<em>a</em> = 8 - a train arrives at the station once every 8 minutes, so for any given 8 minute interval, a randomly selected train has uniform probability of arriving at the station at some point in this time.
<em>f(x)</em> = 1/8 - the area under the graph of <em>f(x)</em> must be equal to 1. This area corresponds to a rectangle with length <em>a</em> = 8 and height <em>x</em> such that 8<em>x</em> = 1. Solving for <em>x</em> gives 1/8.
<em>P</em> = 5/8 - this is equal to the area under the graph over the interval [0, 5], which is the area of a rectangle with length 5 and height 1/8.
X=33
Image of my work is attached
Answer:
(-1, -1) and (2, 2)
Step-by-step explanation:
Substitute for y in the first equation and solve the quadratic.
x = x^2 -2
x^2 -x -2 = 0 . . . . subtract x
(x -2)(x +1) = 0 . . . .factor
Solutions are the values of x that make these factors be zero:
x = 2, x = -1
Since y=x, the solutions are ...
(x, y) = (-1, -1) and (2, 2)
The employee discount is 30% off. Here's the process to find this answer:
Calculate the difference between the original price and the discounted price. We're trying to find the percentage of the discount, not the percentage 38.50 is of 55.
55 - 38.5 = 16.5
Multiply the difference by 100 as part of the percentage formula. (is over of is equal to the percentage over one hundred)
16.5 * 100 = 1,650
Divide your result by 55 as the final part of the percentage formula.
1,650 / 55 = 30