(C)Copyright 2018, C. Burke.
Someone has to be the last to know.
This was supposed to be Wednesday's comic, and today's comic will hopefully appear Monday. Yeah, school started again.
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Someone has to be the last to know.
This was supposed to be Wednesday's comic, and today's comic will hopefully appear Monday. Yeah, school started again.
Come back often for more funny math and geeky comics.
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I prefer let no one 'put us under', but no one catches that when I say it out loud.
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Would a polar bear be a 'bear north'? Like a compass? Would it live in a concave?
Oddly, I enjoyed the titular pun because it could refer to an actual measurement, or what actions Dec and the team undertake!
The Polar Treasure was both the fourth pulp adventure and the fourth Bantam paperback.
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The design flaw is the bottoms of your feet. You don't want to get burned down to your soles.
Yes, I feel like a heel for telling that joke.
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If I had to hypothesize, I'd go with 30*ln(x), where x is the number of coats.
Or just wear coats for the Sun can't get to you. But you might pass out from the heat that way.
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Even as I type "8-sider", I'm thinking "octahedron" not "octagon".
I haven't read Quest for the Spider yet, and I didn't know that it was so early in the series because it wasn't reprinted as a Bantam paperback until #68.
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The limit is on the allowed amount of fun.
The bigger joke is that people think Mike is a stand-in for me, but Mike has never raised his voice to express himself.
Once again, this comic is semi-autobiographical. I can invoke Murphy's here because I've been saying that due to all the rain this summer, I haven't had to top off the pool (or water the garden as much), so the water bill should go down. And now there's a week of Sun ahead of us, and I'm topping off the pool. With cold water. That likely won't warm up too quickly.
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Don't try to steal it! It's already taken!
So this happened:
A Twitter colleague, Taylor Grant, @teachbarefoot, announced his new blog
To which I replied, Now that is a great name for a bln(x)!
Taylor liked my pun better, and re-christened his bln(x) to include the "b".
Obviously, I'm not stealing his idea because a) I suggested the "b", and b) I skipped the parentheses to save space.
Enjoy his blog. My blog will remain the usual comics, test questions and answers, and the occasional mathematical insights, which are hopefully my own and not someone else's restated in (mostly) my own words.
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More Algebra 2 problems.
June 2017, Part I
All Questions in Part I are worth 2 credits. No work need be shown. No partial credit.
13. A student studying public policy created a model for the population
of Detroit, where the population decreased 25% over a decade. He
used the model P = 714(0.75)^{d}, where P is the population, in
thousands, d decades after 2010. Another student, Suzanne, wants
to use a model that would predict the population after y years.
Suzanne’s model is best represented by
Which explanation is appropriate for Miles and his dad to make?
1) P = 714(0.6500)^{y}
2) P = 714(0.8500)^{y}
3) P = 714(0.9716)^{y}
4) P = 714(0.9750)^{y}
Answer: 3) P = 714(0.9716)^{y}
There are 10 years to 1 decade, so d = 10y
So P = 714(0.75)^{d} = 714(0.75)^{10y} = 714(0.75^{10})^{y}
And P = 714(0.9716)^{y}
14. The probability that Gary and Jane have a child with blue eyes is 0.25, and the probability that they have a child with blond hair is 0.5. The probability that they have a child with both blue eyes and blond hair is 0.125. Given this information, the events blue eyes and blond hair are
Answer: (2) II, only
They are independent because P(A and B) = P(A) * P(B). That is 0.125 = 0.5 * 0.25.
This eliminates choices 1 and 3.
The events are not mutually exclusive, because P(A or B) = P(A) + P(B) - P(A and B) = 0.25 + 0.5 - 0.125 = 0.625, but 0.625 =/= 0.5 + 0.25.
15. Based on climate data that have been collected in Bar Harbor, Maine, the average monthly temperature, in degrees F, can be modeled by the equation B(x) = 23.914sin(0.508x - 2.116) + 55.300. The same governmental agency collected average monthly temperature data for Phoenix, Arizona, and found the temperatures could be modeled by the equation P(x) = 20.238sin(0.525x - 2.148) + 86.729.
Which statement can not be concluded based on the average monthly temperature models x months after starting data collection?
1) The average monthly temperature variation is more in Bar
Harbor than in Phoenix.
2) The midline average monthly temperature for Bar Harbor is
lower than the midline temperature for Phoenix.
