ACCUPLACER Next Generation Quantitative Reasoning Algebra and Statistics Version 1 Questions

Explanation

<h2>The point (-1,1) lies in the shaded region of the xy-plane above.</h2> This point, when plotted on a Cartesian plane, falls within the given shaded region. The x-coordinate and y-coordinate of this point correspond respectively to -1 and 1, placing it within the boundaries of the shaded area. <b>A) (-1,1)</b> This is the correct answer. The coordinates (-1,1) fall within the shaded region of the xy-plane when plotted accordingly. The x-coordinate is -1 and the y-coordinate is 1, both of which place the point inside the shaded region. <b>B) (0,1)</b> The coordinates (0,1) do not fall within the shaded region. The x-coordinate is 0 and the y-coordinate is 1, which lie outside of the boundaries of the shaded area. <b>C) (1,2)</b> The coordinates (1,2) do not fall within the shaded region. The x-coordinate is 1 and the y-coordinate is 2, which also lie outside of the boundaries of the shaded area. <b>D) (2,-1)</b> The coordinates (2,-1) do not fall within the shaded region. The x-coordinate is 2 and the y-coordinate is -1, which place the point outside of the boundaries of the shaded area. <b>Conclusion</b> In the context of the xy-plane, a point is defined by its x (horizontal) and y (vertical) coordinates. The point (-1,1) is the only one among the provided options that falls within the boundaries of the shaded region when plotted on the plane. All the other points, namely (0,1), (1,2), and (2,-1) are located outside the shaded area. Therefore, the point (-1,1) is the correct answer.

Explanation

<h2>14/18 is the correct probability.</h2> The probability of a household on Malia's block being selected at random that subscribes to both cable television and home phone service is calculated by dividing the number of households that subscribe to both services by the total number of households that subscribe to cable television. <b>A) 14/18</b> This is the correct answer. It's calculated by dividing the number of households subscribed to both services (14) by the total number of households subscribed to cable television (18). This gives the probability of a household that subscribes to cable television also subscribing to home phone service. <b>B) 14/26</b> This is not correct because it incorrectly assumes that the denominator should be the total number of households that subscribe to either cable television or home phone service. But the question asks for the probability of a household that subscribes to cable television also subscribing to home phone service, so the denominator should be the total number of households that subscribe to cable television (18), not the total number of households that subscribe to either service (26). <b>C) 18/36</b> This is not correct because it incorrectly assumes that the denominator should be the total number of households on Malia's block. But the question asks for the probability of a household that subscribes to cable television also subscribing to home phone service, so the denominator should be the total number of households that subscribe to cable television (18), not the total number of households on the block (36). <b>D) 14/36</b> This is not correct because it incorrectly assumes that the denominator should be the total number of households on Malia's block. But the question asks for the probability of a household that subscribes to cable television also subscribing to home phone service, so the denominator should be the total number of households that subscribe to cable television (18), not the total number of households on the block (36). <b>Conclusion</b> The probability of a randomly selected household that subscribes to cable television also subscribing to home phone service is determined by dividing the number of households subscribed to both services by the total number of households subscribed to cable television. This is correctly represented by the ratio 14/18. Any other ratio either misrepresents the total number of households or incorrectly calculates the probability based on irrelevant parameters.

Explanation

<h2>42 is the average number of comic books owned by Fred and Norman.</h2> To find the average number of comic books owned by Fred and Norman, we have to first determine the total number of comic books they own together. We know that Fred, Norman, and Dave own a total of 128 comic books and Dave owns 44. Therefore, Fred and Norman together own 128 - 44 = 84 comic books. The average is then found by dividing this total by the number of people, which is 2 in this case. Hence, the average number owned by Fred and Norman is 84 ÷ 2 = 42 comic books. <b>A) 42</b> This is the correct choice because Fred and Norman together own 84 comic books, and the average number of comic books they own is found by dividing this total by the number of people, which gives us 42 comic books each. <b>B) 44</b> This answer would be correct if Dave's ownership of 44 comic books was applied to Fred and Norman. However, Dave's ownership does not affect the average number of comic books owned by Fred and Norman, as we are only interested in the average of the comic books owned by Fred and Norman. <b>C) 46</b> This answer is incorrect because it is greater than the calculated average. An average of 46 comic books each would mean Fred and Norman together own more than 128 comic books, which is not the case. <b>D) 48</b> This answer is incorrect because it is greater than the calculated average. An average of 48 comic books each would mean Fred and Norman together own more than 128 comic books, which is not the case. <b>Conclusion</b> The average number of comic books owned by Fred and Norman is 42. This is calculated by first determining the total number of comic books owned by Fred and Norman, which is 84, and then dividing this total by the number of people, which is 2. The other options are incorrect because they are either based on incorrect assumptions or they are greater than the calculated average.

