5155 Pennsylvania Grades 4 to 8 Core Assessment Mathematics Version 1 Questions

Explanation

<h2>$1,060</h2> To determine the total cost of the landscaping items, we need to sum all the individual costs accurately, leading us to the closest total of $1,060. <b>A) $1,010</b> This choice is significantly lower than the actual total cost. It likely results from an underestimation of one or more item costs or an error in the addition process. Given the higher prices typically associated with landscaping materials, this figure does not reflect the realistic expenses involved. <b>B) $1,030</b> While this option is closer than $1,010, it still falls short of the correct total. This amount may arise from missing costs or miscalculating the addition of the landscaping items. Thus, it does not accurately represent the overall expenditure Alfred would incur. <b>C) $1,040</b> This choice is slightly more accurate but still does not reach the correct total. It indicates an undercalculation of the overall landscaping costs, potentially omitting certain items or misestimating their prices. Consequently, it remains inadequate for covering the total expenses. <b>D) $1,060</b> This option correctly represents the total cost of all landscaping items when summed properly. It accounts for each individual item's price, providing an accurate reflection of Alfred's landscaping expenses. <b>Conclusion</b> Accurate calculation of landscaping costs is essential for budgeting. By totaling the prices of all necessary items, we arrive at $1,060, confirming that this figure encompasses the complete financial requirement for Alfred's landscaping project. The other options underestimate the total, emphasizing the importance of thorough calculation in financial planning.

Explanation

<h2>27 and 35 can be written in the blanks to maintain a constant difference between consecutive numbers.</h2> To find the two missing numbers between 19 and 43 that maintain a constant difference, we first determine the total difference: 43 - 19 = 24. This difference must be evenly distributed across the three gaps, resulting in a common difference of 8. Therefore, the sequence is 19, 27, 35, 43. <b>A) 25, 31</b> If we substitute 25 and 31 into the sequence, we get 19, 25, 31, and 43. The differences would be 6 (25 - 19), 6 (31 - 25), and 12 (43 - 31), which are not constant. Thus, this choice fails to satisfy the condition. <b>B) 26, 36</b> Using 26 and 36 results in the sequence 19, 26, 36, and 43. The differences here are 7 (26 - 19), 10 (36 - 26), and 7 (43 - 36). Again, these differences are not consistent, which disqualifies this option. <b>C) 27, 35</b> By inserting 27 and 35, we have 19, 27, 35, and 43. The differences are 8 (27 - 19), 8 (35 - 27), and 8 (43 - 35), which are all equal. This option successfully maintains a constant difference of 8, making it the correct answer. <b>D) 28, 37</b> Inserting 28 and 37 gives us the sequence 19, 28, 37, and 43. The differences calculated are 9 (28 - 19), 9 (37 - 28), and 6 (43 - 37). Since these differences are not uniform, this choice does not fulfill the requirement for a constant difference. <b>Conclusion</b> To establish a consistent difference between consecutive numbers, the sequence must maintain equal spacing. The combination of 27 and 35 achieves this with an even difference of 8, while all other options fail to provide a uniform difference among the numbers. Therefore, 27 and 35 are the only valid solutions to the problem.

Explanation

<h2>(0, -4) are the coordinates of point A.</h2> In the xy-plane, point A is located on the y-axis at the coordinate (0, -4), indicating that it is 4 units below the origin. <b>A) (4, 0)</b> This coordinate represents a point on the x-axis, specifically 4 units to the right of the origin. It does not match the vertical position of point A, which is located on the y-axis. <b>B) (0, 4)</b> This coordinate indicates a point on the y-axis, 4 units above the origin. While it is on the correct axis, it does not represent the correct vertical position of point A, which is actually below the origin. <b>C) (-4, 0)</b> This coordinate signifies a point on the x-axis, 4 units to the left of the origin. Similar to option A, it does not align with point A's location on the y-axis and therefore cannot be the correct answer. <b>D) (0, -4)</b> This coordinate accurately describes point A's position on the y-axis, located 4 units below the origin. It is the only option that correctly matches the specified location of point A in the xy-plane. <b>Conclusion</b> Identifying coordinates in the xy-plane requires understanding the relationship between x and y values. Point A is specifically positioned at (0, -4), placing it on the y-axis below the origin. The other choices misplace point A either on the x-axis or above the origin, confirming that (0, -4) is the only correct answer.

Explanation

<h2>-2x + 14</h2> To solve the expression 2(x + 3) - 4(x - 2), we first distribute the constants to the terms inside the parentheses and then combine like terms. This process reveals that the equivalent expression simplifies neatly to -2x + 14. <b>A) -2x - 2</b> This option results from incorrect calculations. After distributing and combining like terms, we obtain a positive constant instead of a negative one. The mistake likely arises from miscalculating either the distribution or the combination of terms, leading to an incorrect constant term. <b>B) -2x + 14</b> This expression correctly represents the simplified form of 2(x + 3) - 4(x - 2). When we distribute and simplify, we find 2x + 6 - 4x + 8, which combines to yield -2x + 14. <b>C) 2x - 2</b> This choice incorrectly suggests a positive coefficient for x and a negative constant. The error may stem from a misunderstanding of the distribution process or an oversight during the combination of like terms, leading to incorrect signs in the final expression. <b>D) 2x + 14</b> This option incorrectly maintains a positive coefficient for x while adding a constant of 14. The error likely arises from failing to properly account for the negative term from the second distribution, which alters the sign of the x term. <b>Conclusion</b> The expression 2(x + 3) - 4(x - 2) simplifies to -2x + 14 through careful distribution and combination of like terms. While options A, C, and D reflect various miscalculations, option B accurately captures the correct simplified form. Understanding the distribution and combining like terms correctly is crucial for achieving the right answer in algebraic expressions.

Explanation

<h2>Mary will save approximately $20.00 if she uses her 15% off coupon on the humidifier.</h2> To calculate her savings, we multiply the cost of the humidifier, $129.95, by the discount rate of 15%. This results in a savings amount that is closest to $20.00. <b>A) $15.00</b> Calculating 15% of $129.95 yields a savings amount of $19.49. Therefore, $15.00 is significantly lower than the actual savings Mary would realize with her coupon. <b>B) $18.00</b> While $18.00 is closer than $15.00, it still does not accurately reflect the savings. The calculation shows that Mary will save approximately $19.49, which is higher than this amount. <b>C) $20.00</b> This is the closest estimate to the actual savings Mary will achieve. By calculating 15% of $129.95, we find her savings to be approximately $19.49, which rounds to about $20.00, making it the most accurate choice. <b>D) $22.00</b> This option overestimates the savings, as 15% of $129.95 is below $22.00. Hence, it does not represent a realistic amount that Mary would save using the coupon. <b>Conclusion</b> Mary's coupon for 15% off on a humidifier priced at $129.95 results in a savings of approximately $19.49, which is best approximated by $20.00. The other options either underestimate or overestimate her savings, highlighting the importance of accurate percentage calculations in determining discount values.