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: Soft Drinks Orange: Two 24-packs for $18; one 24-pack for $10 Root Beer: One 24-pack for $12 Cream Soda: One 12-pack for $5 A consumer needs to purchase at least 50 soft drinks for a picnic. Which of the following combinations is the most cost-effective?

A. 2 packs of Orange and 1 pack of Cream Soda

B. 3 packs of Orange

C. 2 packs of Root Beer and 1 pack of Cream Soda

D. 5 packs of cream Soda

Answer Explanation

To find the cost-effective option, we need to find how much the consumer will spend for the given options:

2 packs of Orange and 1 pack of Cream Soda will cost $18+$5= $23

3 Packs of Orange will cost $18+$10=$28

2 packs of Root Beer and 1 pack of Cream Soda will cost 2($12)+$5=$29

5 packs of cream Soda will cost 5($5)=$25

From the above evaluation, the consumer will spend $23 for a cost effective package of soft drinks. Thus, 2 packs of Orange and 1 pack of Cream Soda will be cheaper to purchase compared to other options.
Q #3: A macaroni and cheese recipe calls for 1/3 cup of flour for every 1 1/5 cup of milk. To make a bigger batch, the chef uses 2 cups of flour. Which of the following would be the amount of milk needed for the bigger batch?

A. 7 1/5 cups

B. 2 2/5 cups

C. 3 8/15 cups

D. 6 cups

Answer Explanation

We are being asked to find the amount of milk needed. This is a proportion problem, which compares the amount of flour to that of milk. Letting x represent the amount of milk required, we set up the proportion with flour on the numerator and amount of milk in denominator as follows:

Change the mixed fraction of 1 1/5 into improper fraction as follows

The proportion equation becomes

Cross-multiply to solve for x

As an mixed fraction, 36/5 becomes 7 1/5. Therefore, 7 1/5 cups of milk are needed to make a big batch of 2 cups.