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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:
In 3 seconds the cup is filled with <u>.</u>
Step-by-step explanation:
Given:
2 seconds = water
We need to find the percent of the cup that is filled with water after 3 seconds.
Solution:
Now Given:
The cup was filled at a constant rate.
First we will find the volume of water filled in the cup after 1 seconds.
2 seconds = water
1 seconds = Volume of water filled in 1 second.
By Using Unitary method we get;
Volume of water filled in 1 second =
Now we will find the volume of water filled in the cup after 3 seconds.
1 second = of water is filled
3 seconds = volume of water filled in the cup after 3 seconds
Again by using Unitary method we get;
volume of water filled in the cup after 3 seconds =
Hence In 3 seconds the cup is filled with .
To find the percent of the cup filled with water after 3 seconds we would required the dimensions of the cup which is not available in the question.
There are two ways to work this out: normal variables or using "imaginary" numbers.
Normal variables:
![(7+2i)(3-i)\\(7*3)+[7*(-i)]+(3*2i)+[2i*(-i)]\\21-7i+6i-2i^{2}\\\\21-i-2i^{2}](https://tex.z-dn.net/?f=%20%287%2B2i%29%283-i%29%5C%5C%287%2A3%29%2B%5B7%2A%28-i%29%5D%2B%283%2A2i%29%2B%5B2i%2A%28-i%29%5D%5C%5C21-7i%2B6i-2i%5E%7B2%7D%5C%5C%5C%5C21-i-2i%5E%7B2%7D)
Imaginary numbers:
Using the result from earlier:
Now since
, then the expression becomes:
Normal variables:
Imaginary numbers:
Using the result from earlier:
Now since