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If the right triangle is isosceles, the two legs must be equal. By using Pythagorean Theorem, we can get \(2(a^2) = (4\sqrt{2})^2\) which equals \(2(a^2) = 32\). So \(a^2 = 16\). This gives us \(a = 4\). If the legs of the triangle are \(4\), we can get the area to be \(8\).

- Daisy

I can be one of the 2 hungry people who knows where the glass is so I am not going to eat one of those. 

I guess this is not the answer that you are hoping for :)

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How about.

Let the 2 who know each chose a good peice, then allow them to eat the peice they chose. They are hungry so it they really have chosen a good peice they will eat it and they were telling the truth. If they don't eat it it is because there is glass in that slice and they are lying.

If they both eat it then you can just ask them to sort the good from the bad, they are both telling the truth so they will agree on the out come and the 3 remaining good pieces will be identified.

If neither eat it then they are both liars. You can get them to sort out the 5 good and 5 bad ones 

If neither eat it then you can again ask them to sort the good from the bad, they are both lying so they will agree on the out come.  The 5 that they say are good are the bad ones

If one eats the cake and one doesn't then it is obvious that the eater is telling the truth and the onther is lying.

Get the truth teller to point out the other 4 good ones. 

Yes x=7 but  hectictar I have no idea why you say that x is the solution to this .....

B)     2l x-12 l = 10  

Ther is no l in the question ???

Because F = ma, if the acceleration is 0, then the forces are in equilibrium.

First, the man have weight(of course!), so there is a force pointing downwards labeled W(stands for weight).

And then, there is tension in the string, so there is a force pointing upwards labeled T(stands for tension).

Also, there is normal force, so there is another force pointing upwards labeled N(stands for normal force).

Finally, the normal force and tension balances the weight, so it should be in equilibrium.

P.S.: I am not specifically good at Physics, but I tried my best to help. If anyone sees mistake in my solution, please teach me. Thank you.

"The interior acute angles are congruent" tells you it is a regular pentagram, so the measure of interior acute angle = 180/5 = 36 degrees. (I divided by 5 because it is a pentagram(5-gram) .)

Now you draw a straight line like this:

Calculate the angles in the triangle formed:

the base angles of the isosceles triangle is 72 degrees.

As the line drawn is a straight line, so the exterior angle is 108 degrees.

Measure of internal reflex angle = 72 * 2 + 108 degrees = 252 degrees

It’s very easy to tell you what this means.

This means you know how to ask a computer a question, but not the correct question.

WolfRam correctly answered the question you asked.

You need to ask it this conditional question: Four (4) dice sum to eight (8). What’s the probability the four (4) dice are all twos (2).

If you phrase this correctly, WolfRam wil answer it correctly.

GA

You see, the first one is a hexagon(6-gon), so the sum of interior angle is: 

\((6-2)\cdot(180^{\circ}) = 720^{\circ}\)

The second one is a pentagon(5-gon) although it is a concave pentagon. But in fact, you still use the same formula for this.

The sum of interior angle is:

\((5-2)\cdot(180^{\circ}) = 540^{\circ}\)

Edit:

Explanation for (n-2)*(180 degrees):

For any polygon, start from one of the vertices, then repeatedly draw an edge to another vertice, until all the vertices are directly connected with an edge. If the polygon is an n-gon, then it should now be divided into (n-2) triangles. So the sum of  interior angles should be (n-2)*(180 degrees).

Notice: \(\dfrac{n(2n+1)(7n+1)}{6} = (n+1)^2+(n+2)^2+\dots+(2n)^2\)

So the question is equivalent to: Find all integers n such that \((n+1)^2+(n+2)^2+\dots+(2n)^2\) is an even number.

But if x^2 is an odd number, then x is an odd number, also if x^2 is an even number, then x is an even number(why?)

So the question is just asking: Find all integers n such that \((n+1)+(n+2)+\dots+(2n)\) is an even number.

Next, we will find the formula for \((n+1)+(n+2)+\dots+(2n)\).

\(\quad(n+1)+(n+2)+\dots+(2n)\\ =n^2+(1+2+3+\dots+n)\\ =n^2+\dfrac{1}{2}(n)(n+1) \\ = \dfrac{n}{2}(3n+1)\)

So, finally, the question is equivalent to: Find all integers n such that n(3n+1) is divisble by 4.

