Consumer Reports

Problem:
In the August 2005 issue of Consumer Reports, readers suffering from depression reported that alternative treatments were less effective than prescription drugs. Suppose that 550 readers felt better taking prescription drugs, 220 felt better through meditation, and 45 felt better taking St. John’s wort. Furthermore, 95 felt better using prescription drugs and meditation, 17 felt better using prescription drugs and St. John’s wort, 35 felt better using meditation and St. John’s wort, 15 improved using all three treatments, and 150 improved using none of these treatments. (Hypothetical results are partly based on percentages given in Consumer Reports.)

a. How many readers suffering from depression were included in the report? Of those included in the report.
b.How many felt better using prescription drugs or mediation?
c. How many felt better using St. John’s wort only?
d. How many improved using prescription drugs and meditation, but not St. John’s wort?
e. How many improved using prescription drugs or St. John’s wort, but not meditation?
f. How many improved using exactly two of these treatments?
g.How many improved using at least one of these treatments?

Answer the questions in Chapter 3: Section 3.6, Problem #58.

Problem #58:
Automobile accidents reduce life expectancy by 500 days or drowning does not reduce life expectancy by 30 days.

1.Use the information given by the graph to determine the truth value of the compound statement.

2. Write the compound statement’s negation.

3. Use the information given by the graph to determine the truth value of the negation in part 2.

Answer the questions in Chapter 5: Section 5.7, Problem #128.

Problem #128:
Company A pays $23,000 yearly with raises of $1200 per year. Company B pays $26,000 yearly with raises of $800 per year. Which company will pay more in year 10? How much more?

Answer the questions in Chapter 8: Section 8.3, Problem #50.

Problem #50:
Two accounts each began with a deposit of $10,000. Both accounts have rates of 6.5%, but one account compounds interest once a year while the other account compounds interest continuously. Make a table that shows the amount in each account and the interest earned after one year, five, years, ten years, and 20 years.

Answer the questions in Chapter 10: Section 10.5, Problem #40.

Problem #40:
What is the cost of concrete for a walkway that is 15 feet long, 8 feet wide, and 9 inches deep if the concrete costs $30 per cubic yard?

Answer the questions in Chapter 11: Section 11.5, Problem #6.

Problem #6:
A political discussion group consists of five Democrats and six Republicans. Four people are selected to attend a conference.
a. In how many ways can four people be selected from this group of eleven?
b. In how many ways can four Republicans be selected from the six Republicans?
c. Find the probability that the selected groups will consist of all Republicans.