Answers
Assuming [tex]A'[/tex] denotes the complement of the set [tex]A[/tex], i.e. all elements in the universal set that do not belong to [tex]A[/tex], then we can prove this in general.
To establish equality between two sets, you need to show that they are both subsets of one another.
Prove [tex](A\cup B)'\subseteq A'\cap B'[/tex]:Let [tex]x\in(A\cup B)'[/tex].
By definition of set complement, this means [tex]x\not\in A\cup B[/tex].
By definition of set union, [tex]x\not\in A[/tex] and [tex]x\not\in B[/tex].
By definition of complement, [tex]x\in A'[/tex] and [tex]x\in B'[/tex].
By definition of set intersection, [tex]x\in A'\cap B'[/tex].
Therefore [tex](A\cup B)'[/tex] is a subset of [tex]A'\cap B'[/tex], because membership of some arbitrary element in the first set directly implies membership in the second set.
Prove [tex]A'\cap B'\subseteq(A\cup B)'[/tex]:Let [tex]x\in A'\cap B'[/tex]. The proof follows similarly as above.
By definition of intersection, [tex]x\in A'[/tex] and [tex]x\in B'[/tex].
By definition of complement, [tex]x\not\in A[/tex] and [tex]x\not\in B[/tex].
By definition of union, [tex]x\not\in(A\cup B)[/tex].
By definition of complement, [tex]x\in(A\cup B)'[/tex].
Therefore [tex]A'\cap B'[/tex] is a subset of [tex](A\cup B)'[/tex].
And hence both sets are equal, regardless of what the sets may be.
Related Questions
An aquarium 8 m long, 1 m wide, and 1 m deep is full of water. Find the work needed to pump half of the water out of the aquarium. (Use 9.8 m/s2 for g and the fact that the density of water is 1000 kg/m3.) Show how to approximate the required work by a Riemann sum. (Let x be the height in meters below the top of the tank. Enter xi* as xi.)
Answers
Answer:
9800Joules
Step by step Explanations
Before we can set the integral up, let the upper half the aquarium be divided into horizontal slices for easy calculation
Then we will represent distance from the top of the tank as X and also
2 its thickness as ∆x
We will be working on the horizontal slices , since in the horizontal slices each drop of water in a given slice will be have the same distance from the top of the tank.
Given that An aquarium has;
Length = 8 m long,
Width = 1 m wide,
Dept =1 m deep
And ∆x m,
density of water is 1000 kg/m3
g = 9.8 m/s2
CHECK THE ATTACHMENT FOR DETAILED EXPLANATION
A manufacturer claims that fewer than 6% of its fax machines are defective. In a random sample of 97 such fax machines, 5% are defective. Find the P-value for a test of the manufacturer's claim. Group of answer choices 0.3264 0.1736 0.3409 0.1591
Answers
Answer:
[tex]z=\frac{0.05 -0.06}{\sqrt{\frac{0.06(1-0.06)}{97}}}=-0.415[/tex]
Now we can find the p value with the following probability:
[tex]p_v =P(z<-0.415)=0.3409[/tex]
Step-by-step explanation:
Information given
n=97 represent the random sample taken
[tex]\hat p=0.05[/tex] estimated proportion of defective
[tex]p_o=0.06[/tex] is the value to verify
z would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to tests
We want to tet if the true proportion is less than 6%, the system of hypothesis are:
Null hypothesis:[tex]p\geq 0.06[/tex]
Alternative hypothesis:[tex]p < 0.06[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info given we got:
[tex]z=\frac{0.05 -0.06}{\sqrt{\frac{0.06(1-0.06)}{97}}}=-0.415[/tex]
Now we can find the p value with the following probability:
[tex]p_v =P(z<-0.415)=0.3409[/tex]
A cone and a cylinder have the same base and height, as shown below. A cone is inside of a cylinder with same base and height. The volume of the cylinder is 84 pi inches squared What can be concluded about the volume of the cone? Check all that apply.
Answers
Answer:
The volume of the cone = 28 inch³
Step-by-step explanation:
First let's consider the formula for the volume of the shapes
For cylinder
Volume= πr²h
For cone
Volume= 1/3 πr²h
So we'd notice that no much difference except that the volume if a cylinder is divided by two to get that off a cone.
So if the volume of the cylinder is
84π inch
The volume of the cone is 84/3 = 28
The volume of the cone = 28 inch³
what’s the area of this triangle?
