Solution :
We have to prove that [tex]$\overline{A \cup B} = \overline{A} \cap \overline{B}$[/tex] (De-Morgan's law)
Let [tex]$x \in \bar{A} \cap \bar{B}, $[/tex] then [tex]$x \in \bar{A}$[/tex] and [tex]$x \in \bar{B} $[/tex]
and so [tex]$x \notin \bar{A}$[/tex] and [tex]$x \notin \bar{B} $[/tex].
Thus, [tex]$x \notin A \cup B$[/tex] and so [tex]$x \in \overline{A \cup B}$[/tex]
Hence, [tex]$\bar{A} \cap \bar{B} \subset \overline{A \cup B}$[/tex] .........(1)
Now we will show that [tex]$\overline{A \cup B} \subset \overline{A} \cap \overline{B}$[/tex]
Let [tex]$x \in \overline{A \cup B}$[/tex] ⇒ [tex]$x \notin A \cup B$[/tex]
Thus x is present neither in the set A nor in the set B, so by definition of the union of the sets, by definition of the complement.
[tex]$x \in \overline{A}$[/tex] and [tex]$x \in \overline{B}$[/tex]
Therefore, [tex]$x \in \overline{A} \cap \overline{B}$[/tex] and we have [tex]$\overline{A \cup B} \subset \overline{A} \cap \overline{B}$[/tex] .............(2)
From (1) and (2),
[tex]$\overline{A \cup B} = \overline{A} \cap \overline{B}$[/tex]
Hence proved.
Juan bought a laptop for $650 and a power adapter for $59. If the sales tax rate is 6%,
what was the total tax that Juan paid?
Answer:
$42.54
Step-by-step explanation:
total spent- 709
6/100*709= 42.54
if my answe helps please mark as brainliest.
help plzz WILL MARK BRAINLIST
Answer:
224
Step-by-step explanation:
Given
f(x) = 4x² - 4x
f(-7) = 4 * (-7)² - 4 * (-7)
= 196 + 28
= 224
Hope it will help :)
4
What is the result of 2-10?
.
1
5
Answer:
-3.14530027393739338363829263839
-Step-by-step explanation:
Is a bucket used to carry water more likely to have a capacity of a pint or a gallon
Answer:
well it depends on the size of the bucket but some buckets may be a gallon but then some are bigger id-k if this makes sense im srry
Step-by-step explanation:
Hello!! I have a question, can you please answer it. ^^
The school nurse is assembling first-aid kits for the teachers. She has 75 bandages and 90 throat lozenges.
All the kits must have the same number of each supply, and all supplies must be used.
a. What is the largest number of kits the nurse can make?
b. How many bandages and lozenges will be in each kit?
Answer:
1. 75
2. 1
Step-by-step explanation:
Simplify 2x + 1 -x + 2.
Answer:
x+3
Step-by-step explanation:
Hope you have a good day, Loves!
Also if I'm right can you let me know please?
Also Also if I am right can I please have Brainliest??
(How in the hecc are three people answering this?)
Functions:Question 5
What is the y-intercept of the line whose equation is shown below?
y = - 3.3 +7
Select one:
3
-3
4
7
In ARST, the measure of T=90°, ST = 7.7 feet, and RS = 9.7 feet. Find the measure
of R to the nearest degree.
9.7
7.7
X
T
R
Answer:
Submit Answer
Answer: 53
Step-by-step explanation:
Answer:
53
Step-by-step explanation:
..................Help please!
Answer:
with
Step-by-step explanation:
what
Carter is going to invest $210 and leave it in an account for 5 years. Assuming the interest is compounded annually, what interest rate, to the nearest tenth of a percent, would be required in order for Carter to end up with $250?
Answer:360
Step-by-step explanation:g-g5
The rate of interest will be 0.35.
What is compound interest?
Compound interest is the interest calculated on the principal and the interest accumulated over the previous period.
Compound interest formula[tex]CI = P(1+\frac{r}{n}) ^{nt} -P[/tex]
and, the Amount is given by
[tex]A = P(1+\frac{r}{n} )^{nt}[/tex]
Where,
A is amount
P is principal
r is rate of interest
n is number of times interest is compounded per year
t is time
According to the given question
Principal, P = $210
Amount, A = $250
Time, t = 5 years
n = 1
Therefore, the interest rate is given by
Amount = [tex]P(1+\frac{r}{n}) ^{nt}[/tex]
⇒[tex]250 = 210(1+\frac{r}{1}) ^{5}[/tex]
⇒[tex]\frac{250}{210} =(1+r)^{5}[/tex]
⇒[tex]1.19 = (1+r)^{5}[/tex]
⇒[tex]\sqrt[5]{1.19} = 1+r\\[/tex]
⇒ 1.035 = 1 + r
⇒ r = 1.035 - 1
⇒ r = 0.35
Hence, the interest rate is o.35.
Learn more about compound interest here:
https://brainly.com/question/14295570
#SPJ2
7. Look at this figure
There are different shapes in the figure (Do not count the
trapezoid itself)
b2
9:24 AM
2/9/2029
Answer:
thx for the 32 points
Step-by-step explanation:
What is 10x+ 5y =30 in function form
What is the volume of the pyramid?
Answer: 484
Step-by-step explanation:
12x11x11=1,452
1,452/3=484
Pls help pls thank you
Answer:
2 1/2 pounds
Step-by-step explanation:
3^-7
Simplify please.
Answer:
0.000457 what I got
Step-by-step explanation:
Solve for q.
7(q + 7) = 5q + 59
Answer:
5.
Step-by-step explanation:
7(q + 7) = 5q + 59
7q + 49 = 5q + 59
7q - 5q = 59 - 49
2q = 10
q = 5.
Use distributive property to write an equivalent expression. Use paper and pencil to
work the problems out, and then check your answers once you have submitted the
practice. (Answers will be in the bubbled comments after the problem.)
A. 6 Gn+2)
B.p(4p +9)
C. 5r (r + 4
Answer:
A) 6Gn + 12 (or 6n+12, if that’s what you meant)
B) 4p²+9p
C) 5r²+20r
Step-by-step explanation:
A. If you meant 6(n+2)...
Multiply 6 by n and also 6 by 2:
6n + 12
B. Multiply p by 4p and also p by 9
4p²+9p
C. Multiply 5r by r and also 5r by 4
5r²+20r
Hope this helped!
Someone please help :( ?????
Solve for x.
(x + 10)°
(4x - 35)°
Answer:
x = 15
Step-by-step explanation:
x+10=4x−35
x+10−4x=4x−35−4x
−3x+10−10=−35−10
−3x=−45
x = 15
Can someone answer this question please ASAP
Answer:
x = 2
Step-by-step explanation:
a) 82
b) 42
c) 98
d) 70
Answer:
option d.
let the two angle of mnp be x and y
in the trapezoid NO and MP are parallel.
so the 28° = y and 42°=x(by alternate interior angle)
so the angle mnp= x+y
angle mnp=28°+42°=70°
A rectangle has length 6 cm and width 4 cm. Give the length and width of another rectangle with the same area but a different perimeter.
Answer:
length could be 8 cm and width would be 3 cm and that would have a perimiter of 24 cm also
Can you please tell me the equation to solve for x
Answer:
53 + 67 + x = 180
Step-by-step explanation:
Answer:
180 = 53 + x + 67
(A straight line equals 180°)
good luck, hope this helped :)
Put the following numbers in order from least to greatest 6.-3, 0, 4.-5
Answer:
-5, -3, 0, 4, 6
Step-by-step explanation:
Answer:
-5,-3,6,4,0
Step-by-step explanation:
I just did least to greatest
What is the greatest common factor (GCF) of 12x and (3x^2 + 6x)?
(B) 3x
(C) X + 2
(D) 3x(x + 2)
(A) 3
Hey I'm Chloe, Can You Help Me Thank you :)
y varies proportionally with x. When x = 2, y = 18.
What is the constant of proportionality for this relationship?
Answer:
y = 9x
Step-by-step explanation:
which algebraic expression represents the word expression "three times the square of a number, n, subtracted from 54. ANSWER ASAP
High-definition televisions have an aspect ratio of 16: 9. The following answer choices are television screen sizes rounded to the nearest inch. Which could be a High-definition television?
Answer:
18.5 in approx
Step-by-step explanation:
Given data
aspect ratio of 16: 9
L= 16in
W= 9 in
We want to find the diagonal of the TV
applying Pythagoras theorem
d^2= l^2+w^2
d^2= 16^2+ 9^2
d^2=256+81
d^2= 337
d= √337
d= 18.35 in
Hence the tv is 18.5 in approx
Hakeem left his house and drove to the store. He stopped and went inside. From there, he drove in the same direction until he got to the bank. He stopped and went inside the bank. Then he drove home. The graph below shows the number of blocks away from home Hakeem is xx minutes after he left his house, until he got back home.
Answer:
where is the pic of the graph?
8x8x8=_______=_______
Answer:
8*8*8= 8^3= 512
Step-by-step explanation:
Answer:
8x8x8= 8^3 = 512
Step-by-step explanation:
Hope this helps