The opera theater manager calculates that 15% of the opera tickets for tonight's show have been sold. If the manager is accurate, what is the probability that the proportion of tickets sold in a sample of 690 tickets would differ from the population proportion by more than 4% ? Round your answer to four decimal places.

Twenty people check their hats at a theater. In how many ways can their hats be returned so that

(a) no one receives his or her own hat?

(b) at least one person receives his or her own hat?

(c) exactly one person receives his or her own hat?

At the movies: A movie theater is considering a showing of Puppet Master for a 80's thowback night. In order to ensure the success of the evening, they've asked a random sample of 53 patrons whether they would come to the showing or not. Of the 53 patrons, 30 said that they would come to see the film. Construct a 95% confidence interval to determine the true proportion of all patrons who would be interested in attending the showing.

a) What is the point estimate for the true proportion of interested patrons? (please input a proportion accurate to four decimal places)

b) Complete the interpretation of the confidence interval. Please provide the bounds for the confidence interval in decimal form, accurate to four decimal places, and list the lower bound first.
"We are ... % confident that the true proportion of patrons interested in attending the showing of Puppet Master is between ... and ... "

c) The theater is only willing to show Puppet Master if they are confident that at least 40% of their patrons would be interested in seeing the film. Should they show it?

A movie theater has at most 90 seats available. Each adult movie ticket costs $14, and each child movie ticket costs $8. To make a profit, the theater must bring in more than $852 in ticket sales per show. A) In terms of A and C, write an inequality that represents the restriction on total occupancy. B) In terms of A and C, write an inequality that represents the restriction on total ticket sales. C) Make a graph that represents your inequalities. D) Which scenario satisfies the restriction on total occupancy but does not produce enough ticket sales? E) Which scenario does not satisfy the restriction on total occupancy but does produce enough ticket sales? F) Which scenario does not satisfy the restriction on total occupancy but does produce enough ticket sales? G) Which scenario satisfies the restriction on total occupancy and also produces enough ticket sales? 

part 2

Duque Vergere manages a Do or Die Theater complex called Cinema I, II, III, and IV. Each of the four auditoriums plays a different film; the schedule staggers starting times to avoid the large crowds that would occur if all four movies started at the same time. The theater has a single ticket booth and a cashier who can maintain an average service rate of 280 patrons per hour. Service times are assumed to follow an exponential distribution. Arrivals on a normally active day are Poisson distributed and average 210 per hour. To determine the efficiency of the current ticket operation, Duque Vergere wishes to examine several queue-operating characteristics.

d.) What is the average time spent waiting in line to get to the ticket window?
e.) What is the probability that there are more than two people in the system? More than three people? More than four?

Write a javascript code to Create a function called Hotel that takes Room no, Customer name. amount paid. Write a code to call hotel function for each customer and display details of customers lodging in rooms with even room numbers.
I need only js and html code. no css
pls take screenshot of output , else I might dislike
thanks

Consider the case of a sheep farmer who lives next door to an African Safari theme park with dangerous lions. If the lions come in contact with the sheep, they kill them and eat them, costing the sheep farmer damages of $15,000. However, the theme park can build a fence around the lions for $6000. In the alternative, the sheep farmer can fence off his pasture for $8000. Assume that it costs the sheep farmer and the Safari park each $2000 to hire a lawyer if they have to negotiate an agreement between them. What is the efficient outcome here? Why? Suppose that the Safari Park is granted a right of free roaming so that it does not have to fence off its animals and is not liable for any damages they cause. What is the likely outcome now? Will the sheep farmer and the Safari negotiate? Why or why not? Now suppose that the cost of legal advice drops to $500 in part b). How does that change the likely outcome? Why? Assume the legal rule changes, so that the sheep farmer is granted right to safe grazing. If the Safari is held liable for damages to sheep, what is the likely outcome?

Suppose Tokyo is planning to construct a new public park. Based on some market research, they have determined that the town’s 50 residents can be divided into two types with respect to their benefit from this public good. 20 of the town’s residents are of Type 1 and the other 30 residents are of Type 2. Each resident's individual demand for acres of park space is given by:

Type 1: Q_D = 20 – P

Type 2: Q_D = 40 – 2P

a. Solve for the aggregate demand of Tokyo’s 50 residents as a function of the number of acres. Be sure to write down equations for each section of the aggregate demand curve, as well as the interval of quantities each section spans.

b. Graph the aggregate demand curve calculated in part a. Make sure to label both intercepts, slopes, and the intersection of the two sections.

c. Suppose each acre of public park has a marginal cost of MC = 200 + Q . Solve for the socially efficient number of acres for the town to construct.

d. Calculate the total surplus the 50 residents of Tokyo's gain from constructing this public park.