<span>To do these you will be adding or subtracting 2pi (or integer multiples of .
Since the given angles are in fraction form, it will help to have 2pi in fraction form, 2pi=10/5=6pi/3=4pi/2=18pi/9 NOTE: this>(/) stands for over like 1 over 2 EX. 1/2
too, so the addition/subtraction is easier.
Hint: When deciding if you have a number between 0 and 2pi, compare it to the fraction version of 2pi that you've been adding/subtracting.
For 17pi/5...
First we can see that 17pi/5 is more than 10pi/5 (aka 2pi). So we need to start subtracting: 17pi/5 - 10pi/5 = 7pi/5
Now we have a number between 0 and 10pi/5. So 7pi/5 is the co-terminal angle between 0 and 2pi.
I'll leave the others for you to do. Just remember that you might have to add or subtract multiple times before you get a number between 0 and 2pi.
P.S don't add or subtract at all if the number starts out between 0 and 2pi.</span>
Answer:
a) The probability of selling less than 100 gallons (x≤1) is P=0.16.
b) The mean number of gallons is M=80 gallons.
Step-by-step explanation:
The probability of selling x, in hundred of gallons, on any day during the summer is y(x)=0.32x, in a range for x from [0;2.5].
The probability of selling less than 100 gallons (x≤1) is then:
The mean number of gallons can be calculated as:
1 apple + 1 banana
1 apple + 1 orange
1 apple + 1 peach
1 banana + 1 apple
1 banana + 1 orange
1 banana + 1 peach
1 orange + 1 apple
1 orange + 1 banana
1 orange + 1 peach
1 peach + 1 apple
1 peach + 1 orange
11 combinations of food
Hope this helped
![\bf \begin{cases} x=1\implies &x-1=0\\ x=1\implies &x-1=0\\ x=-\frac{1}{2}\implies 2x=-1\implies &2x+1=0\\ x=2+i\implies &x-2-i=0\\ x=2-i\implies &x-2+i=0 \end{cases} \\\\\\ (x-1)(x-1)(2x+1)(x-2-i)(x-2+i)=\stackrel{original~polynomial}{0} \\\\\\ (x-1)^2(2x+1)~\stackrel{\textit{difference of squares}}{[(x-2)-(i)][(x-2)+(i)]}](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Bcases%7D%0Ax%3D1%5Cimplies%20%26x-1%3D0%5C%5C%0Ax%3D1%5Cimplies%20%26x-1%3D0%5C%5C%0Ax%3D-%5Cfrac%7B1%7D%7B2%7D%5Cimplies%202x%3D-1%5Cimplies%20%262x%2B1%3D0%5C%5C%0Ax%3D2%2Bi%5Cimplies%20%26x-2-i%3D0%5C%5C%0Ax%3D2-i%5Cimplies%20%26x-2%2Bi%3D0%0A%5Cend%7Bcases%7D%0A%5C%5C%5C%5C%5C%5C%0A%28x-1%29%28x-1%29%282x%2B1%29%28x-2-i%29%28x-2%2Bi%29%3D%5Cstackrel%7Boriginal~polynomial%7D%7B0%7D%0A%5C%5C%5C%5C%5C%5C%0A%28x-1%29%5E2%282x%2B1%29~%5Cstackrel%7B%5Ctextit%7Bdifference%20of%20squares%7D%7D%7B%5B%28x-2%29-%28i%29%5D%5B%28x-2%29%2B%28i%29%5D%7D)
![\bf (x^2-2x+1)(2x+1)~[(x-2)^2-(i)^2] \\\\\\ (x^2-2x+1)(2x+1)~[(x^2-4x+4)-(-1)] \\\\\\ (x^2-2x+1)(2x+1)~[(x^2-4x+4)+1] \\\\\\ (x^2-2x+1)(2x+1)~[x^2-4x+5] \\\\\\ (x^2-2x+1)(2x+1)(x^2-4x+5)](https://tex.z-dn.net/?f=%5Cbf%20%28x%5E2-2x%2B1%29%282x%2B1%29~%5B%28x-2%29%5E2-%28i%29%5E2%5D%0A%5C%5C%5C%5C%5C%5C%0A%28x%5E2-2x%2B1%29%282x%2B1%29~%5B%28x%5E2-4x%2B4%29-%28-1%29%5D%0A%5C%5C%5C%5C%5C%5C%0A%28x%5E2-2x%2B1%29%282x%2B1%29~%5B%28x%5E2-4x%2B4%29%2B1%5D%0A%5C%5C%5C%5C%5C%5C%0A%28x%5E2-2x%2B1%29%282x%2B1%29~%5Bx%5E2-4x%2B5%5D%0A%5C%5C%5C%5C%5C%5C%0A%28x%5E2-2x%2B1%29%282x%2B1%29%28x%5E2-4x%2B5%29)
of course, you can always use (x-1)(x-1)(2x+1)(x²-4x+5) as well.
