Math's Got Problems

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(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

The two problems are left as exercises for the reader. It's a math blog after all.

That said, there are answers. And I even worked them out. So it's your turn.

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.

Come back often for more funny math and geeky comics.

Algebra Problems of the Day (Integrated Algebra Regents, June 2013)

While I'm waiting for new Regents exams to come along, I revisiting some of the older NY Regents exams.

More Regents problems.

Administered June 2013

Part I: Each correct answer will receive 2 credits.


16. If rx - st = r, which expression represents x?

(1) (r + st) / r
(2) r / (r + st)
(3) r / (r - st)
(4) (r - st) / r

Answer: (1) (r + st) / r
Use inverse operations isolate x:

rx - st = r
rx = r + st
x = (r + st) / r

17. What is the solution of the equation (x + 2) / 2 = 4 / x?

(1) 1 and -8
(2) 2 and -4
(3) -1 and 8
(4) -2 and 4

Answer: (2) 2 and -4
Cross-multiply and solve the quadratic equation:

(x + 2) / 2 = 4 / x
x(x + 2) = (2)(4)
x² + 2x = 8
x² + 2x - 8 = 0
(x + 4)(x - 2) = 0
x + 4 = 0 OR x - 2 = 0
x = -4 or x = 2

Or you could have substituted the values in the choices into the original equation and checked which ones made a true statement.

(1 + 2) / 2 ?= 4 / 1
3/2 =/= 4 (No need to check -8)

(2 + 2) / 2 ?= 4 / 2
4/2 = 4/2 (YES!)

(-4 + 2) / 2 ?= 4 / -4
-2 / 2 ?= 4 / -4
-1 = -1 (YES!)



18.Which type of function is graphed below?

(1) linear
(2) quadratic
(3) expotential
(4) absoulte value

Answer: (3) expotential
Linear is a straight line. A quadratic function would go up toward infinity on both sides, down on both sides, but not to the left. An absolute value function is V shaped.

Exponetial functions go almost horizontal on end, and ever-upward on the other.

19. What is the slope of the line represented by the equation 4x + 3y = 12?

(1) 4/3
(2) 3/4
(3) -3/4
(4) -4/3

Answer: (4) -4/3
If you didn't know that the slope of a line in Standard Form (Ax + By = C) is -A/B, then you could have found the answer by converting the equation to slope-intercept form:

4x + 3y = 12
3y = -4x + 12
y = (-4/3)x + 12/3



20. The diagram below shows the graph of which inequality?

(1) y > x - 1
(2) y > x - 1
(3) y < x - 1
(4) y < x - 1

Answer: (4) y < x - 1
It has a solid line which is shaded below. That makes it equal and less than.



More to come. Comments and questions welcome.

More STAAR problems.

Algebra Problems of the Day (Integrated Algebra Regents, June 2013)

While I'm waiting for new Regents exams to come along, I revisiting some of the older NY Regents exams.

More Regents problems.

Administered June 2013

Part I: Each correct answer will receive 2 credits.


11. The solutions of x² = 16x - 28 are

(1) -2 and -14
(2) 2 and 14
(3) -4 and -7
(4) 4 and 7

Answer: (2) 2 and 147
Rewrite x² = 16x - 28 with all the terms on one side and solve the equation by factoring.

x² = 16x - 28
x² - 16x + 28 = 0
(x - 2)(x - 14) = 0
x - 2 = 0 and x - 14 = 0
x = 2 and x = 14

Notice that -28 would have factored into -2 and 14 or 2 and -14. Luckily, neither of those were choices if you had made that mistake with the sign.

12. If the expression (2y^a)⁴ is equivalent to 16y⁸, what is the value of a?

(1) 12
(2) 2
(3) 32
(4) 4

Answer: (2) 2
If (2y^a)⁴ = 16y⁸ then 16y^4a = 16y⁸. That means that 4a = 8, and a = 2.

Remember that the exponent of 4 is applied to everything inside the parentheses, and that the rule for raising a power to a power is to multiply the exponents.



13. Which table shows bivariate data?

Answer: (2)
Bivariate means that you are measuring two kinds of data. In choice (1), only Age is being measured and the frequency of each number is listed. In choices (3) and (4), Type of Car and Day are qualitative, and cannot be measured. You could make bar graphs from these but you couldn't make a histogram out of it.

14. The box-and-whisker plot below represents the results of test scores in a math class.

What do the scores 65, 85, and 100 represent?

(1) Q1, median, Q3
(2) Q1, Q3, maximum
(3) median, Q1, maximum
(4) minimum, median, maximum

Answer: (2) Q1, Q3, maximum
According to the graph, the minimum is 20, Q1 is about 65, the median is about 72, Q3 is about 85, and the maximum is 100. Since the questions asks about 65 and 85, we can assume these are Q1 and Q3. We can't tell exactly what value the median has, but it's in the low 70s, and it isn't put of the question.



