A circle has an area of 49 in2. Which of the following is the circumference of the circle in terms of pi ( )?

A. 7 π in

B. 14 π in

C. 28 π in

D. 3.5 π in

Answer Explanation:

We need to find the circumference of the circle from the given area.

To find the circumference, we need to find the radius of the circle from the given area.

Let r be the radius of the circle, and the area of the circle is given by

Substituting the value of area in the above equation becomes

Dividing both sides by pi and taking square root on both sides yields

The radius of the circle is 7 in. and the circumference of the circle is given by the relation:

Therefore, the Correct Answer is B.

Q #1: Which of the following is the length of the unknown leg of a right triangle that has one leg length of 8 feet and a hypotenuse of 12 feet? (Round to the nearest tenth.)

A. 4 feet

B. 14.4 feet

C. 8.9 feet

D. 40 feet

Answer Explanation

We are asked to find the one of the lengths of a right-angled triangle, we use the Pythagoras theorem to find the unknown length.

First, we label the triangle as below and let the unknown length be x.

Then, we apply the Pythagoras theorem to find the value of x as:

The value of the unknown length is approximately 8.9 feet.
Q #2: Simplify the expression above. Which of the following is correct?

A. 6

B. 8

C. 1

D. 12

Answer Explanation

We follow the order of operations to solve the given expression.

First, we start with the numerator and solve it as follows

[2(3+5*3)]

We start with multiplication in inner brackets, 5*3=15. The expression becomes

[2(3+15)]

Then, we conduct the addition of 3+15=18. Then, the expression yields

[2(18)]=2*18=36

Now, we solve for denominator, which is 12/2=6.

Thus, the expression is reduced into

The expression reduces into 6.
Q #3: As the number of credit hours a student takes in a semester increases, the amount of tuition, the amount of access fees, and the number of student loans available also increase. Which of the following is the independent variable?

A. Amount of access fees

B. Amount of tuition

C. Number of student loans available

D. Number of credit hours

Answer Explanation

A change in number of credit hours result in a change in the amount of access fees, amount of tuition, and availability of student loans. Thus, number of credit hours is the independent variable.