ACCUPLACER Next Generation Quantitative Reasoning Algebra and Statistics

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Question 1

Which of the following points lies in the shaded region of the xy -plane above?

Your Answer: Option(s)

Correct Answer: Option(s) A

Rationale

(-1,1) lies in the shaded region of the xy-plane above.

The point (-1,1) is situated in the shaded area defined by the conditions of the problem, confirming its position within the specified region of the xy-plane.

A) (-1,1)
This point has an x-coordinate of -1 and a y-coordinate of 1, placing it in the upper-left quadrant of the xy-plane. Given the criteria of the shaded region, (-1,1) fits perfectly within the designated area, meeting all relevant inequalities or conditions.

B) (0,1)
While this point has a valid y-coordinate of 1, its x-coordinate of 0 places it on the y-axis. Depending on the specific boundaries of the shaded region, (0,1) may or may not be included, which typically indicates that it does not lie within the shaded area if the region does not extend to include the y-axis.

C) (1,2)
This point is located in the upper-right quadrant of the xy-plane with coordinates that likely exceed the boundaries defined by the shaded region. The x-coordinate of 1 and y-coordinate of 2 may place it outside the constraints set by the inequalities, thus excluding it from the shaded area.

D) (2,-1)
The coordinates for this point place it in the lower-right quadrant, where the y-coordinate of -1 indicates that the point lies below the x-axis. Typically, shaded regions in such problems are defined by positive y-values, making (2,-1) an unlikely candidate for inclusion in the shaded area.

Conclusion
In evaluating the points based on their coordinates and the defined shaded region in the xy-plane, only (-1,1) satisfies the conditions necessary for inclusion. The other points either fall outside the shaded area or do not meet the specified criteria, underscoring the importance of understanding the geometric representation of inequalities in two-dimensional space.

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(-1,1) lies in the shaded region of the xy-plane above.

14/18 represents the probability that a household subscribing to cable television also subscribes to home phone service.

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(-1,1) lies in the shaded region of the xy-plane above.

14/18 represents the probability that a household subscribing to cable television also subscribes to home phone service.

The average number of comic books owned by Fred and Norman is 42.

Janelle will take approximately 2.5 hours to travel 20 miles.

Trevani paid $1.00 in sales tax on the book.

Free Preview Ended

Unlock Full Access

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