Answer:
Triangle PQR is a right triangle therefore you can use the pythagorean theorem to find the length of PR which is the same as the hypothenuse
Step-by-step explanation:
Theorem:
(QP)² + (QR)² = (PR)²
(6)² + (14)² = 232 ⇒ (PR)² = 232 then PR = √232 = 15.23
If PR is adjusted to 16 feet then we use the Pythagorean theorem again to find the height QR
(QR)² + (14)² = (16)²
(QR)² = 256 - 196 = 60 ⇒ QR = √60 = 7.75.
Answer:
y = -2(x+2)(x-1)/((x+3)(x-6)) = (-2x^2 -2x +4)/(x^2 -3x -18)
Step-by-step explanation:
A polynomial function will have a zero at x=a if it has a factor of (x-a). For the rational function to have zeros at x=-2 and x=1, the numerator factors must include (x+2) and (x-1).
For the function to have vertical asymptotes at x=-3 and x=6, the denominator of the rational function must have zeros there. That is, the denominator must have factors (x+3) and (x-6). Then the function with the required zeros and vertical asymtotes must look like ...
f(x) = (x+2)(x-1)/((x+3)(x-6))
This function will have a horizontal asymptote at x=1 because the numerator and denominator degrees are the same. In order for the horizontal asymptote to be -2, we must multiply this function by -2.
The rational function may be ...
y = -2(x +2)(x -1)/((x +3)(x -6))
If you want the factors multiplied out, this becomes
y = (-2x^2 -2x +4)/(x^2 -3x -18)
Answer: 2.308 .
Step-by-step explanation:
Let X denotes the number of earthquakes in SanFernando valley region of Los Angeles in 1994.
Given: 
Probability is 0.87 that there will be at least 15 earthquakes .
i.e. 
![\Rightarrow\ P(\dfrac{X-\mu}{\sigma}\geq\dfrac{15-17.6}{\sigma})=0.87\\\\ \Rightarrow\ P(Z\geq\dfrac{-2.6}{\sigma})=0.87\ \ \ [Z=\dfrac{X-\mu}{\sigma}]](https://tex.z-dn.net/?f=%5CRightarrow%5C%20P%28%5Cdfrac%7BX-%5Cmu%7D%7B%5Csigma%7D%5Cgeq%5Cdfrac%7B15-17.6%7D%7B%5Csigma%7D%29%3D0.87%5C%5C%5C%5C%20%20%5CRightarrow%5C%20P%28Z%5Cgeq%5Cdfrac%7B-2.6%7D%7B%5Csigma%7D%29%3D0.87%5C%20%5C%20%5C%20%5BZ%3D%5Cdfrac%7BX-%5Cmu%7D%7B%5Csigma%7D%5D)
Z-value corresponding to p-value 0.87 is -1.1263 .
So, 

Hence, the required standard deviation = 2.308 .
Answer:
26%
Step-by-step explanation:
percent change = (new number - old number)/(old number) * 100%
Here, the new number is £504, and the old number is £400.
percent change = (£504 - £400)/(£400) * 100% =
= £104/£400 * 100% = 0.26 * 100% = 26%
If w is real then we need ignore negative sign and consider it as a mod value. So the answer will be 2