Answer:

Step-by-step explanation:
Given


Required
Determine the final score
Final score is calculated as follows:



to get the slope of any line, all we need is two points off of it, so let's get the slope and thus its equation, hmmmm let's see points (-2,-3) and the origin are the obvious ones =)
![\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{0}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{0-(-3)}{0-(-2)}\implies \cfrac{0+3}{0+2}\implies \cfrac{3}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-3)=\cfrac{3}{2}[x-(-2)]\implies y+3=\cfrac{3}{2}(x+2) \\\\\\ y+3=\cfrac{3}{2}x+3\implies y=\cfrac{3}{2}x](https://tex.z-dn.net/?f=%5Cbf%20%28%5Cstackrel%7Bx_1%7D%7B-2%7D~%2C~%5Cstackrel%7By_1%7D%7B-3%7D%29%5Cqquad%20%28%5Cstackrel%7Bx_2%7D%7B0%7D~%2C~%5Cstackrel%7By_2%7D%7B0%7D%29%20%5C%5C%5C%5C%5C%5C%20slope%20%3D%20m%5Cimplies%20%5Ccfrac%7B%5Cstackrel%7Brise%7D%7B%20y_2-%20y_1%7D%7D%7B%5Cstackrel%7Brun%7D%7B%20x_2-%20x_1%7D%7D%5Cimplies%20%5Ccfrac%7B0-%28-3%29%7D%7B0-%28-2%29%7D%5Cimplies%20%5Ccfrac%7B0%2B3%7D%7B0%2B2%7D%5Cimplies%20%5Ccfrac%7B3%7D%7B2%7D%20%5C%5C%5C%5C%5C%5C%20%5Cbegin%7Barray%7D%7B%7Cc%7Cll%7D%20%5Ccline%7B1-1%7D%20%5Ctextit%7Bpoint-slope%20form%7D%5C%5C%20%5Ccline%7B1-1%7D%20%5C%5C%20y-y_1%3Dm%28x-x_1%29%20%5C%5C%5C%5C%20%5Ccline%7B1-1%7D%20%5Cend%7Barray%7D%5Cimplies%20y-%28-3%29%3D%5Ccfrac%7B3%7D%7B2%7D%5Bx-%28-2%29%5D%5Cimplies%20y%2B3%3D%5Ccfrac%7B3%7D%7B2%7D%28x%2B2%29%20%5C%5C%5C%5C%5C%5C%20y%2B3%3D%5Ccfrac%7B3%7D%7B2%7Dx%2B3%5Cimplies%20y%3D%5Ccfrac%7B3%7D%7B2%7Dx)
Your answer would be 3/50 reduced.
Answer:
20160 ways
Probability = 0.0556
Step-by-step explanation:
We have 9 different letters, so the total number of words we can make is:

If we want just the words that begin with L and end with a vowel, we would have the first letter "locked", so we have 8 letters remaining, and it must end with a vowel, so the last "slot" has just 4 possible values (A, E, I or O). Then we would have 4 possible values for the last letter and 7 remaining letters in the middle of the word:

The probability is calculated by the division of the number of words we want over the total number of words:

To find all the positive integers less than 2018 that are divisible by 3, 11, and 61, you will use what you know about factors.
3, 11, and 61 are all answers. So are 33, 183, 671, and 2013.
If you put these in factors, the product will be divisible by them!
3 x 11 = 33
3 x 61 = 183
11 x 61 = 671
3 x 11 x 61 = 2013
Take each number and square it, cube it, etc...
9, 27, 81, 243, 729
121, 1331
9 x 11 = 99
27 x 11 = 297
81 x 11 = 891
121 x 9 =1089
121 x 3 = 363
61 x 9 = 549
61 x 27 = 1647
Everything in bold is a correct answer.