Answers
Answer:
hi there, the answer is
A=45 cm2
Step-by-step explanation:
A= 1/2 x 10 x 9
A=5 x 9
A=45 cm2
35 games a different team has 50pts 14 games were draws how many games was lost
Answers
Answer:
9 losts
The team had 14 draws which is 14points. So you will substrate 14points from the total 50point, which will left with 36point.
The 36point constitutes 12 wins
Therefore 12wins + 14draws = 26 matches.
You then substrate 26 matches from the 35total matches to get your lose matches.
: 35 - 26 = 9
Therefore, there was 9 lost matches
The owner of a rental company rents bicycles and tricycles and keeps inventory by counting seats and wheels. One day, he counts 25 seats and 60 wheels. The equation representing the total number of seats is b + t = 25, where b is the number of bicycles and t is the number of tricycles. Which equation represents the number of wheels?
Answers
Answer:
2b + 3t = 60
Step-by-step explanation:
2b is the number of wheels on a bicycle
3t is the number of wheels on a tricycle
and 60 is the total number of wheels
"Rebecca walks 100 feet in a straight line. She then turns 20 degrees to her left and walks another 100 feet, and then turns 20 degrees to her left again. She continues this pattern until she reaches the point where she started. How far did she walk
Answers
Answer:
1,800 ft
Step-by-step explanation:
Rebecca will walk in the pattern of a regular polygon with 'n' sides and internal angles of 160 degrees (180 at a straight line - 20 degrees from each turn).
The equation that describes the internal angle of a regular polygon is:
[tex]A = \frac{(n-2)*180}{n}[/tex]
For A = 160 degrees:
[tex]160n=(n-2)*180\\(180-160)n=360\\n=18\ sides[/tex]
If each side is 100 ft long, the total distance that Rebecca has walked is:
[tex]d = 18*100\\d=1,800\ ft[/tex]
She walked 1,800 ft.
Please help! Correct answer only, please! Consider the matrix shown below: Find the determinant of the matrix A. Group of answer choices A. The Determinant cannot be found for a matrix with these dimensions B. 11 C. 7 D. 23
Answers
Answer: d) 23
Step-by-step explanation:
Consider matrix [tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right][/tex]. The determinant is: ad - bc
In the matrix given, a = 5, b = -1, c = 3, d = 4
det A = ad - bc
= 5(4) - 3(-1)
= 20 - (-3)
= 20 + 3
= 23
Solve the system by graphing. (Enter your answers as a comma-separated list. If the system is inconsistent, enter INCONSISTENT. If the system is dependent, enter DEPENDENT.) x + y = 6 x − y = 2
Answers
Answer:
(4,2). DEPENDENT
Step-by-step explanation:
As each equation consist on two variable, both can be represented graphically on a cartesian plane. First, each expression is rewritten in explicit form:
[tex]y = 6 - x[/tex] (red line) and [tex]y = x - 2[/tex] (blue line)
By the resource of graphing software, the solution is (4,2). The representation is presented below as attachment. As solution exists, both expression are linearly DEPENDENT.
Brainliest for anyone who gets this correct , Which of the graphs below would result if you made the leading term of the following function negative?
Answers
Answer:
i think its D. i might be wrong sorry.
Step-by-step explanation:
Answer:D
Step-by-step explanation:
ones that go down are negative, and this is a cubic function
Robert is 40 years older than Brittany. the sum of their ages is 82. find their ages.
Answers
Answer:
brittany is 42
Step-by-step explanation:
if he is 40 years older than her and the sum of there ages is 82
82-40 = 42
If -3+i is a riot of the polynomial function f(x), which of the following must also be a root of f(x)
Answers
Answer:
-3-i
Step-by-step explanation:
imaginary roots always occur in pairs.
so second root=-3-i
Answer:
A) -3-i
Step-by-step explanation:
imaginary roots always occur in pairs.
Which numbers belong to the solution set of the Inequality? x + 9 < 78
Answers
Answer: x<69
Step-by-step explanation:
For this problem, we solve is just as we would if it was an equal sign.
x+9<78 [subtract 9 on both sides]
x<69
Suppose that 75% of adult Americans agree that, while downloading music from the Internet and then selling it is piracy and should be prohibited, downloading for personal use is an innocent act and should not be prohibited.We will take a random sample of 30 American adults and ask them if they agree with the statement. Then the sampling distribution of the sample proportion of people who answer yes to the question is:
Answers
Answer:
The sampling distribution of the sample proportion of people who answer yes to the question is approximately normal with mean of 0.75 and standard deviation of 0.0791.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question:
[tex]p = 0.75, n = 30[/tex]
So
[tex]\mu = 0.75, s = \sqrt{\frac{0.75*0.25}{30}} = 0.0791[/tex]
The sampling distribution of the sample proportion of people who answer yes to the question is approximately normal with mean of 0.75 and standard deviation of 0.0791.
Solving Division Story Problems: Tutorial
52 of 54
E Save & Exit
Geri ran in a marathon race. It took her 3 hours and 28 minutes to run
26 miles. how many minutes did it take her to run 1 mile if she ran at the
same rate for the whole race?
Answer the question below. Type your response in the
space provided.
(1 hour = 60 minutes)
Answer the question.
minutes
Clear
832 PM
O Type here to search
na do
Answers
Answer:
8 minutes
Step-by-step explanation:
Let t represent the time for one mile. We are told the ratio of minutes to miles is constant, so we have the proportion ...
time / distance = t/(1 mi) = (208 min)/(26 mi)
Multiplying both sides of the equation by (1 mi), we have ...
t = (208/26) min = 8 min
Geri's average pace was 8 minutes to run 1 mile.
Burnwood Tech plans to issue some $50 par preferred stock with a 8% dividend. A similar stock is selling on the market for $65. Burnwood must pay flotation costs of 6% of the issue price. What is the cost of the preferred stock? Round your answer to two decimal places.
Answers
Answer:
6.5%
Step-by-step explanation:
The formular used to calculate the cost of preferred stock is:
= Fixed dividend/Net proceeds
Fixed dividend= $50 × 8/100
= $50×0.08
=$4
Net proceeds= Market price-Flotation costs
= $65-(6/100×$65)
= $65-(0.06×$65)
= $65-3.9
= $61.1
Therefore cost of preferred stock is
= 4/61.1 ×100
= 0.065×100
= 6.5%
Hence the cost of preferred stock is 6.5%
What’s the correct answer for this question?
Answers
Answer:
PQ = 6
Step-by-step explanation:
Using tangent-secant theorem,
(PQ)² = (PR)(PS)
(PQ)² = (4)(9)
(PQ)² = 36
Taking square root on both sides, we get
PQ = 6
Molly, Nathan, and Sam own a
bookstore. They agree to share
the profit equally. If the profit is
$8,822, which is the best estimate
of each owner's share?
A $2,000
B $3,000
C $4,000
D $5.000
PLEASE HELP QUICKLY ! THANK YOU
Answers
At least 2,000
Step-by-step explanation:
I divided 8,822 by 3 and got 2940.66666....
If you basically round that, you get to 2,000
You could get 3,000 but they need to share their profit equally
(hopefully this helped :P)
Puerto Rico is a spanish speaking territory of the United States functioning as a self governing _____.
A.commonwealth
B. Settlement
C.state
D. Colony
Answers
Answer:
It is a colony. hope i helped :)
Step-by-step explanation:
The lengths of two sides of a right triangle are given. Find the length of the third side. Round to the nearest tenth if
necessary.
legs: 18 in, and 17 in.
24.8 in.
a.
b.
5.9 in.
c. 27.7 in.
d. 19.5 in.
Answers
Answer:
A)24.8in
Step-by-step explanation:
17^2 + 18^2 =613
sq root of 613 = 24.758...
24.8in
The adjustment of the thickness of the lens to make close vision possible is ca
Answers
Answer: Accommodation
Step-by-step explanation:
Accommodation is the adjustment of the optics of the eye to keep an object in focus on the retina as its distance from the eye varies.
How much of other chemicals must be evaporated from 400 grams of a hand sanitizer that is 24% alcohol to strengthen it to a hand sanitizer that is 30% alcohol? Correct your answer to the nearest whole number.
Answers
Answer:
80 g
Step-by-step explanation:
mass of sanitizer = 400 g
percentage of alcohol = 24%
mass of alcohol in the sanitizer = 24% of 400 g = 0.24 x 400 = 96 g
this means that the mass of other chemicals = 400 - 96 = 304 g
If alcohol content is increased to 30% by removing more of the other chemicals, then mass of alcohol will still remain 96 g
this means that 96 g becomes 30% of the resulting hand sanitizer, we write mathematically as
96 g = 30% of y
where y is the new mass of the sanitizer
96 = 0.3y
y = 96/0.3 = 320 g
The remaining mass of other chemicals = 320 - 96 = 224 g
the total mass of other chemical lost is
304 - 224 = 80 g
What is the product
46 times 10 (the ten has a exponent number) and the exponent number is 2
Answers
Answer:
The answer is 4600. 10 with the exponent of 2 is 100, so 100 times 46 is 4600. Hope this helps;)
Step-by-step explanation:
pleaseee answer this exponentt! 4ba^-4
Answers
Answer:
the answer would be (4b)/(a^4)
Step-by-step explanation:
At a Psychology final exam, the scores are normally distributed with a mean 73 points and a standard deviation of 10.6 points. The lower 5% of the class will not get a passing grade. Find the score that separates the lower 5% of the class from the rest of the class. 58.0 56.6 55.6 57.2
Answers
Answer:
The score that separates the lower 5% of the class from the rest of the class is 55.6.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
[tex]\mu = 73, \sigma = 10.6[/tex]
Find the score that separates the lower 5% of the class from the rest of the class.
This score is the 5th percentile, which is X when Z has a pvalue of 0.05. So it is X when Z = -1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.645 = \frac{X - 73}{10.6}[/tex]
[tex]X - 73 = -1.645*10.6[/tex]
[tex]X = 55.6[/tex]
The score that separates the lower 5% of the class from the rest of the class is 55.6.
Filmore has invested $10,000 in an account to help pay for his grandson’s education. He expects the account to return 4.5% annually. Use the rule of 72 to estimate how long it will take the $10,000 to double in value.
Answers
Answer:
16 years
Step-by-step explanation:
The rule of 72 says you can estimate the doubling time in years by dividing 72 by the interest rate in percent.
__
For an interest rate of 4.5%, the rule of 72 says the doubling time is ...
72/4.5 = 16 . . . years
It will take about 16 years for the investment to double in value.
An object is dropped off a building that is 144 feet tall. After how many seconds does the object hit the ground? (
Answers
Answer:
t = 3 seconds
Step-by-step explanation:
16t^2=144
Simplify by dividing both sides by 16:
t^2=9
t=3
Hope this helped!
A garage charges $24 an hour for labour. The garage charges Nigel $336 labour to replace the engine in his car. For how many hour labours was he charged?
Answers
Answer:
14 hours
Step-by-step explanation:
336/$24 = 14 hours
Answer: 14 hours
Step-by-step explanation:
Total charges = 336
Rate per hour = 24
No. of hours worked
= 336 / 24 = 14 hours
a boy is standing on a pole of height 14.7m throws a stone upwards. it moves in a vertical line slightly away from the pole and falls on the ground. its equation of motion in meters and seconds is x=9.8t-4.9t^2. find time taken for upward and downward motions. also find the maximum height reached by the stone from the ground.
Answers
Answer:
The time taken for the upward motion is 1 second. The same time is taken for the downward motion
It reaches a maximum height of 4.9 meters.
Step-by-step explanation:
The equation of motion is:
[tex]x(t) = -4.9t^{2} + 9.8t[/tex]
Since the term which multiplies t squared is negative, the graph is concave down, that is, x increases until the vertex, where it reaches it's maximum height, then it decreases.
Vertex of a quadratic equation:
Quadratic equation in the format [tex]x(t) = at^{2} + bt + c[/tex]
The vertex is the point [tex](t_{v}, x(t_{v}))[/tex], in which
[tex]t_{v} = -\frac{b}{2a}[/tex]
In this question:
[tex]x(t) = -4.9t^{2} + 9.8t[/tex]
So [tex]a = -4.9, b = 9.8[/tex]
Vertex:
[tex]t_{v} = -\frac{9.8}{2*(-4.9)} = 1[/tex]
The time taken for the upward motion is 1 second.
[tex]x(t_{v}) = x(1) = 9.8*1 - 4.9*(1)^{2} = 4.9[/tex]
It reaches a maximum height of 4.9 meters.
Downward motion:
From the vertex to the ground.
The ground is t when x = 0. So
[tex]-4.9t^{2} + 9.8t = 0[/tex]
[tex]4.9t^{2} - 9.8t = 0[/tex]
[tex]4.9t(t - 2) = 0[/tex]
[tex]4.9t = 0[/tex]
[tex]t = 0[/tex]
Or
[tex]t - 2 = 0[/tex]
[tex]t = 2[/tex]
It reaches the ground when t = 2 seconds.
The downward motion started at the vertex, when t = 1.
So the duration of the downward motion is 2 - 1 = 1 second.
If you roll two fair six-sided dice, what is the probability that at least one die shows a 3?
Answers
Answer:
3
Step-by-step explanation:
you are right
