Answer:
Yes, the function is a kernel
Step-by-step explanation:
Given
Document x an z
Function definition! k(x:z)
We want to show that the above is a kernel.
To do this, we'll explicitly construct feature vectors φ(x) and φ(z)
This gives;
K(x,z) =φ(x)·φ(z).
Given than any document; say x and z
A vocabulary V can be constructed.
Vocabulary V must have a finite size of words in the document set..
The feature mapping is constructed as φ(x) for x by the following:
For the kth word wk in V, if wk appears in document x, assign φ(x) k(the kth element ofφ(x)) to be 1; else φ(x)k to 0.
Then the number of unique words common in x and z is φ(x)·φ(z), giving us the kernel
.
Divide 53.70 by 6 to give you 8.95 and divide 71.60 by 8 to give you 8.95 so they sell it for the exact same unit price
$25 - $4 = $21
You spent $21 on 3 boxes of granola bars.
3 boxes = $21
1 box = $21 ÷ 3 = $7
One box of granola bar costs $7.
1. n^2 -8n +16 = 25
Subtract 25 from both sides
n^2 - 8n + 16 - 25 = 0
Simplify
n^2 - 8n - 9 =0
Factor
(n-9)(n+1) = 0
Solve for n
n-9 = 0, n = 9
n+1 = 0, n = -1
Solution: 9,-1
2. C = b^2/25
Multiply both sides by 25:
25c = b^2
Take square root of both sides
b = +/-√25c
Simplify:
b = 5√C, -5√C
3. d = 16t^2 +12t
subtract d from both side:
16t^2 + 12t -d =0
Use quadratic formula to solve:
t = (3 +/-√(9-4d))/8
4. 5w^2 +10w =40
Subtract 40 from both side:
5w^2 + 10w -40 = 0
Factor:
5(w-2)(w+4)=0
Divide both sides by 5:
(w-2)(w+4)=0
Solve for w:
w-2 = 0, w = 2
w+4=0, w = -4
Solution: 2,-4
