The community park has a small lake where visitors can rent paddle boats at $1 for 15 minutes, up to 2 hours. After 2 hours, the rate increases to $3 for 30 minutes.

Problem Write the piecewise function to model this situation and graph the function.

  1. What is the rental charge at 15 minutes? At 16 minutes? At 45 minutes?

2. If you had only $15, how long could you rent a boat?

3. How are the two lines in the graph the same, and how are they different?

4. How would the graph change if the rate change occurred at ? = 1 hour?

5. How would the graph change if the fee were $2 for 15 minutes?

6. What is the rental fee at 3 hours?

SoakNSun Swim Park sells individual and family tickets. With a​ ticket, each person receives a​ meal, three​ beverages, and unlimited use of the swimming pools. SoakNSun has the following ticket prices and variable costs for 2018​:

SoakNSun expects to sell one individual ticket for every three family tickets. SoakNSun​'s total fixed costs are $61,875.

Requirement 1. Compute the​ weighted-average contribution margin per ticket.

Complete the table below to calculate the​ weighted-average contribution margin. ​(Round the​ weighted-average contribution margin per unit to the nearest​ cent.)

Requirement 2. Calculate the total number of tickets SoakNSun must sell to break even.Start by selecting the formula and entering the amounts to calculate the total number of tickets SoakNSun must sell to break even. ​(Abbreviations used: Weighted avg. CM​ = weighted-average contribution margin. Complete all answer boxes. For items with a zero​ value, enter​ "0".)

Requirement 3. Calculate the number of individual tickets and the number of family tickets the company must sell to break even.

1. Jupiter recently introduced her cousin Letecia to one of her colleagues working for the Avocado Park Development Council, whose name is Scheherazade. Letecia has decided to ask Scheherazade out on a date and her goats have jumped in to help. They don’t really understand human romantic customs, but they reason that humans base most of their behavior on money, so they want to start by estimating how much Letecia should expect to spend on a date. They collect a random sample of 52 first dates from residents of Avocado Park and ask how much money the dater spent (they discarded responses of zero as unhelpful). The results of their survey can be found under the questions. Thanks
   1. Identify the population of interest.
   2. Identify the variable of interest. What type of variable is it?
   3. If the goats want to estimate HOW MUCH Letecia should be expected to spend on this date, what parameter should they try to estimate?
   4. If the goats wish to estimate the parameter you chose in part c using a confidence interval, what conditions would need to be met? What assumptions would be necessary?
   5. Estimate the parameter you chose in part c with a confidence level of 90%.
   6. If Letecia can only afford to spend $80 on this date, should she worry that she’ll come off as cheap? Justify your answer.

Date Expense: 43,96, 70, 92, 87, 92, 70, 89, 65, 67, 43, 61, 57, 61, 75, 46, 83, 27, 81, 22, 127, 94, 86, 69, 102, 96, 59, 98, 72, 115, 117, 67, 55, 73, 84, 64, 62, 45, 51, 84, 74, 60, 82, 69, 41, 81, 62, 83, 120, 72, 97, 66

A theme park owner records the number of times the same kids from two separate age groups ride the newest attraction.

Using the computational formula, what is the SS, sample variance, and standard deviation for the age group of 13–16? (Round your answers for variance and standard deviation to two decimal places.)

SS sample variance standard deviation

theme park owner wants to know if the children’s rides are favoring 10 year old girls over 10 year old boys based on height. In other words, does one group taller than the other and thus can go on more rides?

Part a: The owner gathered height data on 10 year old girls and 10 year old boys, see data below. Determine at the 5% significance level if there is evidence that the two genders are not the same height and thus cannot all go on the same rides. Show your work and give your answer in complete sentences in context of the problem.

Part b: After doing some research, the owner found the following information about the expected height and standard deviation for 10 year olds. Does that change the result of part a? Show your work and give your answer in complete sentences in context of the problem.

use c++

Parking charge application: A parking garage charges a $20.00 minimum fee to park for up to 3 hours. The garage charges an additional $5.00 per hour for hour or part thereof in excess of 3 hours. The maximum charge for any given 24-hour period is $50.00. Assume that no car parks for longer than 24 hours at a time. Write a program that calculates and prints the parking charge for each of 3 customers who parked their cars in this garage yesterday. You should enter the hours parked for each customer. Your program should save the result in a array of Customer. The class customer is the following:

class customer{ string plate; float hour; float fee; }

Your program should use the function calculateCharges to determine the fee for each customer. You should print the result for the 3 customers in the following format:

Plate Hours Charge

132AAC 1.5 20.00

236URT 4.0 25.00

390ROP 24.0 50.00

TOTAL 29.5 95.00

In doing this question make sure to keep the array of customer as global variable.

Northwood Company manufactures basketballs. The company has a ball that sells for $32. At present, the ball is manufactured in a small plant that relies heavily on direct labor workers. Thus, variable expenses are high, totaling $22.00 per ball, of which 69% is direct labor cost.

Last year, the company sold 30,000 of these balls, with the following results:

Required:

1. Compute (a) last year's CM ratio and the break-even point in balls, and (b) the degree of operating leverage at last year’s sales level.

