Answer:
If 6 is an interior entry then it has to appear in one of the subwords 165 or 561. If all three of {2,3,4} are on the same side of these the digit 3 has to be in the middle of the three (gives 4 ways). If one of {2,3,4} stands alone it has to be one of 2 and 4 (gives another 8 ways). In all there are 24 admissible words of this kind.
If 6 is the first or last entry the entry next to 6 has to be 1 or 5. The remaining four digits could be arranged in 4!=24 ways, but we have to exclude the 2⋅3!=12 ways containing 24 or 42 as a subword. It follows that there are 2⋅2⋅(24−12)=48 admissible words of this kind.
The total number of admissible words therefore is 72.
<span>1) 2p = -2.
<span> 4p [ y - k ] = [ x - h) ]² --- > - 4 [ y + 5 ] = [ x + 5 ]²
2) </span></span><span>4p * (y - k) = (x - h)^2 </span>
<span>(h , k) is the vertex </span>
<span>The vertex is halfway between the focus and the directrix (when they're at their closest) </span>
<span>p is that distance </span>
<span>2 - 1 = 1 </span>
<span>4p = 1 </span>
<span>p = 1/4 </span>
<span>(1/4) * (y - k) = (x - h)^2 </span>
<span>y - k = 4 * (x - h)^2 </span>
<span>The vertex is at (6 , 3/2), since that's midway between (6 , 1) and (6 , 2) </span>
<span>y - 3/2 = 4 * (x - 6)^2 </span>
<span>y = (3/2) + 4 * (x - 6)^2
</span><span>
4) </span><span>f(x) = (-1/16)*(x²)
</span><span>
5) </span><span>f(x) = −1/4 x2 − x + 5</span><span>
</span>
5000 * 0.05 * 3.5 = 875
5000 + 875 = 5875
answer: <span>ending balance $5,875</span>
