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Which expression is equivalent to 9x4 + 21x2 + 3x?
Wrong
Correct!
Wrong
Wrong
Wrong
Let's break this down step by step:
The easiest way to solve this problem is to expand the parentheses.
Take the factor outside, 3x, and multiply it by each term inside:
3x(3x³ + 7x + 1) = 3x·3x³ + 3x·7x + 3x·1
So, the full expansion is: 9x⁴ + 21x² + 3x
The expanded form matches exactly the expression in the problem:
9x⁴ + 21x² + 3x
Therefore, option (B) is correct.
In answer (A): 9x⁴ + 3x(7+1) = 9x⁴ + 21x + 3x → the middle term is 21x, not 21x².
In answer (C): 3x²(3x² + 7x) + 3x = 9x⁴ + 21x³ + 3x → the middle term is 21x³.
In answer (D): 3x(3x³ + 7x² + 3x) = 9x⁴ + 21x³ + 3x² → exponents are wrong.
Answer (E): x(9x³ + 21x + 3x) = 9x⁴ + 21x² + 3x² → gives two x² terms instead of one.
Which of the following conclusions can be drawn from the chart?
Wrong
Wrong
Correct!
Wrong
Wrong
Let's break this down step by step:
The chart divides information into three main categories: Sales, Customer Service, and Productivity and Satisfaction. It further separates them by performance level: Exceeds Expectations, Adequate, Needs Improvement, and Unacceptable. To interpret the data accurately, we must note not only how many details appear in each column, but also how they connect across categories.
Within Productivity and Satisfaction, several details provide insight into company trends. In the Needs Improvement column, the chart shows that sales have gone down for three of the company’s best-selling products. These are described as consistently successful, meaning they are older products that have performed steadily over time. In the Adequate column, however, two newly launched items are listed as instant successes, both have sold out, and one has even received public recognition. Finally, the Exceeds Expectations column notes that total sales surpassed company goals. Taken together, these details indicate that even though some older products are declining, new ones are performing so well that they are compensating for those losses.
Answer (A) is incorrect because it cannot be concluded that customer service is the strongest area of the company. It has the most things written in the exceeds expectations column, but this does not make it the strongest. After all, according to that line of reasoning, customer service would also be the weakest because it has the most written in the unacceptable column, and it can’t be the strongest and weakest area at the same time. In truth, one cannot generally conclude from charts such as these which areas are the strongest or the weakest (or any kind of absolute), as the chart only gives examples of specific things that happened; it does not give a full evaluation. Furthermore, customer service does not even appear to be conclusively stronger than productivity and satisfaction, according to the chart. For these reasons, this conclusion cannot be drawn.
Answer (B) is incorrect because it cannot be concluded that “the customer service representatives are better at handling phone calls than answering e-mails.” There are both positive and negative things listed about customer service e-mails and phone calls. In determining whether or not a department is better in one area than another, it is important to distinguish between general points and individual ones. If an entire department is evaluated in a certain area, we can conclude things about the department from that evaluation. However, if one person does something one time, we cannot. In this case, there are general positive points listed about both phone calls and e-mail responses (everyone averaging above three stars in phone calls, and 90% of e-mails being answered on time), and they are both rated as adequate points. There is also one individual negative point listed about each (the unanswered e-mail and the 0-star phone call, which each happened one time to one person), and they are both rated as unacceptable. The only information we have in addition to this is the 5-star rating on the phone calls of two employees. This is an individual point (about two employees, not an entire department), so it is not enough to conclude that the department is better at phone calls in general.
Answer (C) is correct because it can be concluded that “sales of new products are helping to make up for a gap left by older products” through an evaluation of the Productivity and Satisfaction row. Sales have decreased for older products that were once consistently successful, while new products have sold out quickly and even gained publicity. In addition, total sales have exceeded expectations overall. These connected details show that the company’s strong new-product performance is compensating for the decline in older products.
Answer (D) is incorrect because it it cannot be concluded that “the area that needs the most improvement is productivity and satisfaction.” Productivity and satisfaction does indeed have the most things written in the needs improvementcolumn, but answer choice D was not referring to the title of the column but rather to a general need for improvement. Unlike productivity and satisfaction, the other categories have things written in the unacceptable column, and this is worse than the needs improvement column. Overall, this area of the company seems to be very strong according to the chart, and there is nothing that would lead us to believe that it needs the most improvement.
Answer (E) is incorrect because it cannot be concluded that “The most urgent things that need to be fixed are the rudeness in the phone call, late arrivals, and weekly cleaning.” The chart makes no indication as to which unacceptable points are more urgent to fix than others. Using our own judgment, we should likely arrive at the conclusion that these three items are the least urgent of all five unacceptable points. E-mails going unanswered could directly affect the productivity of the company, and the refund is a problem that has still not even been taken care of, and this can reflect very negatively on the company. While the other unacceptable problems are serious, one certainly cannot conclude that they are more urgent than the unanswered e-mail and the refund.
Read the draft of Sofia’s argument:
Many universities have begun adopting test-optional admissions policies. (1)____________, students who choose not to submit standardized test scores are evaluated more heavily on their essays and extracurricular activities. (2) ______________, critics argue that removing test requirements may unintentionally disadvantage applicants from schools with fewer academic resources. (3)______________, universities that have made the change report increases in both diversity and first-generation college enrollment. (4)______________, the data suggest that while test-optional policies are not perfect, they represent a meaningful step toward equity in higher education.
Select the transition word or phrase that best completes each blank and helps readers follow Sofia’s reasoning.
Wrong
Wrong
Wrong
Wrong
Correct!
The correct answer is (E).
Let's break this down step by step:
In blank (1) the writer explains how test-optional admissions policies work in practice. This means the transition should introduce an example or clarification that illustrates the previous statement.
In blank (2) the writer shifts to the concerns of critics. Because this presents an opposing viewpoint, the transition should signal contrast or counterargument, helping readers recognize that a different perspective is being introduced.
In blank (3) the writer describes the results seen in universities that adopted the policy. Here, the transition should indicate a result or consequence, showing the logical connection between the policy and its outcomes.
In blank (4) the writer acknowledges that test-optional policies are not perfect but still argues in their favor. This part of the paragraph needs a concession transition, one that admits a limitation while reaffirming the main claim.
The best transition for blank (1) is “For instance” because it introduces an example that clarifies how the policy works.
The best transition for blank (2) is “On the other hand” because it introduces an opposing viewpoint, showing contrast.
The best transition for blank (3) is “As a result” because it connects the earlier action (the policy change) to the effect that follows (more diversity and first-generation enrollment).
The best transition for blank (4) is “Nevertheless” because it acknowledges criticism but maintains support for the argument.
Therefore, answer (E) is correct.
Answer (A) is incorrect because the flow breaks because the first, third, and fourth connectors do not fit the paragraph’s purpose:
Answer (B) is incorrect because only the third connector fits, and the others make the logic confusing:
Answer (C) is incorrect because the first and fourth connectors do not fit the paragraph’s purpose:
Answer (D) is incorrect because the last connector does not fit and changes the meaning of the ending:
Answer (E) is correct because all four connectors fit the logic and tone of the paragraph:
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