STAAR (State of Texas Assessments of Academic Readiness) Algebra I, May 2019, cont.

Continuing with the State of Texas Assessments of Academic Readiness (STAAR) exam, administered MAY 2019.

More STAAR problems.

Administered May 2019

Read each question carefully. For a multiple-choice question, determine the best answer to the question from the four answer choices provided. For a griddable question, determine the best answer to the question.


21. Which graph best represents y = -x² + 6x - 1?

[SEE IMAGE]

Answer: A
Since the coeffiicient of x² is negative, the parabola opens downward. So choices B and C are eliminated.
When x = 0, y = -1. The point (0, -1) is on the line in graph A but not graph D. So choice D is eliminated. This leaves B as the answer.
You can check by trying any other point, such as the vertex. The zeroes aren't a good choice in this example because they are not integers.

22.Which graph best represents the solution set of y > 3x − 4?

F 77
G 137
H 83
J 105

Answer: H 83
I put all the data into a table in the graphing calculator and did a linear regression to find the line of best fit.
My results were y=5.5392709845975 + 0.051934923490403x (You don't need that many decimals.)
To get a prediction for 1500, substitute 1500 for x.
Then 5.54 + 0.052(1500) = 83.54, which is closest to H. (If you used more decimal places, you would get even closer.)



23. The graph of a linear function is shown in the grid.

Which equation is best represented by this graph?

A y + 2 = 7/5 (x + 7)
B y - 2 = 7/5 (x - 7)
C y + 2 = 5/7 (x + 7)
D y - 2 = 5/7 (x - 7)

Answer: D y - 2 = 5/7 (x - 7)
The choices are given in Point-Slope form, which is written in the form:

y - y₁ = m(x - x₁)
Let's look at the slope first.
There appears to be a point at (0, -3). It looks like there's a point at (4, 0), which would give a slope of 3/4. However, that isn't a choice, so I'm deducing that (4, 0) isn't really a point on the line, but is so close to the line that it is hard to tell.
There also appears to be a point at (7, 2). The choices are all full of 7s and 2s, so this looks good. The slope of a line from (0, -3) to (7, 2) would be found as follows: m = (y2 - y1) / (x2 - x1) = (2 - -3) / (7 - 0) = 5 /7
There is a slope of 5/7 in choices C and D.

Next, notice that the form has minus signs in it. For y + 2 and x + 7 to be in the equation, then the point (-7. -2) would have to be on the line. However, it is not.
On the other hand, we know that the point (7, 2) is on the line. So Choice D is the answer.

24. Which expression is equivalent to (xy^-6)² for all values of x and y where the expression is defined?

F xy^-36
G xy³⁶
H x²y^-12
J x²y¹²

Answer: H x²y^-12
The rule for exponents is that the exponent goes only with the constant or the variable right next to it on its left. If there is a parenthesis there, then the exponent is a applied to everything within the parentheses.
So the x, which doesn't show an exponent, gets an exponent of 2. Because the y already has an exponent of -6, it gets multiplied by 2, which makes it -12.

Another way to look at it is this:

(xy^-6)² = (xy^-6)(xy^-6) = x x y^-6 y^-6 = x² y^-12



25. A college student completed some courses worth 3 credits and some courses worth 4 credits. The student earned a total of 59 credits after completing 18 courses.
How many courses worth 3 credits did the student complete?

A 13
B 5
C 20
D 39

Answer:
You can set up a system of equations that says

3x + 4y = 59
x + y = 18
Multiply the second equation by -4 so we can eliminate the y terms
4x + 4y = 72
3x + 4y = 59
x = 13
The student took 13 three-credit course (which means the student took 5 four-credit courses).
Choices C and D are actually the number of the 59 credits earned from four- and three-credit courses.



More to come. Comments and questions welcome.

More STAAR problems.

STAAR (State of Texas Assessments of Academic Readiness) Algebra I, May 2019, cont.

Continuing with the State of Texas Assessments of Academic Readiness (STAAR) exam, administered MAY 2019.

More STAAR problems.

Administered May 2019

Read each question carefully. For a multiple-choice question, determine the best answer to the question from the four answer choices provided. For a griddable question, determine the best answer to the question.


