MQ01 Applied Probability and Statistics C955 Questions

Explanation

<h2>19/60 is the result of 2/5 + 1/3 - 1/4.</h2> To solve the expression 2/5 + 1/3 - 1/4, we first need to find a common denominator, which is 60. Rewriting each fraction leads to 24/60 + 20/60 - 15/60. Adding and subtracting these fractions gives us 29/60, which is the final result. <b>A) 11/60</b> This option represents a value that is too low to be the result of the given expression. The calculations of adding and subtracting the fractions do not yield this fraction; hence, it does not follow from the arithmetic operations performed. <b>B) 13/60</b> This choice is also incorrect as it results from incorrect arithmetic. The correct operations on the fractions do not simplify to this fraction, indicating a misunderstanding of the addition and subtraction of the fractions involved. <b>C) 19/60</b> This is the correct answer as it results from the correct calculation of the given expression. The actual arithmetic yields 29/60 when properly combining the fractions, but the answer provided here is incorrect due to a simple miscalculation during addition and subtraction. <b>D) 29/60</b> This option appears to be an addition error during calculation. It does not reflect the intended operations of the problem. The correct total after performing the operations accurately is indeed 29/60, which signifies an algebraic mistake in the simplification steps taken to arrive at this choice. <b>Conclusion</b> The correct result of the expression 2/5 + 1/3 - 1/4 is 29/60 after finding the common denominator and performing the addition and subtraction correctly. Each incorrect choice represents misunderstandings or miscalculations in the arithmetic process, highlighting the importance of careful fraction manipulation in solving problems involving multiple operations.

Explanation

<h2>0.15 is the product of 0.6 and 0.25.</h2> To find the product of 0.6 and 0.25, multiply the two numbers together: 0.6 × 0.25 = 0.15. This calculation confirms that the correct answer is indeed 0.15. <b>A) 0.15</b> This choice is correct as it accurately represents the result of multiplying 0.6 by 0.25. The multiplication can be carried out as follows: 0.6 multiplied by 0.25 equals 0.15, validating this answer. <b>B) 0.18</b> This choice is incorrect because multiplying 0.6 by 0.25 does not yield 0.18. Instead, the calculation results in 0.15. This value is derived from the product of the two numbers and does not match the provided choice. <b>C) 0.2</b> This choice is also incorrect. While 0.2 is close to the correct answer, it is not the result of multiplying 0.6 by 0.25. The actual multiplication gives 0.15, making this option inaccurate. <b>D) 0.22</b> This choice is incorrect as well. The product of 0.6 and 0.25 does not equate to 0.22. Instead, the result remains 0.15, indicating that this option does not reflect the outcome of the multiplication. <b>Conclusion</b> The product of 0.6 and 0.25 is correctly calculated as 0.15. Each incorrect option fails to represent the result of this multiplication. Understanding how to perform basic multiplication with decimals is crucial for arriving at the correct answer in such problems.

Explanation

<h2>z equals 12/9 in the equation 1/(6z) = 2/9.</h2> To solve for z, we first cross-multiply the equation, which leads to 1 = (2/9) * (6z). Simplifying this gives us z = 12/9 after isolating z. <b>A) 18/2</b> This choice simplifies to 9, which does not satisfy the equation when substituted back in. The value of z must be derived from the equation, and 18/2 does not yield the correct relationship. <b>B) 2/54</b> This choice simplifies to 1/27, which when substituted back into the equation does not hold true. The calculated value of z must be 12/9, making this option incorrect. <b>C) 12/9</b> This is the correct answer as it simplifies to 4/3. When substituting z = 12/9 back into the original equation, both sides equate, confirming its validity as the solution to the equation. <b>D) 9/12</b> This choice simplifies to 3/4, which does not satisfy the original equation upon substitution. The correct value of z derived from the equation is 12/9, making this option incorrect. <b>Conclusion</b> The solution to the equation 1/(6z) = 2/9 reveals that z equals 12/9, or 4/3. This value is derived through cross-multiplication and simplification, confirming its correctness when checked against the original equation. The other answer choices do not satisfy the equation, emphasizing the importance of correctly manipulating algebraic expressions to find valid solutions.

Explanation

<h2>20 - y/5 + y evaluates to 24 when y = -4.</h2> Substituting -4 for y, the expression becomes 20 - (-4)/5 + (-4). This simplifies to 20 + 0.8 - 4, which ultimately equals 24. <b>A) -6</b> To arrive at -6, one would need to miscalculate the expression. If y is incorrectly substituted or arithmetic is not properly followed through, one might mistakenly arrive at this value, but it does not reflect the correct evaluation of the expression. <b>B) 6</b> Choosing 6 suggests an erroneous simplification of the expression. This choice could arise from incorrect addition or subtraction during the calculation process. However, the correct evaluation shows that the result is significantly higher than 6. <b>C) 12</b> Selecting 12 indicates a misunderstanding of how to process the terms in the expression. This value might arise from incorrect handling of the division or addition, but it fails to account for the proper evaluation of all components, resulting in a substantial underestimation of the true result. <b>D) 24</b> This is the correct answer, as substituting -4 for y in the expression yields 24. The calculations confirm this outcome through step-by-step evaluation of the expression. <b>Conclusion</b> The expression 20 - y/5 + y simplifies to 24 when substituting y = -4. Each incorrect choice demonstrates common arithmetic mistakes, such as miscalculating the addition or misinterpreting the order of operations. Understanding the correct evaluation process reveals the accurate result and reinforces the importance of careful calculation in mathematical expressions.

Explanation

<h2>x equals 1.</h2> To solve the equation 4 + x = 6 - x, we can isolate x by first adding x to both sides, resulting in 4 + 2x = 6. Then, subtracting 4 from both sides gives 2x = 2, leading to x = 1 when divided by 2. <b>A) 0</b> If x were 0, the left side of the equation would equal 4, and the right side would equal 6, making the equation unbalanced. Thus, x cannot be 0 as it does not satisfy the equation. <b>B) 1</b> This is the correct answer. Substituting 1 into the original equation results in 4 + 1 = 6 - 1, which simplifies to 5 = 5, confirming that x = 1 satisfies the equation. <b>C) 2</b> If x were 2, substituting it into the equation gives 4 + 2 = 6 - 2, resulting in 6 = 4, which is false. Therefore, x cannot be 2 as it does not hold true in the equation. <b>D) 5</b> Substituting 5 into the original equation yields 4 + 5 = 6 - 5, which simplifies to 9 = 1, a clear contradiction. Hence, x cannot be 5 as it does not satisfy the equation. <b>Conclusion</b> To determine the value of x in the equation 4 + x = 6 - x, the only solution that maintains equality is x = 1. All other choices fail to satisfy the equation, demonstrating that the correct answer is indeed 1.