Happy Veterans Day 2020

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(C)Copyright 2020, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

Their masks are in their pockets, okay. They'll take them out as they need them.

I would think that if he couldn't go to the American Legion post today, my father would be over in his community garden where he grew tomatoes and peppers. It's actually a nice day outside, except for some light drizzle or mist.

Happy Veterans Day to all verterans, and Thank you.

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Algebra 2 Problems of the Day

Daily Algebra 2 questions and answers.

More Algebra 2 problems.

Welcome back. After a long pause, the Problems of the Day are back. And I'll be honest, the reason I haven't been posting is because I forgot that I hadn't finished all the New York State Regents exams. Otherwise, I would have continued after I posted the January 2020 exam. As far as I can tell, I left off in Part I of the January 2017 exam.
Update: After doing a deep dive on my blog, I discovered that I have answered these questions before -- except that I used the tag "Algebra" instead of "Algebra 2", even though "Algebra 2" was in the title of the posts. Next project: update all those old tags.

January 2017, Part I

All Questions in Part I are worth 2 credits. No work need be shown. No partial credit.


7. The expression [SEE IMAGE BELOW] is equivalent to

[SEE IMAGE]

Answer: 2) SEE IMAGE BELOW
The rules of exponents. A negative exponent indicates a reciprocal. A fractional exponent indicates a root (square, cube, fourth, etc). An exponent outside of the parentheses multiplies all the exponents inside the parentheses (even if those are 1). Exponents appearing in the numerator and denominator of a fraction mean that, if the base is the same, the exponents are subtracted.

Some of the operations shown below could have been done in a different order, but the result should be the same. (If it isn't, then a mistake was made. Please, check your work.)

The -1/2 exponent is resolved by taking the reciprocal of the fraction and changing the -1/2 to +1/2.

The 1/2 exponent is resolved by multiplying, producing m^1/6 in the numerator and m^2/2, which is just m, in the denominator.

Subtract 1/6 - 1, which is -5/6.

Negative exponent. Take the reciprocal and make it +5/6.

Finally, take the sixth root of m⁵, which is Choice (2).

8. What is the inverse of the function y = log₃ x?

1) y = x³
2) y = log_x 3
3) y = 3^x
4) x = 3^y

Answer:(3) y = 3^x then x = 3^y.

The inverse of that would switch the x and the y, so the inverse is y = 3^x.



9. Gabriel performed an experiment to see if planting 13 tomato plants in black plastic mulch leads to larger tomatoes than if 13 plants are planted without mulch. He observed that the average weight of the tomatoes from tomato plants grown in black plastic mulch was 5 ounces greater than those from the plants planted without mulch. To determine if the observed difference is statistically signifi cant, he rerandomized the tomato groups 100 times to study these random differences in the mean weights. The output of his simulation is summarized in the dotplot below.
Given these results, what is an appropriate inference that can be drawn?

1) There was no effect observed between the two groups.
2) There was an effect observed that could be due to the random assignment of plants to the groups.
3) There is strong evidence to support the hypothesis that tomatoes from plants planted in black plastic mulch are larger than those planted without mulch.
4) There is strong evidence to support the hypothesis that tomatoes from plants planted without mulch are larger than those planted in black plastic mulch.

Answer: 2) There was an effect observed that could be due to the random assignment of plants to the groups.
There was an effect, but there isn't strong evidence. It could be random.

Comments and questions welcome.

More Algebra 2 problems.

I also write Fiction! Check out In A Flash 2020, by Christopher J. Burke for 20 great flash fiction stories, perfectly sized for your train rides. Available in softcover or ebook at Amazon. If you enjoy it, please consider leaving a rating or review on Amazon or on Good Reads. Thank you.

Attractive

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(C)Copyright 2020, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

Whether Scott is more attracted to Annie or Barbara is left as an exercise to the reader.

Originally, I had Scott's desk with his computer setup behind him. All that got cut to so I could fit three panels. Also, witty banter is the antithesis of the strategic use of dialogue balloons. As it was, I had to navigate a minefield about being attracted to "large" or "massive" bodies for the sake of the punchline.

And it looks like that punch is coming.

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(x, why?) Mini: Two Pips

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"Place your bet, and let it ride!"

