Tutor profile: Rohun S.
The equation C=5/9(F−32) shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true? I. A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 5/9 degrees Celsius. II. A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit. III. A temperature increase of 5/9 degrees Fahrenheit is equivalent to a temperature increase of 1 degree Celsius. A) I only B) II only C) III only D) I and II only
The statements below the questions are interpretations of the relationship between 2 variables in the context of slope. The given equation, C=5/9(F-32)= 5/9F - 160/9 is in slope-intercept form, so the slope is equal to 5/9. Since slope is equal to rise over run, for every 5 units of rise, there are 9 units of run. In other words, for every 5-degree increase in Celsius (dependent variable), Fahrenheit (independent variable) increases by 9 degrees. With this in mind, let's evaluate the validity of each statement. To find the increase in Celsius resulting from a 1-degree increase in Fahrenheit, we do: 9 degrees Fahrenheit divided by 9 equals 1 degree Fahrenheit and 5 degrees Celsius divided by 9 equals 5/9 degrees Celsius. Therefore, for every 1-degree increase in Fahrenheit, Celsius increases by 5/9 degrees. Statement I is true. To find the increase in Fahrenheit resulting from a 1-degree increase in Celsius, we do: 5 degrees Celsius divided by 5 equals 1 degree Celsius and 9 degrees Fahrenheit divided by 5 equals 9/5 (or 1.8) degrees Fahrenheit. Therefore, for every 1-degree increase in Celsius, Fahrenheit increases by 1.8 degrees. Statement II is true. Statement III contradicts statement II, so it is not correct. Therefore, the correct answer is D) I and II only.
"Also, studies have found that those students who major in philosophy often do better than students from other majors in both verbal reasoning and analytical writing. These results can be measured by standardized test scores." Which choice most effectively combines the sentences at the underlined portion? A) writing as B) writing, and these results can be C) writing, which can also be D) writing when the results are
When combining sentences, we should always focus on concision and logical flow. Although every answer choice is grammatically correct, 3 of the 4 choices are not ideal. Choice B adds an independent clause to a sentence that already has both independent and dependent clauses, which unnecessarily lengthens the sentence. Also, it includes the word "results", which is out of place, since the 1st sentence does not mention any results. Next, Choice C is mediocre because "also" doesn't fit since the sentence hasn't previously mentioned another way of measuring the results before the standardized test scores. Finally, Choice D doesn't fit because "when" implies that the results of other measurements of the verbal reasoning and analytical writing skills of philosophy majors conflict with standardized test scores. We don't have evidence to suggest that this is the case. Further, the word "results" is out of context since results were not mentioned in the 1st sentence. Thus, that leaves Choice A. Not only is it the most concise, but the word "as" implies that evidence for the fact that philosophy majors "do better" exists. Of course, it does, in the form of standardized test scores.
Find the values of x and y. 14x - 4.5y = -29 7x - 9y = -58
This a system of equations. To solve for x and y, we can use substitution, elimination, or graphing. Substitution works well when one of the variables is already isolated, and we use elimination when it is easy to generate equal coefficient values for two of the same variables. Graphing is ideal when the equations are easy to graph quickly—the slope and y-intercepts are small. In this case, we choose elimination because 4.5 multiplies to 9 and 7 multiplies to 14 easily, so we have two approaches to generate equations that can be added (and one variable eliminated). Thus, we will try to "eliminate" y to solve for x. We begin by multiplying the 1st equation by -2 such that -28x + 9y = 58. We then stack the equations to "add them". -28x + 9y = 58 / (+) -7x - 9y = -58 / -35x = 0 / x = 0 /Now that we have a value for x, we will plug it back into one of the equations (original or "-28x + 9y = 58"). 7x - 9y = -58 Substitute 0 for x. 7(0) - 9y = -58 Multiply 7 by 0. -9y = -58 Divide both sides by -9. y = 58/9 or 6 4/9 Our final answer is x = 0 and y = 58/9
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