Tutor profile: Christie L.
The average number of students per classroom, y, at Central High School can be estimated using the equation y = 0.8636x + 27.227, where x represents the number of years since 2004 and x ≤ 10. Which of the following statements is the best interpretation of the number 0.8636 in the context of this problem? A) The estimated average number of students per classroom in 2004 B) The estimated average number of students per classroom in 2014 C) The estimated yearly decrease in the average number of students per classroom D) The estimated yearly increase in the average number of students per classroom
Our objective is to understand the slope or y-intercept of the graph because we're not given a visual graph. We can estimate the independent variable, y, for a given value of x. Based on the standard slope equation on a xy plane: y = mx + b 0.8636 is m which is the slope. This positive number gives us a positive slope which indicates that the average number of students per classroom is increasing. Therefore, choice D is right. Choice A is wrong. Because the average number of students in 2004 is determined by the y-intercept of the graph of the equation which represents the estimated average number of students per classroom in 2004. Choice B is wrong. The limitations of the model are given by x ≤ 10. This statement determines that the model finds the average number of students in 2014. Choice C is wrong. The slope is 0.8636 which is a positive number. Therefore, the rate of change is positive and an increasing slope. Additionally, the y-intercept is added which makes it even less likely that it would be a decreasing function.
All during the financial advisor's presentation on investment options, Tina repeatedly tried, to no avail, to (I)____ Donovan of his positive impression of the speaker's motives. Donovan, however, was (ii)___ in his convictions. Blank (I): a: disabuse, b: advise, c: convince Blank (ii): d: ambivalent, e: stalwart, f: steadfast
A key part to notice is "to no avail" which makes us note that whatever Tina is trying, it is not working no matter what repeatedly tries. For the blanks, we always have to note whether it's a positive or a negative word. Following blank (I) we see that Donovan thinks positively of the speaker's motives. Is Tina trying to make Donovan like the speaker more or dislike? It seems that she is trying to move Donovan from the way he currently thinks about the speaker; so, we want a negative first blank. While (a) convince and (b) advise may seem like viable options because Tina is trying to persuade Donovan in someway, her motives are closer to being warnings and persuading him that he is WRONG. Therefore, we should choose (c) disabuse. Even if we don't necessarily know what disabuse means, it has a -dis- prefix which is a negative connotation. (as it turns out, disabuse means to sway someone from a negative way of thinking) Finally for blank (ii), we see that Donovan holds to his convictions. Fill in the blank yourself before looking at the answer choices. You might think something along the lines of Donovan, however, was steady in his convictions. Looking at the answer choices we first see (d) ambivalent: -Ambi- means both and ambivalent means wishy-washy and not a solid choice. So we can cross it out because it isn't' what we want. (e) stalwart means loyal which seems like a good choice. However, Donovan isn't necessarily loyal like a friend but he is simply sticking to his opinion. He is constant in his thought Therefore, (f) steadfast : unwavering -- is our winner is (f) steadfast because it is strong in its opinion. Answer: blank (I): a : disabuse blank (ii): f : steadfast
Subject: Basic Math
What is the remainder when dividing 491 by 9?
First, you divide 491 by 9. In doing so we see how many times 9 goes into 491. We see that it is 54.555...6. This tells us that we can fit 9 inside of 491 a total of 54 whole times which will leave us with a little leftover. So, we do 54 x 9 = 486. To find the remainder we take 491 and subtract it by 486. 491-486 = 5 We have a remainder of 5. Work to show: 491 / 9 = 54.555...6 54 x 9 = 486 491-486 = 5 Remainder = 5 491 / 9 = 54 r5
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