A small town gets its water supply from three nearby lakes, A, B, and C. Sometimes in the late summer

the water level in a lake falls below a certain critical level. When this occurs, there is a risk that the water

from that lake will become polluted with E-Coli. If the water supply to the town becomes polluted, the

residents are advised to boil their water. If only the water level at lake A falls below the critical level,

experience has shown that the residents will have a 5% chance of a boil water advisory. Similarly, if

only the water levels at lakes B or C fall below the critical level, chances of a boil water advisory are

4% and 7%, respectively. If two or more lakes fall below the critical levels simultaneously, the risk

of a boil water advisory rises to 40%. Lake A falls below the critical level in 30% of the summers,

while this number is 50% and 20% for lakes B and C, respectively. The probability that exactly two

lakes will fall below their critical levels simultaneously is 12%, and it is equally likely to be any two of

the three. Finally, there is a 3% chance that all three lakes will simultaneously fall below their critical

levels. During some summer in the future:

a) What is the probability that the residents will have a boil water advisory? (answer:0.0914)

b) If the residents have a boil water advisory, what is the probability that the water level will fall

below the critical level at lake B alone? (answer:0.1707)

c) If the residents have a boil water advisory, what is the probability that the water level will fall

below the critical levels at two or more lakes simultaneously? (answer:0.6565)

Air Shangrila sells to both tourist and business travelers on its single route. Tourists always stay over on Saturday nights, while business travelers never do. The weekly demand function of tourists is

          QdT=8,000−5P,

and the weekly demand function of business travelers is

          QdB=2,000−0.5P.

The marginal cost of a ticket is $350.

Instructions: Round your answers to 2 decimal places as needed. For elasticities, include a negative sign if necessary.

a. What prices should Air Shangrila set for its tourist ticket and its business ticket?

    P_tourist = $.

    P_business = $.

b. If the government passes a law that says all tickets must cost the same amount, what price will Air Shangrila set? (Assume Air Shangrila sells to both types of consumers. That is, profit from selling to both types of consumers will be greater than profit without price discrimination where price is set so high that only one group demands a positive quantity.)

    P = $.

c. What would be the elasticities of demand for the two groups at that price?

    E^d_tourist = .

    E^d_business = .

A movie monopolist sells to college students and other adults, as in Worked-Out Problem 18.2 (page 635). The demand function for students is

          QdS=1,000−100P,

and the demand function for other adults is

          QdA=4,500−100P.

Marginal cost is $2 per ticket.

Instructions: Round your answers to 2 decimal places.

a. What prices will the monopolist set when she can discriminate? How will discrimination affect the monopolist's profit?     

    P_student = $ per ticket.

    P_adult = $ per ticket.

    Profit = $.

b. What prices will the monopolist set when she cannot discriminate? How will it affect her profit?

    P_everyone = $ per ticket.

    Profit = $.

Use strong induction to show that every positive integer n can be written as a sum of distinct powers of two, that is, as a sum of a subset of the integers 2^0 =1, 2^1 = 2, 2^2 = 4, and so on. [Hint: For the inductive step, separately consider the case where k + 1 is even and where it is odd. When it is even, note that (k + 1)/2 is an integer.]

Problem 4. Assume F is of bounded variation and continuous. Prove that F = F₁ − F₂, where both F₁ and F₂ are monotonic and continuous.

Human Resource Consulting (HRC) surveyed a random sample of 53 Twin Cities construction companies to find information on the costs of their health care plans. One of the items being tracked is the annual deductible that employees must pay. The Minnesota Department of Labor reports that historically the mean deductible amount per employee is $501 with a standard deviation of $102.

1. Point vs. Interval Estimation

Here you will discuss the importance of constructing confidence intervals for the population mean. You want to be sure to address these questions:

• What are confidence intervals?
• What is a point estimate?
• What is the best point estimate for the population mean? Explain why it is the best.
• Why do we need confidence intervals?

