When a <u>set</u> of given <em>numbers</em> or<em> items</em> is to be <u>arranged</u> in a <u>definite</u> way or pattern, permutation can be used to <u>determine</u> the <em>number</em> of ways in which this can be done. Thus the <em>required</em> answer to the question is 990.
When a <u>set</u> of given <em>numbers</em> or<em> items</em> is to be <u>arranged</u> in a <u>definite</u> way or pattern, permutation can be used to <u>determine</u> the <em>number</em> of ways in which this can be done. The applicable formula is:
= ![\frac{n!}{(n - r)!}](https://tex.z-dn.net/?f=%5Cfrac%7Bn%21%7D%7B%28n%20-%20r%29%21%7D)
where: n is the <u>total</u> number of items given, and r is the number of items <u>selected</u>.
Thus the given <u>question</u> can be solved as :
= ![\frac{11!}{(11-3)!}](https://tex.z-dn.net/?f=%5Cfrac%7B11%21%7D%7B%2811-3%29%21%7D)
= ![\frac{11!}{8!}](https://tex.z-dn.net/?f=%5Cfrac%7B11%21%7D%7B8%21%7D)
= ![\frac{11 * 10 * 9 * 8!}{8!}](https://tex.z-dn.net/?f=%5Cfrac%7B11%20%2A%2010%20%2A%209%20%2A%208%21%7D%7B8%21%7D)
= 11 x 10 x 9
= 990
= 990
Therefore, the <em>required</em> answer is 990.
For more clarifications on permutation, visit: brainly.com/question/12468032
#SPJ 1
Answer:
3 or
C
Step-by-step explanation:
(45 - 3x)^1/2 = x - 9 Square both sides
45 - 3x = x^2 - 18x + 81 Switch sides
x^2 - 18x + 81 = 45 - 3x Add 3x to both sides
x^2 - 15x + 81 = 45 Subtract 45 from both sides
x^2 - 15x + 36 = 0 Factor
(x - 12)(x - 3) =0
The answers are
x = 12
x = 3
Now the question asks which is extraneous. The answer will be which ever number won't solve the original equation. Looking at it right now, both look OK.
(45 - 3*12)^1/2 = 12 - 9
(45 - 36)^1/2 = 3
(9)^1/2 = 3
So 12 is a proper solution.
What about 3?
(45 - 3*3)^1/2 = 12 - 3
(45 - 9)^1/2 = 9
36^1/2 = 9
6 does not = 9
The extraneous solution is x = 3
Answer:
![y=\frac{1}{3}x+2](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B3%7Dx%2B2)
Step-by-step explanation:
We can see that the y-intercept is 2. This is because when
,
(for this line). We can also use the
rule for this line. When the <em>x</em> increases by 1, the <em>y</em> increases by 3. Therefore, we know the slope is
. Putting all this information in slope-intercept form
, gives us the following.
![y=\frac{1}{3}x+2](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B3%7Dx%2B2)
There's your answer :) hope this helps!
Answer:
n-1
Step-by-step explanation:
Consecutive means that they have a difference of one, so the expression will be n-1.
![- 5x+2y=9 \\ y=7x](https://tex.z-dn.net/?f=%20-%205x%2B2y%3D9%20%5C%5C%20%3C%2Fp%3E%3Cp%3Ey%3D7x)
We know that y=7x, so we just need tu put it into the 1st equation
![- 5x + 2 \times 7x = 9 \\ - 5x + 14x = 9 \\ 9x = 9 | \div 9 \\ 9x \div 9 = 9 \div 9 \\ x = 1](https://tex.z-dn.net/?f=%20-%205x%20%2B%202%20%5Ctimes%207x%20%3D%209%20%5C%5C%20%20-%205x%20%2B%2014x%20%3D%209%20%5C%5C%209x%20%3D%209%20%7C%20%5Cdiv%209%20%5C%5C%209x%20%5Cdiv%209%20%3D%209%20%5Cdiv%209%20%5C%5C%20x%20%3D%201)
So we found x. Now we can find y
![y = 7 \times 1 \\ y = 7](https://tex.z-dn.net/?f=y%20%3D%207%20%5Ctimes%201%20%5C%5C%20y%20%3D%207)
Answer:
x=1, y=7; or (1;7)