (5 points)

Suppose a 1 kg mass is attached to the end of a string that is stretched 0.2 m by a force of 500 N (newtons). An exterior force F0 cos 50t acts on the mass. Find the position function x(t) if the initial conditions are given by x(0) = 0, x′(0) = 50.

A turbine blade of solution annealed INCOLOY alloy 800 is 18 in long and operates at 1400 degrees Fahrenheit. If the tip clearance is 0.2 in and centrifugal forces induce an average longitudinal stress of 10 ksi. After how many hours is expected the blade to interfere with the turbine stator due to creep?

The posterior probabilities of four hypothesis h1,h2,h3,h4 are (0.2, 0.5,0.2, 0.1) respectively. A new training sample is classified +ve by h2 and h3, while h1 and h4 classify the same data instance as -ve. Find the classification with Bayes Optimal Classifier and Brute Force Classification?

Mass 1 is moving at 6 m/s in the +x direction and it collides in a perfectly elastically with mass 2 of 2 kg moving at 15 in the -x direction. They collide for 0.2 seconds, and the average force on mass 1 is 149 N in the -x direction. What is the mass of mass 1 in kg?

Use the normal distribution to find a confidence interval for a proportion p given the relevant sample results. Give the best point estimate for p, the margin of error, and the confidence interval. Assume the results come from a random sample.

A 99% confidence interval for p given that p^=0.7 (this is p hat) and n=110.

Round your answer for the point estimate to two decimal places, and your answers for the margin of error and the confidence interval to three decimal places.

Air at a pressure of 350 kPa, a temperature of 80°C, and a velocity of 180 m/s enters a convergent–divergent nozzle. A normal shock occurs in the nozzle at a location where the Mach number is 2. If the air mass flow rate through the nozzle is 0.7 kg/s, and if the pressure on the nozzle exit plane is 260 kPa, find the nozzle throat area, the nozzle exit area, the temperatures upstream and downstream of the shock wave, and the change in entropy through the nozzle.

A random sample of 120 observations is selected from a binomial population with an unknown probability of success ?. The computed value of ?̂ is 0.7.
(1)    Test ?0:?=0.55 against ??:?>0.55. Use ?=0.01.

test statistic ?=

critical ? score     


(2)    Test ?0:?=0.5 against ??:?<0.5. Use ?=0.05.

test statistic ?=

critical ? score     


(3)    Test ?0:?=0.55 against ??:?≠0.55. Use ?=0.01.

test statistic ?=

positive critical ? score    

negative critical ? score