TEAs Test Math

An occupational therapist uses a spherical medicine ball in mobility exercises. The diameter of the ball is 43 feet. What is its approximate volume? (Use π = 3.14. The volume of a sphere of radius R is 43πR3.)

1.24 cubic feet (The radius of the sphere is R=12(43)=23 foot. So, the volume is 43π(23)3=43π⋅827≈43(3.14)827≈1.24 feet.)

A patient's IV drips at a rate of 25 mL per minute. What is this rate in cL per second?

1/240 cL per second (Use the facts that 1 cL = 100 mL and 1 minute = 60 seconds. Convert the units as follows: 25 mL1 minute×1 minute60 seconds×1 cL100 mL=2560(100)=1240 cL per seconds)

A blood test must be performed in a centrifuge that can hold eight test tubes of blood. A test tube must be in the centrifuge for 5 minutes to complete the test. How many test tubes can be tested with this centrifuge in 1.5 hours?

144 tubes (First, since 1 hour equals 60 minutes, 1 1/2 hours equals 90 minutes. Let x be the number of test tubes that can be tested in 90 minutes. Set up and solve this proportion: 8 test tubes5 minutes=x test tubes90 minutes 750 = 5x x = 144 So, 144 test tubes can be tested in this amount of time.)

The manager of a hospice center estimates that each of her three staff members can change the sheets on a patient's bed in 8 minutes. Working independently, how long would it take them to make 57 beds?

152 minutes

At 6 AM, all 30 beds in the intensive care unit are occupied. Twenty percent of the patients are scheduled to be moved out of this unit by 9 AM. How many beds will this make available to new patients?

6

Convert 50 centimeters to kilometers.

0.0005 kilometers

A patient's Bivalirudin medication is infused at a rate of 16 mL per hour via an infusion pump. The IV bag of fluid is a mixture of 24,000 units of Bivalirudin with 500 mL of saline. What dosage is the patient receiving every 15 minutes?

192 units (The pump rate is 16 mL per hour. So, in 15 minutes, 4 mL are dispensed. There are 24,000500=48 units of Bivalirudin per mL in the IV fluid bag. So, in 15 minutes, 48(4) = 192 units of Bivalirudin are dispensed to the patient.)

Water drains from a soaking tub used for hydrotherapy at a rate of 5 gallons per minute. What is this rate in pints per second?

2/3 pint per second

An 8-year-old child weighing 95 pounds is prescribed Cefazolin in the amount of 25 mg per kg of body weight daily, to be divided into equal doses every 6 hours. Approximately how many milligrams should the nurse administer with each dose? (Use 1 kg = 2.205 pounds, if necessary.)

270 mg per dose (First, convert body weight from pounds to kg by dividing 95 by 2.205. This yields 95 pounds = 43.084 kg. So, the amount of Cefazolin to be administered daily is 25(43.084) = 1,077.1 mg. Since there are 24 hours in one day, this amount should be divided in to 4 equal doses each: 1,077.14=269.2, or approximately 270 mg.)

Because of a MRSA outbreak, the walls, ceiling, and floor of all patient rooms on the 8th floor of a hospital wing must be sterilized using industrial strength disinfectant. A one-gallon jug will disinfect 2,000 square feet. The dimensions of a patient's room are 10 feet by 10 feet by 12 feet and there are 18 patient rooms in the wing. How many gallons of disinfectant are needed to complete the job?

6.12 Gallons (Start by computing the square footage of the area to be treated for one patient's room. The wall, floor and ceiling are all rectangles, so to compute their area multiply length times width. Then, the surface area to be treated is the sum of these six areas: 10(10) + 10(10) + 10(10) + 10(10) +10(12) + 10(12) = 680 square feet Next, multiply this by the number of rooms to get the total square footage to be disinfected: 680(18) = 12,240 square feet Finally, to get the number of gallons needed, divide the total square footage by 2,000 to get 6.12 gallons.)

It takes a physical therapist, on average, 30 minutes to work through a stretching regimen per patient. If she takes one hour for lunch, which of these inequalities describes the number of patients, x, with whom she can work in an 8-hour workday? A.1/2x+1≤8 B.30x≤8 C.30x+1≤8

A.1/2x+1≤8

A nurse rounds a patient's weight to the nearest kilogram and records it as 78 kg. Which of the following is the largest possible actual weight of the patient? A.78.48 kg B.78.52 kg C.77.91 kg D.77.46 kg

A.78.48 kg

Which of these expressions is equivalent to the phrase, "three less than one-half of a number?" A.1/2(x−3) B.1/2x−3 C.(1/2−3)x D.3x−12

B.1/2x−3

A cancer patient is prescribed 10 mg of Phenergan every 12 hours for nausea. A 150 mL bottle that indicates "4 milligrams of Phenergan are contained in one teaspoon" is available. How many mL must the nurse administer for a single dose? (Remember that 1 teaspoon = 5 mL) A.2.5 mL B.12.5 mL C.25 mL D.50 mL

B.12.5 mL (First, determine the number of teaspoons equal to 10 mg by dividing 10 mg by 4 mg. So, one dose equals 2.5 teaspoons. Now, multiply by the number of mL in one teaspoon: 2.5(5) = 12.5 mL.)

A full IV bag contains 1 liter of fluid. The fluid leaves the bag at a rate of 150 liter per minute. Which of these equations can be used to determine the number of minutes, m, it takes for the bag to empty completely? A.1−50m=0 B.150m+1=0 C.1−150m=0 D.150m=0

C.1−150m=0 (The portion of a liter that has left the bag after m minutes is 150m. So, the amount remaining in the bag after m minutes is 1−150m. The number of minutes it takes the bag to completely empty is the value of m for which this expression equals zero. So, the desired equation is 1−150m=0.)

Which of these equations is equivalent to "the sum of three and a number is twice the number?" A .x + 3 = 2 + x B. 3x = 2 + x C. 3x = 2x D. x + 3 = 2x

D. x + 3 = 2x