These are the events in the question above:
<span>D - has disease
</span>
<span>H - healthy (does not have disease)
</span>
<span>P - tests positive </span>
<span>It is the probability that a person has the disease AND tests positive divided by the probability that the person tests positive.
</span>
Sick, + [.04*.91] = .0364
<span>Sick, - [.04*.09] = .0036 </span>
Healthy, + [.96*.04] = 0.0384
<span>Healthy, - [.96*.96] = .9216
</span>
.0364 / (.0364 + .0.0384) = 0.487
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.
The question does not make sense.
The commutative property applies to addition and multiplication, not addition and subtraction.
The commutative property does not apply to subtraction or division because in those operations, the order of the numbers makes a difference, whereas in addition and subtraction the order does not make a difference.
For example:
Addition
5 + 4 = 9
4 + 5 = 9
5 + 4 = 4 + 5
Changing the order of the 4 and the 5 gives the same answer.
The commutative property does apply to addition.
Multiplication
5 * 4 = 20
4 * 5 = 20
5 * 4 = 4 * 5
Changing the order of the 4 and the 5 gives the same answer.
The commutative property does apply to multiplication.
Subtraction
5 - 4 = 1
4 - 5 = -1
5 - 4 is not equal to 4 - 5
Changing the order of the 4 and the 5 gives a different answer.
The commutative property does not apply to subtraction.
Division
5/4 = 1.25
4/5 = 0.8
1.25 is not equal to 0.8.
Changing the order of the 4 and the 5 gives a different answer.
The commutative property does not apply to division.
The standard form is 24,000,011
Answer:
$90,962.66
Step-by-step explanation:
The formula for this is, where V = amount after t years:
V = P(1 + r/n)^nt where P is the amount invested, r = the rate as a decimal fraction, n is the number of times interest compounded each year and t = the number of years.
Here, V = 340,000, r = 0.07, n = 4 , t = 19 and P is to be found.
340,000 = P(1 + 0.07/4)^(4*19)
340,000 = P( 1.0175)^76
P = 340,000 / (1.0175^76)
P = $90,962.66
