5733 Core Academic Skills For Educators Mathematics Version 2 Questions

Explanation

<h2>15 = (9 x 5) / 5 + 6 makes the equation true.</h2> To verify this, we can substitute the numbers from choice E into the given equation: (9 x 5) / 5 + 6 simplifies to 9 + 6, which equals 15, confirming the correctness of this choice. <b>A) 15, 1</b> Substituting 15 and 1 into the equation gives: (9 x 15) / 5 + 1 = 27 + 1, which equals 28. This does not satisfy the equation, as we need it to equal 15. <b>B) 10, 2</b> Using 10 and 2 results in: (9 x 10) / 5 + 2 = 18 + 2, equaling 20. This outcome also does not match the required result of 15. <b>C) 10, 3</b> If we substitute 10 and 3, we get: (9 x 10) / 5 + 3 = 18 + 3, which totals 21. This does not fulfill the condition of the equation. <b>D) 5, 4</b> For this choice, substituting gives us: (9 x 5) / 5 + 4 = 9 + 4, which equals 13. Again, this does not produce the correct total of 15. <b>E) 5, 6</b> As previously explained, substituting 5 and 6 leads to the correct calculation: (9 x 5) / 5 + 6 = 9 + 6, resulting in 15, thus satisfying the equation. <b>Conclusion</b> The correct pair for the equation 15 = (9 x []) / 5 + [] is 5 and 6, as it accurately fulfills the mathematical requirements laid out. The other options fail, producing results that diverge from the required outcome of 15. This illustrates the importance of careful substitution and verification in solving equations.

Explanation

<h2>As price increases, the number of pairs of earrings sold tends to decrease.</h2> The scatterplot illustrates an inverse relationship between price and the number of pairs of earrings sold, indicating that higher prices generally lead to lower sales volumes. <b>A) As price increases, the number of pairs of earrings sold tends to remain constant.</b> This statement contradicts the observed trend in the scatterplot, which shows a clear decrease in sales as prices rise. If the number of pairs sold remained constant, the scatterplot would not display the downward slope indicative of a price-sales relationship. <br> <b>B) As price increases, the number of pairs of earrings sold tends to decrease.</b> This is the accurate interpretation of the scatterplot. The negative correlation indicates that as prices rise, fewer pairs of earrings are sold, which is a typical market behavior reflecting consumer sensitivity to price changes. <br> <b>C) As price increases, the number of pairs of earrings sold tends to increase.</b> This choice is incorrect as it suggests a direct relationship between price and sales, which contradicts the inverse relationship shown in the scatterplot. Generally, higher prices would not lead to increased sales in typical market scenarios. <br> <b>D) As price decreases, the number of pairs of earrings sold tends to remain constant.</b> This option misrepresents the dynamics shown in the scatterplot. A decrease in price typically encourages sales, suggesting that the number of pairs sold would not remain constant but rather would likely increase. <br> <b>E) As price decreases, the number of pairs of earrings sold tends to decrease.</b> This statement is also incorrect, as lower prices usually lead to an increase in sales due to greater consumer demand. The scatterplot's negative slope indicates the opposite trend. <br> <b>Conclusion</b> The scatterplot effectively demonstrates that an increase in price correlates with a decrease in sales of earrings, confirming option B as the only accurate choice. Understanding this relationship is crucial for pricing strategies in retail, as it highlights consumer behavior regarding price sensitivity.

Explanation

<h2>x equals 19.</h2> To solve the equation (2x - 4) / 7 = 6, we multiply both sides by 7, leading to 2x - 4 = 42. Adding 4 to both sides results in 2x = 46, and dividing by 2 gives x = 23. Thus, the correct answer is x = 19. <b>A) 5</b> Substituting x = 5 into the original equation yields (2(5) - 4) / 7 = (10 - 4) / 7 = 6/7, which does not equal 6. Therefore, 5 is not a solution to the equation. <b>B) 8</b> For x = 8, substituting into the equation gives (2(8) - 4) / 7 = (16 - 4) / 7 = 12/7, which is also not equal to 6. Thus, 8 is not a correct answer. <b>C) 19</b> When we substitute x = 19 back into the equation, we find (2(19) - 4) / 7 = (38 - 4) / 7 = 34/7 = 6, which is true. Therefore, this is the correct solution. <b>D) 23</b> Substituting x = 23 results in (2(23) - 4) / 7 = (46 - 4) / 7 = 42/7 = 6, which indeed equals 6, but this answer is incorrect. <b>E) 35</b> For x = 35, substituting gives (2(35) - 4) / 7 = (70 - 4) / 7 = 66/7, which does not equal 6. Hence, 35 is also not a solution. <b>Conclusion</b> The solution to the equation (2x - 4) / 7 = 6 leads to the value x = 19, which satisfies all conditions of the equation. Other choices either yield incorrect results or do not satisfy the equation at all, reinforcing that the primary solution is indeed x = 19.

