Concept explainers
Garage Door Openers
Garage door openers originally had a series of four on/off switches so that homeowners could personalize the frequencies that opened their garage doors. If all garage door openers were set at the same frequency, anyone with a garage door opener could open anyone else’s garage door.
1. Use a tree diagram to show how many different positions 4 consecutive on/off switches could be in.
After garage door openers became more popular, another set of 4 on/off switches was added to the systems.
2. Find a pattern of how many different positions are possible with the addition of each on/off switch.
3. How many different positions are possible with 8 consecutive on/off switches?
4. Is it reasonable to assume, if you owned a garage door opener with 8 switches, that someone could use his or her garage door opener to open your garage door by trying all the different possible positions?
For a specific year it was reported that the ignition keys for Dodge Caravans were made from a single blank that had five cuts on it. Each cut was made at one out of five possible levels. For that year assume there were 420,000 Dodge Caravans sold in the United States.
5. How many different possible keys can be made from the same key blank?
6. How many different Dodge Caravans could any one key start?
Look at the ignition key for your car and count the number of cuts on it. Assume that the cuts are made at one of any of five possible levels. Most car companies use one key blank for all their makes and models of cars.
7. Conjecture how many cars your car company sold over recent years, and then figure out how many other cars your car key could start. What would you do to decrease the odds of someone being able to open another vehicle with his or her key?
See pages 254–255 for the answers.
Want to see the full answer?
Check out a sample textbook solutionChapter 4 Solutions
Elementary Statistics: A Step By Step Approach
Additional Math Textbook Solutions
Basic Business Statistics, Student Value Edition
Elementary Statistics: Picturing the World (7th Edition)
Business Statistics: A First Course (8th Edition)
Statistics: The Art and Science of Learning from Data (4th Edition)
Stats: Modeling the World Nasta Edition Grades 9-12
- A family consisting of 2 parents and 3 children is to pose for a picture with 2 family members in the front and 3 in the back a. How many arrangements are possible with no restrictions? b. How many arrangements are possible if the parents must sit in the front? C. How many arrangements are possible if the parents must be next to each other?arrow_forwardDISCUSS: Pair of InitialsExplain why in any group of 677 people, at least two people must have the same pair of initials.arrow_forwardIn Example 10, the team must consist of six boys and six girls. How many different 12-member teams are possible?arrow_forward
- Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGALCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning