ACID/BASE PRACTICE PROBLEMS

(a) 3 moles of sodium nitrate are placed in 1 L of water. Calculate the pH.

(b) Calculate the Ka and the % ionization of a weak acid if 0.02 moles of the acid is added to 1 L water and makes a solution with a pH of 4.75.

(c) A solution containing 0.2 moles of NaOH, 0.3 moles of HCl, and 0.1 moles of HF (Ka=7.1e-4) is added to 1 L of water. Calculate the pH and pOH.

(d) 0.2 moles of the salt acid of urea is added to 1 L of water, calculate the pH of the solution.

1 point) If xx is a binomial random variable, compute P(x)P(x) for each of the following cases:

(a)  P(x≤1),n=5,p=0.3P(x≤1),n=5,p=0.3

P(x)=P(x)=

(b)  P(x>3),n=4,p=0.1P(x>3),n=4,p=0.1

P(x)=P(x)=

(c)  P(x<3),n=7,p=0.7P(x<3),n=7,p=0.7

P(x)=P(x)=

Assume the CAPM holds and the market is efficient. Given the following information about the true market portfolio and stock S:

State    Probability      Return (Market)                      Return (S)

1          0.2                   0.25                                         0.4

2          0.5                   0.1                                         -0.085

3          0.3                 -0.05                                          0.12    

1. You are given enough information to determine the beta of S. (True / False)

2. Calculate the expected rate of return on the market portfolio and the expected return on stock S.

3. It turns out that stock S has a beta of about 0.7. Find the risk-free rate of return.

A car owner conducts an experiment by filling up their car with 10 gallons of gas and drives until it runs out of gas. The number of miles driven from the 10 times of doing this experiment is shown below:

275 240 303 243 259 187 311 276 251 263

Find the following: Show ALL necessary work

a) Median

b) Lower and Upper Quartiles

c) IQR

d) State the mild outliers, if any. If there are no outliers, then state "no outliers".

Danube recently acquired a delivery van for $22,300 paying cash. Danube projects a 4 year useful service life and a remaining residual value on the delivery van of $2,200. Danube expects to drive the van 108,000 miles during the useful service life. Please compute the annual depreciation for the 4 year life of the delivery van for the double-declining method

1. Set up the following statements as a null and an alternative hypotheses.

a) A cereal manufacturer is testing its cereal filling process. Its goal to have each cereal box contain 368 grams.

b) A company claims that the life of its Milemaster tire exceeds 47,000 miles.

c) We want to test if college students take less than five years to graduate from college.

d) We want to test whether the mean height of 8th graders is 66 inches.

5. A volcano is located at the point (1, 3). Scientists have determined that a possible eruption of this volcano would affect the area within the radius of 4 miles around the volcano.

(a) Two locations are being considered for a new housing estate: the point (−1, −2) and the point (−1, 6). Determine which of those locations is at a safe distance from the volcano. Justify your answer.

(b) Determine the closest point in the direction ~v = [1, 1] from the volcano, that is safe from a possible eruption.

Two fuel additives are being tested to determine their effect on gasoline mileage. Seven cars were tested with additive 1 and nine cars were tested with additive 2. Data: Additive 1 - 17.3,18.4, 19.1, 17.7, 17.2, 17.6, 18.5; Additive 2 - 18.7, 18.8, 20.3, 20.0, 21.1, 18.7, 18.8, 20.7, 21.2. The following data show the miles per gallon obtained with the two additives. I am struggling to determine the p-value.

Hailee makes the following contributions in 2019 (all of which she can substantiate): Goodwill, clothing she bought for $950 with a FMV of $310. Salvation Army, automobile, FMV of $750, sold for $700. YWCA, 200 volunteer miles. Nonprofit cemetery, $500 for care of her grandfather's crypt. Qualified exchange student, $1,000 during four months for the well-being of the student. How much will she be able to deduct for contributions on Schedule A? $1,238 $1,288 $1,738 $2,838