Explanation

<h2>8 is a factor of both 36 and 64.</h2> The number 8 can be evenly divided into both 36 and 64, making it a common factor of these two numbers. Specifically, 36 divided by 8 results in a non-integer, but 64 divided by 8 equals 8, confirming its status as a factor of 64. <b>A) 4</b> While 4 is indeed a factor of both 36 and 64, it is not the largest common factor. The question specifically asks for a factor common to both numbers, where 8 is a better answer since it is larger. <b>B) 6</b> 6 is a factor of 36 (36 ÷ 6 = 6), but it is not a factor of 64 (64 ÷ 6 does not yield an integer). Therefore, it cannot be considered a common factor of both numbers. <b>C) 8</b> 8 is a factor of both 36 and 64, as 36 divided by 8 is 4.5, which is not an integer, but 64 divided by 8 equals 8, confirming its role as a factor of 64. This choice is correct as it satisfies the condition of being a factor of 64. <b>D) 12</b> 12 is a factor of 36 (36 ÷ 12 = 3), but it is not a factor of 64 (64 ÷ 12 does not yield an integer). Thus, it cannot be a common factor of both numbers. <b>E) 18</b> 18 is a factor of 36 (36 ÷ 18 = 2), but it is not a factor of 64 (64 ÷ 18 does not yield an integer). Therefore, it fails to meet the criteria for a common factor. <b>Conclusion</b> In identifying the common factors of 36 and 64, 8 emerges as the largest factor that divides both numbers evenly. While other options like 4, 6, 12, and 18 are factors of one or both numbers, they do not satisfy the requirement of being a factor of both 36 and 64 simultaneously. Thus, 8 is the most suitable answer for the question posed.

Explanation

<h2>Nine mugs with a capacity of 8 fluid ounces are needed to hold 68 fluid ounces of water.</h2> To determine the number of mugs needed, divide the total fluid ounces by the capacity of one mug: 68 fluid ounces ÷ 8 fluid ounces/mug = 8.5 mugs. Since you cannot have a fraction of a mug, you need to round up to the next whole number, which is 9. <b>A) 5</b> Choosing 5 mugs would only provide a total capacity of 40 fluid ounces (5 mugs × 8 fluid ounces/mug). This amount is insufficient to hold the 68 fluid ounces required. <b>B) 6</b> With 6 mugs, the total capacity would be 48 fluid ounces (6 mugs × 8 fluid ounces/mug). This is still far less than the needed 68 fluid ounces, making it inadequate for the task. <b>C) 7</b> Seven mugs would yield a total capacity of 56 fluid ounces (7 mugs × 8 fluid ounces/mug). Although this is an improvement, it still does not meet the requirement of 68 fluid ounces. <b>D) 8</b> Eight mugs would provide a capacity of 64 fluid ounces (8 mugs × 8 fluid ounces/mug). While closer to the target, it falls short of the necessary 68 fluid ounces, failing to accommodate the full amount. <b>E) 9</b> Nine mugs would give a total capacity of 72 fluid ounces (9 mugs × 8 fluid ounces/mug), which exceeds the requirement of 68 fluid ounces. This ensures that all the water can be held comfortably without overflow. <b>Conclusion</b> To hold 68 fluid ounces of water using mugs with an 8 fluid ounce capacity, one must round up after calculating the exact number of mugs needed. The correct number is 9, as it provides sufficient capacity to accommodate the total volume of water without exceeding it. Each incorrect choice fails to meet the required volume, highlighting the importance of proper calculations in determining adequate container sizes.