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3 years ago

How do you simplify(n!)^2/(n+1)!(n-1)!

1 answer:

5 0

We haven n! = (n-1)! x n and (n+1)! = n! x (n + 1);
Then, (n!)^2 = n! x n! = n! x (n-1)! x n;
And (n+1)!(n-1)! = n! x (n + 1) x (n-1)!;
Finally, [n! x (n-1)! x n] / [n! x (n + 1) x (n-1)!] = (n+1)/n;

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Given the data points, (x, y) of a linear function: (2, 11), (4, 10), (6, 9), (12, 6), what is the function? What is the slope?

NeX [460]

Answer:

The function is $y~=~12 ~-~ 0.5 \cdot x$ .

The slope is $m=-0.5$ .

The y-intercept is $b=12$ .

Step-by-step explanation:

Our aim is to calculate the values m (slope) and b (y-intercept) in the equation of a line :

$y=mx+b$

We have the following data:

$\begin{array}{c|cccc}x&2&4&6&12\\y&11&10&9&6\end{array}$

To find the line of best fit for the points given, you must:

Step 1: Find $X\cdot Y$ and $X\cdot X$ as it was done in the table below.

Step 2: Find the sum of every column:

$\sum{X} = 24 ~,~ \sum{Y} = 36 ~,~ \sum{X \cdot Y} = 188 ~,~ \sum{X^2} = 200$

Step 3: Use the following equations to find b and m:

$\begin{aligned} b &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 36 \cdot 200 - 24 \cdot 188}{ 4 \cdot 200 - 24^2} \approx 12 \\ \\m &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 4 \cdot 188 - 24 \cdot 36 }{ 4 \cdot 200 - \left( 24 \right)^2} \approx -0.5\end{aligned}$

Step 4: Assemble the equation of a line

$\begin{aligned} y~&=~b ~+~ m \cdot x \\y~&=~12 ~-~ 0.5 \cdot x\end{aligned}$

The graph of the regression line is:

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3 years ago

Find the slope and the y-intercept of the graph of the linear equation. Then, graph the equation.

Anni [7]

Answer:

$slope \: = - 2x \\ y - intercept \: = 0 \: or \: (0,0)$

I inserted an image of the equation.

Step-by-step explanation:

Hope this helps!

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2 years ago

Write and solve the sentence as an inequality. A number minus 3 is less than -5.

Lorico [155]

Answer:

x - 3 < -5 is the inequality x < -2 is the solution

Step-by-step explanation:

x - 3 < -5

add 3

x < -2

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3 years ago

Write the equation of a line perpendicular to y= -5/6x-3 and whose y-intercept is (0,11).

worty [1.4K]

Answer:

y=6/5x+11

Step-by-step explanation:

Perpendicular lines have the opposite sign and reciprocal of the original line. Since the y-intercept is 11 we know that it is 6/5x+11

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Colt1911 [192]

Answer:

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