Answer:
C
Step-by-step explanation:
If the average wasn't shifted at all, that means the third value must've been the same as the average to not shift it.
Answer:
The tower is 61.65 meters tall.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Given that a bag contains 40 cards numbered 1 through 40 that are either red or blue. A card is drawn at random and placed back in the bag.
This is done four times. Two red cards are drawn, numbered 31 and 19, and two blue cards are drawn, numbered 22 and 7.
From the above we cannot conclude that red cards and even numbers are mutually exclusive
Just drawing two red cards and because the two happen to be odd we cannot generalize the red cards have odd numbers.
This might have occurred due to simple chance from a comparatively large number of 40 cards.
Suppose say we have red cards 20, and 19 red 1 blue.
Then drawing 2 from 19 red cards have more probability and this can occur by chance.
So friend's conclusion is wrong.
Answer: 3π in terms of pi or 9.42 if in π or pi= 3.14
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, .
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