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alekssr [168]
3 years ago
8

Evaluate C_n.xP^xQn-x For the given n=7, x=2, p=1/2

Mathematics
1 answer:
r-ruslan [8.4K]3 years ago
7 0

Answer:

The value of given expression is \frac{21}{128}.

Step-by-step explanation:

Given information: n=7, x=2, p=1/2

q=1-p=1-\frac{1}{2}=\frac{1}{2}

The given expression is

C(n,x)p^xq^{n-x}

It can be written as

^nC_xp^xq^{n-x}

Substitute n=7, x=2, p=1/2 and q=1/2 in the above formula.

^7C_2(\frac{1}{2})^2(\frac{1}{2})^{7-2}

\frac{7!}{2!(7-2)!}(\frac{1}{2})^2(\frac{1}{2})^{5}

\frac{7!}{2!5!}(\frac{1}{2})^{2+5}

\frac{7\times 6\times 5!}{2\times 5!}(\frac{1}{2})^{2+5}

21(\frac{1}{2})^{7}

\frac{21}{128}

Therefore the value of given expression is \frac{21}{128}.

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Solve the system of equations.<br> 5y – 4c = -7<br> 2y + 4x = 14
Lesechka [4]

c=\frac{5y}{4\\} + \frac{7}{4\\}

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Step-by-step explanation:

if 'c' is meant to be another 'x' the answer is

(3, 1)

x = 3,y = 1

4 0
3 years ago
What is 1/6+7/10 as a equivalent fraction
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Step-by-step explanation:

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The area is 30 m!


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6 0
2 years ago
What are the explicit equation and domain for an arithmetic sequence with a first term of 8 and a second term of 5? 20 pts.
fgiga [73]

ANSWER

a_n = 11 - 3n

EXPLANATION

The explicit rule for an arithmetic sequence is given by:

a_n = a_1 + d(n - 1)

It was given that:

a_1 = 8

and

a_2 = 3

The common difference is

d = 5 - 8 =  - 3

We plug in the values into the explicit formula to get,

a_n = 8+  - 3(n - 1)

Expand to get,

a_n = 8 - 3n  + 3

The explicit rule is

a_n = 11 - 3n

6 0
3 years ago
What is the equation of the line that passes through the points (5, 3) and (-3,-1)?
Liono4ka [1.6K]

Answer:

y=1/2x+1/2

m=1/2

Step-by-step explanation:

You want to find the equation for a line that passes through the two points:

(5,3) and (-3,-1).

First of all, remember what the equation of a line is:

y = mx+b

Where:

m is the slope, and

b is the y-intercept

First, let's find what m is, the slope of the line...

The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.

For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:

So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (5,3), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=5 and y1=3.

Also, let's call the second point you gave, (-3,-1), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=-3 and y2=-1.

Now, just plug the numbers into the formula for m above, like this:

m=

-1 - 3 over

-3 - 5

or...

m=

-4 over

-8

or...

m=1/2

So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:

y=1/2x+b

Now, what about b, the y-intercept?

To find b, think about what your (x,y) points mean:

(5,3). When x of the line is 5, y of the line must be 3.

(-3,-1). When x of the line is -3, y of the line must be -1.

Because you said the line passes through each one of these two points, right?

Now, look at our line's equation so far: y=1/2x+b. b is what we want, the 1/2 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (5,3) and (-3,-1).

So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!.

You can use either (x,y) point you want..the answer will be the same:

(5,3). y=mx+b or 3=1/2 × 5+b, or solving for b: b=3-(1/2)(5). b=1/2.

(-3,-1). y=mx+b or -1=1/2 × -3+b, or solving for b: b=-1-(1/2)(-3). b=1/2.

See! In both cases we got the same value for b. And this completes our problem.

The equation of the line that passes through the points

(5,3) and (-3,-1)

is

y=1/2x+1/2

7 0
3 years ago
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