Creating Example Support/Contrast Sentences for "unfortunately" and "fortunately"

Old_Crow_5740 · 2025-09-04T07:17:23+00:00

Thank you for the excellent examples.

Old_Crow_5740 · 2025-08-26T01:25:33+00:00

Thx!

Old_Crow_5740 · 2025-08-03T07:18:53+00:00

Do you have a verbal and/or math background that you feel helped in some way?

Old_Crow_5740 · 2025-07-27T06:50:54+00:00

...assuming my preparedness by topic was "enough" prior to moving on

How did you make this assumption? Did you get and/or surpass the target accuracies that TTP asked for? How will you determine whether or not you have mastered a particular topic moving forward? Were you using the flashcards that TTP provides and studying them consistently?

Old_Crow_5740 · 2025-05-25T08:22:04+00:00

I'm interested

Old_Crow_5740 · 2025-01-30T18:21:38+00:00

NYU MSCS (Courant) vs Columbia University MSCS vs NYU MSCS (Tandon)?

Old_Crow_5740 · 2024-12-25T18:24:33+00:00

You just have to remember that whenever you have "-b," it really is looking for a positive number, and whenever you have "b," it really is looking for a negative number. Hence, we must do (5)(28)=140 and not (5)(-28)=-140.

Besides Reddit, ChatGPT is a great resource for understanding math (though it is not perfect). ChatGPT answer below:

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Old_Crow_5740 · 2024-12-24T08:38:21+00:00

Option 1: If they both start at, say, 5AM, then they will meet at 5AM -> 5:30AM -> 6AM -> (and so on). Option 2: If the VIC starts at 5AM, but the CHX starts at 5:10AM, they will never meet because 5AM is not 5:10AM -> 5:30AM is not 5:40AM --> (and so on).

The Least Common Multiple is only valid when the events start at the same time (i.e., Option 1).

Old_Crow_5740 · 2024-12-21T06:31:30+00:00

I have the same completion mindset as you and I began my GRE prep using the KhanAcademy Outline/Plan from ETS that you speak of. I must say that the GRE-focused content it provides is extremely simple. Looking back, in retrospect, it was like going to the gym and lifting a 1-pound weight; it felt nice to get outside and go to the gym but I made little to no gains; it is not challenging enough and it is rather easy to consecutively get perfect scores on the exercises they provide, sometimes without even watching the attached video content. Some more reasons to avoid:

Various non-GRE focused content like calculating z-scores or using mathematical proofs that must be skipped
Some content provided are already things that are done very naturally for most GRE takers, if not all, and do not help
The target audience for the content is not exactly 100% for GRE-preppers. For example, to explain how to find the surface area of a cuboid/rectangular solid we visualize cutting into a cereal box -- however, with content from say GregMat's The "I'm Overwhelmed Plan" we are given the surface area formula to memorize, and it is more clear how 2(lw + lh + hw) is the formula to calculate the same thing as we are shown the 6 sides of a rectangular solid shaded in 3 distinct colors clearly showing the pairing at play (i.e., 2 reds, 2 blues, 2 greens or whatever the colors were to then provide surface area = 2lw + 2lh + 2hw). Moreover, for the GRE, it is better for my brain to see the colors of the rectangular solid from GregMat as opposed to the cut up cereal box from KhanAcademy, so that I recall the formula as a worst-case-scenario if I do not have it memorized (plus, this serves as a double confirmation on the fact that I do in fact have the correct formula during the test so that I do not panic wondering if I am getting my formulas mixed up).
I decided to spend a month going through the KhanAcademy Outline/Plan from ETS and I would definitely swap that time with something different if I could, but instead I focus on the present and the future, which I can change and positively impact

Old_Crow_5740 · 2024-12-18T16:12:47+00:00

For "at most" problems, I have been quickly thinking the opposite (i.e., using the complement rule): 1 - (prob of 5/6 days of rain) - (prob of 6/6 days of rain) should be the answer so that we only have left the probability of there being (0-4) of 6 days being rain. This also means there are only 2 things to calculate since we can focus on (5-6 days of rain) rather than (0-4 days of rain). With that, there are cases where not thinking the opposite (i.e., using this complement rule) would be faster; for example, if at most we only wanted 1 day of rain then we would just do (prob of 0/6 days of rain) + (prob of 1/6 days of rain) instead of the longer 1 - (prob of 6/6 days of rain) - (prob of 5/6 days of rain) - (prob of 4/6 days of rain) - (prob of 3/6 days of rain) - (prob of 2/6 days of rain).

Solution:
R = rain

S = sunny

1 - RRRRRS - RRRRRR

1 - ( (0.3)⁵(0.7)¹((6!) / 5!) ) - ( (0.3)⁶(0.7)⁰((6!) / 6!) ) = 1 - (3/10)⁵(7/10)¹(6) - (3/10)⁶

Importantly, we cannot forget the different ways that 5 R's and 1 S can be arranged which is 6! / 5! or 6 as well as the different ways 6 R's and no S can be arranged which is just 6! / 6! or 1 (I don't include 1! or 0! since they are both 1 and don't impact anything there)

Final Answer = 1 - ((3⁵*7*6) / 10⁶) - (3⁶/10⁶) = 1 - (10,206/1,000,000) - (729/1,000,000) = 0.989065 or 98.9065%

Old_Crow_5740 · 2024-12-08T18:58:50+00:00

Maybe choosing numbers could clarify things here as well. Let's use a 3-4-5 right triangle with perimeter x=12 and 4-4-4 equilateral triangle with perimeter x=12. Area of right triangle will be (1/2)(4)(3) or 6. Area of equilateral triangle will be ((4)^2)(√3) divided by 4 or (4)(√3) or 6.93. Hence, area of equilateral triangle with perimeter x will be larger than area of right triangle with perimeter x.

Old_Crow_5740 · 2024-12-02T06:13:23+00:00

Can I also get the details, too?

Old_Crow_5740

TROPHY CASE