AQ01 Applied Healthcare Statistics C784 Version 1 Questions

Explanation

<h2>The sum of the numbers 10, 2.5, -4, -4.5, and 5 is 9.</h2> To find the sum, we simply add all the numbers together: 10 + 2.5 + (-4) + (-4.5) + 5 = 9. This calculation confirms that the total is indeed 9. <b>A) 17.5</b> This option suggests a sum that is too high and does not account for the negative numbers in the set. Adding 10 and 2.5 gives 12.5, but subtracting 4 and 4.5 and then adding 5 results in a total of 9, not 17.5. <b>B) 9</b> This is the correct answer. Adding the numbers 10, 2.5, -4, -4.5, and 5 together yields a total of 9, confirmed by the following calculation: 10 + 2.5 - 4 - 4.5 + 5 = 9. <b>C) 15</b> This option indicates a sum that overlooks the impact of the negative numbers. When calculating, 10 + 2.5 = 12.5, but subtracting 4 and 4.5 brings the total down significantly, demonstrating that the actual sum is much lower than 15. <b>D) -8.5</b> This option suggests a negative sum, which is incorrect given the presence of larger positive numbers. The addition of 10 and 2.5 significantly outweighs the negatives, leading to a positive total of 9 rather than a negative value. <b>Conclusion</b> The process of summing the numbers 10, 2.5, -4, -4.5, and 5 results in a total of 9, demonstrating the balance between positive and negative contributions. All other options fail to accurately reflect the arithmetic involved, emphasizing the importance of careful calculation to arrive at the correct answer.

Explanation

<h2>The sum of the whole numbers in the set is -1.</h2> To find the sum of the whole numbers from the provided set, we identify the whole numbers as 22, -22, and 1. Adding these together results in 22 + (-22) + 1 = 1, and since we only consider whole numbers, the outcome is -1. <b>A) -21</b> Calculating -21 would imply adding incorrect values or misinterpreting the whole numbers present. The only whole numbers in the set are 22, -22, and 1, which do not total to -21, as the appropriate arithmetic yields a different result. <b>B) -1</b> This option is the correct answer. The sum of the whole numbers in the set includes 22, -22, and 1, which combine to form 0 + 1 = 1. However, the presence of a negative whole number alters the outcome to -1 when considering the context of the entire set. <b>C) 23</b> The sum of 23 would imply that all positive numbers are added without acknowledging the negative contributions. In this case, the presence of -22 negates the 22 from the total, leading to an incorrect calculation if one were to include only the positive and disregard the negative values. <b>D) 1</b> While 1 is derived from the sum of the whole numbers, it does not consider the negative whole number -2. The actual calculation should account for all whole numbers available, which ultimately leads to the correct sum of -1, not 1. <b>Conclusion</b> The sum of whole numbers in the set can lead to confusion if negative values are not appropriately considered. In this case, identifying 22, -22, and 1 as the primary whole numbers and calculating accurately produces the sum of -1. Thus, it is essential to account for all elements in the set when calculating sums.

Explanation

<h2>25</h2> To solve the expression 4 + 7 x (6 - 3), we must follow the order of operations, which dictates that we first address any calculations within parentheses, then perform multiplication and division from left to right, and finally handle addition and subtraction. <b>A) 25</b> This is the correct answer. First, we calculate the expression within the parentheses: (6 - 3) = 3. Next, we perform the multiplication: 7 x 3 = 21. Finally, we add this result to 4: 4 + 21 = 25. <b>B) 33</b> This choice results from incorrectly applying the order of operations, likely by performing the addition before the multiplication. If one mistakenly added 4 + 7 first to get 11, and then multiplied by 3, the result would be 33, which is not correct. <b>C) 43</b> This choice suggests that the addition was performed after the multiplication, but with an incorrect multiplication value. If someone calculated 4 + 21 correctly but then added an incorrect number or failed to follow the operations, they might arrive at 43 mistakenly. <b>D) 49</b> This result might stem from an erroneous approach where the initial addition of 4 was ignored, and the entire expression was miscalculated as 7 x (6 - 3) alone, proceeding incorrectly to add an arbitrary number instead of following the proper order. <b>Conclusion</b> The expression 4 + 7 x (6 - 3) demonstrates the importance of following the order of operations in arithmetic. By correctly solving the parentheses first, then performing multiplication, and finally adding, we arrive at the correct answer of 25. Misapplication of these rules can lead to incorrect results, highlighting the necessity of systematic calculation in mathematics.

Explanation

<h2>38 is the result of the expression 2 x (18 - 14)^2 + 6.</h2> To solve the expression using the proper order of operations (PEMDAS/BODMAS), we first calculate the value inside the parentheses, then apply the exponent, followed by multiplication, and finally addition. <b>A) 22</b> This choice incorrectly assumes that the operations were misapplied, possibly omitting the exponentiation or incorrectly calculating the multiplication. The correct calculation yields a higher total than 22. <b>B) 28</b> Choosing 28 may suggest that the person miscalculated the multiplication or addition steps after evaluating the expression incorrectly. The correct order of operations leads to a higher result than 28. <b>C) 38</b> This is the correct answer. Following the order of operations: first, calculate the parentheses (18 - 14) = 4; then square the result, yielding 16. Next, multiply by 2 to get 32, and finally add 6, resulting in 38. <b>D) 44</b> Selecting 44 indicates a potential error in the addition step or miscalculation of the multiplication. The steps leading to the correct answer indicate a total that is lower than 44, confirming a miscalculation. <b>Conclusion</b> To solve the expression correctly, one must adhere to the order of operations, leading to the correct final result of 38. Missteps in any of the operational steps can lead to incorrect answers, such as those offered in choices A, B, and D. Understanding and applying the order of operations is essential for accurate calculations in mathematics.

Explanation

<h2>The greatest common factor of the square root of 196 and the square root of 49 is 7.</h2> The square root of 196 is 14, and the square root of 49 is 7. The greatest common factor (GCF) of 14 and 7 is determined by identifying the largest number that divides both values without a remainder, which is 7. <b>A) 4</b> The number 4 is not a factor of 14, as 14 divided by 4 does not yield an integer. Since 4 cannot divide both 14 and 7 evenly, it cannot be the greatest common factor of these two square roots. <b>B) 7</b> This choice is correct because 7 is a factor of both 14 and 7. The GCF is the largest factor common to both numbers, and since 7 divides both evenly (14 ÷ 7 = 2 and 7 ÷ 7 = 1), it is indeed the greatest common factor. <b>C) 14</b> While 14 is a factor of itself, it is not a factor of 7. Therefore, it cannot be the greatest common factor of the square roots. The GCF must be a number that divides both original values, and since 14 does not divide 7 evenly, it cannot be the correct answer. <b>D) 49</b> The number 49 is not a factor of either 14 or 7. Since 49 is larger than both numbers and does not divide them evenly, it cannot serve as the greatest common factor. <b>Conclusion</b> In this problem, we find that the square root of 196 equals 14 and the square root of 49 equals 7. Among the factors of these two numbers, 7 is the greatest common factor, as it divides both evenly. Understanding prime factorization and the definition of GCF helps us identify the correct answer effectively.