15. Give an example of disjoint closed sets F, F, such that 0 inf{|x; – xzl : x; € F;}.
Answers
The example of disjoint closed sets F and G such that inf{|x - y| : x ∈ F, y ∈ G} = 2 is F = {x ∈ ℝ : x ≥ 1} and G = {x ∈ ℝ : x ≤ -1}.
Whst is an an example of the disjoint closed sets?Let's consider the set F = {x ∈ ℝ : x ≥ 1} and G = {x ∈ ℝ : x ≤ -1}. Both F and G are closed sets.
In order to show that they are disjoint, we can observe that for any x ∈ F, we have x ≥ 1, and for any x ∈ G, we have x ≤ -1. Therefore, there is no value of x that satisfies both conditions simultaneously, which means F and G have no common elements and are disjoint.
Now, let's calculate the infimum of the absolute difference |x - y| for all x ∈ F and y ∈ G:
inf{|x - y| : x ∈ F, y ∈ G}
Since F consists of values greater than or equal to 1, and G consists of values less than or equal to -1, the absolute difference between any x ∈ F and y ∈ G will always be greater than or equal to 2:
|x - y| ≥ |1 - (-1)| = 2
Therefore, the infimum of the absolute difference is 2.
In summary, the example of disjoint closed sets F and G such that inf{|x - y| : x ∈ F, y ∈ G} = 2 is F = {x ∈ ℝ : x ≥ 1} and G = {x ∈ ℝ : x ≤ -1}.
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Related Questions
The box plot shows the statistics for the weight, in pounds, of some dogs.
Are there any outliers? Explain how you know.
i will give brainliest :)
Answers
No , there are no outliers.
A box plot is there which shows the statistics for the weight in pounds of some dogs.
We have to find , are there any outliers in the given plot.
What do you mean by average ?
The average is the ratio of sum of all numbers to the total no. of numbers.
We know that ;
An outlier is an observation which lies at an abnormal distance from other values in a random sample.
As per the question ;
The box ranges from 35 to 55.
The average of weight of dogs is ;
= (35 + 40 + 45 + 50 + 55) / 5
= 225 / 5
= 45 pounds
By this data we can conclude that the dog is neither underweight nor overweight.
Thus , there are no outliers in the data given.
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For positive acute angles A and B, it is know that tan A= 8/15 and sin B= 11/61. Find the value of cos (a+b) in simplest form
Answers
Answer:
812/1037
Step-by-step explanation:
To solve this, we have to use trigonometric identities.
Cos (A + B) is given as Cos A Cos B - Sin A Sin B. And from the question, we have that
Tan A = 8/15.
We know that in a triangle, the Tan angle is represented Opp/Adj and thus the Opp is 8, and the Adj is 15. Using Pythagoras, we have
hyp² = opp² + adj²
hyp² = 8² + 15²
hyp² = 64 + 225
hyp² = 289
hyp = √289 = 17
The identity of Cos is Adj/Hyp and that of Sin is Opp/Hyp.
Cos A = 15/17
Sin A = 8/17
Repeating the same process for B, we have
Sin B = 11/61
adj² = hyp² - opp²
adj² = 61² - 11²
adj² = 3721 - 121
adj² = 3600
adj = √3600 = 60
Cos B = 60/61
Now, using the earlier stated trigonometric identity, we have
cos (a + b) = CosA CosB - SinA SinB
cos (a + b) = 15/17 * 60/61 - 8/17 * 11/61
cos (a + b) = 900/1037 - 88/1037
cos (a + b) = 812/1037
Please answer please
Answers
Answer:
C. m < 1 + m < 2 = 90
Step-by-step explanation:
It is clear that the line separating angles 1 and 2 is a perpendicular bisector, which means that the measures of angles 1 and 2 must add up to 90.
To check that x = 49, we can use the equation x + x - 8 = 90 and solving for x gives us 49.
PLEEEEEEEEEEEEEEEASE HELP ME WITH THIS. IT IS DUE TOMORROW!!!
Answers
Answer:
Line CA is parrallel to Line HR and Line MC is parallel to line HA.
Step-by-step explanation:
This is because Angle CAM and Angle HAR are equal. Also because Angle CMA and Angle HAR are equal because Angle CAM and Angle HAR are equal.
a person leaves home at 8:00 am and drives to a destination at a rate of 40 miles per hour. the person returns at a rate of 25 miles per hour and arrives at 2:30 pm. how far was the destination?
Answers
Answer:
100mi
Step-by-step explanation:
which ordered pairs is the solution to this set of linear inequalities?
y < 2x +2 and y ≥ -x -1
a.(-1,0)
b(0,3)
c(2,0)
d(-1,-4)
Answers
Answer:
c (2,0)
Step-by-step explanation:
One way to solve this system of inequalities is to graph the inequalities and see which ordered pair lies in the shaded region that is common to both inequalities
See the graph and each of the ordered pairs. Only (2, 0) lies entirely within the shaded region
(-1, 0) lies on the intersection of the two lines so it will satisfy the >= inequality but not the < inequality
Answer (2, 0)
However if you cannot use graphing then a brute force method must be used to see which ordered pair satisfies both inequalities
a. (-1, 0)
Check y < 2x + 2 ?
=> 0 < 2(-1) + 2 ?
=> 0 < -2 + 2
0 < 0 ? False
Eliminate option a
b. (0, 3)
y < 2x + 2?
=> 3 < 2(0) + 2?
3 < 2? False
Eliminate option b
c. (2, 0)
y < 2x + 2?
=> 0 < 2(2) + 2 ?
=> 0 < 4 + 2
=> 0 < 6 True
Move to the second inequality
y ≥ -x - 1?
0 ≥ -2 - 1
0 ≥ -3 True
So option c is the correct choice
While it is not necessary to check option d, let's do it anyway
d. (-1, -4)
y < 2x + 2 ?
-4 < 2(-1) + 2 ?
-4 < -2 + 2 ?
-4 < 0 ? True
Move to the second inequality
y > -x - 1 ?
-4 > -(-1) - 1
-4 > -2? False
Option d is eliminated
Correct answer: (2, 0) which is option c
solve for x, Give your answer as a fraction or decimal rounded to the nearest hundredth.
Answers
Using the fact that the triangles are similar, we will see that:
x = 5.626
How to find the value of x?On the image we can see two triangles, such that one is inscribed on the other.
Just because of that, it is obvious that the two triangles are similar.
And because the triangles are similar, the quotients between correspondent sides must be equal, that allows us to write the equation:
3/x = 8/15
The quotient is "left side over the bottom side"
We can solve that equation for x:
3/x = 8/15
3 = (8/15)*x
(15/8)*3 = x
45/8 = x
5.625 = x
That is the value of x.
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figure out the questions do all give brainliest
Answers
c) 1hr
d)2 pieces of pizza
d)3 rows
A florist ordered a shipment of red, blue, and white carnations to use for table decorations at a banquet. The ratio of red : blue : white carnations in the shipment is 3:1:2. There are 60 white carnations in the shipment. What is the total number of carnations in the shipment?.
Answers
Answer:
165
Step-by-step explanation:
What this ratio means is that for every 2 white carnations, there is 1 blue and 3 red.
We have 60 white, or 30 groups of 2
We have 3 red carnations for each group of two:
3 * 30 = 90
And we have 1 blue for each group of two:
30 / 2 = 15
So, our total number of carnations would be 90 + 15 + 60
Or: 165
If I ran 10x-2 now and then ran 2x+18 tommarow how much have I ran in total
Answers
Answer:
10x-2+2x+18
=10x+2x+18-2
=12x+16
Answer:8x-16
Step-by-step explanation:
Which expression is equivalent to (m−2n−3)−4?
m−6n−7
m8n12
m−8n−12
1 over the quantity m raised to the sixth power times n raised to the seventh power end quantity
Answers
Answer:
B
Step-by-step explanation:
(m^-2 n^-3)^-4
-2 x -4 = 8
-3 x -4 = 12
m^8n^12
The given expression (m − 2n − 3) − 4 is equivalent to →
(m - 2n - 7).
