Answer:
46 housewives read all three magazines.
Step-by-step explanation:
Given:
n(A) = 150
n(B) = 200
n(C) = 156
n(A∩B) = 48
n(B∩C) = 60
n(A∩C) = 52
n(A∪B∪C) = 300
so we know the relation as:
n(A∪B∪C) = n(A) + n(B) + n(C) - n(A∩B) - n(B∩C) - n(A∩C) + n(A∩B∩C)
∴ n(A∩B∩C) = n(A) + n(B) + n(C) - n(A∩B) - n(B∩C) - n(A∩C) - n(A∪B∪C)
= 150 + 200+ 156 - 48 - 60 - 52 - 300
= 46
Hence the number of housewives that had read all three magazine is 46.
Answer:
5% with the information I'm provided with. I need more info
if that's wrong
Step-by-step explanation:
Since the chance of getting an even number on every roll is 3/6 or 1/2
We have to multiply 1/2 by 138
The answer is 69.
Hope this is correct, and pls correct me if I'm wrong :)
Answer:
Part c: Contained within the explanation
Part b: gcd(1200,560)=80
Part a: q=-6 r=1
Step-by-step explanation:
I will start with c and work my way up:
Part c:
Proof:
We want to shoe that bL=a+c for some integer L given:
bM=a for some integer M and bK=c for some integer K.
If a=bM and c=bK,
then a+c=bM+bK.
a+c=bM+bK
a+c=b(M+K) by factoring using distributive property
Now we have what we wanted to prove since integers are closed under addition. M+K is an integer since M and K are integers.
So L=M+K in bL=a+c.
We have shown b|(a+c) given b|a and b|c.
//
Part b:
We are going to use Euclidean's Algorithm.
Start with bigger number and see how much smaller number goes into it:
1200=2(560)+80
560=80(7)
This implies the remainder before the remainder is 0 is the greatest common factor of 1200 and 560. So the greatest common factor of 1200 and 560 is 80.
Part a:
Find q and r such that:
-65=q(11)+r
We want to find q and r such that they satisfy the division algorithm.
r is suppose to be a positive integer less than 11.
So q=-6 gives:
-65=(-6)(11)+r
-65=-66+r
So r=1 since r=-65+66.
So q=-6 while r=1.
Answer: the number of tiles will be 49
Step-by-step explanation:
Let x represent the number of tiles that Joshua can buy at either stores.
one store for $0.99 per tile but he he will have to rent a tile saw for $25. Let the total cost of buying x tiles in this store be y. Therefore
y = 0.99x + 25
At another store, he can buy a tile for $1.50 per tile and borrow a tile saw for free. Let the total cost of buying x tiles in this store be z. Therefore
z = 1.5x
To determine the number of tiles for which both costs will be the same, we will equate y to z. It becomes
0.99x + 25 = 1.5x
1.5x - 0.99x = 25
0.51x = 25
x = 25/0.51
x = 49