3) The maximum average monthly temperature for Bar Harbor is
79° F, to the nearest degree.
4) The minimum average monthly temperature for Phoenix is
20° F, to the nearest degree.
Answer: 4) The minimum average monthly temperature for Phoenix is
20° F, to the nearest degree.
If you graph both of these functions you will find the following information:
For Bar Harbor: the minimum value is 31.39, the midline 55.3, the maximum is 79.21 and the range is 47.83.
For Phoenix, min is 66.49, mid is 86.73, max is 106.97 and range is 40.48.
Choices 1, 2, and 3 can be seen in the data. Choice 4 is incorrect, the minimum average monthly temperature for Phoenix is approximately 66° F, to the nearest degree.
Comments and questions welcome.
More Algebra 2 problems.
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Dammit, I'm mad.
I guess that was, you know, "palindrome weak".
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Are the odds stacked against Dec?
I'm still decided on the format. I'll probably use the pulp order (or publication order) but parody the Bantam covers.
I fiddled with the logo, and I made the image taller so I could include a "cover blurb", which makes up for the lack of dialogue. Also, the blurb means people who see the image away from the blog or the comic page will see that text and not miss the joke. Without context, it's just an odd image.
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Historically, the expression is *pleased as Punch & Judy*.
And Ken is the puppet master.
I had more exposition, but it was just a recap of last week's comic and blog notes. Who needs that, right? what we really need is
a wacky Wikipedia link!
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When you beat bosses together, it's getting serious.
My intent had been to have more updates this week, but this one took a lot longer than anticipated, even in black and white.
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Well, someone's got to get these two together, right?
Debated whether or not to do "School Life" in the summer, and then whether or not this strip would fall into that category. (For one thing, it's in color, not black and white.) That's what I get for starting so many sub-series within the main series. Why am I even numbering these things?
How should things work out for Vanessa and Sven? Or Missy and Vaughn? Or the green-haired kid whom I don't think I created a name for...
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''Doc? Are we going to Widow's Peak?'' ''No!''
Something old becomes something new. I had a bit of debate with myself about how to do this. Just the covers? Do I need dialogue? If so, where to add it? Maybe underneath, or just the "alt" text. I don't know.
If it's just the covers, with no dialogue, then I spent too much time -- including a Twitter poll -- deciding on the supporting characters. We'll see as time moves on.
Also, if anyone knows how to *easily* remove the shadows from WordArt, or knows a similar program to produce the titles, that would be great.
By the way, the alternate title was going to be Dec Visage, to remove it further from the original, but I thought that that might be too far. "Visage", of course, is a word refering to a face, which 3-D objects, like prisms and pyramids, have.
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ObMath: The mean age of the guys should equal the mean age of the girls. And other mean stuff going on.
The dialogue for this comic was originally wordier, trying to get it where it needed to go (and even included, sort of, a reference to the above fact, giving their relative ages). Judy and Chuck have been together almost as long as Ken and Michele (possibly longer, but I'm only going by first mentions).
Stranger fact: even though Chuck has been mentioned a few times, I don't think he's appeared since comic #321 on the Fourth of July in 2009. NINE YEARS! He was supposed to be shown at the wedding, but I simplified that strip as much as I could, so none of the +1's were shown.
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Stand back. You don't to get into the thick of it!
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Don't stand in the amplitude. Don't block the wave.
Yeah, that's about all I had. That's why this became a "mini". For what it's worth, this looks like the 100th Mini I've done.
I say "looks like" because my count has been off once before due to mislabeling a file. But this is the 100th entry that has the
Mini tag.
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Doctor Woo Hoo and his Companion. Or Doctor Cutey and her Companion.
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They were complementary, and it turned out so right.
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Don't be the negative one here. That's his job.
I can't believe I haven't done this before. And there may be more of this to come.
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He is happy just as He is. Say what you want, you won't get a reaction.
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Mr. & Mrs. Wayne will pop up any time now.
I wanted a Ken-and-Michele-are-back comic, and then I left them out of it.
I also left out the math -- probability that two people would capsize the chair was approximately 1.0.
I also figured that they would have gone out with Judy and Chuck first, but where's the math in that? Other than figuring the tip? (Chuck might be the least mature of the group, but I didn't want him to be a dweeb or anything.)
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It's only skew if the dancer *misses* the pole. But that wouldn't be as funny!
