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C  Read explanation for full answer!

Step-by-step explanation:

Assuming you are learning about combinatrics, both A and B would be talking about relatively the same thing. 17 books, you can choose three, how many combinations, well, 17x16x15. Same goes for B. 56 students, four positions, 56x55x54x53. This is because only one person or book can fill one spot, and after that there are only 16 which can fill the other spot and then only 15 and so on. Therefore, 17x16x15. So, now we know its C, but what is the answer. Well we know 72% will get an A and 28% will not, so how could we make this into a combinatrics problem? Well we know that 72% will get an A, and 28% will get anything else which could include B's or C's etc, however we don't know the exact percentage so we will stay away from that. We could probably use something involving the class instead, similar to the choosing part of the election and book problem. So maybe something like this, "There are 50 boys and 50 girls in a class who are taking a test in which 72% of them will get A's, while 28% will not, so how many combinations could be made in order that the boys achieve more A's than the girls." That way, you are using the 72% and 28%, and you'd have to adjust so that the boys get more than the girls. This is a combination problem because it could be 50 boys and 22 girls got A's, while the other 28 girls got lower. Or 49 boys and 23 girls got A's, while 1 boy and 27 girls got lower.  That is where the combination problem would be found, and that would be what I would put for my answer with the knowledge I have.

Hope this helps!

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation: