Answer:
1) Juans claim is incorrect. The correct experimental probablilty is 2/9
Step-by-step explanation:
Answer:
1. (6, 2) and (-3, -6) 2. (-4 and -6) and (3, -8) 3.(-2, -8) and (6, 4) 4.(-3, 9) and (0, 1) 5.(2, -2) and (8, 1) 6.(-12, 4) and (0, 2) 7.(-8, -4) and (4, -7) 8.(-4, 13) and (-2, 6)
Step-by-step explanation:
Let p(x) be a polynomial, and suppose that a is any real
number. Prove that
lim x→a p(x) = p(a) .
Solution. Notice that
2(−1)4 − 3(−1)3 − 4(−1)2 − (−1) − 1 = 1 .
So x − (−1) must divide 2x^4 − 3x^3 − 4x^2 − x − 2. Do polynomial
long division to get 2x^4 − 3x^3 − 4x^2 – x – 2 / (x − (−1)) = 2x^3 − 5x^2 + x –
2.
Let ε > 0. Set δ = min{ ε/40 , 1}. Let x be a real number
such that 0 < |x−(−1)| < δ. Then |x + 1| < ε/40 . Also, |x + 1| <
1, so −2 < x < 0. In particular |x| < 2. So
|2x^3 − 5x^2 + x − 2| ≤ |2x^3 | + | − 5x^2 | + |x| + | − 2|
= 2|x|^3 + 5|x|^2 + |x| + 2
< 2(2)^3 + 5(2)^2 + (2) + 2
= 40
Thus, |2x^4 − 3x^3 − 4x^2 − x − 2| = |x + 1| · |2x^3 − 5x^2
+ x − 2| < ε/40 · 40 = ε.
Answer:
y < 1/2x -5
Step-by-step explanation:
1/2 is the slope
-5 is the y intercept
<h3>Solution and Explanation:</h3>
If 
and 
are directly proportional, then they must have a common scalar.
To find we must first find its scalar. If we let 
be the scalar we can form the equation, 
.
We are given the information that if 
then 
. We can use that in finding the scalar.
Now we can solve for when 
knowing that our scalar is 
.
<h3>Answer:</h3>
when
