Find a counterexample to show that we don't always have equality.
Answers
Answer:
Hello your question is incomplete below is the complete question
Let R be a relation from A to B and S a relation from B to C.
(a) Prove that . [tex]Dom(S \circ R) \subseteq Dom(R)[/tex]
(b) Find a counterexample to show that we don’t always have equality.
answer : (b) Dom ( S o R ) = [ 1 ] and Dom ( R ) = [ 1, ∝ ]
hence: Dom ( S o R ) ≠ Dom ( R )
Step-by-step explanation:
Note : R ⊆ A * B and S ⊆ B * C
A) To prove that [tex]Dom(S \circ R) \subseteq Dom(R)[/tex]
we take note that : S o R ⊆ A x C
ATTACHED BELOW IS THE REMAINING PART OF THE SOLUTION
B) A counterexample to show that we don't always have equality
attached below is a assumptions and solution on how we arrived at the value below
Dom ( S o R ) = [ 1 ] and Dom ( R ) = [ 1, ∝ ]
hence: Dom ( S o R ) ≠ Dom ( R )
Related Questions
In December, the amount of snowfall was 3 2/3 feet. In January, the amount of snowfall was 4 1/8 feet. What was the amount of snowfall in the two months combined? Write your answer as a mixed number in simplest form.
Answers
Answer:
7 19/24
Step-by-step explanation:
Add. That is your answer.
Jan completes 60 trials of pulling colored marbles out of a bag. She pulled green 15 times. If there are 250 marbles in the bag, how many of them are probably green?
Answers
Answer:
the answer is 63 green marbles
Step-by-step explanation:
Answer:
Green marbles are probably = 62.5.
Step-by-step explanation:
Since Jan completes 60 trials and pulled green 15 times, the probability of any marble being green can be calculated as:
= 15/60
= 0.25
With 250 marbles in the bag, using the probability value of green marbles calculated above, the number of green marbles can be estimated as:
= 0.25 of 250
= 62.5
This shows that since there is a 25% probability of obtaining a green marble from 60 trials of pulling colored marbles out of the bag containing 250 marbles, then the total number of green marbles will be equal to 62 or 63.
Which of the following is a solution to the equation −25x = 10?
x = -4
x = -4
x = -25
x = -25
x = 4
x = 4
x = 25
Answers
Answer: x=-0.4
Step-by-step explanation:
From long experience, it is known that the time it takes to do an oil change and lubrication job on a vehicle has a normal distribution with a mean of 17.8 minutes and a standard deviation of 5.2 minutes. An auto service shop will give a free lube and oil change service to any customer who must wait beyond the guaranteed time to complete the work. If the shop does not want to give more than 1% of its customers a free lube and oil change service, how long should the guarantee be
Answers
Answer: 29.916 minutes
Step-by-step explanation:
Given the following :
Mean of distribution = 17.8 minutes
Standard deviation of distribution = 5.2 minutes
Percentage of customers to give free lube and oil change service should not exceed 1% if the customer waits beyond the guaranteed time ;
Length of guarantee :
Since % of customers should not exceed 1%
Then probability of not being chosen = (1 - 0.01) = 0.99
Using the z table to find the Zscore of 0.99,
Zscore of 0.99 = 2.33
This is 2.33 standard deviations above the mean
(2.33 × standard deviation) + mean value
(2.33 × 5.2 minutes) + 17.8 minutes
12.116 + 17.8
= 29.916 minutes
20. Solve for r
T=1+r/n
Answers
Answer:
r = nT-n
Step-by-step explanation:
T = 1 + r/nT-1 = r/nn(T-1) = rnT-n = rStep-by-step explanation:
T = 1 + r/n
T-1 = r/n
n(T-1) = r
nT-n = r
Answer:
r = nT-n
Write the equation of a line that passes through (2,-1) and is PARALLEL to y = -3x + 4
The equation is ______
Answers
Answer:
y = -3x + 5
Step-by-step explanation:
Since the line is parallel, we know that the slope of our line must be equal to the one given.
The given equation is:
y = -3x + 4
and thus, it has a slope of -3
As such, our unknown equation...
y = kx + m
...must have the same k-value, or the same slope, of -3.
y = -3x + m
Now we just need to find m. We know that our line passes through the point (2, -1), or in other words, when x = 2, y = -1
We can put these values for x and y into our equation.
y = -3x + m
-1 = -3 * 2 + m
-1 = -6 + m
Adding 6 to both sides:
5 = m
m = 5
Putting m = 5 into our equation:
y = -3x + m
y = -3x + 5
..we find that our equation is
y = -3x + 5
The required equation of a line is y = -3x + 5 that passes through (2,-1) and is parallel to y = -3x + 4.
