EinsteinJr

... Yup. Lazy 😂

HINT: I am waiting you to use a confidence interval, that gives you the upper and lower bounds the proportion of supporters of Emmanuel, depending on the frequency observed (in that case, 52 %), and with a confidence of about 95 %.

Here is the formula:

\(f-\frac{1}{\sqrt{n}}\leq p \leq f+\frac{1}{\sqrt{n}}\)

where p corresponds to the proportion of people who will actually vote for Emmanuel, f is the proportion of the people surveyed who said they would vote for him, and n is the size of our sample (the number of people surveyed).

That's right:

(and yeah, I still give those brownie pictures for right answers).

That's right, your answers are exact!

Here's a brownie for getting all questions all right:

OK I'll try not to forget that and to put it in my next topic

I already have the answers, that's just some "brain food"

The answer is simple: the triangle can't have an area because there is no such triangle.

Why? That's because any right triangle (I made a typo in the question, I apologize for that) can be inscribed in a circle with the hypotenuse as its diameter.

So, if the triangle is inscribed in a circle with a diameter of 10 cm (the lenght of the hypotenuse), then the max lenght of the altitude to the hypotenuse is 5 cm; 6 cm is bigger than 5 cm, so the triangle can not exist.

So, the ONLY correct answer is: there is NO such triangle. Anyone who gives me a value is wrong.

That's not right.

Another hint? If you find a value for the area, then you are wrong.

That's right rarinstraw1195; here is a triangular pyramid (or a tetrahedron; let's call a spade a spade):

Congratulations to Hayley1, Guest, CPhill and rarinstraw1195 for solving those problems; you each deserve a brownie!

Yum...

CPhill, your answer is correct; one to go!

Melody, you're right, breaking the matches isn't allowed (but 3D is allowed; I just gave you all a huge hint!)

That's correct Guest!

Since I think there won't be one person who answer all four questions, I'll give a cookie to everyone who has reolved one or more of the problems when the four are solved.

Good, you got the answer to one question; three to go!

There are one googol or 10¹⁰⁰ or 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000  zeroes in a googolplex.

Hint:

Pythagorus's theorem:

“In any triangle right-angled at B, the lenght of the hypotenuse squared is equal to the sum of the squares of the lenghts of the two other sides” or, in other words:

AC²=AB²+BC²

Trigonometric functions:

In a right triangle, for any non-right angle α:

\(\sin(\alpha)=\frac{\text{opposite side}}{\text{hypotenuse}} \\\cos(\alpha)=\frac{\text{adjacent side}}{\text{hypotenuse}} \\\tan(\alpha)=\frac{\text{opposite side}}{\text{adjacent side}}\)

Respectively the sinus, the cosinus and the tangent of α.

Of course I am! (just kidding...)

"The world won't be destroyed by those who do evil, but by those who watch them without doing anything."

Albert Einstein