Answer:
B. (-1, 2)
Step-by-step explanation:
A piecewise-defined function may be discontinuous at the boundaries of its pieces, and it may be discontinuous if it is undefined anywhere within one of its pieces. So, you need to check all of these possibilities.
The boundary locations are x = -1, 0, and 4.
At x=-1, the function has the value e^-1 on one side of the boundary and -1 on the other side, so is discontinuous at x=-1. This rules out choice A.
At x=0, the function has the value 0 on both sides of the boundary, so it is continuous there.
At x=4, the function has the value 10 on one side of the boundary and the value cos(12) on the other side, so is discontinuous at x=4.
In the piece between 0 and 4, the function is defined as 5x/(x-2), so will be undefined where the denominator is zero, at x=2.
__
In summary, the function is discontinuous at x=-1, x=2, x=4. So, any interval containing these x-values can be ruled out. The only remaining possibility is ...
B. (-1, 2)
6 pints = .75 gallon
4 cups = .25 gallon
so if you add .75 and .25, it should equal 1 gallon.
Answer:
-$9.6
Step-by-step explanation:
X : ___ 1000 ____600 ____300 ___200
P(x): __ 1/1000 _ 2/1000 _ 2/1000 _ 5/1000
Expected winning per ticket :
Σ(X * p(X)) = [(1000 * 1/1000) + (600 * 2/1000) + (300 * 2/1000) + (200 * 5/1000) - price per ticket
= 1 + 1.2 + 0.6 + 1 - 7
= 3.8 - 7
= - $3.2
Expextwd winning if 3 tickets Is purchased :
3 * - 3.2= - $9.6
The answer is C. m∠1 + m∠4 = 180°
Let x be the distance of the additional water stations from the starting line.
We want on that is 1.5 miles behind the 8-mile water station, and one that is 1.5 miles ahead. The following absolute value function describes x:
|x-1.5| = 8
Two numbers comply: x= 9.5 and 6.5.
The additional water stations will be 6.5 and 9.5 miles from the starting line.
