The interior angles of a quadrilateral have to add to 360 degrees.
Add 41 + 88 + 114 = 243 Then subtract from 360. 360-243 = 117 degrees
If <em>f(x)</em> is a linear function, then
<em>f(x)</em> = <em>ax</em> + <em>b</em>
for some constants <em>a</em> and <em>b</em>.
Given that <em>f</em> (1) = 4 and <em>f</em> (4) = 1, these constants are such that
<em>f</em> (1) = <em>a</em> + <em>b</em> = 4
<em>f</em> (4) = 4<em>a</em> + <em>b</em> = 1
Solve for <em>a</em> and <em>b</em> : eliminate <em>b</em> by subtracting the two equations,
(<em>a</em> + <em>b</em>) - (4<em>a</em> + <em>b</em>) = 4 - 1
-3<em>a</em> = 3
<em>a</em> = -1
Then
-1 + <em>b</em> = 4
<em>b</em> = 5
So we have
<em>f(x)</em> = -<em>x</em> + 5
You have all five questions correct. Nice work
-------------------------------
Problem 1: There are 8 spaces labeled 1 though 8 so the proper sample space is {1,2,3,4,5,6,7,8} which is basically all the possible outcomes
Problem 2: There is one "3" out of 8 total, so 1/8 is the probability of landing on 3
Problem 3: There are 4 spaces that are even {2,4,6,8} out of 8 total {1,2,3,4,5,6,7,8}. So 4/8 = 1/2
Problem 4: There are 4 blue out of 3+5+4 = 12 total, so 4/12 = 1/3
Problem 5: We got 24 red out of 40 total, so 24/40 = 3/5
