1. Calculate the pH of a 0.434 M aqueous solution of acetylsalicylic acid (aspirin)(HC₉H₇O₄, K_a = 3.0×10^-4).

2. Calculate the pH of a 0.0420 M aqueous solution of hydrofluoric acid (HF, K_a = 7.2×10^-4).

3. Calculate the pH of a 0.0973 M aqueous solution of hydrofluoric acid (HF, K_a = 7.2×10^-4).

1. Calculate the pH of a 0.434 M aqueous solution of acetylsalicylic acid (aspirin)(HC₉H₇O₄, K_a = 3.0×10^-4).

2. Calculate the pH of a 0.0420 M aqueous solution of hydrofluoric acid (HF, K_a = 7.2×10^-4).

3. Calculate the pH of a 0.0973 M aqueous solution of hydrofluoric acid (HF, K_a = 7.2×10^-4).

Calculate the ​(a​) net present value​ (NPV), ​(b​) profitability index​ (PI), and ​(c​) internal rate of return​ (IRR) for Projects 1 and 2​ (cash flows shown​ below), assuming a required return of 13%.

a.  What is the NPV of Project​ 1? $___ ​​(Round to the nearest​ cent.) What is the NPV of Project​ 2? ​ $___ ​(Round to the nearest​ cent.)

b. What is the PI of Project​ 1? ____ ​(Round to two decimal​ places.) What is the PI of Project​ 2? ​___ (Round to two decimal​ places.)

c. What is the IRR of Project​ 1? __​% (Round to two decimal​ places.) What is the IRR of Project​ 2? __​% (Round to two decimal​ places.)

In order to test ?0:?=.5 vs. ??:?<.5 using the .10 level of significance, a sample of ?=100 will be selected. Suppose that, in reality, the population proportion is .4.

(a) The probability the test will commit a type II error is   .___

(b) The power of the test is ___ .

Independent random samples, each containing 50 observations, were selected from two populations. The samples from populations 1 and 2 produced 30 and 25 successes, respectively.
Test ?0:(?1−?2)=0 against ??:(?1−?2)≠0. Use ?=0.05.

(a) The test statistic is  

(b) The P-value is

(c) The final conclusion is
A. There is not sufficient evidence to reject the null hypothesis that (?1−?2)=0
B. We can reject the null hypothesis that (?1−?2)=0 and conclude that (?1−?2)≠0

The Columbus Dispatch conducted a study. Two identical football, one filled with helium and one filled with ordinary air, were used. A casual observer was unable to detect a difference in the two footballs. A novice kicker was used to punt the footballs. A trial consisted of kicking both footballs in a random order. The kicker did not know which football he was kicking. The distance of each punt was recorded, then another trial was conducted. A total of 39 trials were run. Do the data indicate that helium-filled footballs travel farther than air-filled footballs? Give a confidence interval and significance test. (Data: FTBALL)

Given the following sample information, test the hypothesis that the treatment means are equal at the 0.10 significance level:

a. State the null hypothesis and the alternative hypothesis.

H₀ : μ₁ =  Correctμ₂   =  Correctμ₃

H₁ : Treatment means are not  Correct all the same.

b. What is the decision rule? (Round the final answer to 2 decimal places.)

Reject H₀ if F >                2.58 2.58 Incorrect .

c. Compute SST, SSE, and SS total. (Round the final answers to 2 decimal places.)

SST =                46.96 46.96 Incorrect

SSE =                53 53 Incorrect

SS total =                99.96 99.96 Incorrect  

d. Complete the ANOVA table. (Round the SS, MS, and F values to 2 decimal places.)

e. State your decision regarding the null hypothesis.

Decision: Reject  CorrectH_0.

f.Find the 95% confidence interval for the difference between treatment 2 and 3. (Round the final answers to 2 decimal places.)

95% confidence interval is: 0.13 0.13 Incorrect   ±   3.37 3.37 Incorrect  

We can conclude that the treatments 2 and 3 are different  Correct .

2–1. Using the Comprehensive Annual Financial Report obtained for Exercise 1–1, answer the following questions: a. Compare the items discussed in the MD&A in your CAFR with the list of items in this chapter. Which topics listed in this chapter are not in your CAFR? Which topics are in your CAFR that are not listed in this chapter? Do you think your CAFR has a reasonably complete discussion?

b. From the MD&A in your report, write a short summary of (1) the financial condition of your government, (2) a comparison of revenues compared with the prior year, (3) a comparison of expenses compared with the prior year, and (4) a comparison of budgeted and actual activity.

c. From the Statement of Net Position, identify the following: (1) unrestricted net position—governmental activities; (2) unrestricted net position— business-type activities; (3) restricted net position by restriction— governmental activities; (4) restricted net position by restriction—business-type activities; and (5) unrestricted and restricted net position—component units (if any).

d. From the Statement of Activities, identify the following: (1) net program expense (or revenue)—governmental activities; (2) net program expense (or revenue)—business-type activities; (3) net program expense (or revenue)—component units; (4) change in net position— governmental activities; (5) change in net position—business-type activities; and (6) change in net position—component units. Does the ending net position in this statement agree with the net position figures in the Statement of Net Position?

e. From the Statement of Revenues, Expenditures, and Changes in Fund Balances for Governmental Funds, identify the names of the major governmental funds. List the net change in fund balance for each major fund.

f. From the governmental fund statements, take one major fund (other than the General Fund) and prove, using the 10 percent and 5 percent criteria described in this chapter, that the fund is required to be reported as a major fund.

g. From the Statement of Revenues, Expenses, and Changes in Fund Net Position, list the major enterprise funds. For each, identify: (1) the operating income, (2) the income (loss) before contributions and transfers, and (3) the change in net position.

1. Describetherelationshipbetweentwovariableswhenthe correlation coefficient r is a) near –1 b) near 0 c) near +1

2. What is the meaning of the “least-squares” criterion?

3. “Correlation does not imply causation.” Explain.

Find

(f ⁻¹)'(a).

f(x) = 6 + x² + tan(πx/2),    −1 < x < 1,    a = 6