Given that the first pair of snake eyes has already been rolled, the probablity of a second pair is only 1 in 36.

However, if we wanted to know the probability of rolling snake eyes twice, it would be (1/36)(1/36) or 1 in 1296. If you roll the dice and scoop them up every two seconds, then you should see it happen in less than an hour, on average.

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After Halloween

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(C)Copyright 2020, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

After Halloween? All Saints Day. All Souls Day. And there's something after that, I think.

This is as close as I get to dipping a toe in the water. And only because I had all the characters in existence, even if he's not the new number 2 any more. There was too much of this 12 years ago. Looking back at my first year, these are the strips I hate, and the reason I never did a "First 100 Strips" book.

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School Life #18: Happy Halloween 2020

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I don't know how happy it'll be. Maybe it'll be more stealthy.

In years past, no facial coverings were allowed in school. Face makeup is fine, but not actual masks. (I have twice, at different schools, gone as Green Lantern using face paint.) This year, everyone is masked up.

The other amusing thing is how many heroes have masks that don't cover their mouths. This works well visually for comics and movies so the characters can be more expressive.

Non-turtle ninjas seem an obvious choice for a costume that covers the face but leaves the eyes visible. The problem is that it looks like regular dark clothing that's been accessorized.

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Math Horror Movies: THEm!

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>Spoiler: There's no top. That's anticlimactic, I know.

So this one came about accidentally while I was working on "The y". I almost made a joke in the aftertext and then realized I had a comic.

And top of this, I borrowed the spider from the work files from Ants vs. Spiders, which had all those lovely ants as well.

The one thing that killed me was that I found the background and started making the comic, forgeting that I needed to fit it into my screen. I could have avoided a couple of problems. For one thing, I would have made the slope less steep, and fit more ants on it. Second, I actually had to slightly rotate the ants to fit them on this line when they would have fit a more gentle slope just fine.

Planning always helps. Having time to plan ... well, that's a different buggy situation. Anyway, que sera, sera, whatever plus b plus b.

And as these are all "B" films, don't expect to see The b any time soon. Not until next year when I'm either desperate enough to use it, or forgetful enough to think I thought of it for the first time!

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Math Horror Movies: (x, why?) The 13th

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>Accept no similarities! It's the same or it's not.

I overthought a compilation before simplifying, so to speak.

When I first started this, I never expected to still be doing this years later. Many of the webcomics I read back in 2007 have fallen by the dustbits (some have been reclaimed). Others are still going strong. Me? To quote (then paraphrase) Luke Coombs: "They say I'm middle of the road, not much to show, underachieving average Joe." But I wear my heart of my sleeve, and that might not mean much to them, but it does to me.

For thsoe who I left waiting for this one: my apologies, but family first. They were here for a good part of the day, which prevented me from finishing up. But that's fine with me.

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Math Horror Movies: THE y

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What will it intercept?

I don't know how many Math Horror Movies there will be this year because I've run through most of the obvious and quite a few obscure movie references, and they'll get more repetitive than a math drill.

This one was a little truoublesome. I originally thought to call it The Return of the y or somesuch because I thought "The y" might not be obvious. Once I drew it, I didn't feel that way. Except ... !

Then I had the logo (and post title) problem that is looks like "They"! So I played some font games. I'm happy with the result.

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Congruent

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A Pythagorean Triple whammy.

Originally, I was going to use WALK and RIDE before I decided I wanted Pentagons, for whatever reason. Oddly, it was difficult finding lists of 6-letter words with no repeated letters. Maybe I was using poor search terms.

EDIT: This was supposed to have been added when I got home last night and was sitting at my own computer. That obviously did not happen.
A congurent number is an integer that is the area of a right triagnle with three rational sides, which are not necessarily integers.
In the case of this comic, a triangle with sides of 24/5, 35/12, and 337/60 would have an area of (1/2)(24/5)(35/12), or 7.

No, not an obvious solution. I saw the list of congruent numbers before I found a list of triangles that created them. I wouldn't have wanted to have worked that out. For starters, I probably would've been stuck on the 7-24-25 triangle, trying to get an area of 7 out of that!

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Families of Functions

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It's a Not All in the Family moment.

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Time Remaining

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The moment after they post those ''Time Remaining'' announcements, they're incorrect.

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