1. Given a group of n people. There are C(n, r) ways of forming groups of r out of n.
2. Where C(n, r)=
3. For example, given {Andy, John, Julia}. We want to pick 2 people to give a gift: we can pick {(Andy, John), (Andy, Julia), (John, Julia)}, so there are 3 ways. So we can list and count.
4. Or we could do this with the formula C(3, 2)=
5. C(8, 6)=
So there are C(8,6)=28 ways of chosing 6 out of 8 people to form the subcommittees. <span />
Check the picture below, so the parabola looks more or less like that.
now, the vertex is half-way between the focus point and the directrix, so that puts it where you see it in the picture, and the horizontal parabola is opening to the left-hand-side, meaning that the distance "P" is negative.
![\textit{horizontal parabola vertex form with focus point distance} \\\\ 4p(x- h)=(y- k)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h+p,k)}\qquad \stackrel{directrix}{x=h-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\supset}\qquad \stackrel{"p"~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}](https://tex.z-dn.net/?f=%5Ctextit%7Bhorizontal%20parabola%20vertex%20form%20with%20focus%20point%20distance%7D%20%5C%5C%5C%5C%204p%28x-%20h%29%3D%28y-%20k%29%5E2%20%5Cqquad%20%5Cbegin%7Bcases%7D%20%5Cstackrel%7Bvertex%7D%7B%28h%2Ck%29%7D%5Cqquad%20%5Cstackrel%7Bfocus~point%7D%7B%28h%2Bp%2Ck%29%7D%5Cqquad%20%5Cstackrel%7Bdirectrix%7D%7Bx%3Dh-p%7D%5C%5C%5C%5C%20p%3D%5Ctextit%7Bdistance%20from%20vertex%20to%20%7D%5C%5C%20%5Cqquad%20%5Ctextit%7B%20focus%20or%20directrix%7D%5C%5C%5C%5C%20%5Cstackrel%7B%22p%22~is~negative%7D%7Bop%20ens~%5Csupset%7D%5Cqquad%20%5Cstackrel%7B%22p%22~is~positive%7D%7Bop%20ens~%5Csubset%7D%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D)
![\begin{cases} h=-7\\ k=-2\\ p=-4 \end{cases}\implies 4(-4)[x-(-7)]~~ = ~~[y-(-2)]^2 \\\\\\ -16(x+7)=(y+2)^2\implies x+7=-\cfrac{(y+2)^2}{16}\implies x=-\cfrac{1}{16}(y+2)^2-7](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D%20h%3D-7%5C%5C%20k%3D-2%5C%5C%20p%3D-4%20%5Cend%7Bcases%7D%5Cimplies%204%28-4%29%5Bx-%28-7%29%5D~~%20%3D%20~~%5By-%28-2%29%5D%5E2%20%5C%5C%5C%5C%5C%5C%20-16%28x%2B7%29%3D%28y%2B2%29%5E2%5Cimplies%20x%2B7%3D-%5Ccfrac%7B%28y%2B2%29%5E2%7D%7B16%7D%5Cimplies%20x%3D-%5Ccfrac%7B1%7D%7B16%7D%28y%2B2%29%5E2-7)
Answer:
Step-by-step explanation:
Sin 58° = 0.848 = BC/13
So
BC = 0.848*13 = 11.024
Let's solve your equation step-by-step.<span><span>−<span>4<span>(<span>r+2</span>)</span></span></span>=<span>4<span>(<span>2−<span>4r</span></span>)</span></span></span>Step 1: Simplify both sides of the equation.<span><span>−<span>4<span>(<span>r+2</span>)</span></span></span>=<span>4<span>(<span>2−<span>4r</span></span>)</span></span></span><span>Simplify</span><span><span><span><span>(<span>−4</span>)</span><span>(r)</span></span>+<span><span>(<span>−4</span>)</span><span>(2)</span></span></span>=<span><span><span>(4)</span><span>(2)</span></span>+<span><span>(4)</span><span>(<span>−<span>4r</span></span>)</span></span></span></span>(Distribute)<span><span><span><span>−<span>4r</span></span>+</span>−8</span>=<span><span>8+</span>−<span>16r</span></span></span><span><span><span>−<span>4r</span></span>−8</span>=<span><span>−<span>16r</span></span>+8</span></span>Step 2: Add 16r to both sides.<span><span><span><span>−<span>4r</span></span>−8</span>+<span>16r</span></span>=<span><span><span>−<span>16r</span></span>+8</span>+<span>16r</span></span></span><span><span><span>12r</span>−8</span>=8</span>Step 3: Add 8 to both sides.<span><span><span><span>12r</span>−8</span>+8</span>=<span>8+8</span></span><span><span>12r</span>=16</span>Step 4: Divide both sides by 12.<span><span><span>12r</span>12</span>=<span>1612</span></span><span>r=<span>43</span></span>Answer:<span>r=<span>4<span>3</span></span></span>
Answer:
198.75
Step-by-step explanation:
Multiply 795 by .25
$795 - $198.75= new price
