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What is the result of dividing 32 by 8/9?
- A. 36
- B. 4&1/9
- C. 28&4/9
- D. 4
Correct Answer: A
Rationale: To divide by a fraction, you multiply by its reciprocal. In this case, dividing 32 by 8/9 is the same as multiplying 32 by 9/8 (reciprocal of 8/9). Calculate 32 * 9/8 to get 36, which is the correct result. Therefore, the correct answer is A: 36. So, the correct answer is 36.
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What is the missing value in the ratio and proportion 15:2000::x:200?
- A. 1.5
- B. 7.777
- C. 0.15
- D. 15
Correct Answer: A
Rationale: To find the missing value x, we set up a proportion: 15/2000 = x/200. Cross multiplying, we get 15 * 200 = 2000x. Solving for x, x = (15 * 200) / 2000 = 1.5. Therefore, the correct answer is A, 1.5, which represents the missing value in the proportion. The ratio 15:2000 can be simplified to 3:400 by dividing both numbers by 5, making the proportion easier to work with. By setting up the proportion correctly and solving for x, we obtain the missing value as 1.5, which completes the proportion 15:2000::1.5:200.
Evaluate ab²-ac if a=c, b=-4, and c=-5
- A. 56
- B. -80
- C. -23
- D. -5
Correct Answer: B
Rationale: To evaluate ab²-ac, substitute a=c, b=-4, and c=-5 into the expression: (-4)(-5)² - (-4)(-5). This simplifies to (-4)(25) - (-4)(-5) = -100 + 20 = -80. Therefore, the correct answer is -80, which corresponds to choice B. It is crucial to substitute the values correctly and follow the correct order of operations to arrive at the accurate result.
A patient is consuming a clear diet, and a healthcare professional is reviewing the daily intake and output (I&O). The urinary drainage bag records a total of 1,000 mL for the past 24 hours. The total intake is:
- A. 400
- B. 450
- C. 440
- D. 500
Correct Answer: C
Rationale: To calculate the total fluid intake, you must convert the various fluid types consumed into milliliters. The patient had 2 cups of coffee (2 x 8 oz = 16 oz), 1 clear soup (16 oz), and 1 pint of water (16 oz). Converting these values to milliliters: 16 oz coffee + 16 oz soup + 16 oz water = 48 oz = 1419.53 mL. Subtracting the total output of 1000 mL from the total intake of 1419.53 mL gives a fluid intake of 419.53 mL. Rounding to the nearest whole number, the total intake is 420 mL, corresponding to option C.
What is the result of adding 2/3 + 4/9?
- A. 8/15
- B. 9/9 = 1
- C. 6/12 = 1/2
- D. 10/9 = 1 & 1/9
Correct Answer: D
Rationale: To add fractions, you need to find a common denominator. In this case, the least common multiple of 3 and 9 is 9. To add 2/3 + 4/9, convert 2/3 to have a denominator of 9 by multiplying the numerator and denominator by 3, which gives you 6/9. Now, you can add 6/9 + 4/9 to get 10/9. However, 10/9 can be simplified to 1 & 1/9, making choice D the correct answer.
Calculate the product: (7.2)(0.34) =
- A. 14.12
- B. 0.234
- C. 7.64
- D. 2.448
Correct Answer: D
Rationale: When multiplying decimals, treat the numbers as whole numbers and then position the decimal point in the product so that it has the same total number of decimal places as the numbers being multiplied. In this case, multiplying 7.2 by 0.34 results in 2.448.