Answer:
We use Baye's theorem: P(A)P(B|A) = P(B)P(A|B)
with (A) being defective and
(B) marked as defective
we have to find P(B) = P(A).P(B|A) + P(¬A)P(B|¬A). .......eq(2)
Since P(A) = 0.1 and P(B|A)=0.9,
P(¬A) = 1 - P(A) = 1 - 0.1 = 0.9
and
P(B|A¬) = 1 - P(¬B|¬A) = 1 - 0.85 = 0.15
put these values in eq(2)
P(B) = (0.1 × 0.9) + (0.9 × 0.15)
= 0.225 put this in eq(1) and solve for P(B)
P(B) = 0.4
To determine the median, we need to set up our numbers from least to greatest, and then place T in later to figure out what T is.
8, 9, 9, 9, 10, 11, 12, 15. Cross out the smallest number with the largest number.
9, 9, 9, 10, 11, 12.
9, 9, 10, 11.
9, 10.
9.5 is our median currently.
Since we need to get a number after 10 to make 10 the median, let's use 12.
8, 9, 9, 9, 10, 11, 12, 12, 15.
9, 9, 9, 10, 11, 12 ,12.
9, 9, 10, 11, 12.
9, 10, 11.
10 is now our median since we inserted 12 into our list.
Your answer is 12.
I hope this helps!
9514 1404 393
Answer:
p(x) = x³ -3x²+4x -2
Step-by-step explanation:
When the polynomial has real coefficients, the complex roots come in conjugate pairs. You are given one root as 1+i, so there is another that is 1-i.
Each root r gives rise to a factor (x -r). Then the three roots tell you the factorization is ...
p(x) = (x -1)(x -(1+i))(x -(1-i))
The last two factors can be recognized as the factors of the difference of squares:
((x -1) +i)((x -1) -i) = (x -1)² -i²
= (x² -2x +1) -(-1) = x² -2x +2
Now the whole polynomial can be seen to be ...
p(x) = (x -1)(x² -2x +2) = x(x² -2x +2) -1(x² -2x +2)
p(x) = x³ -2x² +2x -x² +2x -2 . . . . eliminate parentheses
p(x) = x³ -3x²+4x -2
Answer:
<h2>2.) When dividing by −2, he did not change the direction of the sign. </h2>
Step-by-step explanation:
-4(x + 8) ≤ -2x + 50 <em>use the distributive property: a(b + c) = ab + ac</em>
-4x - 32 ≤ -2x + 50 <em>add 2x to both sides</em>
-4x + 2x - 32 ≤ -2x + 2x + 50
-2x - 32 ≤ 50 <em>add 32 to both sides</em>
-2x - 32 + 32 ≤ +50 + 32
-2x ≤ 82 <em>divide both sides by (-2) / </em><em>flip the inequality sign</em><em>/</em>
x ≥ -41
Andrew's mistake:
2.) When dividing by −2, he did not change the direction of the sign.