Answer:
His homework isn't finished.
Step-by-step explanation:
As in this sentence: "If the trash is taken out, and Theodore is watching television, then he has finished his homework.". It says that if trash is taken out, then Theodore has not finished his homework He has just taken out the trash.
Answer:
a) P(X = 0) = 0.5997
b) P(X = 9) = 0.0016
c) P(X = 8) = 0.0047
d) P(X = 5) = 0.4018
Step-by-step explanation:
These following problem are examples of the binomial probability distribution.
Binomial probability
Th binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
![P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.%5Cpi%5E%7Bx%7D.%281-%5Cpi%29%5E%7Bn-x%7D)
In which
is the number of different combinatios of x objects from a set of n elements, given by the following formula.
![C_{n,x} = \frac{n!}{x!(n-x)!}](https://tex.z-dn.net/?f=C_%7Bn%2Cx%7D%20%3D%20%5Cfrac%7Bn%21%7D%7Bx%21%28n-x%29%21%7D)
And
is the probability of X happening.
(a) for n = 4 and π = 0.12, what is P(X = 0)?
![P(X = 0) = C_{4,0}.(0.12)^{0}.(0.88)^{4} = 0.5997](https://tex.z-dn.net/?f=P%28X%20%3D%200%29%20%3D%20C_%7B4%2C0%7D.%280.12%29%5E%7B0%7D.%280.88%29%5E%7B4%7D%20%3D%200.5997)
(b) for n = 10 and π = 0.40, what is P(X = 9)?
![P(X = 9) = C_{10,9}.(0.4)^{9}.(0.6)^{1} = 0.0016](https://tex.z-dn.net/?f=P%28X%20%3D%209%29%20%3D%20C_%7B10%2C9%7D.%280.4%29%5E%7B9%7D.%280.6%29%5E%7B1%7D%20%3D%200.0016)
(c) for n = 10 and π = 0.50, what is P(X = 8)?
![P(X = 8) = C_{10,8}.(0.5)^{8}.(0.5)^{2} = 0.0047](https://tex.z-dn.net/?f=P%28X%20%3D%208%29%20%3D%20C_%7B10%2C8%7D.%280.5%29%5E%7B8%7D.%280.5%29%5E%7B2%7D%20%3D%200.0047)
(d) for n = 6 and π = 0.83, what is P(X = 5)?
![P(X = 5) = C_{6,5}.(0.83)^{5}.(0.17)^{1} = 0.4018](https://tex.z-dn.net/?f=P%28X%20%3D%205%29%20%3D%20C_%7B6%2C5%7D.%280.83%29%5E%7B5%7D.%280.17%29%5E%7B1%7D%20%3D%200.4018)
Answer:
x = 100°
y = 125°
z = 55°
Step-by-step explanation:
A straight line is 180°
A triangle is 180°
Solve in this order:
X: 180 - 80 = 100
Z: 180 - 80 - 45 = 55
Y: 180 - 55 = 125
Answer:
$5.29
Step-by-step explanation:
If a total of 6 gloves are $31.74, you divide by the number of gloves (6) to get your answer
31.74/6= 5.29
Answer:
An equation in standard form for the line is:
![\frac{5}{2}x-y=-4](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B2%7Dx-y%3D-4)
Step-by-step explanation:
Given the points
The slope between two points
![\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5Cmathrm%7BSlope%5C%3Abetween%5C%3Atwo%5C%3Apoints%7D%3A%5Cquad%20%5Cmathrm%7BSlope%7D%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
![\left(x_1,\:y_1\right)=\left(-2,\:-1\right),\:\left(x_2,\:y_2\right)=\left(0,\:4\right)](https://tex.z-dn.net/?f=%5Cleft%28x_1%2C%5C%3Ay_1%5Cright%29%3D%5Cleft%28-2%2C%5C%3A-1%5Cright%29%2C%5C%3A%5Cleft%28x_2%2C%5C%3Ay_2%5Cright%29%3D%5Cleft%280%2C%5C%3A4%5Cright%29)
![m=\frac{4-\left(-1\right)}{0-\left(-2\right)}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B4-%5Cleft%28-1%5Cright%29%7D%7B0-%5Cleft%28-2%5Cright%29%7D)
![m=\frac{5}{2}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B5%7D%7B2%7D)
Writing the equation in point-slope form
As the point-slope form of the line equation is defined by
![y-y_1=m\left(x-x_1\right)](https://tex.z-dn.net/?f=y-y_1%3Dm%5Cleft%28x-x_1%5Cright%29)
Putting the point (-2, -1) and the slope m=1 in the line equation
![y-\left(-1\right)=\frac{5}{2}\left(x-\left(-2\right)\right)](https://tex.z-dn.net/?f=y-%5Cleft%28-1%5Cright%29%3D%5Cfrac%7B5%7D%7B2%7D%5Cleft%28x-%5Cleft%28-2%5Cright%29%5Cright%29)
![y+1=\frac{5}{2}\left(x+2\right)](https://tex.z-dn.net/?f=y%2B1%3D%5Cfrac%7B5%7D%7B2%7D%5Cleft%28x%2B2%5Cright%29)
![y=\frac{5}{2}x+4](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B5%7D%7B2%7Dx%2B4)
Writing the equation in the standard form form
As we know that the equation in the standard form is
![Ax+By=C](https://tex.z-dn.net/?f=Ax%2BBy%3DC)
where x and y are variables and A, B and C are constants
so
![y=\frac{5}{2}x+4](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B5%7D%7B2%7Dx%2B4)
![\frac{5}{2}x-y=-4](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B2%7Dx-y%3D-4)
Therefore, an equation in standard form for the line is:
![\frac{5}{2}x-y=-4](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B2%7Dx-y%3D-4)