What is the slope of the line?The slope of the line is defined as the gradient of the line.
The given equation is:
y = -3x + 4
And, it has a slope of -3
We know that the slope of our line must be equal to the one given because the line is parallel.
y = mx + c
Here the same slope, of -3, so m = -3
y = -3x + c ....(i)
The required line passes through point (2, -1),
Substitute the values of x = 2, and y = -1 in equation (i), and solve for c
y = -3x + c
-1 = -3(2) + c
-1 = -6 + c
Add 6 to both sides of the equation,
5 = c
c = 5
Substitute the values of c = 5 = 2 in equation (i),
y = -3x + 5
Thus, the required equation of a line is y = -3x + 5 that passes through (2,-1) and is parallel to y = -3x + 4.
Learn more about Slope of Line here:
brainly.com/question/14511992
#SPJ2
The salt water fish tank at your house is filled with 22 inches of water. The water evaporates at a steady rate of 2 inches per week. Write an equation that approximates the depth y of water in the aquarium x weeks after you fill it.
Answers
Answer:
y = 22 - 2x
Step-by-step explanation:
Given the following :
Amount of water in salt water fish tank = 22 inches
Evaporation occurs steadily at the rate ; 2 inches per week
The depth y of water in the aquarium x weeks after filling :
The depth of water reduces as evaporation occurs ; and as such reduces by 2 inches per week
Hence,
After x weeks, the depth 'y' of water in the aquarium will be :
y = Initial position of water - 2(number of weeks)
y = 22 - 2x
y = new depth
x = number of weeks
Can someone Help me with this Question.
Answers
Answer:
D.
Step-by-step explanation:
A secret government agency has developed a scanner which determines whether a person is a terrorist. The scanner is fairly reliable; 95% of all scanned terrorists are identified as terrorists, and 95% of all upstanding citizens are identified as such. An informant tells the agency that exactly one passenger of 100 aboard an aeroplane in which you are seated is a terrorist. The police haul off the plane the first person for which the scanner tests positive. What is the probability that this person is a terrorist
Answers
Answer:
The probability of a person is a terrorist is [tex]0.161.[/tex]
Step-by-step explanation:
Let,
[tex]A=[/tex] Your neighbor is a terrorist
[tex]B=[/tex] Your neighbor tested positive
Now we want to find the value of [tex]P(A|B)[/tex] where
[tex]P(A|B)=\frac{P(B|A)P(A)}{P(B|A)P(A)+P(B|A^c)P(A^c)}[/tex]
where [tex]P(A)=\frac 1{100}=1-P(A^c), P(B|A)=0.95,[/tex]
[tex]P(B|A^c)=1-0.95=0.05[/tex]
Therefore, [tex]P(A|B)=\frac{\frac{0.95}{100}}{\frac{0.95}{100}+0.05\times \frac{99}{100}}[/tex]
[tex]=\frac{\frac{0.95}{100}}{\frac{0.95+0.05\times 99}{100}}=\frac{0.95}{0.95+4.95}[/tex]
[tex]=0.161[/tex]
Hence, the probability of a person is a terrorist is [tex]0.161.[/tex]
Given: Lines a and b are parallel and line c is a transversal.
Prove: ∠2 is supplementary to ∠8
What is the missing reason in the proof?
Statement Reason
1. a || b, is a transv 1. given
2. ∠6 ≅ ∠2 2. ?
3. m∠6 = m∠2 3. def. of congruent
4. ∠6 is supp. to ∠8 4. def. of linear pair
5. ∠2 is supp. to ∠8 5. congruent supplements theorem
A: vertical angles theorem
B: alternate interior angles theorem
C: corresponding angles theorem
D: alternate exterior angles theorem
Answers
Answer:
C: corresponding angles theoremStep-by-step explanation:
The angles in matching corners are called Corresponding Angles.
The Corresponding Angles Theorem: If a transversal cuts two parallel lines, their corresponding angles are congruent
∠6 ≅ ∠2 as per above statementCorrect answer choice is C.
The missing reason is corresponding angles theorem.