16. Which expression is equivalent to (10 + 7r - r²) + (−6r² − 18 + 5r)

F -7r² + 2r + 8
G 7r² + 12r + 8
H -7r² + 12r - 8
J 7r² + 2r - 8

Answer: H -7r² + 12r - 8
Combine the like terms: r² goes with r², r goes with r, and constant goes with constant. Then, arrange them in standard order, which is from highest exponent to lowest.
10 + 7r - r² + −6r² − 18 + 5r
-r² − 6r² + 7r + 5r + 10 − 18
-7r² + 12r − 8

17.Which graph best represents the solution set of y > 3x − 4?

[SEE IMAGE]

Answer: D
The inequality have a > sign, not a > sign. Therefore, it will have a broken (dotted or dashed) line to represent the boundary that is NOT part of the solution. And since it is "greater" and not "less than", the points above the line are the ones that have to be shaded.
That's Choice D.



18. A bank account earning annual compound interest was opened, and no additional deposits or withdrawals were made after the initial deposit. The balance in the account after x years can be modeled by b(x) = 850(1.025)^x.
Which statement is the best interpretation of one of the values in this function?

F The initial balance of the account decreases at a rate of 97.5% each year.
G The balance in the account increases at a rate of 2.5% each year.
H The initial balance of the account was $1,025.
J The balance in the account at the end of one year is $850.

Answer: G The balance in the account increases at a rate of 2.5% each year.
Looking at the numbers in the equation:
850 represents the opening balance before any time has passed.
1.025 is the growth rate, which as a percentage is 102.5%. That means an additional 2.5% is being added to the balance
x is the number of years that pass, the more years, the bigger the balance.

The initial balance is increasing, not decreasing, so F is eliminated
2.5% is the rate of increase, so this is the answer.
The initial balance is $850. 102.5% represents the growth. Eliminate H.
The initial balance of $850 is at Year 0 before any time has passed. It is not the balance after one year. Eliminate choice J.

19. A company collected data for the number of text messages sent and received using a text-message application since October 2011. The table shows the number of text messages sent and received in billions over time. The data can be modeled by a quadratic function.

Which function bests models the data?

Which function best models the data?
A n(t) = −0.002t² + 0.55t + 5.02
B n(t) = 0.072t² − 0.15t + 2.73
C n(t) = −0.002t² + 5.02
D n(t) = 0.072t² + 2.73

Answer: B n(t) = 0.072t² − 0.15t + 2.73
You have a few options here.
You can plot each of the four graphs in your calculator and do a visual check. You can enter the data into a table and do a quadratic regression. Or you can reason out which choices to eliminate.
For example, in Choices C and D, the middle coefficent, b is 0, so the vertex is 0. The positive x values are rising, so the t² term can't have a negative coefficient. So C is eliminated.
Calculating -b/2a for A, we get -.55/(2(-0.002)) = 137.5. The values would be rising for x < 137.5, but the rate of change would be decresasing. Choice A can be eliminated.
Calculating -b/2a for B, we get -0.15/(2(0.072)) = 1.041666..., so this is also a possibility.
Now there are only two formulas to check.
0.072(40)² - 0.15(40) + 2.73 = 111.93
0.072(40)² + 2.73 = 117.93
Choice B is a better fit.
0.072(10)² - 0.15(40) + 2.73 = 8.43
0.072(20)² - 0.15(20) + 2.73 = 28.53
0.072(30)² - 0.15(30) + 2.73 = 63.03
This look pretty close with the -0.15t middle term.

All of that said, I put all of the numbers into a Desmos quadratic regression calcuator and got the following results:
a = 0.0721429, b = -0.14881, c = 2.73214. Which is Choice B.



20. The graph of a linear function is shown on the grid.

What is the rate of change of y with respect to x for this function?
Record your answer and fill in the bubbles on your answer document.

Answer:
What is the rate of change? That is, what is the slope of this line?

Change in y / change in x = (y2 - y1) / (x2 - x1) = (2 - 3.6) / (5 - -3)
= - 1.6 / 8 = -16 / 80 = -1 / 5 or -0.2.



More to come. Comments and questions welcome.

More STAAR problems.

BAD BED BID

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

As long as we need random letters anyway, why not pick words. Easier to say and remember!

Coming up with five words was the easy part, apparently. I had intended for BAD to be 85^o, not 95. Then I looked at the picture was I was done. It was easier to change the number.

Ken could've asked Bibi about minor arc BI and major arc BI, I guess.

The original idea was that BOD would be double the size of BAD, BED, and BID, which are all congruent because they are all inscribed angles that intercept the same arc. Instead, it is double the size of angle BUD. It just doesn't flow as nicely.

Come back often for more funny math and geeky comics.

STAAR (State of Texas Assessments of Academic Readiness) Algebra I, May 2019, cont.

Continuing with the State of Texas Assessments of Academic Readiness (STAAR) exam, administered MAY 2019.

More STAAR problems.

Administered May 2019

Read each question carefully. For a multiple-choice question, determine the best answer to the question from the four answer choices provided. For a griddable question, determine the best answer to the question.


11. A student worked out at a gym continuously for 50 minutes. The graph shows the remaining percentage of the workout as a linear function of x, the time in minutes.

Which answer choice best describes the domain and range of the function for this situation?

A Domain: All real numbers greater than or equal to 0 and less than or equal to 100
     Range: All real numbers greater than or equal to 0 and less than or equal to 50
B Domain: {-2}
     Range: {100}
C Domain: All real numbers greater than or equal to 0 and less than or equal to 50
     Range: All real numbers greater than or equal to 0 and less than or equal to 100
D Domain: {100}
     Range: {-2}

Answer: C Domain: All real numbers greater than or equal to 0 and less than or equal to 50
Range: All real numbers greater than or equal to 0 and less than or equal to 100
The domain is all of the possible x values. The range is all of the possible y values.
The domain goes from 0 to 50. The range goes from 0 to 100.

12.The graph of quadratic parent function f was transformed to create the graph of g(x) = f(x + 2) −5. Which graph best represents g?

[SEE IMAGE]

Answer: G
The parent function would have a vertex at the origin, (0, 0).
The transformation y = a(x - h)² + k moves the graph h units to the left and k units up. However, in this equation, h is +2 and k is -5. We have to flip the signs. So the graph will move two spaces to the right and five units down.



13. Which expression is equivalent to (45 m^-6p²v¹²) / (15 m^-2p⁸v^-4)

A (3 v⁸) / (m⁸p⁶)
B (3 v¹⁶) / (m⁴p⁶)
C (30 m³) / (p⁴p³)
D (30 v³) / (m³p⁴)

Answer: B (3 v¹⁶) / (m⁴p⁶)
Put whatever confusions or misconceptions you may have about exponents aside for one moment. The first thing you need to do is divide 45 by 15 and get 3. Eliminate Choices C and D immediately. If you subtracted 45 - 15 and got 30, you need to review the basics. (Harsh, maybe, and sorry, but very true.)

There are two rules that have to be used here. First, when you have the same variables with exponents in both the numerator and denominator, you subtract the exponents. Second, a negative exponent on top becomes a postive exponent by moving the variable to the bottom, and vice versa.

Let's subtract the exponents: m, -6 - (-2) = -4; p, 2 - 8 = -6; v, 12 - (-4) = 16
So we have m^-4, p^-6 and v¹⁶
Only the v is staying on top. The m and p go to the bottom.
The correct choice is B.

14.What is the positive solution to this equation?

4x² + 12x = 135
Record your answer and fill in the bubbles on your answer sheet.

Answer:
First step in solving a quadratic equation is setting the equation equal to 0. Then we can either factor or use the quadratic formula.

4x² + 12x = 135
4x² + 12x - 135 = 0
Find ac: (4)(135) = -540
Are there factors of -540 that sum to +12?
(-2, 270), (-3, 180), (-4, 135), (-5, 108), (-6, 90),
(-9, 60), (-10, 54), (-12, 45), (-15, 36), (-18, 30) < -- This one.
4x² - 18x + 30x - 135 = 0

At this point, I would usually draw a table, and do the box method in reverse. Instead, we'll work by grouping.
(4x² - 18x) + (30x - 135) = 0

Find the Greatest Common Factor of each pair of terms, and factor it out.
2x(2x - 9) + 15(2x - 9) = 0

Factor (2x - 9) from each expression.
(2x - 9)(2x + 15) = 0
2x - 9 = 0 or 2x + 15 = 0
2x = 9 or 2x = -15
x = 4.5 or x = -7.5

The positive solution is 4.5.

