Scoring exactly 20 would be the least likely...
20 is the bullseye its the circle with the least area therefore the hardest to hit.
Brainliest my answer if it helps you out?
Answer:
Step-by-step explanation:
Let W =
be orthogonal polynomials which is equal to
, which defines the inner products as
![$(f,g)=f(-2)g(-2)+f(-1)g(-1)+f(0)g(0)+f(1)g(1)+f(2)g(2)$](https://tex.z-dn.net/?f=%24%28f%2Cg%29%3Df%28-2%29g%28-2%29%2Bf%28-1%29g%28-1%29%2Bf%280%29g%280%29%2Bf%281%29g%281%29%2Bf%282%29g%282%29%24)
Now, we find the orthogonal projection of
on W.
So the projection is
![$Proj_W p = \frac{(p_0,p)}{(p_0,p_0)}p_0+\frac{(p_1,p)}{(p_1,p_1)}p_1+\frac{(p_2,p)}{(p_2,p_2)}p_2$](https://tex.z-dn.net/?f=%24Proj_W%20p%20%3D%20%5Cfrac%7B%28p_0%2Cp%29%7D%7B%28p_0%2Cp_0%29%7Dp_0%2B%5Cfrac%7B%28p_1%2Cp%29%7D%7B%28p_1%2Cp_1%29%7Dp_1%2B%5Cfrac%7B%28p_2%2Cp%29%7D%7B%28p_2%2Cp_2%29%7Dp_2%24)
![$(p_0,p)=p_0(-2)p(-2)+p_0(-1)p(-1)+p_0(0)p(0)+p_0(1)p(1)+p_0(2)p(2)$](https://tex.z-dn.net/?f=%24%28p_0%2Cp%29%3Dp_0%28-2%29p%28-2%29%2Bp_0%28-1%29p%28-1%29%2Bp_0%280%29p%280%29%2Bp_0%281%29p%281%29%2Bp_0%282%29p%282%29%24)
![$=4(-24)+4(-3)+4(0)+4(3)+4(24)=0$](https://tex.z-dn.net/?f=%24%3D4%28-24%29%2B4%28-3%29%2B4%280%29%2B4%283%29%2B4%2824%29%3D0%24)
![$(p_0,p_0)=p_0(-2)p_0(-2)+p_0(-1)p_0(-1)+p_0(0)p_0(0)+p_0(1)p_0(1)+p_0(2)p_0(2)$](https://tex.z-dn.net/?f=%24%28p_0%2Cp_0%29%3Dp_0%28-2%29p_0%28-2%29%2Bp_0%28-1%29p_0%28-1%29%2Bp_0%280%29p_0%280%29%2Bp_0%281%29p_0%281%29%2Bp_0%282%29p_0%282%29%24)
![$=4(4)+4(4)+4(4)+4(4)+4(4)=80$](https://tex.z-dn.net/?f=%24%3D4%284%29%2B4%284%29%2B4%284%29%2B4%284%29%2B4%284%29%3D80%24)
![$(p_1,p)=p_1(-2)p(-2)+p_1(-1)p(-1)+p_1(0)p(0)+p_1(1)p(1)+p_1(2)p(2)$](https://tex.z-dn.net/?f=%24%28p_1%2Cp%29%3Dp_1%28-2%29p%28-2%29%2Bp_1%28-1%29p%28-1%29%2Bp_1%280%29p%280%29%2Bp_1%281%29p%281%29%2Bp_1%282%29p%282%29%24)
![$=(-6)(-24)+(-3)(-3)+0(0)+3(3)+6(24)=306$](https://tex.z-dn.net/?f=%24%3D%28-6%29%28-24%29%2B%28-3%29%28-3%29%2B0%280%29%2B3%283%29%2B6%2824%29%3D306%24)
![$(p_1,p_1)=p_1(-2)p_1(-2)+p_1(-1)p_1(-1)+p_1(0)p_1(0)+p_1(1)p_1(1)+p_1(2)p_1(2)$](https://tex.z-dn.net/?f=%24%28p_1%2Cp_1%29%3Dp_1%28-2%29p_1%28-2%29%2Bp_1%28-1%29p_1%28-1%29%2Bp_1%280%29p_1%280%29%2Bp_1%281%29p_1%281%29%2Bp_1%282%29p_1%282%29%24)
![$=(-6)(-6)+(-3)(-3)+0(0)+3(3)+6(6)=90$](https://tex.z-dn.net/?f=%24%3D%28-6%29%28-6%29%2B%28-3%29%28-3%29%2B0%280%29%2B3%283%29%2B6%286%29%3D90%24)
![$(p_2,p)=p_2(-2)p(-2)+p_2(-1)p(-1)+p_2(0)p(0)+p_2(1)p(1)+p_2(2)p(2)$](https://tex.z-dn.net/?f=%24%28p_2%2Cp%29%3Dp_2%28-2%29p%28-2%29%2Bp_2%28-1%29p%28-1%29%2Bp_2%280%29p%280%29%2Bp_2%281%29p%281%29%2Bp_2%282%29p%282%29%24)
![$=2(-24)+(-1)(-3)+(-2)(0)+(-1)(3)+2(24)=0$](https://tex.z-dn.net/?f=%24%3D2%28-24%29%2B%28-1%29%28-3%29%2B%28-2%29%280%29%2B%28-1%29%283%29%2B2%2824%29%3D0%24)
![$(p_2,p_2)=p_2(-2)p_2(-2)+p_2(-1)p_2(-1)+p_2(0)p_2(0)+p_2(1)p_2(1)+p_2(2)p_2(2)$](https://tex.z-dn.net/?f=%24%28p_2%2Cp_2%29%3Dp_2%28-2%29p_2%28-2%29%2Bp_2%28-1%29p_2%28-1%29%2Bp_2%280%29p_2%280%29%2Bp_2%281%29p_2%281%29%2Bp_2%282%29p_2%282%29%24)
![$=(2)(2)+(-1)(-1)+(-2)(-2)+(-1)(-1)+2(2)=14$](https://tex.z-dn.net/?f=%24%3D%282%29%282%29%2B%28-1%29%28-1%29%2B%28-2%29%28-2%29%2B%28-1%29%28-1%29%2B2%282%29%3D14%24)
Therefore,
![$Proj_W p = \frac{(p_0,p)}{(p_0,p_0)}p_0+\frac{(p_1,p)}{(p_1,p_1)}p_1+\frac{(p_2,p)}{(p_2,p_2)}p_2$](https://tex.z-dn.net/?f=%24Proj_W%20p%20%3D%20%5Cfrac%7B%28p_0%2Cp%29%7D%7B%28p_0%2Cp_0%29%7Dp_0%2B%5Cfrac%7B%28p_1%2Cp%29%7D%7B%28p_1%2Cp_1%29%7Dp_1%2B%5Cfrac%7B%28p_2%2Cp%29%7D%7B%28p_2%2Cp_2%29%7Dp_2%24)
![$=\frac{0}{80}(4)+\frac{306}{90}(3t)+\frac{0}{14}(t^2-2)$](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B0%7D%7B80%7D%284%29%2B%5Cfrac%7B306%7D%7B90%7D%283t%29%2B%5Cfrac%7B0%7D%7B14%7D%28t%5E2-2%29%24)
![$=\frac{51}{5}t$](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B51%7D%7B5%7Dt%24)
Hi there!
The question here gives us an inequality, and it tells us to solve for x.
![\frac{1}{3} (6x+24)-20 \ \textless \ - \frac{1}{2} (6x-36)](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B3%7D%20%286x%2B24%29-20%20%5C%20%5Ctextless%20%5C%20%20-%20%5Cfrac%7B1%7D%7B2%7D%20%286x-36%29)
First, use the distributive property to simplify both sides of the equation.
![2x+8-20\ \textless \ -3x+18](https://tex.z-dn.net/?f=2x%2B8-20%5C%20%5Ctextless%20%5C%20-3x%2B18)
Now, on the left side of the inequality, combine like terms.
![2x-12\ \textless \ -3x+18](https://tex.z-dn.net/?f=2x-12%5C%20%5Ctextless%20%5C%20-3x%2B18)
Add 12 to both sides.
![2x\ \textless \ -3x+30](https://tex.z-dn.net/?f=2x%5C%20%5Ctextless%20%5C%20-3x%2B30)
Add 3x to both sides.
![5x\ \textless \ 30](https://tex.z-dn.net/?f=5x%5C%20%5Ctextless%20%5C%2030)
Divide 5 from both sides.
![x\ \textless \ 6](https://tex.z-dn.net/?f=x%5C%20%5Ctextless%20%5C%206)
Therefore, the solution to the inequality is anything less than 6, or
x < 6. Hope this helped!
Answer: ![9\times10^7\ miles](https://tex.z-dn.net/?f=9%5Ctimes10%5E7%5C%20miles)
Step-by-step explanation:
Given: The estimated distance from Earth to the moon![=2.25\times10^5\ miles](https://tex.z-dn.net/?f=%3D2.25%5Ctimes10%5E5%5C%20miles)
If the distance from Earth to the sun is approximately 400 times farther.
Then, the distance from Earth to the sun![=400\times2.25\times10^5](https://tex.z-dn.net/?f=%3D400%5Ctimes2.25%5Ctimes10%5E5)
![=900\times10^5\ miles\\=9\times10^7\ miles](https://tex.z-dn.net/?f=%3D900%5Ctimes10%5E5%5C%20miles%5C%5C%3D9%5Ctimes10%5E7%5C%20miles)
Therefore, the approximate distance from Earth to the sun=![9\times10^7\ miles](https://tex.z-dn.net/?f=9%5Ctimes10%5E7%5C%20miles)
Answer:
1 4/13
Step-by-step explanation:
![6 \frac{7}{13} \div 5 = \frac{85}{13} \div 5 = \frac{85}{13} \times \frac{1}{5} = \frac{17}{13} = 1 \frac{4}{13}](https://tex.z-dn.net/?f=6%20%5Cfrac%7B7%7D%7B13%7D%20%20%5Cdiv%205%20%3D%20%5Cfrac%7B85%7D%7B13%7D%20%20%5Cdiv%205%20%3D%20%20%5Cfrac%7B85%7D%7B13%7D%20%20%5Ctimes%20%20%5Cfrac%7B1%7D%7B5%7D%20%20%3D%20%20%5Cfrac%7B17%7D%7B13%7D%20%3D%20%201%20%5Cfrac%7B4%7D%7B13%7D%20)