Answer:
steps below
Step-by-step explanation:
post here 16 and 17, should be able to do 18 and 19 yourself
16.
y=-8 for x≤-6
y=-1/4 x + 2 for -4≤x≤4
y=4 for x>4
17.
y=-x-4 for x<-3
y=x+1 for -3≤x≤1
y=-6 for x>4
The sum of 5/30 + 4/6 would equal 25/30 because you would want to find a common denominator, which would be 30, but then you would want to simplify 25/30 because both the numerator and the denominator are both divisible by 5. so the final answer would be 5/6. Hope this helped! -Julia
Answer:
The possible values of c are 1 or 2. There are 13 hearts in a deck of cards and 52-13 = 39 cards that are not. There are a total of 52 cards to choose from, so the possibilities for each value of c are found by dividing the number of results for that value by 52. (Image 1)
Histogram is attached for your reference.
Answer:
a. dQ/dt = -kQ
b. 
c. k = 0.178
d. Q = 1.063 mg
Step-by-step explanation:
a) Write a differential equation for the quantity Q of hydrocodone bitartrate in the body at time t, in hours, since the drug was fully absorbed.
Let Q be the quantity of drug left in the body.
Since the rate of decrease of the quantity of drug -dQ/dt is directly proportional to the quantity of drug left, Q then
-dQ/dt ∝ Q
-dQ/dt = kQ
dQ/dt = -kQ
This is the required differential equation.
b) Solve your differential equation, assuming that at the patient has just absorbed the full 9 mg dose of the drug.
with t = 0, Q(0) = 9 mg
dQ/dt = -kQ
separating the variables, we have
dQ/Q = -kdt
Integrating we have
∫dQ/Q = ∫-kdt
㏑Q = -kt + c

when t = 0, Q = 9

So, 
c) Use the half-life to find the constant of proportionality k.
At half-life, Q = 9/2 = 4.5 mg and t = 3.9 hours
So,

taking natural logarithm of both sides, we have
d) How much of the 9 mg dose is still in the body after 12 hours?
Since k = 0.178,

when t = 12 hours,

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