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Solve the equation if X = 3: 3X² - 21/(3X) = ?
- A. 1 1/3 or 1.33
- B. 2/6 or 0.33
- C. 1/3 or 0.33
- D. 2/3 or 0.67
Correct Answer: D
Rationale: To solve the equation, substitute X = 3 into the expression: 3(3²) - 21/(3*3) = 3(9) - 21/9 = 27 - 7 = 20. Simplify further to get 20/30 = 2/3. Therefore, the correct answer is D (2/3 or 0.67). The critical step is correctly simplifying the expression by dividing 21 by 3 times 3 (3X) instead of just 3X.
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Subtract 5/6 - 3/4.
- A. 1/2
- B. 1/12
- C. 2/24
- D. 1
Correct Answer: B
Rationale: To subtract fractions, you need a common denominator. The common denominator between 6 and 4 is 12. Convert both fractions to have a denominator of 12. 5/6 becomes 10/12 and 3/4 becomes 9/12. Subtracting 10/12 - 9/12 results in 1/12. Therefore, the correct answer is 1/12.
Ratio and Proportion: 0.3:2 = 15:X (Enter numeric value only.)
- A. 50
- B. 75
- C. 100
- D. 125
Correct Answer: C
Rationale: To find the value of X, first, we need to set up a proportion using the given equation: 0.3/2 = 15/X. Cross multiply to solve for X: 0.3X = 2 * 15. Simplify to get 0.3X = 30. Divide by 0.3 to solve for X: X = 30 / 0.3 = 100. Therefore, the correct answer is C. Choice A (50), B (75), and D (125) are incorrect as they do not satisfy the proportion equation given. A summary of the incorrect choices: A is too low, B is also too low, and D is too high compared to the correct answer of 100.
One side of a 6-sided die is numbered 4, 9, 12, 16, 20, and 24. What is the probability of rolling an even number?
- A. 5/6
- B. 3/4
- C. 2/3
- D. 1/3
Correct Answer: A
Rationale: To find the probability of rolling an even number, we identify the even numbers on the die, which are 4, 12, 16, 20, and 24 (5 even numbers). Since there are 6 total outcomes on a 6-sided die, the probability of rolling an even number is the number of favorable outcomes (5) divided by the total number of outcomes (6), resulting in a probability of 5/6.
A mother is planning a birthday party. She will give each child 15 balloons. There are 50 balloons per packet. How many packets does the mother need if there will be 16 children?
- A. 5
- B. 6
- C. 17
- D. 50
Correct Answer: A
Rationale: To determine the number of packets the mother needs, you must calculate the total number of balloons required for all children. With 16 children receiving 15 balloons each, the total number of balloons needed is 15 x 16 = 240. As each packet contains 50 balloons, divide the total balloons needed by the number of balloons per packet: 240 · 50 = 4.8. Since packets cannot be in fractions, round up to the nearest whole number, which means the mother needs 5 packets to provide balloons for all 16 children.
What is 5 & 3/4 divided by 1/2 when reduced?
- A. 5 & 1/2
- B. 2 & 3/8
- C. 11 & 1/2
- D. 18
Correct Answer: C
Rationale: To divide a mixed number by a fraction, first convert the mixed number to an improper fraction. 5 & 3/4 as an improper fraction is 23/4. Next, invert the divisor to find its reciprocal, making it 2/1. Now, multiply the dividend by the reciprocal: (23/4) · (2/1) = (23/4) * (1/2) = 23/8 = 2 & 7/8. This result as a mixed number is 11 & 1/2, which is the correct answer. Therefore, the correct answer is 11 & 1/2.