Imcool

The numbers \(x_1,x_2,x_3,x_4\) are chosen at random in the interval \([0,1]\)  Let \(I\) be the interval between \(x_1,x_2\) and let \(J\) be the interval between \(x_3,x_4\)  Find the probability that intervals \(I,J\) both have length greater than \(\frac{3}{4}\). 

Ok, so this implies that \(x_2-x_1>3/4\), same thing for the other pair.

We'll just assume that the numbers go from least to greatest.

This means that \(x_1<1/4\), which is 1/4 chance, times the chance that \(x_2>3/4\), which is also 1/4. multiplying, we get 1/16, which we multiplu by 2 since they don't have to go from least to greatest, we just assumed. This gives us 1/8.

We do the same for \(x_3,x_4\) and get the same result. Adding these together will give us our final answer, \(\fbox{1/4}\)

...really?

First of all, at least try the problem before copy and pasting it onto this site

Second of all, you didn't even copy it RIGHT. I would expect you put a little more effort so that people can READ your problem, and answer it occordingly. 

You can post it again and I will answer it. Post it with the corrections.

We can imagine a coordinate grid The right-most point he can travel to is (2,0), left-most is (-2,0), top and down is (0,2) and (0,-2) respectively.

Now, in between those points, the furthest the fly can go is (1,1),(1,-1),(-1,1), and (-1,-1). Therefore, the total number of possible points Franklin can end up at is \(\fbox{12}\)

\(400000a+40000b+4000c+400d+40e+4f=300000d+30000e+3000f+300a+30b+3c\)

\(3997(\overline{abc})=2996(\overline{def})\)

\(\overline{abcdef} = 29963997\)

Alrighty..

1. For this one, the diagonal of the base ABCD is \(\sqrt{12^2+12^2}\) which is \(12\sqrt2\). Dividing that by 2 gives \(6\sqrt2\).

Now, to find the height, we use the pythagorean theroem.

\(10^2={6\sqrt2}^2+b^2\)

\(100 = 72+b^2\)

\(b^2 = 28\)

\(b = 2\sqrt7\)

by the way, b is the height.

now, we get the area of the pyramid is \(\frac{12\cdot12\cdot2\sqrt7}{3}\)

which gives us \(96\sqrt7\)

Looks like your HW, with the last sentence and all. Why don't you try it yourself, give it some effort, and when you cannot do it, can ask for help. and put what you've tried.

For the second part, there are 18 people, and the 2 people have to be different, so its just 18 * 17 divided by 2 which is 153 ways

Umm.. What is the (18 18)? Is there suppose to be like a symbol or something? Also what is it equal too..?

Hello Cphill, do you mind telling me how to post a desmos picture? I've been answering questions and its very frustrating to only describe the picture

Mean: 

​107​+​74​​+86+​51​+67​+33​+53 divided by 7. 

Median: The middle number when the numbers are sorted from least to greatest.

Mode: The number that appears most often

Mid range: The smallest number + the largest number divided by 2. 

I suggest you be familiar with how to calculate average. You can search it up online or ask your teacher about it, as it is very important to know this concept.

I noticed that in your numbers, there is no single mode. I am guessing that in this case, since every number appears exactly once, you just average them for the mode, which is the same as the mean a.k.a average of the set.