What are corresponding angles?Corresponding angles are angles that have the same relative position or measurement in two similar figures. They are formed when two lines, parallel or not, are intersected by a transversal.
Given that, lines a and b are parallel and line c is a transversal.
We need to prove ∠2 is supplementary to ∠8.
The proof:-
1. a || b, c is a transv. 1. given
2. ∠6 ≅ ∠2 2. corresponding angles theorem
3. m∠6 = m∠2 3. def. of congruent
4. ∠6 is supp. to ∠8 4. def. of linear pair
5. ∠2 is supp. to ∠8 5. congruent supplements theorem
Hence the missing reason is corresponding angles theorem.
Learn more about corresponding angles click;
https://brainly.com/question/1597341
#SPJ7
Please help me with this homework equation
I don’t understand and need help someone please do step by step
Answers
Step-by-step explanation:
f'(x) = 6x-12
in vertex : f'(x) = 0
6x-12 =0 => x=2
f(2) = 3 ( 2² ) -12 (2 ) +1 = -11
vertex ( 2 , -11 )
Which of the following reltions is not a function?
a
{(- 1, 4), (1, 6), (4, 10)}
b
{(- 1, 2), (1, 3), (- 1, 4)}
c
{(- 1, 6), (4, 7), (5, 6)}
d
{(- 1, 2), (1, 2), (3, 3)}
Answers
Answer:
B is the correct answer
Step-by-step explanation:
There are two y coordinates for one x coordinate
Find the shortest distance, d, from the point (5, 0, −6) to the plane x + y + z = 6.
Answers
Answer:
[tex]\frac{7}{\sqrt{3}}[/tex]
Step-by-step explanation:
The shortest distance d, of a point (a, b, c) from a plane mx + ny + tz = r is given by:
[tex]d = |\frac{(ma + nb + tc - r)}{\sqrt{m^2 + n^2 + t^2}} |[/tex] --------------------(i)
From the question,
the point is (5, 0, -6)
the plane is x + y + z = 6
Therefore,
a = 5
b = 0
c = -6
m = 1
n = 1
t = 1
r = 6
Substitute these values into equation (i) as follows;
[tex]d = |\frac{((1*5) + (1*0) + (1 * (-6)) - 6)}{\sqrt{1^2 + 1^2 + 1^2}} |[/tex]
[tex]d = |\frac{((5) + (0) + (-6) - 6)}{\sqrt{1 + 1 + 1}} |[/tex]
[tex]d = |\frac{(-7)}{\sqrt{3}} |[/tex]
[tex]d = \frac{7}{\sqrt{3}}[/tex]
Therefore, the shortest distance from the point to the plane is [tex]d = \frac{7}{\sqrt{3}}[/tex]
Need help on this question
Answers
Consider a medical study that is being performed to test the effect of smoking on lung cancer. Two groups of subjects are identified; one group has lung cancer and the other one doesn't. Both are asked to fill out a questionnaire containing questions about their age, gender and occupation. What is the response variable
Answers
Answer:
Lung cancer
Step-by-step explanation:
The response variable is lung cancer. From the question we are testing to find out what effect smoking has on lung cancer. Therefore lung cancer is our response variable.
Another name for the response variable is the dependent variable. And it is the variable that we are testing for. This variable would respond to changes that are being made to the independent variable.
What is the constant of proportionality in the equation?
y=5x
0
1
4 or
5
Answers
Answer:
hope it helps...
Step-by-step explanation:
The value of the constant of proportionality is k=5k=5
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y/x=ky/x=k or y=kxy=kx
The value of the constant k is equal to the value of the slope
In this problem we have
y=5xy=5x ------> is a linear direct variation
The slope is m=5m=5
therefore
The value of the constant of proportionality is k=5k=5
Answer:
5 is the constant of proportionailty
show how are 5 hundreds and 4 tens the same as 4 hundreds and 14 tens.
Answers
The value of the 5 hundreds and 4 tens is the same as 4 hundreds and 14 tens.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
5 hundreds and 4 tens can be written as,
⇒ 5 × 100 + 4 × 10
⇒ 500 + 40
⇒ 540
4 hundreds and 14 tens can be written as,
⇒ 4 × 100 + 14 × 10
⇒ 400 + 40
⇒ 540
The value of the 5 hundreds and 4 tens is the same as 4 hundreds and 14 tens.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ2
1) What should h be so that the expression h? - 2h has a value of 3 ?
