Answer:
x²-8x-1=0
comparing above equation with ax²+bx+c=0
a=1
b=-8
c=-1
x=

=(--8+-√(64-4×1×-1)/2×1
=8+-√(64+4)/2
taking positive
x=(8+√68)/2=2(4+√17)/2=4+√17
taking negative
x=(8-√68)/2=2(4-√17)/2=4-√17
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The best and most correct answer among the choices provided by the question is </span><span>A. Between 0.05 and 0.01 </span> .
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Hope my answer would be a great help for you. </span>
Answer:
0.2941 = 29.41% probability that it was manufactured during the first shift.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is

In which
P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Defective
Event B: Manufactured during the first shift.
Probability of a defective item:
1% of 50%(first shift)
2% of 30%(second shift)
3% of 20%(third shift).
So

Probability of a defective item being produced on the first shift:
1% of 50%. So

What is the probability that it was manufactured during the first shift?

0.2941 = 29.41% probability that it was manufactured during the first shift.
The solution is 
<em><u>Solution:</u></em>
Let us assume,

<em><u>Given system of equations are:</u></em>


<em><u>Rewrite the equation using "a" and "b"</u></em>
2a - 3b = -5 ------------ eqn 1
4a + 6b = 14 -------------- eqn 2
<em><u>Let us solve eqn 1 and eqn 2</u></em>
<em><u>Multiply eqn 1 by 2</u></em>
2(2a - 3b = -5)
4a - 6b = -10 ------------- eqn 3
<em><u>Add eqn 2 and eqn 3</u></em>
4a + 6b = 14
4a - 6b = -10
( - ) --------------------
8a = 4

Substitute a = 1/2 in eqn 1

Now let us go back to our assumed values
Substitute a = 1/2 in assumed values

Substitute b = 2 in assumed value

Thus the solution is 
Answer:
1. The expected pay-out on each policy is 250 * 1/90 + 12000 * 1/100 + 17000 * 1/400 = $165. So that's what the premium would have to be in order to get a profit of 0.
2. The profit per policy is the premium the company receives minus the expected payout = 350 - 165 = $185.
3. The expected profit on 375 policies would be 375 * 185 = $69375
Step-by-step explanation: