B) state the minimum monthly income and hourly wage per worker needed to cover monthly expenses for the family you used in part a. then, explain how to calculate the hourly wage based on the monthly income and state the hourly wage. assume that each full-time worker works four 40-hour work weeks per month, and each part-time worker works two 40-hour weeks per month.

Five more than the product of a number n and 8 is at least 100. write an inequality that can be used to find all positive values of n

1. spending nights at a 3 star hotel in paris, france or spending nights at a 5 star hotel in new york city. 2. cell phone plans, comparing monthly fee and price per text message. you must use basic phones for the purpose of this project. vacation situation: you have graduated from high school and you are planning to go on a vacation by yourself. you have always wanted to travel to paris, france, but you need to consider the price of the ticket as well as the cost of hotel per night. as an alternative, you want to look into spending the same number of nights in new york city at a luxurious 5 star hotel. now you need to determine whether you should go to paris which will cost you for flight and hotel or stay in nyc that will cost you only for the hotel. note: you are spending the same number of nights at each destination. assignment: gather information from travel agencies, such as american airline, orbitz, expedia, or kayak, through their website for cost of flight and cost of hotel. then write a system of linear equations for the two plans and create a graph. use the methods we have been studying to determine which plan is better based on the number of nights you decide to stay if you had $1500 to spend for this vacation. cell phone plans situation: you have graduated from high school and moved away to college. your parents have decided that it’s time for you to pay for your own cell phone. you have to stick to a strict budget. now you need to determine whether you should go with a plan that costs more per month but charges less per text message or a cheaper plan that charges more per message. assignment: you are to choose from a cellphone company that offers two talk and text plans. the company charges a monthly service fee of $20 for either plan the customer chooses: talk and text plan a charges five cents a minutes and twenty dollars for 250 texts. talk and text plan b charges ten cents a minute (first 100 minutes free) and fifteen dollars for 200 texts. note: assume you are purchasing a basic phone, which is $0 with 2-year contract. you cannot purchase unlimited text messaging for this exercise. use the methods we have been studying to determine which plan is better based on the number of text messages you send per month if you only have $75 to spend each month. project details you will decide which project you want to do. after you decide on a project, you will need to: 1) collect the data if necessary. 2) write the system of linear equations and a word problem once the data has been collected. 3) use the methods we have been studying (graphing and solving algebraically) to find the solution to the written system. 4) design the final display of the project on a poster board. be creative! project rubric 2 points = data for the scenarios. (only applicable to vacation plans) 1 points = data 1 points = sources documented 8 points = word problem and the system of equations 2 points = all variables are defined 6 points = both equations are accurate 8 points = graphic solution 4 points = each line is correctly graphed 2 points = labels and titles 2 points = point of intersection 8 points = algebraic solution and explanation 4 points = correct solving 2 points = explain your work and how you came up with the parameters 2 points = check 14 points = final project 4 points = creativity 4 points = contains the analysis of your equations 6 points = final product is organized and clear final project checklist – refer to the rubric above make sure you have the following items on your final project… • collected data (if necessary) • system of linear equations with variables defined • graphs of both equations (this can be done on desmos and printed or drawn by hand) • algebraic solution with work and units • analysis: o if you chose vacation plan: for how many nights are the prices going to be same? if you had $1500 to spend for your vacation, which plan would you choose and why? o if you chose talk and text plan: for how many minutes will both plans hare the same cost? if you had $75 to spend each month, which plan should you choose and why? vacation – data organizer 1) define the variables 2) complete the following chart to you come up with a systems of linear equations destination paris, france new york city hotel rating   name of hotel price of hotel (per night) compare same nights price of flight linear equation 3) write an equation for staying in paris, france. 4) write an equation for staying in new york, ny. talk and text plans – data organizer 1) define the variables. 2) express plan a as an equation. 3) express plan b as an equation. *make sure you take into consideration that first 100 minutes of talking on the phone is free!

Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .