Answer:
Step-by-step explanation:
Triangle XYZ is a right angle triangle.
From the given right angle triangle
XZ represents the hypotenuse of the right angle triangle.
With ∠34 as the reference angle,
YZ represents the adjacent side of the right angle triangle.
XY represents the opposite side of the right angle triangle.
To determine x, we would apply the Cosine trigonometric ratio
Cos θ = opposite side/hypotenuse. Therefore,
Cos 34 = x/28
x = 28Cos34 = 28 × 0.8290
x = 23.212
To the nearest tenth, it becomes
23.2
I got 3.75. not sure if it’s right but hope i helped
Answer:
b
Step-by-step explanation:
The volume (V) of a sphere is calculated as
V = 
πr³ ( where r is the radius )
Here r = 3, thus
V = π × 3³
= π × 27 = 4π × 9 = 36π in³ → b
Answer:
Step-by-step explanation:
Area is half base × height
If area = 140 and height = 20 inches
base =140 ÷ 20 = 7 × 2 = 14 inches
Answer:
a) 7.79%
b) 67.03%
c) Cumulative Distribution Function
Step-by-step explanation:
We are given the following in the question:
where x is the duration of a call, in minutes.
a) P( calls last between 2 and 3 minutes)
![=\displaystyle\int^3_2 p(x)~ dx\\\\= \displaystyle\int^3_20.1e^{-0.1x}~dx\\\\=\Big[-e^{-0.1x}\Big]^3_2\\\\=-\Big[e^{-0.3}-e^{-0.2}\Big]\\\\= 0.0779\\=7.79\%](https://tex.z-dn.net/?f=%3D%5Cdisplaystyle%5Cint%5E3_2%20p%28x%29~%20dx%5C%5C%5C%5C%3D%20%5Cdisplaystyle%5Cint%5E3_20.1e%5E%7B-0.1x%7D~dx%5C%5C%5C%5C%3D%5CBig%5B-e%5E%7B-0.1x%7D%5CBig%5D%5E3_2%5C%5C%5C%5C%3D-%5CBig%5Be%5E%7B-0.3%7D-e%5E%7B-0.2%7D%5CBig%5D%5C%5C%5C%5C%3D%200.0779%5C%5C%3D7.79%5C%25)
b) P(calls last 4 minutes or more)
![=\displaystyle\int^{\infty}_4 p(x)~ dx\\\\= \displaystyle\int^{\infty}_40.1e^{-0.1x}~dx\\\\=\Big[-e^{-0.1x}\Big]^{\infty}_4\\\\=-\Big[e^{\infty}-e^{-0.4}\Big]\\\\=-(0- 0.6703)\\= 0.6703\\=67.03\%](https://tex.z-dn.net/?f=%3D%5Cdisplaystyle%5Cint%5E%7B%5Cinfty%7D_4%20p%28x%29~%20dx%5C%5C%5C%5C%3D%20%5Cdisplaystyle%5Cint%5E%7B%5Cinfty%7D_40.1e%5E%7B-0.1x%7D~dx%5C%5C%5C%5C%3D%5CBig%5B-e%5E%7B-0.1x%7D%5CBig%5D%5E%7B%5Cinfty%7D_4%5C%5C%5C%5C%3D-%5CBig%5Be%5E%7B%5Cinfty%7D-e%5E%7B-0.4%7D%5CBig%5D%5C%5C%5C%5C%3D-%280-%090.6703%29%5C%5C%3D%200.6703%5C%5C%3D67.03%5C%25)
c) cumulative distribution function
