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.
Answer:
Therefore, the probability is P=0.74.
Step-by-step explanation:
We know that Jose estimates that if he leaves his car parked outside his office all day on a weekday, the chance that he will get a parking ticket is 26%.
Therefore the probability that he will get a parking ticket is P1=0.26.
We calculate the probability that he will not get a parking ticket.
We get:
P=1-P1
P=1-0.26
P=0.74
Therefore, the probability is P=0.74.
Answer:
21
Step-by-step explanation:
Let x represent the number of dimes and y represent the number of nickels. The total number of coins is 37; this gives us the equation
x+y = 37
Each dime is worth ten cents, or 0.10, and each nickel is worth five cents, or 0.05. The total amount of money is given by
0.10x+0.05y = 2.65
This gives us the system
To solve this, we will use substitution. We will isolate x in the first equation:
x+y=37
Subtract y from each side:
x+y-y = 37-y
x = 37-y
Substitute this into the second equation:
0.10(37-y)+0.05y = 2.65
Using the distributive property,
0.10(37)-0.10(y)+0.05y = 2.65
3.70-0.10y+0.05y = 2.65
Combining like terms,
3.70-0.05y = 2.65
Subtract 3.70 from each side,
3.70-0.05y-3.70 = 2.65-3.70
-0.05y = -1.05
Divide both sides by -0.05:
-0.05y/-0.05 = -1.05/-0.05
y = 21
There were 21 nickels.
For a parabola that opens upward, it must be a quadratic equation whose coefficient of x2 is a positive number.
So, I'll say x2+5x+6.
Answer:
3/14
Step-by-step explanation:
6/7 ÷ 4
Copy dot flip
6/7 * 1/4
Rewriting
6/4 * 1/7
Divide the top and the bottom of the first fraction by 2
3/2 * 1/7
3/14
