Use the formula for nPr to evaluate the following expression. 5P5

Mathematics

1 answer:

Cloud [144]4 years ago

7 0

Answer: 120

Step-by-step explanation:

The permutation of n things taken r at a time is given by expression :-

$^nP_r$

The formula to evaluate $^nP_r$ is given by :-

$^nP_r=\dfrac{n!}{(n-r)}$

Then , $^5P_5$ will be :-

$^5P_5=\dfrac{5!}{(5-5)!}$

Since , $n!=n(n-1)(n-2).......(2)(1)$

Then , $^5P_5=\dfrac{5\times4\times3\times2\times1}{0!}=120\ \ \ \text{Also,}0!=1$

Therefore, the value of the expression $^5P_5=120$

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Pleasee helppp fastt

Phoenix [80]

Not sure if this is how your teacher wants it, but here is how I would approach it in high school geometry:

To find the area of a rectangle, you need the base and the height.

The radius is 28 mm however the radius only covers half of one circle. Multiply 28 by 2 to get the length of one circle (56) and multiply 56 by 2 to get the length of your base of your rectangle (112).

Now to find the height: the center of the circles creates an equilateral triangle with the side length of 2r or 56 in this case. This means each angle of that triangle is 60 degrees, and when split in half, this creates two triangles both with angles of 30, 60, and 90. The altitude of this triangle is r√3 because of the “special right triangle rule” or 28√3 in this case. This comes to 48.497 mm. To find the remaining length of the height, you can use the radii of the top and bottom circle which add to 56. Add this to the previous number. So...

Height: 104.497
Base: 112

Now multiply the base times height to get:

216.497 mm.

Hope that helps!

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4 years ago

I need help with this question

vekshin1

Answer:

m = 2 /5

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

The entire graph of the function h is shown in the figure below. Write the domain and range of h using interval notation.

LiRa [457]

Answer:

(A) Domain : (-4, 3]

(B) Range : [ -2, 4)

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3 years ago

What’s the definition of input and output?

Vika [28.1K]

Input is the same as the x-term and output is the same as the y-term.

For example, take a look at the image provided with thee table.

Looking at the first box of our table, notice that if we subtract 5 from 1, we get -4 and if we subtract 5 from 2 we get -3 and if we subtract 5 from 3, we get -2. Notice that in each case, we're subtracting 5 from the input to get the output.

I attached a table so you can practice if you'd like to. All you have to do is subtract 5 from each input and you will end up with the output. The first few are done for you. I also provided an answer key in the next image so you can check your work.

The last one might be a little trick. In the input, we have n which is a variable that represents any number. If we want to find the nth term, we simply subtract 5. So we have n - 5.

First image is practice if you'd like and the second is the key.

If you don't want to do it, no worries.