Confused so help needed. On a number line where would 6/10 be located choose all answers that make a true statement 
1 answer:
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Answer:
Husband:
The husband will have 16.35 mg of caffeine in his body at 7 pm.
Woman:
The pregnant woman will have 51.33 mg of caffeine in her body at 7 pm.
Step-by-step explanation:
The amount of caffeine in the body can be modeled by the following equation:
In which C(t) is the amount of caffeine t hours after 8 am, C(0) is how much coffee they took and r is the rate the the amount of caffeine decreases in their bodies.
110 mg of caffeine at 8 am,
So
Husband
Half life of 4 hours. So
Applying ln to both sides
So for the husband
At 7 pm
7 pm is 11 hours after 8 am, so this is C(11)
The husband will have 16.35 mg of caffeine in his body at 7 pm.
Pregnant woman
Half life of 10 hours. So
Applying ln to both sides
At 7 pm
7 pm is 11 hours after 8 am, so this is C(11)
The pregnant woman will have 51.33 mg of caffeine in her body at 7 pm.
x = number of messages sent or received
y = total cost per month
Plan A costs $30 per month plus $0.10 per text message. So the cost for plan A is y = 0.10*x + 30. The portion 0.10*x represents just the cost of the 10 cents per message, and then we add on the fixed cost of $30 to get the total cost.
In a similar fashion, plan B's cost is y = 60. There is no cost per message, so we don't have to include x in the picture. The cost is a flat fee, which leads to a flat horizontal line graph (as shown in the attachment below)
Our two equations are: y = 0.10x+30 and y = 60. Let's use substitution to find x
y = 0.10x + 30
60 = 0.10x + 30 ... replace y with 60 (works because y = 60)
60-30 = 0.10x
30 = 0.10x
0.10x = 30
x = 30/0.10
x = 300
If you send or receive 300 messages, then both plans will cost the same. We can see this on the graph below where the two lines cross at (300,60). Note how plugging x = 300 into the first equation simplifies to y = 60.
