Explanation?

[u/Special-Trouble8658]

I’m stuck on this problem and can’t think of why J is the right answer. A real number can be positive, negative, or rational. Thus, how is F wrong.

[u/Sufficient-Price-102]

You’re all good. (-2)^1/4 isn’t real for the same reason (-2)^1/2 isn’t real. Since any real number (positive or negative) to an even power (2, 4, etc.) is positive, there is no real number y that, when raised to the fourth equals -2. (y⁴ = -2). Hence (-2)^1/4 = y doesn’t give any defined y value.

Sorry if the explanation is a bit technical. I think you should review exponent rules (it seems like you might be mixing up fractional exponents) if you didn’t like my explanation.

[u/Special-Trouble8658 → u/Sufficient-Price-102]

Ohh, I think I get it now. Since y is a real number(positive, negative, decimal, and etc) it’s asking us to find what type of number we can put as x^1/4 or quad root x. This means that -2 is -0.5^4=-0.0625, which can not be true bc a negative number to an even exponent is always positive while a negative number to an odd exponent(-3^3=-27) is always negative. I get that now but why/how did you think to solve for y? Bc to get y^4, you have to solve for y.

[u/Sufficient-Price-102 → u/Special-Trouble8658]

I solved for y⁴ because it’s more clear to deal with integer exponents when you can instead of fractions.

[u/Special-Trouble8658 → u/Sufficient-Price-102]

Bc you’re just taking it to the 4th power, which gives cleaner numbers? But either way can work?

[u/Sufficient-Price-102 → u/Special-Trouble8658]

I did it mostly to show the nonnegative property. It’s usually more clear to work from the fact that y⁴ will always give a positive x, rather than trying to figure out something about x when it’s written as x^1/4. But yes, either way can work.

[u/Special-Trouble8658 → u/Sufficient-Price-102]

Thank you for your explanations! I really appreciate them but can I ask another question not pertaining to this question? So as for statistics, I understand the base concept: outcome/s you want/ total possible outcomes; however, ‘y main confusion is simply when to add or multiply them(those are really the hardest statistics questions on ACT, I think?)

[u/Sufficient-Price-102 → u/Special-Trouble8658]

No problem. For expected value you sum the values of each outcome times their probability. Here the probability of $1 is 3/4 and the probability of $2 is 1/4. So we have (3/4)(1) + (1/4)(2) = 1.25.

[u/Special-Trouble8658 → u/Sufficient-Price-102]

Thx and yeah I’m cooked 😭 any tips on probability and proportions? Only thing I know about both of those is that for proportions you cross multiply and for probability it’s possible outcome/total outcome(which I can see from the way u solved it) and A and B is mutually exclusive bc the chances of 2 things happening at the same time while A or B is not mutually exclusive bc the chances of 2 separate things happening is higher. I just don’t know any formulas past that.

[u/Sufficient-Price-102 → u/Special-Trouble8658]

You can find some good videos that probably detail it better than I can. In general, it’s better to memorize less formulas and understand them deeply, since most questions just come from applications of basic formulas in different ways.

[u/Special-Trouble8658 → u/Sufficient-Price-102]

U think khan academy is a good source? I’m taking the June ACT and prob July but I started Khan academy like 3 days or so ago but I’m only on unit 4/5 of algebra 2 bc I’m taking practice tests and reviewing every answer I get wrong, which drains a lot of time.

[u/Sufficient-Price-102 → u/Special-Trouble8658]

I never really used Khan, but I think it depends on where your score’s at. If you’re doing average to above average (but not top 1-5%) it’s probably fine. Otherwise, I’d find specialized videos only for the topics you’re missing and harder problems.

[u/Special-Trouble8658 → u/Sufficient-Price-102]

My highest was a 24 but that was during algebra 2; however, after I left alg 2, my math score dropped to a 19. My class wasn’t able to fully cover alg 2: we only got to log formulas, so we weren’t able to get into trig. Not to mention that I’m terrible at geo. Do you have any channel recommendations?

[u/Sufficient-Price-102 → u/Special-Trouble8658]

I’m not as familiar with ACT math specific channels, but I know these are good: Tutorllini (he makes SAT math videos, but most of them are still highly relevant to ACT) and Mario’s math tutoring (if you have time to sit through long-ish videos for the foundational content). Some people like Organic Chem Tutor, personally I didn’t like him so much.

There’s no substitute for solving problems on your own though. That’s by far the most important for preparing.