A recent study reported that 40% of community college students in the U.S. Receive federal loans to pay for college tuition and
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Answer: 167
Step-by-step explanation: To find the 76th term of this arithmetic sequence, we will be using our explicit formula which is shown below.
Since we want to determine the 76th term, we are going
to substitute 76 in for <em>n</em> in our explicit formula.
Then, will be our first term in our sequence which is 17.
Lastly, <em>d</em> is our common difference or the difference between each of the terms in our arithmetic sequence which is 2.
So we have .
Now we have all the information we need. Just simplify from here.
Make sure to apply order of operations because this is where many
students make mistakes. Inside the parentheses first!
(76 - 1) is going to be 75.
So we have .
Then, we have to make sure we multiply before we add.
So (75)(2) is going to give us 150.
So we have .
Now just add to find that .
So the 76th term is 167.
<u>Given</u>:
Given that the radius of the circle is 2 inches.
We need to determine the area of the remaining square.
<u>Area of a square:</u>
Given that each circle has a radius of 2 inches.
Then, the diameter of each circle is 4 inches.
Hence, the side length of the square is 2 × 4 = 8 inches.
The area of the square is given by
Thus, the area of the square is 64 square inches.
<u>Area of the four circles:</u>
The area of one circle is given by
Substituting r = 2, we have;
Thus, the area of one circle is 4π in²
The area of 4 circles is 4 × 4π =16π in²
Hence, the area of the 4 circles is 16π in²
<u>Area of the remaining square:</u>
The area of the remaining square is given by
Area = Area of the square - Area of four circles.
Substituting the values, we get;
Thus, the area of the remaining square is (64 - 16π) in²
Hence, Option c is the correct answer.