Mr. Smith works on the 13th floor of a 15 floor building. The only elevator moves continuously through floors 1, 2, . . . , 15, 14, . . . , 2, 1, 2, . . . , except that it stops on a floor on which the button has been pressed. Assume that time spent loading and unloading passengers is very small compared to the travelling time.
Mr. Smith complains that at 5 pm, when he wants to go home, the elevator almost always goes up when it stops on his floor. What is the explanation?
Now assume that the building has n elevators, which move independently. Compute the proportion of time the first elevator on Mr. Smith’s floor moves up.

Step-by-step explanation:

Solution:

Think of it this way. The elevator could be on

floor 1 moving up

floor 2 moving up

floor 2 moving down

floor 3 moving up

floor 3 moving down

floor 4 moving up

floor 4 moving down

5 up

5 down

6 up  

6 down

7 up  

7 down

8 up

8 down

9 up

9 down

10 up

10 down

11 up

11 down

12 up

12 down

- All of these would mean that the guy on the 13th floor would get on an elevator that was moving up.

The rest :-

13 moving up

13 moving down

14 moving up

14 moving down

15 moving down

- 13 up is still moving up but the other 4 possibilities is the only way for the elevator to be coming down when he gets on.

- So there are 28 possibilities and only 4 where the guy is lucky. So the probability that he gets an elevator coming down is 4/28 or 1/7leaving 6/7 that the elevator is moving up.

- As for the second part of question, Since the elevators are independent and you are asking only about one of the elevators, each one of those elevators moves up 6/7 of the time, regardless of how many elevators.

- Now if the question said that you had 7 elevators stop on the floor all at the same time, the probability would say that 1 of the seven would be going down.

a

step-by-step explanation:

when functions are first introduced, you will probably have some simplistic "functions" and relations to deal with, usually being just sets of points. these won't be terribly useful or interesting functions and relations, but your text wants you to get the idea of what the domain and range of a function are. small sets of points are generally the simplest sorts of relations, so your book starts with those.

step-by-step explanation:

state the domain and range of the following relation. is the relation a function?

{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}

the above list of points, being a relationship between certain x's and certain y's, is a relation. the domain is all the x-values, and the range is all the y-values. to give the domain and the range, i just list the values without duplication:

domain: {2, 3, 4, 6}

range: {–3, –1, 3, 6}

(it is customary to list these values in numerical order, but it is not required. sets are called "unordered lists", so you can list the numbers in any order you feel like. just don't duplicate: technically, repetitions are okay in sets, but most instructors would count off for this.)

while the given set does indeed represent a relation (because x's and y's are being related to each other), the set they gave me contains two points with the same x-value: (2, –3) and (2, 3). since x = 2 gives me two possible destinations (that is, two possible y-values), then this relation is not a function.

note that all i had to do to check whether the relation was a function was to look for duplicate x-values. if you find any duplicate x-values, then the different y-values mean that you do not have a function. remember: for a relation to be a function, each x-value has to go to one, and only one, y-value.

state the domain and range of the following relation. is the relation a function?

{(–3, 5), (–2, 5), (–1, 5), (0, 5), (1, 5), (2, 5)}

i'll just list the x-values for the domain and the y-values for the range: