Answer:
Follows are the solution to this question:
Step-by-step explanation:
In point a:
![\to \frac{5 \pi }{6}](https://tex.z-dn.net/?f=%5Cto%20%5Cfrac%7B5%20%5Cpi%20%7D%7B6%7D)
calculating a positive coterminal angle:
![\to \frac{5 \pi }{6} + 2 \pi \\\\ \to \frac{5 \pi +12 \pi }{6} \\\\ \to \frac{17 \pi }{6} \\\\](https://tex.z-dn.net/?f=%5Cto%20%5Cfrac%7B5%20%5Cpi%20%7D%7B6%7D%20%2B%202%20%5Cpi%20%5C%5C%5C%5C%20%5Cto%20%5Cfrac%7B5%20%5Cpi%20%2B12%20%5Cpi%20%7D%7B6%7D%20%5C%5C%5C%5C%20%5Cto%20%5Cfrac%7B17%20%5Cpi%20%7D%7B6%7D%20%5C%5C%5C%5C)
calculating negative coterminal angle:
![\to \frac{5 \pi }{6} -2\pi \\\\ \to \frac{5 \pi - 12 \pi }{6} \\\\ \to \frac{ - 7 \pi }{6} \\\\](https://tex.z-dn.net/?f=%5Cto%20%5Cfrac%7B5%20%5Cpi%20%7D%7B6%7D%20-2%5Cpi%20%5C%5C%5C%5C%20%5Cto%20%5Cfrac%7B5%20%5Cpi%20-%2012%20%5Cpi%20%7D%7B6%7D%20%5C%5C%5C%5C%20%5Cto%20%5Cfrac%7B%20-%207%20%5Cpi%20%7D%7B6%7D%20%5C%5C%5C%5C)
In point b:
![\to \frac{-9 \pi }{4}](https://tex.z-dn.net/?f=%5Cto%20%5Cfrac%7B-9%20%5Cpi%20%7D%7B4%7D)
calculating a positive coterminal angle:
![\to \frac{ -9 \pi }{4} + 2 \pi \ \ = \frac{-9 \pi + 8 \pi }{4} \\\\](https://tex.z-dn.net/?f=%5Cto%20%5Cfrac%7B%20-9%20%5Cpi%20%7D%7B4%7D%20%2B%202%20%5Cpi%20%20%5C%20%5C%20%20%20%3D%20%5Cfrac%7B-9%20%5Cpi%20%2B%208%20%5Cpi%20%7D%7B4%7D%20%5C%5C%5C%5C)
![\to \frac{ - \pi }{4} + 2 \pi \ \ = \frac{- \pi + 8 \pi }{4} \\\\](https://tex.z-dn.net/?f=%5Cto%20%5Cfrac%7B%20-%20%5Cpi%20%7D%7B4%7D%20%2B%202%20%5Cpi%20%20%5C%20%5C%20%20%20%3D%20%5Cfrac%7B-%20%5Cpi%20%2B%208%20%5Cpi%20%7D%7B4%7D%20%5C%5C%5C%5C)
![= \frac{ 7 \pi}{4}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B%207%20%5Cpi%7D%7B4%7D)
calculating a negative coterminal angle:
![\to \frac{ -9 \pi }{4} - 2 \pi \\\\ \to \frac{-9 \pi - 8 \pi }{4} \\\\ \to \frac{-17 \pi }{4}](https://tex.z-dn.net/?f=%5Cto%20%5Cfrac%7B%20-9%20%5Cpi%20%7D%7B4%7D%20-%202%20%5Cpi%20%20%5C%5C%5C%5C%20%20%20%5Cto%20%5Cfrac%7B-9%20%5Cpi%20-%208%20%5Cpi%20%7D%7B4%7D%20%5C%5C%5C%5C%20%5Cto%20%20%5Cfrac%7B-17%20%5Cpi%20%7D%7B4%7D)
Alyssa's ratio of correct questions to total questions is 16 : 20. 16 divided by 20 = 0.80 x 100% = 80%, Alyssa got a B on her quiz.
In order to get an A on the exam, Alyssa needs a ratio of 90 : 100. Looking at the solutions in part (a), 100 is 5 times 20 so to see how many questions Alyssa needs to answer correctly out of 20 we can divide 90 by 5. Since 90 ÷ 5 = 18, Alyssa needs to answer 18 questions correctly. The ratios 18 : 20 and and 90 : 100 are equivalent since both numbers are scaled by the same factor, 5, to get from the first pair of numbers to the second.
Jessie answered 3 times as many questions correctly than she did incorrectly. This means that for every 1 question Jessie answered incorrectly, she answered 3 questions correctly. In other words, Jessie's ratio of correct answers to incorrect answers is 3 : 1.
Answer:
12
Step-by-step explanation:
1
2
3
4
5
6
7
8
9
10
11
12
1+2+3+4+5+6+7+8+9+10+11+12=78
About 84.82
Step-by-step explanation:
The formula to find the volume of a cone is pi*r^2*(h/3). The formula to find radius is diameter/2. 6/2=3. Since r=3 and h=9, pi*3^2*(9/3)=84.82
Answer:
$18.90
Step-by-step explanation:
Multiply the original price by the percentage
$21 x 10% = $2.10
You then subtract this from the original to get the discounted price
$21 - $2.10 = $18.90