Answer:
So the number of total combinations is 35.
Step-by-step explanation:
We know that Ellen must take 4 courses this semester. She has a list of 3 math courses and 4 science courses.
Therefore, she have total 7 courses.
So, we calculate the number of combinations to choose 4 out of 7 courses.
We get:
So the number of total combinations is 35.
Answer:
About 0.6548 grams will be remaining.
Step-by-step explanation:
We can write an exponential function to model the situation. The standard exponential function is:
The original sample contained 510 grams. So, a = 510.
Each half-life, the amount decreases by half. So, r = 1/2.
For t, since one half-life occurs every 38 days, we can substitute t/38 for t, where t is the time in days.
Therefore, our function is:
One year has 365 days.
Therefore, the amount remaining after one year will be:
About 0.6548 grams will be remaining.
Alternatively, we can use the standard exponential growth/decay function modeled by:
The starting sample is 510. So, C = 510.
After one half-life (38 days), the remaining amount will be 255. Therefore:
Solving for k:
Thus, our function is:
Then after one year or 365 days, the amount remaining will be about: