Answer:
Step-by-step explanation:
Consider the sets A and B
(A − (A ∩ B)) ∩ (B − (A ∩ B))
= (A ∩ (A ∩ B)c) ∩ (B ∩ (A ∩ B)c) by the set difference law
= (A ∩ (Ac ∩ B)c) ∩ (B ∩ (Ac ∩ B)c) by De Morgan's law
= {(A ∩ Ac) ∪ (A ∩ Bc)} ∩ {(B ∩ Ac) ∪ (B ∩ Bc)} by the distributive law
= {∅ ∪ (A ∩ Bc)} ∩ {(B ∩ Ac) ∪ ∅} by complementation
= {A ∩ Bc} ∩ {B ∩ Ac} by identity law
= (A ∩ Ac) ∩ (B ∩ Ac) by the associative law
= ∅ ∩ ∅ by complementation
= ∅ by the universal bound law
Therefore, (A − (A ∩ B)) ∩ (B − (A ∩ B)) = ∅
Josh has to mow at least 16 yards. $25 x 16 = $400
Answer:
79/300 mm
Step-by-step explanation:
We can use Ratio and Proportion to answer this question,
We know,
12 sheets of paper = 3.16mm
So,
1 = 3.16/12 mm
So, the thickness of 1 sheet of paper is => 3.16 / 12
=> 79/300
Hope it helps :)
Answer:
x=15 and y=2
Step-by-step explanation:
The given system of equations is
8y - x = 1 ...............(i)
and
10 y = x + 5 ...............(ii)
Now from equation (ii)
10 y = x + 5
subtracting -5 from both sides
10 y - 5 = x + 5 - 5
10 y -5 = x
or
x = 10y -5 ............(iii)
Put this in equation (i)
it becomes
8y - (10y -5) = 1
8y-10y+5=1
-2y+5 =1
subtracting 5 from both sides
-2y + 5 -5 = 1 -5
-2y = -4
dividing both sides by -2 gives
-2y / -2 = -4 / -2
y = 2
We got the value of y putting it in equation (iii) to get the value of x
as from equation (iii)
x = 10y-5
x = 10(2) - 5
x = 20 -5
x = 15
So this is the solution from the equations
Answer:
4) 7.9%
Step-by-step explanation:
Given:
% of milk chocolate = 70%
% of white chocolate = 30%
Total number of chocolate = 20
Number of milk chocolate:
Number of white chocolate:
From the calculations, we now know there are 14 milk chocolates and 6 white chocolates.
2 white chocolates are picked at random without replacement.
Probability first chocolate picked was white:
Probability second chocolate picked was white:
To find probability that both of them are white chocolates, multiply probability of the first and second.
0.3 * 0.2632 = 0.07896
≈ 0.079
Convert to percentage by multiplying by 100.
0.079 * 100 = 7.9%
The probability that they are both
white chocolate is 7.9%