15. The expression (x - 3) / (x + 2) is undefined when the value of x is

(1) -2, only
(2) -2 and 3
(3) 3, only
(4) -3 and 2

Answer: (1) -2, only
The denominator of a fraction cannot have a value equal to 0. The numerator is allowed to be 0. This is because you can divide 0 by any number -- if you split 0 four ways, each person gets 0. However, you cannot divide by 0. You cannot divide 4 zero ways.

So x + 2 =/= 0. Therefor x =/= -2.



More to come. Comments and questions welcome.

More STAAR problems.

Positive Role Models

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(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

What about two negative role models making a positive one? Or would two imaginary role models make a negative one?

I have to find new occupations for old zeroes.

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.

Come back often for more funny math and geeky comics.

I'm Answering Some Writing Prompts

This is a reminder, as if you needed one, that I like to try my hand at writing. One of the things I like to do is answer a few Writing Prompts every week. (I'd do it every day if I could keep up with it.) Most of these are basically first drafts written in under an hour, but I'm happy with how they came out.

If you are on Reddit, you can vote on some of my recent entries. Even if you aren't, you can still read some of them.

Here are links to my last five, with working titles. Check them out and let me know what you think -- either on reddit or here. Thanks!

• Devil With an Angel: An angel accidentally gets her wings clipped and is cared for by an angel
• Not a Hero, Just a Temp: a humorous take on the trope that No Hero Can Kill the Demon Lord ... but what about Larry from Accounting?
• Daughter of Two Fae: A woman made a deal with a faerie in exchange for her firstborn, a man did the same thing before two ever met and had a child
• Diary of an Immortal: every 100 years, an immortal's mind is wiped for the sake of his sanity, but he keeps a journal
• Cead Mile Faulty: a Celt from the year 1021 is transported 1,000 years into the future

Thanks again for reading, and for your votes and comments.

Algebra Problems of the Day (Integrated Algebra Regents, June 2013)

And now for something completely different.

While I'm waiting for new Regents exams to come along, I revisiting some of the older NY Regents exams.

More Regents problems.

Administered June 2013

Part I: Each correct answer will receive 2 credits.


6. The roots of a quadratic equation can be found using the graph below.

What are the roots of this equation?

(1) -4, only
(2) -4 and -1
(3) -1 and 4
(4) -4, -1, and 4

Answer: (3) -1 and 4
The roots of the equation are the points where the line crosses the x-axis. This occurs at -1 and 4.

It should have been obious that choices (1) and (4) were incorrect because there are two places where the lines crosses the x-axis.

7. If the area of a rectangle is represented by x² + 8x + 15 and its length is represented by x + 5, which expression represents the width of the rectangle?

(1) x + 3
(2) x - 3
(3) x² + 6x + 5
(4) x² + 7x + 10

Answer: (1) x + 3
Since the formula for the Area of a rectangle is A = LW then x² + 8x + 15 = (x + 5) W.

Factor x² + 8x + 15 and you get (x + 5)(x + 3). You can check this by multiplying, which will give you x² + 5x + 3x + 15.



8Which set of data describes a situation that would be classified as qualitative?

(1) the colors of the birds at the city zoo
(2) the shoe size of the zookeepers at the city zoo
(3) the heights of the giraffes at the city zoo
(4) the weights of the monkeys at the city zoo

Answer: (1) the colors of the birds at the city zoo
Color is a character trait and is descriptive. That makes it a quality of the object, or qualitative data.

The other three are measurable, or quantifiable, so they are quantative data. You could make an argument about shoe size, as that is an arbitrary scale, and it different measures are usually used for male and female, but it is a size that is quantifiable by some scale.

Color is the better choice.

9. The value of the expression 6! + (5!)(3!)/4! - 10 is

(1) 50
(2) 102
(3) 740
(4) 750

Answer: (3) -1
I will come straight out and say: This is a STUPID Question.

It doesn't mean anything. It is an attempt to see if you understand what a factorial is (the exclamation point) and then can properly perform the Order of Operations.

I remember a student asking me after the exam, "Mr. Burke, what does an exclamation point in a math problem mean?" He, apparently, had never seen it.

For those who don't know what a Factorial (!) is, a number like 6! is calculated as 6 * 5 * 4 * 3 * 2 * 1. Start with that number and multiply it by every integer down to 1. This is something that gets used with combinations and permutations.

But this isn't a combination problem. It's just a mess.

Okay, let's solve it now:

6! + (5!)(3!)/4! - 10
= 720 + (120)(6)/(24) - 10
= 720 + (5)(6) - 10
= 720 + 30 - 10
= 740

If there was a hint, it was that 740 and 750 were both answers. If you forgot to subtract that final 10, you got 750.



10. Which interval notation represents -3 < x < 3?

(1) [-3, 3]
(2) (-3, 3]
(3) [-3, 3)
(4) (-3, 3)

Answer: (1) [-3, 3]
When you see "<", you want to use a square bracket like [ or ]. When you see just <, you want to use a rounded bracket or parenthesis, like ( or ).

There are two < symbols, so both symbols are square brackets.



More to come. Comments and questions welcome.

More STAAR problems.

Algebra Problems of the Day (Integrated Algebra Regents, June 2013)

And now for something completely different.

