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3 years ago

What is the equation of the line that passes through (4, -1) and (-2, 3)?

Mathematics

1 answer:

Mrac [35]3 years ago

7 0

Answer:

2x + 3y - 5 = 0

Step-by-step explanation:

(4 , -1) & (-2,3)

$Slope =\frac{y_{2}-y_{1}}{x_{2}-x_1}}\\\\=\frac{3-[-1]}{-2-4}\\\\=\frac{3+1}{-6}\\\\=\frac{4}{-6}\\\\=\frac{-2}{3}$

m = -2/3; (4 , -1)

y - y1 = m(x - x1)

$y - [-1]= \frac{-2}{3}(x-4)\\\\y + 1 =\frac{-2}{3}x -4*\frac{-2}{3}\\\\y + 1 =\frac{-2}{3}x+\frac{8}{3}$

Multiply the equation by 3

3y + 3 = -2x + 8

3y = -2x + 8 - 3

3y = -2x + 5

2x + 3y - 5 = 0

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Find the mean, variance &a standard deviation of the binomial distribution with the given values of n and p.

MrMuchimi

A random variable following a binomial distribution over $n$ trials with success probability $p$ has PMF

$f_X(x)=\dbinom nxp^x(1-p)^{n-x}$

Because it's a proper probability distribution, you know that the sum of all the probabilities over the distribution's support must be 1, i.e.

$\displaystyle\sum_xf_X(x)=\sum_{x=0}^n\binom nxp^x(1-p)^{n-x}=1$

The mean is given by the expected value of the distribution,

$\mathbb E(X)=\displaystyle\sum_xf_X(x)=\sum_{x=0}^nx\binom nxp^x(1-p)^{n-x}$
$\mathbb E(X)=\displaystyle\sum_{x=1}^nx\frac{n!}{x!(n-x)!}p^x(1-p)^{n-x}$
$\mathbb E(X)=\displaystyle\sum_{x=1}^n\frac{n!}{(x-1)!(n-x)!}p^x(1-p)^{n-x}$
$\mathbb E(X)=\displaystyle np\sum_{x=1}^n\frac{(n-1)!}{(x-1)!((n-1)-(x-1))!}p^{x-1}(1-p)^{(n-1)-(x-1)}$
$\mathbb E(X)=\displaystyle np\sum_{x=0}^n\frac{(n-1)!}{x!((n-1)-x)!}p^x(1-p)^{(n-1)-x}$
$\mathbb E(X)=\displaystyle np\sum_{x=0}^n\binom{n-1}xp^x(1-p)^{(n-1)-x}$
$\mathbb E(X)=\displaystyle np\sum_{x=0}^{n-1}\binom{n-1}xp^x(1-p)^{(n-1)-x}$

The remaining sum has a summand which is the PMF of yet another binomial distribution with $n-1$ trials and the same success probability, so the sum is 1 and you're left with

$\mathbb E(x)=np=126\times0.27=34.02$

You can similarly derive the variance by computing $\mathbb V(X)=\mathbb E(X^2)-\mathbb E(X)^2$ , but I'll leave that as an exercise for you. You would find that $\mathbb V(X)=np(1-p)$ , so the variance here would be

$\mathbb V(X)=125\times0.27\times0.73=24.8346$

The standard deviation is just the square root of the variance, which is

$\sqrt{\mathbb V(X)}=\sqrt{24.3846}\approx4.9834$

7 0

3 years ago

−3=z−8<br><br> Find what Z is

PolarNik [594]

Answer:

z=5

Trust me I don't know how to explain it.

6 0

3 years ago

Read 2 more answers

The temperature at noon was -17 degrees at 6 pm the temperature was -14 degrees. What was the change in temperature degrees?

irina [24]

Answer: the change in tempature was -3 degrees

Step-by-step explanation: hope this helps

5 0

2 years ago

I dont want you to answer question for me, i have already answered it as shown in the picture. I want you to let me know if i ha

Mashutka [201]

Answer:

$\begin{equation}
\sqrt{3}-1,2 \sqrt{10} \div 5, \sqrt{14}, 3 \sqrt{2}, \sqrt{19}+1,6
\end{equation}$

Explanation:

Given the irrational numbers:

$3 \sqrt{2}, \sqrt{3}-1, \sqrt{19}+1,6$, $2 \sqrt{10} \div 5,\sqrt{14}$

In order to arrange the numbers from the least to the greatest, we convert each number into its decimal equivalent.

$\begin{gathered} 3\sqrt{2}=3\times1.414\approx4.242 \\ \sqrt{3}-1\approx1.732-1=0.732 \\ \sqrt{19}+1\approx4.3589+1=5.3589 \\ 6=6 \\ 2\sqrt{10}\div5=2(3.1623)\div5=1.2649 \\ \sqrt{14}=3.7147 \end{gathered}$

Finally, sort these numbers in ascending order..

$\begin{gathered} \sqrt{3}-1\approx1.732-1=0.732 \\ 2\sqrt{10}\div5=2(3.1623)\div5=1.2649 \\ \sqrt{14}=3.7147 \\ 3\sqrt{2}=3\times1.414\approx4.242 \\ \sqrt{19}+1\approx4.3589+1=5.3589 \\ 6=6 \end{gathered}$

The given numbers in ascending order is:

$\begin{equation}
\sqrt{3}-1,2 \sqrt{10} \div 5, \sqrt{14}, 3 \sqrt{2}, \sqrt{19}+1,6
\end{equation}$

Note: In your solution, you can make the conversion of each irrational begin on a new line.

8 0

11 months ago

HELP APPRECIATED <br><br> WILL GIVE BRAINLIEST:))

soldi70 [24.7K]

Answer:

2 1/2= 2 3/6

7 1/6 + 2 3/6 = 9 4/6= 9 2/3

hope this helps!

Please give the brainliest

Step-by-step explanation:

7 0

2 years ago