There are 7 performers who will present their comedy acts this weekend at a comedy club. one of the performers insists on being the last stand-up comic of the evening. if this performer's request is granted, how many different ways are there to schedule the appearances?

720

Step-by-step explanation:

Given : Number of performers who will present their comedy acts  = 7

If one of the performers insists on being the last stand-up comic of the evening and performer's request is granted, then its position got fixed.

Now, the remaining performers = 6

Now , the number of different ways to schedule the appearances is given by :-

Hence, the number of different ways to schedule the appearances =720

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the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet