GingerAle

For the die, think of it as a single six occurring in event one, then a single six occurring in event two.

For the coins, think of it as a set of three heads occurring in event one, then a set of three heads occurring in event two.

The in a row element exists only after two events. 

------

 I am being pedantic with the wording, which is appropriate in mathematics.

Yes, it is. Pedantic wording reduces ambiguity.

My description above provides an interpretation for a solution.

-----

Yes. I’ll post a solution

GA

--. .-

Your answer is more than wrong; it’s atrocious!

GA

--. .-

Hi Melody,

Two events are required to meet the criteria.

First event: roll a die and flip three coins at the same time.

Second event: roll a die and flip three coins at the same time.

At this point, it is now possible to have rolled two sixes twice in a row and/or flip a set of three heads twice on a set of coins two times in a row.

GA

_{Edit: strikeout of redundant word(s) that alters intended meaning of statement.}  

--. .-

Solution:

\(\dfrac{9.41 \text{ d/min/g}} {15.93 \text{ d/min/g}} = 0.590709  |\text{ Fraction of remaining } ^{14}C\)

\( n^\frac{1}{2} = 0.590709  | \text{ Fraction converted to half-lives (n).}\\ \frac{1}{2} log (n) = log (0.590709)  \\ (n) = 0.7594796 \text{ half-lives.}\\ \)

\(\text{Half-life of } ^{14}C  = 5730 \text{ years ± 40 years.}\\ (n)*(5730) =\\ (0.7594796) * (5730) = 4351.82 \text{ years ± 30.4 years.}\\\)

The age of the case: 4351.82 years ± 30.4 years.

Additional notes:  Definitions: The use of "d/min.g" where “.” implies multiplication, –normally presented as (d/min·g), with a center dot rather than a decimal or period.  This presentation is common in many physics texts; however, this is a misnomer, because it implies that the disintegrations per second are multiplied by the mass of the sample, when infact this rate is divided by this mass .  The correct form is "d/min/g" or  "d/(min·g),” which is the form usually presented in biology texts on the same subject. 

GA

--. .-

Oh, gorblimey! Pawsing to read Omi’s post definitely rings a bell and it’s doggone funny.... 

Hi Melody,

So in the USA a kite would qualify as a Trapezium.

. I probably wasn’t paying attention in class, but I don’t remember my geometry teacher referring to a kite to as a trapezium; though I suppose it may be a special case, where the pairs of equidistant lines are always adjacent.  This is similar in scheme to how a square is also a rhombus, rectangle, and parallelogram. LOL.  I have sometimes heard of a kite referred to as a diamond shape.

Oblong is a word I’ve heard since childhood. I think of it as an elongated oval or an ellipsoid blended with a rectangle; or a rectangle with the longer sides parallel, or nearly so, with continuously rounded corners for the width.  In some old texts, I’ve seen the word oblong used to mean rectangle.

Oval comes from the Latin Ovum –for egg, so it is egg-shaped. Specifically the shape refers to the eggs of the Gallus domesticus (domestic chicken), which has been familiar to most people for centuries. 

Most of my early education on shapes was from art classes. My high school Latin teacher also spent many classroom hours teaching the nuances of shapes in second and third-year Latin.  There are many Latin words describing shapes, and most were introduced in very early Latin dialects; the influence of the Greek is notable in many of these words. 

 Later, I learned that shapes that are graphical curves have both precise and general mathematical functions that produce them, such as parabolas, catenaries, ellipsis, and hyperbolas.  Because of the mathematical functions, there is little ambiguity about the shape; for example, how a catenary may be confused for a parabola.

...So much to learn and so little time to learn it....

------------------------------------

It is very nice to see you.

Thank you.

When I open web2.0calc’s forum pages and see posts by Melody, Alan, and ...ah ...ah ..., whoever the third answerer is now, I know that at least one part of the (virtual) world is functioning within normal parameters, even if the forum’s OS  sometimes does not.   

GA

--. .-

Trapezoid and Trapezium are in use in both American (US) and European English; however, the formal meanings are reversed.  

Geometry.   Trapezoid   (Greek)

1. a quadrilateral plane figure having two parallel and two nonparallel sides.
2. British. trapezium (def. 1b).

One more thing:  there are definite advantages in understanding how a computer network’s image proxy algorithm functions, and knowing their limitations. One advantage is allowing for images to display (at least for awhile) that otherwise would not.  I usually refer to this skill set as “being smarter than the computer ...”   

--. .-

There are two types of moderators for this forum: local moderators, (Melody, Alan, ...), and image-moderators, which is an image moderation service (probably) located in India.  

The image-moderators only see the image and approve or block it based on predetermined criteria by the webmaster or administrator.  For this forum, the typical blocked images include:

* Pornography (or any human nudity).

* Subjects that are generally considered gross, disgusting, or repulsive, such as those of diseased, mangled or decomposing remains of humans or animals, and those that are scatological in nature.

* Destructive weaponry, such as guns, knives, and swords –these may include fictional weapons such as ray-guns or laser-swords.  Ironically though, you probably could post mages of atomic bombs, nerve-gas canisters, and deadly biological agents without impediment. 

* Subjects depicting racism, hate-speech, and violence.  

Until recently math related images were not blocked.  These images are not intentionally blocked; they are passively blocked. A probable cause for this nuance is a Covid-related reduction in personnel at the image moderation service company.  The image-moderators have about two minutes to approve or block an image. For this form, the image is processed though a switchable proxy container before it is displayed on the thread. The code for the switch is reported/{null}. The {null} allows the image to display normally. If a decision is not made in the allotted time the default is “report” and this displays a scrambled image.

(The original image is not scrambled, which is why I could reproduce the image in this post.)  

Originally, the form’s local moderators had the option to override a blocked image. This option disappeared in a subsequent update.   The form’s administrator, Herr Massow, periodically resets these block images

Additional notes:

On the questions (contents) page, questions are abbreviated, and those with an image are indicated by an icon; the actual image is not displayed.  The same abbreviated content is used in the profile pages for questions by members.

On the answers (index) page, answers that have an image are displayed. On the index page, these images are displayed, even if the image is blocked on the thread.  This content is also displayed in the profile answers page for members. This content on is not blocked on the profile answer page, and never has been.

Here is an example:

Here is a photo of knives with dried blood.  This would definitely be blocked by the image moderating service; yet, it’s clearly visible in the answer (index) page.  

--. .-

I think it is more an example of the power of suggestion ....

Ok... But why didn’t the suggestion of “...this is NOT the correct equation for this question,” have any power?

...Id est, why did you believe that re-solving the equation would confirm its validity?

I do not think either answer is 'dumb'......just incorrect because of a mistake...

I do not think the answers are dumb either, but I do think ...dumbness is contagious.

--. .-