Find equation to this line

9 friends are lining up. Joe, Susan, John, and Meredith must be beside each other. How many ways can they line up?

ZanzabumX [31]

<h3>Answer: 17,280</h3>

This is one single number slightly over 17 thousand.

You may need to erase the comma when typing the answer in.

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Explanation:

Let's say that another person steps in for Joe, Susan, John, and Meredith. I'll refer to this person as the teacher (perhaps these 9 friends are students on a field trip).

The 9 friends drops to 9-4 = 5 people when those four named people leave the group temporarily. Then it bumps up to 5+1 = 6 people when the teacher steps in. Wherever the teacher is located, the four friends that left will replace the teacher. This guarantees that those four friends stick together.

There are 6! = 6*5*4*3*2*1 = 720 ways to arrange those 6 people. The exclamation mark is a factorial symbol.

Within any of those 720 permutations, we have 4! = 4*3*2*1 = 24 ways to arrange those group of named people when they come back to replace the teacher.

So overall the answer is 4!*6! = 24*720 = 17,280

You may need to erase the comma when typing the answer in.

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Side note: There are 9! = 362,880 ways to arrange all nine friends regardless if those four mentioned people stick together or not. We see that they stick together roughly (17,280)/(362,880) = 0.0476 = 4.76% of the time.

6 0

3 years ago

HELP.... please??????????????

Nostrana [21]

Answers:

Functions

y = -x+11
y = 2x^2-6x+4
y = -7

Not functions

x = 3
x^2+y^2 = 81
y^2 = -5x-12

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Explanation:

A function is possible if and only if any given x input leads to exactly one y output.

For something like x^2+y^2 = 81, we can see that x = 0 leads to either y = 9 or y = -9. So this would <u>not</u> be a function. We would need x to pair with only y value to have it be a function.

We have the same thing going on with y^2 = -5x-12 as well.

For anything of the form x = k, where k is any real number, this is also not a function. We have one single input only and it leads to infinitely many outputs. So in a sense, this is even worse compared to the other examples.

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In summary, we have these three non-functions:

x = 3
x^2+y^2 = 81
y^2 = -5x-12

Everything else is a function. You can use the vertical line test as a visual way to check.

8 0

3 years ago

An inverted pyramid is being filled with water at a constant rate of 35 cubic centimeters per second. The pyramid, at the top, h

Katen [24]

These are the parameters, whats the question?

4 0

3 years ago

5(a−1)−15=3(a+2)+4 <br> a= ?

Alla [95]

Answer:

a = 15

Step-by-step explanation:

screenshots below should explain the answer :)

6 0

3 years ago

Find the y-component of this<br> vector:

irinina [24]

Answer:

The y-component of the vector is approximately -67.844 meters.

Step-by-step explanation:

A vector $\vec v$ in rectangular form are defined by the following form:

$\vec v = (r\cdot \cos \theta, r\cdot \sin \theta)$ (1)

Where:

$r$ - Magnitude, measured in meters.

$\theta$ - Direction with respect to +x semiaxis, measured in sexagesimal degrees.

Please notice that the y-component of the vector corresponds to the second component of the definition. If we know that $r = 101\,m$ and $\theta = 222.2^{\circ}$ , then the y-component of the vector is:

$y = r\cdot \sin \theta$ (2)

$y = (101\,m)\cdot \sin 222.2^{\circ}$

$y \approx -67.844\,m$

The y-component of the vector is approximately -67.844 meters.

5 0

3 years ago

Find equation to this line​

Find equation to this line