NOTE: After you factor, if you aren't sure if you factored correctly, "FOIL" your answer and see if you got your original expression back.
(2x - 9)(2x + 15) = 4x² - 18x + 30x - 135.



15. A grill at a barbecue restaurant will be used to cook sausage links that are 2 lb each and briskets that are 6 lb each. No more than 120 lb of sausage links and briskets will be cooked on the grill.
Which inequality represents all possible combinations of x, the number of sausage links that will be cooked on the grill, and y, the number of briskets that will also be cooked?

A 6x + 2y < 120
B 2x + 6y < 120
C 6x + 2y > 120
D 2x + 6y > 120

Answer: B 2x + 6y < 120
If x is the number of sausage links and each link weighs 2 lbs, then the weight of all the sausage links is 2x. Choices A and C are eliminated.
The weight needs to be "no more than" 120, which means "less than or equal to" 120. Only one choice has a "less than or equal to" symbol, and that's Choice B.



More to come. Comments and questions welcome.

More STAAR problems.

STAAR (State of Texas Assessments of Academic Readiness) Algebra I, May 2019, cont.

And now for something completely different.

While I'm waiting for new Regents exams to come along, I looked to other states for standardized tests that have been made public.

It's nice to say how other states live, right?

More STAAR problems.

Administered May 2019

Read each question carefully. For a multiple-choice question, determine the best answer to the question from the four answer choices provided. For a griddable question, determine the best answer to the question.


6. What is the equation in slope-intercept form of the line that passes through the points(-4, 2)and (12, 6)?

F y = 0.25x + 3
G y = 0.25x - 4.5
H y = 4x + 18
J y = 4x - 42

Answer: F y = 0.25x + 3
First step is to find the slope, which will eliminate two choices immediately.
After that, you have two methods to choose from: you can use slope-intercept form and solve for the y-intercept; or, you can use point-slope form, and rewrite the equation in slope-intercept form.

m = (y2 - y1) / (x2 - x1) = (6 - 2) / (12 - (-4)) = 4 / 16 = 1 / 4 = 0.25. Eliminate choices H and J.
Point-slope form: y - 6 = .25(x - 12) or y = .25(x - 12) + 6 (I prefer the latter because it looks like a transformation.)
y = .25x - 3 + 6
y = .25x + 3, which is choice F.

2. Which graph best represents -5y = -6x + 15?

[SEE IMAGE FOR CHOICES]

Answer: C [SEE IMAGE]
Rewrite in slope-intercept form by dividing the equation by -5: y = 6/5 x - 3
Choices A and B have negative slopes and can be eliminated.
Choice C goes through (0, -3), which is what we want. Choice D goes through (0, 3), which is incorrect.



8. A baker determined the annual profit in dollars from selling pies using p(n) = 52n − 0.05n², where n is the number of pies sold. What is the annual profit if the baker sells 400 pies?

F $20,780
G $12,800
H $28,800
J $20,760

Answer: G $12,800
As I would see on a New York test, this question seems very silly. It would imply that there will come a point where the baker will start to lose money making more pies. Then again, maybe this takes into account that he can only sell so many, and after that the go into the dumpster.

To solve the problem, substitute 400 for n and evaluate the expression.
52(400) - 0.05(400)² = 12,8000

9.An exponential function is graphed on the grid.

Answer: A
The graph is positive, so the rate can't have a negative sign in front of it: C and D are eliminated.
The graph is showing decay, so A is correct. B would show growth.
Of course, you could just put each of these equations into a calculator and look.



10. What is the equation in slope-intercept form of the line that crosses the x-axis at 36 and is perpendicular to the line represented by y = −4/9 x + 5 ?