Don't try this at home. Or on the road.
Don't get ''shiggy'' with it.
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I had a couple different ideas, but thise was the quicker one to do after my day off.
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The following are some of the multiple questions from the recent June 2018 New York State Common Core Geometry Regents exam.
The answers to Part I can be found here
The answers to Part II can be found here
Each correct answer is worth up to 4 credits. Partial credit can be given. Work must be shown or explained.
32. Triangle ABC has vertices with coordinates A(-1,-1), B(4,0), and C(0,4). Prove that ABC is an isosceles triangle but not an equilateral triangle. [The use of the set of axes below is optional.]
Answer:
If it is isosceles, then at least two legs have the same length. If it is not equilateral, then the third leg will have a different length.
Looking at the coordinates of the points, it should be obvious that AB and AC are congruent because you'll be using the same numbers in the calculations.
AB = SQRT ( (-1 - 4)^{2} + (-1 - 0)^{2} ) = SQRT(26)
AC = SQRT ( (-1 - 0)^{2} + (-1 - 4)^{2} ) = SQRT(26)
BC = SQRT ( (4 - 0)^{2} + (0 - 4)^{2} ) = SQRT(32)
There is no need to simplify because you're only looking for equality or inequality.
AB is the same length as AC but not the same as BC. Only two sides are congruent, so ABC is isosceles but not equilateral.
33. The map of a campground is shown below. Campsite C, first aid station F, and supply station S lie along a straight path. The path from the supply station to the tower, T, is perpendicular to the path from the supply station to the campsite. The length of path FS is 400 feet. The angle formed by path TF and path FS is 72°. The angle formed by path TC and path CS is 55°.
Answer:
We can find the length of TS by using the tangent function with triangle TSF.
Once we know TS, we can use the sine function with triangle TSC to find the length of CT, the distance from the campsite to the tower.
Make sure your calculator is in Degree mode.
Tan 72 = x / 400
x = 400 * tan 72 = 1231.07...
Sin 55 = 1231.07 / y
y = 1231.07 / sin 55 = 1502.85897... = 1503 feet.
The distance from the campsite to the tower is 1503 feet.
Note that you could have skipped the intermediary skip and used (x / 400) in the last equation. Finding the length of TS was not required for the problem.
34. Shae has recently begun kickboxing and purchased training equipment as modeled in the diagram below. The total weight of the bag, pole, and unfilled base is 270 pounds. The cylindrical base is 18 inches tall with a diameter of 20 inches. The dry sand used to fill the base weighs 95.46 lbs per cubic foot.
Answer:
Find the Volume of the Base in cubic feet (not cubic inches). Multiply that by .85 to find 85% of the Volume. Multiply that by 95.46 to find the weight of the sand in the base. Then add 270 pounds for the bag, pole and unfilled base.
Remember that the radius is half the diameter: 20 / 2 = 10 inches, which is 10/12 of a foot. The height is 18 inches, which is 18/12 feet.
V = pi * r^{2} * h = (3.141592...)(10/12)^{2} * 18/12 = 3.27249
.85V = .85 * 3.27249 = 2.7816 cubic feet.
The weight of the sand = 2.7816 * 95.46 = 265.53 pounds.
Total weight = 265.53 + 270 = 535.53 or 536 pounds.
End of Part III
A correct answer is worth up to 6 credits. Partial credit can be given. Work must be shown or explained.
35. Parallelogram ABCD, BF ⊥ AFD, and DE ⊥ BEC.
Answer:
BEDF is a rectangle if it is a parallelogram as has a right angle. You need not prove the length of the opposite sides are congruent.
1. ABCD is a parallelogram, BF ⊥ AFD, DE ⊥ BEC: Given
2. BC || AD: Opposite sides of a parallelogram are parallel.
3. BE || DE: Parts of parallel lines are parallel.
4. BF || DE: Two lines that are perpendicular to the same line are parallel.
5. BEDF is a parallelogram: A quadrilateral with two pairs of parallel sides is a parallelogram.
6. Angle DEB is a right angle: Perpendicular lines form right angles.
Note: Line 6 wasn't actually *Given*, even though the boxes for right angles are shown in the diagram. Whatever reason you give, the fact that it is a right angle is important and must be stated!
7. BEDF is a rectangle: A parallelogram with a right angles is a rectangle.
End of Part IV
How did you do?
Questions, comments and corrections welcome.
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