10+3-5=8
That would be how to break it apart
Answer:
The right answer is:
(a) -10.67
(b) 0.7986
Step-by-step explanation:
(a)
According to the question,
<u>X P(X) X.P(X) X2.P(X)</u>
<u>12130 0.002 24.26 294274</u>
<u>-35 0.998 -34.93 1222.55</u>
Now,
![\Sigma x.P(x) = -10.67](https://tex.z-dn.net/?f=%5CSigma%20x.P%28x%29%20%3D%20-10.67)
or,
![\Sigma x^2.P(x) = 295496.35](https://tex.z-dn.net/?f=%5CSigma%20x%5E2.P%28x%29%20%3D%20295496.35)
hence,
The mean will be:
![\Sigma x.P(x) = -10.67](https://tex.z-dn.net/?f=%5CSigma%20x.P%28x%29%20%3D%20-10.67)
(b)
According to the question,
n = 12
p = 0.125
q = 1 - p
= 0.875
Now,
⇒ ![P(X=x) = \binom{n}{x} p^x q^{n-x}](https://tex.z-dn.net/?f=P%28X%3Dx%29%20%3D%20%5Cbinom%7Bn%7D%7Bx%7D%20p%5Ex%20q%5E%7Bn-x%7D)
By substituting the values, we get
⇒ ![P(X \geq 1)=1-(\binom{12}{0} 0.125^0. 0.875^{12-0})](https://tex.z-dn.net/?f=P%28X%20%5Cgeq%201%29%3D1-%28%5Cbinom%7B12%7D%7B0%7D%200.125%5E0.%200.875%5E%7B12-0%7D%29)
⇒ ![=1-(1 (0.125^0) (0.875^{12}))](https://tex.z-dn.net/?f=%3D1-%281%20%280.125%5E0%29%20%280.875%5E%7B12%7D%29%29)
⇒ ![=1-(1(1.0)(0.2014))](https://tex.z-dn.net/?f=%3D1-%281%281.0%29%280.2014%29%29)
⇒ ![=1-(0.2014)](https://tex.z-dn.net/?f=%3D1-%280.2014%29)
⇒
<span>Slope intercept form is always y=mx+b where your
m is your slope and your b is your y-intercept. Knowing this we first need to put your equation into slope intercept form. to do this all we have to do is subtract everything except why across an equal sign to get y=-6x+4. Now all you have to do is figure out what the 'b' is to know that the y-intercept is 4</span>
- Triangle Inequality Theorem: States that the sum of any two sides of a triangle is greater than the length of the third side;
![A+B>C\\B+C>A\\A+C>B](https://tex.z-dn.net/?f=%20A%2BB%3EC%5C%5CB%2BC%3EA%5C%5CA%2BC%3EB%20)
So for this, we are applying the triangle inequality theorem. If any of the inequalities are not true, then this cannot be a triangle. (Let A = 7.7, B = 4.0, and C = 1.7)
![7.7+4.0>1.7\\11.7>1.7\ \textsf{(true)}\\\\4.0+1.7>7.7\\5.7>7.7\ \textsf{(false)}\\\\7.7+1.7>4.0\\9.4>4.0\ \textsf{(true)}](https://tex.z-dn.net/?f=%207.7%2B4.0%3E1.7%5C%5C11.7%3E1.7%5C%20%5Ctextsf%7B%28true%29%7D%5C%5C%5C%5C4.0%2B1.7%3E7.7%5C%5C5.7%3E7.7%5C%20%5Ctextsf%7B%28false%29%7D%5C%5C%5C%5C7.7%2B1.7%3E4.0%5C%5C9.4%3E4.0%5C%20%5Ctextsf%7B%28true%29%7D%20)
<u>Since the second inequality is false, these lengths cannot form a triangle.</u>