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3 years ago

Find the binomial coefficient (4 2)

1 answer:

5 0

$\large\begin{array}{l} \mathsf{\dbinom{4}{2}=\dfrac{4!}{2!\cdot (4-2)!}}\\\\ \mathsf{\dbinom{4}{2}=\dfrac{4!}{2!\cdot 2!}}\\\\ \mathsf{\dbinom{4}{2}=\dfrac{4\cdot 3 \cdot \diagup\!\!\!\! 2!}{2!\cdot \diagup\!\!\!\! 2!}}\\\\ \mathsf{\dbinom{4}{2}=\dfrac{4\cdot 3}{2\cdot 1}}\\\\ \mathsf{\dbinom{4}{2}=\dfrac{12}{2}}\\\\ \boxed{\begin{array}{c}\mathsf{\dbinom{4}{2}=6}\end{array}}\quad\longleftarrow\quad\textsf{this is the answer.} \end{array}$

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Among 320 randomly selected airline travelers, the mean number of hours spent travelling per year is 24 hours and the standard d

Ostrovityanka [42]

The margin of error of the random selection is 0.29

The given parameters are:

$n = 320$ --- the sample size

$\sigma = 2.9$ --- the standard deviation

$\bar x = 24$ --- the mean

$\alpha = 90\%$ --- the confidence level.

The margin of error (E) is calculated as follows:

$E = z \times \sqrt{\frac{\sigma^2}{n}}$

So, we have:

$E = z \times \sqrt{\frac{3.2^2}{320}}$

$E = z \times \sqrt{\frac{10.24}{320}}$

The z-value for 90% confidence level is 1.645.

Substitute 1.645 for z

$E = 1.645 \times \sqrt{\frac{10.24}{320}}$

$E = 1.645 \times \sqrt{0.032}$

Take square roots

$E = 1.645 \times 0.1789$

Multiply

$E = 0.2943$

Approximate

$E = 0.29$

Hence, the margin of error is 0.29

Read more about margin of error at:

brainly.com/question/14396648

5 0

2 years ago

Read 2 more answers

How do i answer this?<br>3(m-2)=2(3m+3)

krek1111 [17]

3 (m - 2) = 2 (3m + 3) Use the Distributive Property on both sides
3m - 6 = 6m + 6 Subtract 6m from both sides
-3m - 6 = 6 Add 6 to both sides
-3m = 12 Divide both sides by -3
m = -4

8 0

3 years ago

Solve this by substitution

frozen [14]

Answer:

y= 1 and x=-2

Step-by-step explanation:

Since they both equal y, you can equal them to each other:

x + 3 = 2x + 5

Then solve:

x - x + 3 = 2x - x + 5

3 - 5 = x + 5 - 5

-2 = x

Substitute x in either equation to solve for y:

y = (-2) +3

y = 1

Or the other equation:

y = 2(-2) + 5

y = -4 + 5

y = 1

hope this helps :)

6 0

2 years ago

Solve the following system by any method. –8x – 8y = 0 –8x + 2y = –20

madam [21]

This one is simple since we already have the two x variables.equal. All we have to do is subtract the equations from one another to get the answer.
So i will subtract the left side by the other left side and the right side by the other right side

-8x - 8y -(-8x + 2y) = 0 -(-20)

distribute negative sign

-8x - 8y + 8x - 2y = 0 + 20

do the math
- 10y = 20
Y = -2

plug t into an equation
-8x -8 (-2) = 0

-8x + 16 = 0
-8x = -16
x = 2
answer (2, -2)

8 0

3 years ago

Will mark as brainliest! 40 points! Thanks!

n200080 [17]

When given a system of equations, the "solutions" are defined where two equations intersect, or meet.

A. The point where the lines p(x) and g(x) meet is (3, -1), and thus this is considered the solution set.

B. Because there are three lines in total, g(x) is able to intersect both lines one time, and so it has two pairs of solutions.

The first is (3, -1), which has already been established with p(x).

The second is (0, 5), and this is where it intersects with f(x).

C. The solution to f(x) = g(x) is 0, as this is the only x value where both equations are equal.

Hope my answer helped!

6 0

2 years ago

Read 2 more answers