CM RATIO = 31.25%

UNIT SALES TO BREAK EVEN = ? BALLS

DEGREE OF OPERATING LEVERAGE = ?

2. Due to an increase in labor rates, the company estimates that next year's variable expenses will increase by $3.00 per ball. If this change takes place and the selling price per ball remains constant at $32.00, what will be next year's CM ratio and the break-even point in balls?

CM RATIO = ?

UNIT OF SALES TO BREAK EVEN = ? BALLS

3. Refer to the data in (2) above. If the expected change in variable expenses takes place, how many balls will have to be sold next year to earn the same net operating income, $90,000, as last year?

NUMBER OF BALLS = ?

4. Refer again to the data in (2) above. The president feels that the company must raise the selling price of its basketballs. If Northwood Company wants to maintain the same CM ratio as last year (as computed in requirement 1a), what selling price per ball must it charge next year to cover the increased labor costs?

SELLING PRICE = ?

5. Refer to the original data. The company is discussing the construction of a new, automated manufacturing plant. The new plant would slash variable expenses per ball by 31.25%, but it would cause fixed expenses per year to double. If the new plant is built, what would be the company’s new CM ratio and new break-even point in balls?

CM RATIO = ? %

UNIT OF SALES TO BREAK EVEN = ? BALLS

6. Refer to the data in (5) above.

a. If the new plant is built, how many balls will have to be sold next year to earn the same net operating income, $90,000, as last year?

NUMBER OF BALLS = ?

b. Assume the new plant is built and that next year the company manufactures and sells 30,000 balls (the same number as sold last year). Prepare a contribution format income statement and Compute the degree of operating leverage.

NORTHWOOD COMPANY

CONTRIBUTION INCOME STATEMENT =

hw 3.2

Northwood Company manufactures basketballs. The company has a ball that sells for $30. At present, the ball is manufactured in a small plant that relies heavily on direct labor workers. Thus, variable expenses are high, totaling $18.00 per ball, of which 60% is direct labor cost.

Last year, the company sold 50,000 of these balls, with the following results:

Northwood Company manufactures basketballs. The company has a ball that sells for $25. At present, the ball is manufactured in a small plant that relies heavily on direct labor workers. Thus, variable expenses are high, totaling $15.00 per ball, of which 60% is direct labor cost.

Last year, the company sold 56,000 of these balls, with the following results:

Required:

1. Compute (a) last year's CM ratio and the break-even point in balls, and (b) the degree of operating leverage at last year’s sales level.

2. Due to an increase in labor rates, the company estimates that next year's variable expenses will increase by $3.00 per ball. If this change takes place and the selling price per ball remains constant at $25.00, what will be next year's CM ratio and the break-even point in balls?

3. Refer to the data in (2) above. If the expected change in variable expenses takes place, how many balls will have to be sold next year to earn the same net operating income, $187,000, as last year?

4. Refer again to the data in (2) above. The president feels that the company must raise the selling price of its basketballs. If Northwood Company wants to maintain the same CM ratio as last year (as computed in requirement 1a), what selling price per ball must it charge next year to cover the increased labor costs?3. Refer to the data in (2) above. If the expected change in variable expenses takes place, how many balls will have to be sold next year to earn the same net operating income, $187,000, as last year?

5. Refer to the original data. The company is discussing the construction of a new, automated manufacturing plant. The new plant would slash variable expenses per ball by 40.00%, but it would cause fixed expenses per year to double. If the new plant is built, what would be the company’s new CM ratio and new break-even point in balls?

6. Refer to the data in (5) above.

a. If the new plant is built, how many balls will have to be sold next year to earn the same net operating income, $187,000, as last year?

b. Assume the new plant is built and that next year the company manufactures and sells 56,000 balls (the same number as sold last year). Prepare a contribution format income statement and compute the degree of operating leverage.

a. Assume that a society is composed of two polluters, with the marginal abatement costs of polluters 1 and 2, respectively, equal to:

MAC1 = 18 – E1

MAC2 = 12 – 2E2

Where MAC1 refers to the marginal abatement costs of polluter 1, and E1 refers to the level of emissions of polluter 1. What is the unregulated level of pollution for each polluter? Find the total level of emissions that would be generated if a per-unit pollution tax of four dollars were imposed. Perform the same exercise for taxes of six dollars and eight dollars.

b. Given the same two marginal abatement cost function in part (a), find the market price of a marketable pollution permit if pollution was limited to eighteen units through the issuance of marketable pollution permits. Assume initially that each polluter is given nine permits (that allow 1 unit of pollution each).

c. Given a societal marginal abatement cost function of:

MAC = 100 – 3E

and a societal marginal damage function of:

MD = 2E,

find the optimal level of pollution and the per-unit pollution tax that would achieve it.

d. MAC1 and MAC2 are two different societal marginal abatement cost functions. Which one is more likely to be associated with an optimal level of pollution that is at or near zero? Why?

MAC1 = 10 – 0.2E

MAC2 = 1/E