2. Mean Estimation

First clearly give the best point estimate for the population mean the data was drawn from. Next you will construct two confidence intervals: a 95% confidence interval and a 99% confidence interval. Bear in mind that the population standard deviation is unknown, but you may assume that the population is approximately normally distributed. Please show your work for the construction of these confidence intervals. If you used technology or a calculator please explain what you used and how you got your intervals.

3. Interpretation and Conclusion

Compare and contrast your findings for the 95% and 99% confidence intervals. Did you notice any changes in your interval estimate? Be specific. What conclusion(s) can be drawn about your interval estimates when the confidence level is increased? Explain why you draw this conclusion.

please explain the solution and what it is wrong with my conception. FOLLOW the COMMENT PLEASE

Question:

Let A and B are nonempty set bounded subset of R, and let A+B be the set of all sums a+b where a belngs to A and b belongs to B

Prove Sup(A+B)=Sup(A)+Sup(B)

Solution: Let ε>0, a is in A and b is in B,

supA<=a+(ε/2), supB<=b+(ε/2)

sup(A + B) ≥ a + b ≥ sup A − ε /2 + sup B − ε /2 = sup A + sup B − ε.

My Question:

1. Why the answer is not sup(A + B) ≥ a+(ε/2)+b+(ε/2)=a+b+ε?

2. I don't understand why supA<=a+(ε/2), supB<=b+(ε/2)

is a+(ε/2) outside the upper bound or inside the lower bound? why upperbound supA will less and equal to a+(ε/2). (please better draw the horizontal line and explain it)

1a. Eliminate the parameter t to rewrite the parametric equation as a Cartesian equation.

1b. A dart is thrown upward with an initial velocity of 68 ft/s at an angle of elevation of 52°. Consider the position of the dart at any time t. Neglect air resistance. (Assume t is in seconds.)

Find parametric equations that model the problem situation.

1c.

A dart is thrown upward with an initial velocity of 61 ft/s at an angle of elevation of 56°. Consider the position of the dart at any time t. Neglect air resistance. (Assume t is in seconds. Round your answer to one decimal place.)

At what time will the dart reach maximum height?
t = ?

In a game show, a wheel of fortune is rotated five times with three sectors of the same size in the colors blue, red and white. What is the probability of the following events?

a.) The wheel does not stop in any of the 5 attempts in the red sector.

b.) The blue sector is hit exactly 4 times.

c.) The sector with the color white occurs at least twice.

• Assignments

  1. Construct ONE inductive Argument by Example.

  2. Construct ONE inductive Argument by Analogy.

  3. Construct ONE inductive Argument from Authority.

• Given what you know so far, evaluate the following instance of the basic form of the Argument about Causes.

  1) Getting a cold drink correlates with the weather getting hotter.
  --------------------------------------------------------------------------------
  2) Thus, getting a cold drink causes the weather to get hotter

a. Using the Euclidean Algorithm and Extended Euclidean Algorithm, show that gcd(99; 5) = 1 and find integers s1 and t1 such that 5s1 + 99t1 = 1.
[Hint: You should find that 5(20) + 99(?1) = 1]

b. Solve the congruence 5x 17 (mod 99)

c. Using the Chinese Remainder Theorem, solve the congruence
x 3 (mod 5)
x 42 (mod 99)

d. Using the Chinese Remainder Theorem, solve the congruence
x 3 (mod 5)
x 6 (mod 9)
x 7 (mod 11)

5. You are looking for a home in three neighborhoods. In one neighborhood, the mean price is much smaller than the median price. In a second neighborhood the mean and median price are the same. In the third neighborhood, the mean price is larger than the median price. What does this information tell you about homes in the three neighborhoods? Would you be more inclined to buy a home in one neighborhood than the two others? Explain your reasoning. Exercise 21 in Section 6.1 is relevant to this topic. What effect might an outlier have on the five-number summary? Exercise 23 in Section 6.1 is relevant to this topic.