Answer:
a. 
b. 
Step-by-step explanation:
First, we need tot find a general expression for the amount of caffeine remaining in the body after certain time. As the problem states that every hour x percent of caffeine leaves the body, we must substract that percentage from the initial quantity of caffeine, by each hour passing. That expression would be:
Then, to find the amount of caffeine metabolized per hour, we need to differentiate the previous equation. Following the differentiation rules we get:
The rate is negative as it represents the amount of caffeine leaving the body at certain time.
To begin, we can simplify the expression's denominator by finding a common denominator between the denominators of the fractions in the denominator. To make them compatible, we can convert
into
:
Next, we can simplify:
Finally, to cancel the denominator within the denominator, we can multiply the whole expression by
, or 1:
The expression simplifies to
, or
as a mixed number.
Answer:
40 more kids chose baseball over basketball.
Step-by-step explanation:
The best way to go about this is to use benchmark percentages.
For baseball, 25% of 800 people chose that, so we can do 800/4 to get 200, so 200 students chose baseball
For basketball, we could do 800/5 but that isn't mental math, so we can do 10% of 800 is 80 and 80*2=160. So 40 more kids chose baseball over basketball.
Answer:
y = 1/3
Step-by-step explanation:
<u>Step 1: Factor</u>
9y^2 - 6y + 1 = 0
(3y - 1)(3y - 1) = 0
(3y - 1)^2 = 0
<u>Step 2: Solve for y</u>
3y - 1 + 1 = 0 + 1
3y / 3 = 1 / 3
y = 1/3
Answer: y = 1/3
