A circle has an area of 169 π in2. Which of the following is the circumference of the circle in terms of pi ( )?

A. 13 π in

B. 26 π in

C. 7.5 π in

D. 20 π in

Answer Explanation:

We need to find the radius of the circle in order to find circumference of the circle. If we let r to be radius of the circle, then

Substituting 169π in place of area

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

The radius of the circle from the given area is 13 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 appropriate unit of a measure to express the weight of a mobile phone?

A. Liter

B. Milliliter

C. Gram

D. Milligram

Answer Explanation

Here, we are required to find the unit of measuring mass. The SI unit of mass is kilogram but other derived units are grams, milligrams, microgram and more.

A kilogram is a large quantity for measuring heavier objects but grams can used to measure small and light objects such as the mass of the mobile phone. Therefore, gram is the appropriate unit for measuring weight of a mobile phone.
Q #2: A circle has an area of 169 π in2. Which of the following is the circumference of the circle in terms of pi ( )?

A. 13 π in

B. 26 π in

C. 7.5 π in

D. 20 π in

Answer Explanation

We need to find the radius of the circle in order to find circumference of the circle. If we let r to be radius of the circle, then

Substituting 169π in place of area

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

The radius of the circle from the given area is 13 in. and the circumference of the circle is given by the relation:
Q #3: Which of the following is the length of the unknown leg of a right triangle that has one leg length of 10 feet and a hypotenuse of 24 feet? (Round to the nearest tenth.)

A. 21.8 feet

B. 25 feet

C. 13.6 feet

D. 17.7 feet

Answer Explanation

Let the unknown length of the x. The resulting triangle is shown below.

We use the Pythagoras theorem as follows to find the unknown value of x as:

Thus, the value of unknown side of the triangle is 21.8 feet.
Q #4: The American with Disabilities Act (ADA) requires that the slope of a wheelchair ramp be no greater than 1:12. Which of the following is the minimum length of a ramp needed to provide access to a door that is 1.5 feet above the sidewalk?

A. 12 feet

B. 4.5 feet

C. 3 feet

D. 18 feet

Answer Explanation

We use the given slope to find the minimum length of the ramp. In this case, slope is the ratio of height to length of the lamp. Thus,

If we let x be the minimum length of the ramp. Then,

Substituting the value of slope into the above equation results in,

Solve for value of x by cross-products

X = 18 Feet

Thus, the minimum length of the ramp needed to provide access to a door that is 1.5 high is 18 feet.
Q #5: Which of the following is an appropriate unit of measure to express the length of a chair?

A. Centimeters

B. Kilometers

C. Micrometers

D. Milligrams

Answer Explanation

The length of the chair could be appropriately measured in centimeters. Kilometers are used to measure long distances while micrometers could be used to measure the length of small microorganism in microbiology lab. However, milligrams are used to measure the masses of small quantities.
Q #6: Which of the following is the independent variable in the equation below? A(f) = 92 + 2f

A. f

B. 2

C. A

D. 92

Answer Explanation

Given the equation A(f)=92+2f

To find the value of A(f), we need to manipulate the value of f. In this case, f is the independent variable while A(f) is the dependent variable.
Q #7: Which of the following is the decimal form of 98.2%?

A. 9.82

B. 9820

C. 982

D. 0.982

Answer Explanation

Percentages are fractions with denominator equal to 100. To convert a percent to decimal form, divide the value by 100.

The decimal form of 98.2% is 0.982.
Q #8: Which of the following is the value of x in the equation below

A. x= -4 or x=2

B. x= -2 or x=3

C. x =-2 or x= 4

D. x= -2 or x= 1

Answer Explanation

we find the value of x by applying the absolute conditions to the given equation.

First, add 2 to both sides of equation

The absolute conditions are:

If , a>0, then u=a or u=-a

In this case a=10, which is greater 0.

The first condition becomes

Add 2 to both sides of the equation

Divide both sides by 4

The second condition becomes

Add 2 to both sides of the equation

Divide both sides by 4

Then, the value of x is 3 or -2.
Q #9: Soft Drinks Orange Two 24-packs for $10; one 24-pack for $8 Root Beer One 24-pack for $11 Cream Soda One 12-pack for $6 A consumer needs to purchase at least 50 soft drinks for a picnic. Which of the following combinations is the most cost-effective?

A. 1 two-24 packs of Orange and 2 packs of Cream Soda

B. 3 one 24-pack of Orange

C. 1 packs of Root Beer and 3 packs of Cream Soda

D. 4 packs of cream Soda

Answer Explanation

To find the cheapest option, we determine how much the consumer will spend in each option given above:

1 two-24 packs of Orange and 2 pack of Cream Soda=1($10)+2($6)=$10+$12=$22

3 one 24-pack of Orange=3($8)=$24

1 pack of Root Beer and 3 packs of Cream Soda=1($11)+3($6)=$11+$18=$29

4 packs of cream Soda=4($6)=$24

The cheapest option is spending $22 and the most expensive one is $29. Thus, the consumer should consider buying 1 two-24 packs of Orange and 2 packs of Cream Soda.
Q #10: There are 1200 students enrolled in four allied health programs at a local community college. The percent students in each program are displayed in the pie chart. Which of the following is the number of students enrolled in the radiologic technology program?

A. 216

B. 504

C. 228

D. 252

Answer Explanation

We are asked to find the number of students enrolled in the radiologic program using the information provided on the pie chart.

If we let x represent the number of students enrolled in the radiologic program, we set a proportion equation with number of students on the numerator and percentages on the denominator.

Total percent in the pie chart adds to 100%, which equals 1200 students. Then, 21% will represent

We solve the value of x by cross-multiplying the equation above.

Therefore, 252 students will enroll for a radiologic program.