Answer:
θ = 36.86°
Step-by-step explanation:
Given that,
The shadow of a 60 foot pole is a 100 feet long.
We need to find the angle of elevation from the end of the shadow to the top of the pole.
Height, h = 60 foot
Hypotenuse, H = 100 feet
Using trigonometry to find it.
![\sin\theta=\dfrac{\text{Height}}{\text{Hypotenuse}}\\\\\sin\theta=\dfrac{60}{100}\\\\\theta=\sin^{-1}(\dfrac{60}{100})\\\\\theta=36.86^{\circ}](https://tex.z-dn.net/?f=%5Csin%5Ctheta%3D%5Cdfrac%7B%5Ctext%7BHeight%7D%7D%7B%5Ctext%7BHypotenuse%7D%7D%5C%5C%5C%5C%5Csin%5Ctheta%3D%5Cdfrac%7B60%7D%7B100%7D%5C%5C%5C%5C%5Ctheta%3D%5Csin%5E%7B-1%7D%28%5Cdfrac%7B60%7D%7B100%7D%29%5C%5C%5C%5C%5Ctheta%3D36.86%5E%7B%5Ccirc%7D)
So, the angle of elevation is 36.86 degrees.
The top 15% (85th percentile) is the cutoff value
![x](https://tex.z-dn.net/?f=x)
such that
![\mathbb P(X\le x)=\mathbb P\left(\dfrac{X-250}{40}\le\dfrac{x-250}{40}\right)=\mathbb P(Z\le z)=0.85](https://tex.z-dn.net/?f=%5Cmathbb%20P%28X%5Cle%20x%29%3D%5Cmathbb%20P%5Cleft%28%5Cdfrac%7BX-250%7D%7B40%7D%5Cle%5Cdfrac%7Bx-250%7D%7B40%7D%5Cright%29%3D%5Cmathbb%20P%28Z%5Cle%20z%29%3D0.85)
where
![z](https://tex.z-dn.net/?f=z)
is the corresponding cutoff for the standardized normal distribution. We have
![z\approx1.0364](https://tex.z-dn.net/?f=z%5Capprox1.0364)
, and so
Answer:
principal (p)=$1895
time (t)=4years
rate(r)=7.9%
Step-by-step explanation:
- compound interest amount=p((1+r/100)^t-1)=$1895((1+7.9/100)^4-1)=$1895×((1.355)-1)=$1895×(0.355)=$672.725
- simple interest=ptr/100=$1895×4×7.9/100=$598.82
Answer:
To find a complex conjugate, simply change the sign of the imaginary part (the part with the i). This means that it either goes from positive to negative or from negative to positive.
As a general rule, the complex conjugate of <span>a+bi</span> is <span>a−bi</span>.
Therefore, the complex conjugate of <span>3−2i</span> is <span>3+2i</span>.
Hope this helped!!... :D
Please correct me if I'm wrong!!.. :3
Answer:
y=60x+14
Step-by-step explanation:
60 is the slope that is going UP at a certain rate and then ur adding 14