Answer: A'(-10, -4) and C''(-6, -8) B. A'(-10, -4) and C"(-18, -24) C. A'(-30, -12) and C"(-18, -24) D. A'(-30, -12) and C"(-4, -6) E. A'(-10, -4) and C"(-4, -6)
Answer:
<u>The probability that carbon emissions from the factory are within the permissible level and the test predicts the opposite to be true is 19.338% (Rounding to the next thousandth place)</u>
Step-by-step explanation:
1. Let's review the information provided to us to answer the question correctly:
Probability that carbon emissions from the company’s factory exceed the permissible level = 35% = 0.35
Accuracy of the test of emissions level = 85% = 0.85
2. The probability that carbon emissions from the factory are within the permissible level and the test predicts the opposite to be true is?
These two events, carbon emissions from the company’s factory and the accuracy of the test are independent events, therefore:
Probability that carbon emissions from the factory are within the permissible level = 1 - 0.35 = 0.65
Probability that the test predicts the opposite to be true = 0..35 * 0.85 = 0.2975 (The opposite is that the carbon emissions from the company exceed the permissible level)
Probability that carbon emissions from the factory are within the permissible level and the test predicts the opposite to be true is:
0.65 * 0.2975 = 0.193375
<u>The probability that carbon emissions from the factory are within the permissible level and the test predicts the opposite to be true is 19.338% (Rounding to the next thousandth place)</u>
Answer:
5)m=11/10
6)m=-17/2
7)m=18.13
8)m=-26/9
BTW The M is an EXAMPLE
Step-by-step explanation:
Answer:
the answer is easy.
Step-by-step explanation:
Answer:
Proofs are in the explantion.
Step-by-step explanation:
We are given the following:
1) 
for integer 
.
1) 
for integer 
.
a)
Proof:
We want to show 
.
So we have the two equations:
a-b=kn and c-d=mn and we want to show for some integer r that we have
(a+c)-(b+d)=rn. If we do that we would have shown that .
kn+mn = (a-b)+(c-d)
(k+m)n = a-b+ c-d
(k+m)n = (a+c)+(-b-d)
(k+m)n = (a+c)-(b+d)
k+m is is just an integer
So we found integer r such that (a+c)-(b+d)=rn.
Therefore, .
//
b) Proof:
We want to show 
.
So we have the two equations:
a-b=kn and c-d=mn and we want to show for some integer r that we have
(ac)-(bd)=tn. If we do that we would have shown that .
If a-b=kn, then a=b+kn.
If c-d=mn, then c=d+mn.
ac-bd = (b+kn)(d+mn)-bd
= bd+bmn+dkn+kmn^2-bd
= bmn+dkn+kmn^2
= n(bm+dk+kmn)
So the integer t such that (ac)-(bd)=tn is bm+dk+kmn.
Therefore, .
//
