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ryzh [129]
3 years ago
8

There are 8 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?
Mathematics
1 answer:
Korvikt [17]3 years ago
7 0
This is a permutations problem. There are only 7 comics you can move into different time slots, the 8th one being fixed in that last position. So you can look at it this way:
For the 1st position, you can choose from all 7 people. Once you've picked that one, you have 6 people to choose from for the 2nd position, and similarly for the remaining ones . This gives you 7x6x5x4x3x2x1 = 5040 ways to arrange them. And the last comic stays in the same position all the time so does not change this number. Make sense? If you need to demonstrate it to yourself, use a smaller number of comics, like 3 or 4, and write out the combinations to see that it works.
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mrs_skeptik [129]

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3.5

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Find the equation of the line the line is perpendicular to the graph of x - 5y=6 and contains 2,-10
qaws [65]
<h3>Answer:   </h3><h3>y + 10  =  - 5 (x - 2)  [point-slope form]  OR</h3><h3>y = - 5 x     [slope-intercept form]</h3><h2 /><h3>Step-by-step explanation:</h3>

<u>Identify the slope of the given line</u>

If we rewrite the equation given, we can easily identify the slope

                 x - 5y = 6

                    - 5y = - x + 6

                        y  = ¹/₅ x  - ⁶/₅

                                ∴ the slope of x - 5y = 6  is  ¹/₅

<u>Find the slope of the perpendicular line</u>  

When two lines are perpendicular, the product of their slopes is -1. This means that the slopes are negative-reciprocals of each other.

                 ⇒  since the slope of this line = ¹/₅

                      then the slope of the perpendicular line (m) =  - 5

<u>Determine the equation of perpendicular line</u>  

We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line:  

                             ⇒  y - (-10) =  - 5 (x - 2)

<h3>                                          ∴  y + 10  =  - 5 (x - 2)</h3><h3 />

We can also write the equation in the slope-intercept form by making y the subject of the equation and expanding the bracket to simplify:

                                   since    y + 10  =  - 5 (x - 2)

<h3>                                                y  =  - 5 x</h3><h3 /><h3>∴ the slope-intercept equation of the perpendicular line is y + 10  =  - 5 (x - 2)  OR  y = - 5 x. </h3><h3 /><h3 />

<em>To test my answer, I have included a Desmos Graph that I graphed using the information provided in the question and my answer.</em>

4 0
3 years ago
Suppose point X has a coordinate of 5 and XY = 10 what are the possible coordinates of point Y
vladimir2022 [97]
The answer is 2 because if the variable or numbers are close together you have to multiply those 2 numbers so that means it would look like this --->        XY=10=5 X 2=10. :)
4 0
3 years ago
Which of the following are remote interior angles of &lt;6? check all that apply
vlada-n [284]

Answer:

C. <3, E. <1

Step-by-step explanation:

A triangle has 3 vertices, so it has exactly 3 interior angles, one at each vertex.

A triangle has 2 exterior angles at each vertex, so a triangle has 6 exterior angles. Each exterior angle is adjacent to an interior angle. The interior angles that are not adjacent to an exterior angle are that exterior angle's remote interior angles.

<6 is an exterior angle of the triangle. <5 is the other exterior angle at that vertex. <2 is an interior angle of the triangle and is adjacent to <6, so <2 is not a remote interior angle to <6.

The other two interior angles of the triangle are <1 and <3.

<1 and <3 are interior angles that are not adjacent to <6, so they are the remote interior angles to <6.

Answer: <1, <3

8 0
3 years ago
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