Th = 1
Oh=-1
h = 2
h = -2
Answers
Divided by -2 both sides
-2h/-2=3/-2
h=-1.5
I need a little more help
Answers
The owner of a local nightclub has recently surveyed a random sample of n = 300 customers of the club. She would now like to determine whether or not the mean age of her customers is over 35. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. The appropriate hypotheses to test are:
Answers
Answer:
We cannot determine the appropriate hypotheses to test this study because we are only given the data for the sample size and the population mean. Meanwhile, we need to know the data of the sample mean, the standard deviation and the level of significance before we can state the appropriate hypotheses for this test.
Step-by-step explanation:
Given that:
sample size n = 300
population mean μ = 35
The null hypothesis and the alternative hypothesis can be computed as follows:
Null hypothesis
[tex]H_o: \leq 35[/tex]
Alternative hypothesis
[tex]H_1 > 35[/tex]
The degree of freedom df = n -1
df = 300 - 1
df = 299
RS = 7y - 4
ST = y +5
RT = 28
Answers
Explanation:
RS + ST = RT
(7y - 4) + (y + 5) = 28
7y - 4 + y + 5 = 28
8y + 1 = 28
8y = 28 - 1
8y = 27
y = 27/8
The values of RS = 19.625 and ST is 8.375.
What is segment Addition Postulate?The segment addition postulate states that if we are given two points on a line segment, A and C, a third point B lies on the line segment AC if and only if the distances between the points meet the requirements of the equation AB + BC = AC.
Given:
RS= 7y-4, ST= y+5, and RT= 28
Suppose that S is between R and T, then:
RS + ST = RT
Putting the values
7y-4+y+5 = 28
7y+y-4+5 = 28
8y + 1 = 28
Subtract 1 from both sides
8y+1-1 = 28 - 1
8y = 27
y = 27/8
y = 3.375
So, length of RS = 7y - 4 = 23.625 - 4 = 19.625.
and, ST = y+5
ST = 3.375+5
ST = 8.375
Hence, the value of RS = 19.625 and ST is 8.375.
Learn more about segment Addition Postulate here: brainly.com/question/17247176
#SPJ2
will give away lots of points! 25 total!!!!
Answers
Answer:
maybe the answer is or "ABC" or "BCA" hope i halp :)
Answer:
mmk
Step-by-step explanation:
What is the solution to the following equation? (4 points) 5(2x − 6) + 20 = 10 Group of answer choices
Answers
Answer:
x=2
Step-by-step explanation:
Solve the system of equations using linear combination method or substitution method. Show all steps.
2x + 5y = 1
-3x + 4y = -13
Answers
Answer:
{x,y} = {19/12,5/6}
Step-by-step explanation:
I NEED HELP QUICKLY... The Student Council is selling raffle tickets to raise money for the Winter Dance. They have a total of 275 tickets to sell and are told they must sell at least 82% of them to raise enough money. How many do they need to sell? [A] Set up a proportion that can be used to solve this problem. [B] Show all steps to solve the problem.
Answers
A)
82/275
B)
100%/x%=275/82
(100/x)*x=(275/82)*x
multiply both sides of the equation by x
100=3.4*x
divide both sides of the equation by (3.4) to get x
100/3.4=x
29.8=x
x=29.8
12-(-5) subtract using a number line
Answers
Answer:17
Step-by-step explanation:
Gabriel determined that his total cost would be represented by 2.5x + 2y – 2. His sister states that the expression should be x + x + 0.5x + y + y – 2. Who is correct? Explain
Answers
Answer:
Both Gabriel and his sister are correct. The two expressions are equivalent. Gabriel’s sister just needs to combine her like terms to get the same expression as Gabriel.
Step-by-step explanation:
sample response for ed 20202
Write the equation of a line through (1,2), parallel to y=4x+1
Answers
Answer:
Step-by-step explanation:
y - 2 = 4(x - 1)
y - 2 = 4x - 4
y = 4x - 2
A doctor give his patient liquid medicine and told him to drink 99 cups over the next 10 days. How much should the patient drink each day
Answers
Answer:
If he had to take it evenly, he'd take 9.9 cups a day.
Step-by-step explanation:
I found this by dividing 99 cups over 10 days. 99/10
Need help please. In this number, 4,001,982.57....What digits is in the hundredths place. ..
Answers
Answer:
the number to the right of the 7
Step-by-step explanation:
