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1.1 Order of Operations & Formulas

1.1 Order of Operations & Formulas
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  • 19. Equal-Payment Plan for Electric Bills

    From May through March, on an equal-payment plan, you pay $90 each month on your electric bill.

    1. How much do you owe in April?
    2. Interpret your answer to part (a).
    3. What should you pay each month to have 12 equal monthly payments?

    data

    • Worked-Out Solution
      1. Add the 12 monthly usage amounts and subtract the 11 equal payments already made to find the amount you owe in April.



        You owe -$21.49 in April.

      2. When you "owe" -$21.49, it means that the electric company actually owes you money and will credit your account.
      3. To have 12 equal monthly payments, you should pay

        $968.51 ÷ 12  months   $80 .71 per month.

        $968.51 divided by 12 months equals approximately $80.71 per month

      You owe $47.08 in September.

      Try downloading the spreadsheet with the data. Enter 80.71 as the monthly payment. How much do you owe in April?

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      _____     _____     _  _    __   __    _  _   
     /  ___||  |  ___||  | \| ||  \ \\/ //  | \| || 
    | // __    | ||__    |  ' ||   \ ` //   |  ' || 
    | \\_\ ||  | ||__    | .  ||    | ||    | .  || 
     \____//   |_____||  |_|\_||    |_||    |_|\_|| 
      `---`    `-----`   `-` -`     `-`'    `-` -`  
                                                    
    
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  • 20. Finding the Total Number of Ink Cartridges

    A combo pack has 2 cubed ink cartridges. A shipment has 6 squared combo packs. Which of the following keystroke sequences is better for finding the total number of ink cartridges in a shipment? Explain your reasoning.

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       _____     ___      ______    ______    _____   
      / ___//   / _ \\   /_   _//  /_   _//  / ____|| 
      \___ \\  / //\ \\    | ||     -| ||-  / //---`' 
      /    // |  ___  ||  _| ||     _| ||_  \ \\___   
     /____//  |_||  |_|| /__//     /_____//  \_____|| 
    `-----`   `-`   `-`  `--`      `-----`    `----`  
                                                      
    
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    system user
    Guest   9 months ago |
    I am learning alot.
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  • 21. Tiling a Hot Tub

    The inside of a circular hot tub is lined with 1-inch by 1-inch tiles.

    1. Explain how to estimate the number of tiles needed for the hot tub.
    2. The hot tub is 3.5 feet deep and has a diameter of 6 feet. What is the minimum number of tiles needed? (The formula for the circumference of a circle is
    • Worked-Out Solution
      1. The hot tub can be modeled using a cylinder. The interior consists of the circular base and the vertical wall.

        You can estimate the number of tiles by estimating the area of the circular base and the vertical wall.

      2. In square feet, the base and wall have the following areas.

        Area of the Circular Base:

        Area of the Vertical Wall:

        If you imagine the wall of the hot tub being "unwrapped," you would have a rectangle whose height is 3.5 feet and whose length is the circumference of the hot tub. So, the area of the vertical wall is

        Area of the Tiled Portion of Hot Tub:

        Because the hot tub is lined with 1-inch by 1-inch tiles, use unit analysis to convert the area to square inches.

        You need a minimum of about 13,565 one-inch tiles, but 14,000 will allow for waste.

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                 ___      ______   __   __            
      ____      / _ \\   /_   _//  \ \\/ //     ___   
     |    \\   / //\ \\  `-| |,-    \ ` //     /   || 
     | [] ||  |  ___  ||   | ||      | ||     | [] || 
     |  __//  |_||  |_||   |_||      |_||      \__ || 
     |_|`-`   `-`   `-`    `-`'      `-`'       -|_|| 
     `-`                                         `-`  
    
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  • 22. Comparing Job Offers

    What are the minimum and maximum yearly total compensations for each job offer?

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      _  __     ___     ______      ___              
     | |/ //   / _ \\  |      \\   / _ \\    ____    
     | ' //   / //\ \\ |  --  //  | / \ ||  |    \\  
     | . \\  |  ___  |||  --  \\  | \_/ ||  | [] ||  
     |_|\_\\ |_||  |_|||______//   \___//   |  __//  
     `-` --` `-`   `-` `------`    `---`    |_|`-`   
                                            `-`      
    
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  • 23. Comparing Job Offers

    Which job offer do you think is better? Explain your reasoning.

    • Worked-Out Solution

      There are many reasons why a person would accept one job offer over another. In real life, the decision is probably more often made "with the heart" rather than "with the head." Even so, you can objectively compare the first 3 parts of each offer.

      You have the opportunity to earn more with Offer A, but "potential income" like sales commission and profit sharing are not guaranteed. Offer B has a higher total compensation, which would be a guaranteed income.

      When two financial offers are close, you would probably make the choice depending on other factors, such as the following:

      • Reputation of the company
      • The work itself (interest, challenge, etc.)
      • Quality of community (life, schools, etc.)
      • Dependent care
      • Professional memberships
      • Health club memberships
      • Vacation time
      • Sick/Personal days
      • Telecommuting options
      • Corporate culture
      • Timeframe for advancement
      • Relocation expenses
      • Overtime/Comp. Time policies
      • Bonus/Raise policies
      • Paid holidays
      • Work hours, including flex-time
      • Parking, expense reimbursement
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               __   __             _    _   __    __  
        ___    \ \\/ //     ___   | || | || \ \\ / // 
       /   ||   \ ` //     /   || | || | ||  \ \/ //  
      | [] ||    | ||     | [] || | \\_/ ||   \  //   
       \__ ||    |_||      \__ ||  \____//     \//    
        -|_||    `-`'       -|_||   `---`       `     
         `-`                 `-`                      
    
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  • 24. Comparing Job Offers

    You decide to make a counteroffer to the company you did not choose in Exercise 23. How does your counteroffer differ from the original? Explain your reasoning.

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      ____     _    _    _    _    _    _      _____  
     |  _ \\  | || | || | |  | || | || | ||   / ___// 
     | |_| || | || | || | |/\| || | || | ||   \___ \\ 
     | .  //  | \\_/ || |  /\  || | \\_/ ||   /    // 
     |_|\_\\   \____//  |_// \_||  \____//   /____//  
     `-` --`    `---`   `-`   `-`   `---`   `-----`   
                                                      
    
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