2/3 of all the people who attended a certain party arrived by 8: 00 pm. how many people arrived by 8: 00 pm?
(1) 9 people arrived after 9: 00 pm.
(2) 21 people arrived between 8: 00 pm and 9: 00 pm, and by 9: 00 pm 90% of all the people who attended the party had arrived.

a) How many people who attended a certain party arrived by  8 PM           60 people

Step-by-step explanation:

2/3 of all people who attended a certain party arrived by  8 P.M . That means that  1/3  arrived in other time. But  2/3  +  1/3 is total number of people in the party.

1) 9 people arrived after 9 PM

And in 2

2) By 9 .00 PM  90 % of people were already in the party and. That means

that 9 people who arrived after are 10 %

Then if      9  people are    10 %

                 x   people are   100%

x  =  (100*9)/10      ⇒   x  =  900/10

x =  90

Here we got total number of people in the party  90

Then    2/3 of   90     is    180/3       60

1/3  0f  90      is   30

the range of a function is the range of y-values for which it is defined, or exists. given that we are only looking at the y-values, we can already discount the first two answers as they deal with the domain of the function (range of x-values).

now, what we need to do is find the smallest and highest y-values for which the function is defined. if you'd like, you could take a ruler and start at the very bottom of the graph, find the lowest point, then move the ruler higher and higher until you reach the highest point. doing so either in your head or with an actual ruler, we can see that the lowest y-value is -5 and the highest y-value is -1.

the question now remains as to whether they are included in the range (fourth answer) or excluded (third answer). the key here is to recognise whether they are marked with an open or a closed circle. since both (-2, -5) and (2, -1) are marked with a closed circle, they are points that exist on the graph and are thus included in the range (note that if they were marked with an open circle like (4, -2) then that would signify that there is a break in the graph at that point).

thus, the fourth answer, (y | -5 ≤ y ≤ -1), is correct.

also note that usually it is good practice to scan your eye inbetween the highest and lowest point for any breaks in the graph - we do have one here at (4, -2), however -2 is still included in the range because there is another point that is included in the graph with the same y-value, ie. point (1, -2).

i hope that but if you require any further explanation don't hesitate to comment below.

stops on an even number.