Step-by-step explanation:
![M=\left[\begin{array}{ccc}1&-1/f_2\\0&1\end{array}\right] \left[\begin{array}{ccc}1&0\\d&0\end{array}\right] \left[\begin{array}{ccc}1&-1/f_1\\0&1\end{array}\right]\\=\left[\begin{array}{ccc}1&-1/f_2\\0&1\end{array}\right]\left[\begin{array}{ccc}1&-1/f_1\\d&-d/f_1\end{array}\right]\\=\left[\begin{array}{ccc}1-d/f_2&-1/f_1+d/f_1f_2\\d&-d/f_1\end{array}\right]\\\\|M|=[-d/f_1+d^2/f_1f_2]-[-d/f_1+d^2/f_1f_2]=0\\\\-1/f=M_{12}=-1/f_1+d/f_1f_2\\1/f=M_{12}=+1/f_1-d/f_1f_2\\](https://tex.z-dn.net/?f=M%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26-1%2Ff_2%5C%5C0%261%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%5C%5Cd%260%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26-1%2Ff_1%5C%5C0%261%5Cend%7Barray%7D%5Cright%5D%5C%5C%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26-1%2Ff_2%5C%5C0%261%5Cend%7Barray%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26-1%2Ff_1%5C%5Cd%26-d%2Ff_1%5Cend%7Barray%7D%5Cright%5D%5C%5C%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1-d%2Ff_2%26-1%2Ff_1%2Bd%2Ff_1f_2%5C%5Cd%26-d%2Ff_1%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%7CM%7C%3D%5B-d%2Ff_1%2Bd%5E2%2Ff_1f_2%5D-%5B-d%2Ff_1%2Bd%5E2%2Ff_1f_2%5D%3D0%5C%5C%5C%5C-1%2Ff%3DM_%7B12%7D%3D-1%2Ff_1%2Bd%2Ff_1f_2%5C%5C1%2Ff%3DM_%7B12%7D%3D%2B1%2Ff_1-d%2Ff_1f_2%5C%5C)
Simple. The answer is 3.2.
Answer:
Remember that the slope of perpendicular lines are negative reciprocals of each other.
Step-by-step explanation:
y = 1 - 2x the slope is -2 the value of the x term.
So the slope of the new line using point (- 1, 2) is 1/2.
Now use y = mx + b where y = -1, x = 2, and m = 1/2 .
y = mx + b
-1 = 1/2(2) + b solve for "b", the y-intersect
-1 = 1 + b
-2 = b
The line that is perpendicular to y = 1 - 2x is y = 1/2x - 2
The 85th percentile is the cutoff time

such that

In other words, the 85th percentile refers to the time needed to belong to the top 15% of the distribution; more generally, the

percentile is the top

of the distribution.
Anyway, to find this value of

, transform

to a random variable

with the standard normal distribution using

where

is the mean of

and

is the standard deviation of

.

Here

is used to denote the z-score corresponding to the cutoff time

. Referring to a z-score table, you find that this occurs for

. So,