For some reason, we arrived at a simpler question. Let's try to solve it now.

n = 4k for k = 1,2,3,4,... is a trivial solution, because if n is divisible by 4, then n(3n+1) is also divisible by 4.

n = 4k+1 for k = 0,1,2,3,4,... is another set of solution. Let's substitute n = 4k+1 into n(3n+1) to see why.

n(3n+1) = (4k+1)(12k+3+1) = (4k+1)(12k+4) = 4(4k+1)(3k+1)

Therefore, when n = 4k+1, for k = 0,1,2,3,4,..., it is also a solution.

Final solution: n = 4k for \(k\in \mathbb Z^+\), or n = 4k+1 for \(k\in \mathbb Z^*\)

The number of permutations for screwing up a simple statistics question is truly mind boggling. I’ve always wondered what the number actually is. It may not actually have a ceiling --it seems as vast as space, and the time to do it is limited only by the imagination and cogitative lifespan of humankind.  

GA

First we need to find how far it moves in an hour.

1 year = 365 1/4 days = 8766 hours

So the plate moves 1/5844 inches/hour

Multiplying by 14: The plate moves 7/2922 inches in 14 hours.

Patients! Goddamn it!

Writing a good troll post isn’t as easy as solving probability problems.

Solution:

The sum of four (4) dice is eight (8).

There are five (5) ways to roll four (4) dice for a sum of eight (8).

5, 1, 1, 1

4, 2, 1, 1

3, 3, 1, 1

3, 2, 2, 1

2, 2, 2, 2

One of these five (5) are four (4) twos (2).

The probability is 1/5 = 20%

GA

There are 5 ways of getting a total of 8 on a roll of 4 dice and each has the following number of prmutations:
5 + 1 + 1 + 1 = 8=4!/3! =4 permutations
4 + 2 + 1 + 1 = 8=4!/2!=12 permutations
3 + 3 + 1 + 1 = 8=4!/2!. 2!=6 permutations
3 + 2 + 2 + 1 = 8=4!/2!=12 permutations
2 + 2 + 2 + 2 = 8=4!/4!=1 permutation
4 + 12 + 6 + 12 + 1 = 35 ways of getting a total of 8. And only 1 of them is 4 twos. Therefore, the probability of throwing 4 twos given a total of 8 is:
1/35 =0.028571.

@above, sorry, but your response is incorrect, because you didnt account for the conditions...thats why it was titled conditional probability lol xD! I know that your answer is right without conditions, but how do i do it with these conditions??? ANyone help???

anyone can help?

I'll help you with the first two!

#18(a) Diameter=2*radius, so Diameter=2*3=6m

#18(b) radius=Diameter/2, radius=18/2=9 inches

0.1X + 180 =X
180 = 0.9X
X =180/0.9
X=200 - He must contibute 20 gold coins for a minimum of 10%.
0.2X + 180 = X
180 =0.8X
X=180/0.8
X=225 - He must contribute 45 gold coins for a maximum of 20%.
45 - 20 = 25 - gold coins-the difference between maximum and minimum.

I had figured it out on my own yesterday. But thank you. 

We can add all these values up!: Thus, we get $2240, so she's not in credit overload!

Let x be the number of hockey cards he sells and y be the number of baseball  cards he sells ....so we have these inequalities

x ≥ 6y

x + y ≤ 525

And we wish to  maximize this objective  revenue function, R

R = .03x  + .05y

Here's the graph of the inequalities  :   https://www.desmos.com/calculator/h7qwjcc9g2

It can be shown that the max  revenue  occurs at the  corner point  (x, y)  = (450, 75)

So...the max revenue is  

.03(450) + .05(75)  =  $17.25

(1/8)x−5<−8  or  7x−4 ≥38

In the first inequality, add 5 to both sides

(1/8)x < -3  multiply both sides by 8

  x < -24

In the second inequality  add 4 to both sides

7x  ≥ 38     divide both sides by 7

x  ≥ 38/7

So..the answer is

(-infinity, -24) U [ 38/7, infinity )