Show that the formula an = 2n+1 - 2 for the nth term in the sequence satisfies the recurrence relation an+1 = 2an + 2 .

Discuss the ways in which electronic information associated with payments is addressed in terms of security. include encryption, secure sockets layers, and secure electronic transactions in your discussion. are there any other ways that consumers and businesses can keep their payment information secure in an electronic commerce environment? do you feel that your information is safe when conducting electronic business? why or why not?

Which of these is a benefit of using objects in a powerpoint presentation? a. collaborators can create the external files while you create and edit the slide show. b. you can easily change the theme and design of the presentation. c. you can have older data in the source file while having up-to-date data in the presentation. d. collaborators can easily share the presentation.

When making changes to optimize part of a processor, it is often the case that speeding up one type of instruction comes at the cost of slowing down something else. for example, if we put in a complicated fast floating-point unit, that takes space, and something might have to be moved farther away from the middle to accommodate it, adding an extra cycle in delay to reach that unit. the basic amdahl's law equation does not take into account this trade-off. a. if the new fast floating-point unit speeds up floating-point operations by, on average, 2ă—, and floating-point operations take 20% of the original program's execution time, what is the overall speedup (ignoring the penalty to any other instructions)? b. now assume that speeding up the floating-point unit slowed down data cache accesses, resulting in a 1.5ă— slowdown (or 2/3 speedup). data cache accesses consume 10% of the execution time. what is the overall speedup now? c. after implementing the new floating-point operations, what percentage of execution time is spent on floating-point operations? what percentage is spent on data cache accesses?