Answer:
The probability that the first failure occurs among the five devices is given by
(a) 9 months =![\frac{9}{15} or =0.6](https://tex.z-dn.net/?f=%5Cfrac%7B9%7D%7B15%7D%20or%20%20%3D0.6)
(b) 12 months=![\frac{12}{15} or = 0.8](https://tex.z-dn.net/?f=%5Cfrac%7B12%7D%7B15%7D%20or%20%3D%200.8)
Step-by-step explanation:
probability is given as the; number of required outcome/ total number of possible outcome.
Answer:
sin(2θ) = 24/25
Explanation:
In order to find the value of sin 2θ, first, recall the double-angle formula for sine.
![\sin 2\theta=2\sin \theta\cos \theta](https://tex.z-dn.net/?f=%5Csin%202%5Ctheta%3D2%5Csin%20%5Ctheta%5Ccos%20%5Ctheta)
From the right-triangle:
![\begin{gathered} \sin \theta=\frac{\text{Opposite}}{\text{Hypotenuse}}=\frac{3}{5} \\ \cos \theta=\frac{\text{Adjacent}}{\text{Hypotenuse}}=\frac{4}{5} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Csin%20%5Ctheta%3D%5Cfrac%7B%5Ctext%7BOpposite%7D%7D%7B%5Ctext%7BHypotenuse%7D%7D%3D%5Cfrac%7B3%7D%7B5%7D%20%5C%5C%20%5Ccos%20%5Ctheta%3D%5Cfrac%7B%5Ctext%7BAdjacent%7D%7D%7B%5Ctext%7BHypotenuse%7D%7D%3D%5Cfrac%7B4%7D%7B5%7D%20%5Cend%7Bgathered%7D)
Substitute these values into the double-angle formula obtained earlier.
![\begin{gathered} \sin 2\theta=2\sin \theta\cos \theta \\ =2\times\frac{3}{5}\times\frac{4}{5} \\ =\frac{24}{25} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Csin%202%5Ctheta%3D2%5Csin%20%5Ctheta%5Ccos%20%5Ctheta%20%5C%5C%20%3D2%5Ctimes%5Cfrac%7B3%7D%7B5%7D%5Ctimes%5Cfrac%7B4%7D%7B5%7D%20%5C%5C%20%3D%5Cfrac%7B24%7D%7B25%7D%20%5Cend%7Bgathered%7D)
The exact value of sin(2θ) is 24/25.
X² + x¹ 11+1
--------- =. ------= 6
2. 2
y² + y¹. 5+(-3).
-------- = ---------- = 1
2. 2
So the midpoint is a) (6,1)
7/16 is your answer to this problem
The slope of the line that passes through (5, 4) and (-4,3) is ![\frac{1}{9}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B9%7D)
<u>Solution:</u>
Given, two points are (5, 4) and (-4, 3)
We have to find the slope of a line that passes through the above given two points.
Slope of a line that pass through
is given as:
![m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_%7B2%7D-y_%7B1%7D%7D%7Bx_%7B2%7D-x_%7B1%7D%7D)
![\text { Here, in our problem, } x_{1}=-4, y_{1}=3 \text { and } x_{2}=5, y_{2}=4](https://tex.z-dn.net/?f=%5Ctext%20%7B%20Here%2C%20in%20our%20problem%2C%20%7D%20x_%7B1%7D%3D-4%2C%20y_%7B1%7D%3D3%20%5Ctext%20%7B%20and%20%7D%20x_%7B2%7D%3D5%2C%20y_%7B2%7D%3D4)
![\text { slope } m=\frac{4-3}{5-(-4)}=\frac{1}{5+4}=\frac{1}{9}](https://tex.z-dn.net/?f=%5Ctext%20%7B%20slope%20%7D%20m%3D%5Cfrac%7B4-3%7D%7B5-%28-4%29%7D%3D%5Cfrac%7B1%7D%7B5%2B4%7D%3D%5Cfrac%7B1%7D%7B9%7D)
Hence, the slope the line that passes through the given points is ![\frac{1}{9}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B9%7D)