Explanation

<h2>Janelle will most likely take about 2.5 hours to travel 20 miles at the same rate.</h2> The time it takes to travel a certain distance is calculated by dividing the total distance by the speed. In this case, Lanelle's speed is 9.7 miles divided by 1.2 hours, which is approximately 8.08 miles per hour. Using this speed, Janelle would travel 20 miles in approximately 2.47 hours, which is closest to 2.5 hours. <b>A) 2 hours</b> Janelle traveling 20 miles in 2 hours would mean she is moving at a speed of 10 miles per hour. This is faster than Lanelle's speed of approximately 8.08 miles per hour, so this time is too short. <b>B) 2.5 hours</b> At Lanelle's speed of approximately 8.08 miles per hour, Janelle would take approximately 2.47 hours to travel 20 miles, which is closest to 2.5 hours. This is the correct answer. <b>C) 5 hours</b> Traveling 20 miles in 5 hours would mean a speed of 4 miles per hour. This is much slower than Lanelle's speed of approximately 8.08 miles per hour, so this time is too long. <b>D) 5.5 hours</b> Travelling 20 miles in 5.5 hours would represent a speed of approximately 3.64 miles per hour. This speed is significantly slower than Lanelle's approximate speed of 8.08 miles per hour, so this time is far too long. <b>Conclusion</b> To find the time it would take Janelle to travel a certain distance at the same speed as Lanelle, we first need to calculate Lanelle's speed. Once we have that, we divide the total distance Janelle needs to travel by Lanelle's speed. In this case, Janelle would take approximately 2.47 hours to travel 20 miles, which is closest to 2.5 hours. Other options either underestimate or overestimate the time it would take based on Lanelle's speed.

Explanation

<h2>Trevani paid a sales tax of $1.00 on the book.</h2> To calculate the sales tax, one must first find the pre-tax price of the book. Given that $13.50 includes an 8% sales tax, we can determine the original price by dividing $13.50 by 1.08. The result, $12.50, is the original price before tax. Subtracting this from the total price gives us the sales tax paid, which is $1.00. <b>A) $0.96</b> This answer incorrectly assumes that the 8% sales tax is applied to the total cost of $13.50. However, the sales tax is applied to the pre-tax price of the book, not the total cost with tax. Therefore, $0.96 is not the correct amount of sales tax. <b>B) $1.00</b> As calculated earlier, $1.00 is the correct amount of sales tax paid. We found this by first determining the pre-tax price of the book ($12.50) and then subtracting this from the total price paid ($13.50). <b>C) $1.04</b> This answer is incorrect because it seems to be based on a misunderstanding of how to calculate sales tax. The tax is computed based on the pre-tax price, not the total price paid, and in this case, the sales tax paid is less than $1.04. <b>D) $1.08</b> This answer is incorrect as it doesn't align with the actual sales tax that was paid. It seems to be based on a misinterpretation of the 8% sales tax, incorrectly assuming that $1.08 was the sales tax paid. <b>Conclusion</b> In order to find the amount of sales tax paid, it's necessary to first determine the pre-tax cost of the item. In this case, Trevani's book cost $12.50 before tax, and the total price with an 8% sales tax was $13.50. By subtracting the pre-tax price from the total price, we can find that Trevani paid $1.00 in sales tax. The other choices represent common misunderstandings of how to calculate sales tax.