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If a die is rolled, what is the probability of getting a 5?
- A. 50%
- B. 20%
- C. 16.67%
- D. 83.33%
Correct Answer: C
Rationale: When rolling a fair six-sided die, there are a total of 6 possible outcomes (numbers 1 to 6). The probability of rolling a 5 is 1 out of 6, as there is only one 5 on the die. To calculate the probability, you divide the number of favorable outcomes by the total number of outcomes. Therefore, the probability of rolling a 5 is 1/6 which equals 0.1667 or 16.67%.
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Evaluate ab^2 - ac if a=c, b=-4, and c=-5
- A. 56
- B. 63
- C. -23
- D. -5
Correct Answer: C
Rationale: To evaluate the expression ab^2 - ac when a=c, b=-4, and c=-5, substitute these values into the expression. We get (-4)(-5)^2 - (-5) = (-4)(25) + 5 = -100 + 5 = -95. Therefore, the correct answer is -95, not 63 as previously stated. Hence, the correct answer is option C, which is -95.
A dairy farmer wants to measure the milk production of his cows. He determines that the herd has produced a total of 250 gallons of milk this morning. How many quarts is this? (Enter numeric value only.)
- A. 500
- B. 750
- C. 1000
- D. 1250
Correct Answer: C
Rationale: The correct answer is C: 1000 quarts. To convert gallons to quarts, you need to know that 1 gallon is equal to 4 quarts. Therefore, to convert 250 gallons to quarts, you would multiply 250 by 4, which equals 1000 quarts. Choice A (500 quarts), B (750 quarts), and D (1250 quarts) are incorrect because they do not correctly convert the given amount of gallons to quarts. Be sure to always remember the conversion factor of 1 gallon to 4 quarts when solving such conversion problems.
If a die is rolled, what is the probability of getting an odd number?
- A. 50%
- B. 75%
- C. 16.70%
- D. 33%
Correct Answer: A
Rationale: When a fair six-sided die is rolled, there are 3 odd numbers (1, 3, 5) out of a total of 6 possible outcomes (1, 2, 3, 4, 5, 6). The probability of rolling an odd number is calculated by taking the number of favorable outcomes (3) divided by the total number of outcomes (6), which simplifies to 3/6 or 1/2, equivalent to 50%. Therefore, the correct answer is 50%. This means that when rolling a fair six-sided die, there is a 50% chance of getting an odd number.
How many shipping labels are needed each day if 9 boxes are shipped, and each box must contain 3 shipping labels?
- A. 7
- B. 3
- C. 27
- D. 24
Correct Answer: C
Rationale: To determine the total number of shipping labels required, you need to multiply the number of boxes by the number of shipping labels per box. In this case, 9 boxes * 3 shipping labels per box = 27 shipping labels needed each day. Therefore, the correct answer is 27.
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.