While I'm waiting for new Regents exams to come along, I revisiting some of the older NY Regents exams.

More Regents problems.

Administered June 2013

Part I: Each correct answer will receive 2 credits.


1. Which expression represents “5 less than twice x”?

(1) 2x - 5
(2) 5 - 2x
(3) 2(5 - x)
(4) 2(x - 5)

Answer: (1) 2x - 5
If you have "5 less than" something, then you are taking 5 away from that something.
If I have "5 less dollars" than you, and you have $20, then I would have 20 - 5 = 15.

2. Gabriella has 20 quarters, 15 dimes, 7 nickels, and 8 pennies in a jar. After taking 6 quarters out of the jar, what will be the probability of Gabriella randomly selecting a quarter from the coins left in the jar?

(1) 14/44
(2) 30/44
(3) 14/50
(4) 20/50

Answer: (1) 14/44
There were originally 50 coins in the jar and 20 of them were quarters. However, 6 coins were removed from the jar, meaning that there are only 44 coins remaining. All of the coins that were removed were quarters, so the number of quarters has dropped from 20 to 14.

That means the probability is 14/44.



3.Based on the line of best fit drawn below, which value could be expected for the data in June 2015?

(1) 230
(2) 310
(3) 480
(4) 540

Answer: (3) 480
If you go to June 2015 on the graph and go up to the line, you will reach a point that is just below the 500 level. This makes 480 the best choice.

4.If the point (5,k) lies on the line represented by the equation 2x + y = 9, the value of k is

(1) 1
(2) 2
(3) -1
(4) -2

Answer: (3) -1
Substitute 5 and k in for x and y in the equation. Then solve for k.

2(5) + k = 9
10 + k = 9
k = -1



5. A soda container holds 5 1/2 gallons of soda. How many ounces of soda does this container hold? 1 quart = 32 ounces
1 gallon = 4 quarts

(1) 44
(2) 176
(3) 640
(4) 704

Answer: (4) 704
Convert the units
5.5 gallons = 5.5 (4 quarts) = 5.5 (4) (32 ounces) = 704



More to come. Comments and questions welcome.

More STAAR problems.

Co-medians Getting Coffee

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(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

Of course, they drove down the middle of the street.

They also thought about tea, but it wasn't alliterative. Not even chai.

You know, there are so many numbers involved with cars and their engines, but they took up too much space and weren't funny.

Would the Cocoa Channel broadcast from Hershey, PA? Or maybe Paris, France?

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.

Come back often for more funny math and geeky comics.

Belle & Mr. Whiskers: Skew

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(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

It's just the mean to the left, and a shift to the right.

Either way, Mr. Whiskers is not amused. He's a grumpy boxplot. (You know, I have to see when that other grumpy cat first appeared.)

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.

Come back often for more funny math and geeky comics.

Setting the Table

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(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

A setting for every place, and every place a setting.

Whether than's dinner or supper, I have no idea.

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.

Come back often for more funny math and geeky comics.

Scatter Plot

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(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

Scatter plot a course for home!

Don't connect the dots for these old TV show plots. But you can draw a trend line. If you do that, you can calculate your residuals. It's all about the residuals.

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.

Come back often for more funny math and geeky comics.

(x, why?) Mini: Futile

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(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

Things that make you go Ohm!

I hope repetition of themes doesn't begin to borg you.

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.

Come back often for more funny math and geeky comics.

Happy Mother's Day 2021!

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(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

It almost defies the laws of science, but neither of them are science teachers!

Yes, it's been awhile, and that actually had been the plan, even before the pandemic. Most of the characters are stuck in Temporal Status, which will make the references and relationships in this strip as outdated as early Simpsons episodes if I keep doing this comic. Unless I have a Crisis in Finite Panels.

Side note: there was a couple on Will & Grace in their earlier run who would appear on game nights where the wife was always pregnant, and this went on for a couple of seasons. No mention was ever made to her ever had any actual babies. It was just a running gag that was never mentioned. It would have been a "brick joke" if she'd delivered in the final season.

Happy Mother's Day to everyone, whether you're a Mom, thinking about becoming a Mom, or just thinking about your Mom at all.

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.

Come back often for more funny math and geeky comics.

Things I Can Count On

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(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

Don't you hate when your creations criticize you?

Hands would be challenging even if I used a larger canvas, I think, but I know that I'm in great company when it comes to how difficult hands are to draw.

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.

Come back often for more funny math and geeky comics.

P(C3PO)

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(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

There's no replacing them!

While I'm pretty much over the joke of "May the Fourth", I will continue to acknowledge it. It's odd that I didn't hear it at all for the first 25 years or so, and then couldn't get away from it. Also, I think "Revenge of the Si(x)th" makes more sense than "Revenge of the Fifth", with the side benefit of leaving Cinco de Mayo alone.

As for the problem above there is a 1 in 5 chance of selecting the correct protocol droid and a 1 in 4 chance of selected the correct astromech, meaning that there is only a 1 in 20 chance of selecting the pair of droids you're looking for.

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.

Come back often for more funny math and geeky comics.