F y = 4/9 x + 16
G y = 4/9 x - 16
H y = 9/4x + 81
J y = 9/4 x - 81

Answer: J y = 9/4 x - 81
A slope that it perpendicular to a slope of -4/9 would be its negative multiplicative inverse -- that is, the inverse reciprocal.
Flip the fraction and switch the sign and -4/9 becomes +9/4.
Two slopes are perpendicular if their product is -1, and (-4/9)(9/4) = -1.

We've eliminated F and G.
To finish the problem, check H and J for the point (36, 0)

y = 9/4 (36) + 81 = 9 (9) + 81 = 162 =/= 0
y = 9/4 (36) - 81 = 9 (9) - 81 = 0
Hopefully, it was obvious that it you were adding two positive numbers, you could get a sum of 0 in choice H.



More to come. Comments and questions welcome.

More STAAR problems.

(x, why?) Mini: Transformation

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

It'll drive you insa-a-a-a-ane!

Come back often for more funny math and geeky comics.

STAAR (State of Texas Assessment of Academic Readiness) Algebra I

And now for something completely different.

While I'm waiting for new Regents exams to come along, I looked to other states for standardized tests that have been made public.

It's nice to say how other states live, right?

More STAAR problems.

Administered May 2019

Read each question carefully. For a multiple-choice question, determine the best answer to the question from the four answer choices provided. For a griddable question, determine the best answer to the question.


1. What is the slope of the graph of y = 12x - 19?

A -19
B -12/19
C 19/12
D 12

Answer: D 12
The exquation is in slope-intercept form, y = mx + b. The slope, m, is the coefficient of the variable x, which in this case is 12.
The 19 represents the y-intercept and isn't relevant to this questions.

2. A golfer hit a golf ball from a tee box that is 6 yards above the ground. The graph shows the height in yards of the golf ball above the ground as a quadratic function of x, the horizontal distance in yards of the golf ball from the tee box.

What is the domain of the function for this situation?
F 0 < x < 230
G 6 < y < 36
H 0 < x < 36
J 6 < y < 230

Answer: F 0 < x < 230
The domain refers to the x values, not the y values, so choices G and J are immediately eliminated. Also, the 36 refers to the height, which is y. The horizontal distance is 230.



3. Which value of x makes the equation 1.25(4x − 10) = 7.5 true?

A 3.5
B -1
C -0.5
D 4

Answer: D 4
Since it is multiple choice, you could just check each solution.
In fact, with the TI calucluators you could enter

1.25(4*{3.5 -1 -0.5 4} - 10) and see which value gives you 7.5.\

Or you can solve it

1.25(4x - 10) = 7.5
4x - 10 = 6
4x = 16
x = 4

4.Which function is equivalent to g(x) = x² + 15x - 54 ?
F g(x) = (x + 9)(x - 6)
G g(x) = (x + 18)(x - 3)
H g(x) = (x - 9)(x + 6)
J g(x) = (x - 18)(x + 3)

Answer: G g(x) = (x + 18)(x - 3)
Which pair of binomials has a product that is equivalent to the given statement? Or, how do you factor the given quadratic function?

The factors of -54 are -6 and +9, +9 and -9, -3 and + 18, and +3 and -18. Of those pairs, which sums to +15? The answer is +18 and -3.

Tricky question because they could have asked about x² + 15x + 54 and got an entirely different answer that doesn't involve just flipping signs.



5. The table shows the linear relationship between the average height in feet of trees on a tree farm and the number of years since the trees were planted.

What is the rate of change of the average height in feet of the trees on the farm with respect to the number of years since the trees were planted?

A 14 ft/yr
B 3 ft/yr
C 7 ft/yr
D 10 ft/yr

Answer: C 7 ft/yr
To find the average, find the rate of change from the first and the last point, (1, 10) and (15, 108).
So m = (108 - 10) / (15 - 1) = 98 / 14 = 7.



More to come. Comments and questions welcome.

More STAAR 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.

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.

Come back often for more funny math and geeky comics.

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.

Come back often for more funny math and geeky comics.

(x, why?) Mini: Two Pips

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

"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.

Come back often for more funny math and geeky comics.

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.

Come back often for more funny math and geeky comics.