What is a mathematical function, equation and expression?function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.
Given is the expression -
(m − 2n − 3) − 4
The given expression is -
(m − 2n − 3) − 4
m - 2n - 3 - 4
m - 2n - 7
Therefore, the given expression (m − 2n − 3) − 4 is equivalent to →
(m - 2n - 7).
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Find the value of X and Y: 3x+9y=30 2(3x+9y)+x=64
pls help.
Answers
Answer:
x = 4 , y = 2
Step-by-step explanation:
3x+9y = 30 --------- (1)
2(3x+9y)+x = 64 ---------(2)
substitute (1) into (2)
2(30)+x = 64
60+x = 64
x = 64-60
x = 4
substitute x=4 into (1)
3x+9y = 30
3(4)+9y = 30
12+9y = 30
9y = 30-12
9y = 18
y = 18/9
y = 2
thus, x = 4 and y = 2
the mean monthly electric bill for 71 residents of the local apartment complex is $62. what is the best point estimate for the mean monthly electric bill for all residents of the local apartment complex?
Answers
If the mean monthly electric bill for 71 residents of the local apartment is $62 , then the best point estimate is $62 .
In the question ,
it is given that ,
the number of residents in the local apartment complex is = 71
the mean electric bill for the 71 residents = $62 ;
we know that the sample mean is itself called as the best point estimate ;
So , best point estimate for mean monthly electric bill for all residents of local apartment complex will be = mean monthly bill for 71 residents of local apartment complex which is given as $62 .
Therefore , the best point estimate is $62 .
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i will mark brainlist!!
Answers
= 3/5 + 11/4
= 12/20 + 55/20
= 67/20
= 3 7/20
Answer:
3/5 + 2 3/4 = 3 7/20
Step-by-step explanation:
2 = 8/4
2 3/4 = 2 + 3/4
then:
3/5 + 2 3/4 = 3/5 + 8/4 + 3/4
= 3/5 + (8+3)/4
= 3/5 + 11/4
3/5 = 12/20
11/4 = 55/20
then:
3/5 + 11/4 = 12/20 + 55/20 = 67/20
67/20 = 60/20 + 7/20 = 3 + 7/20
= 3 7/20
Which pair of functions represents a decomposition of f(g(x)) = | 2(x + 1)^2 + (x + 1) | ?
A) f(x) = (x + 1)^2 and g(x) = | 2x + 1 |
B) f(x) = (x + 1) and g(x) = | 2x^2 + x |
C) f(x) = | 2x + 1 | and g(x) = (x + 1)^2
D) f(x) = | 2x^2 + x | and g(x) = (x + 1)
Answers
Answer:
\(\Large \boxed{\mathrm{\bold{D.}} \ f(x) = | 2x^2 + x | \ \mathrm{and} \ g(x) = (x + 1)}\)
Step-by-step explanation:
\(f(g(x)) = | 2(x + 1)^2 + (x + 1) |\)
The first option :
\(f(x) = (x + 1)^2 \ \mathrm{and} \ g(x) = | 2x + 1 |\)
\(f(g(x))=(|2x+1|+1)^2\)
The second option :
\(f(x) = (x + 1) \ \mathrm{and} \ g(x) = | 2x^2 + x |\)
\(f(g(x))=(|2x^2 +x|+1)\)
The third option :
\(f(x) = | 2x + 1 | \ \mathrm{and} \ g(x) = (x + 1)^2\)
\(f(g(x))=|2(x+1)^2 +1 |\)
The fourth option :
\(f(x) = | 2x^2 + x | \ \mathrm{and} \ g(x) = (x + 1)\)
\(f(g(x))= | 2(x + 1)^2 + (x + 1) |\)
Answer:
D
Step-by-step explanation:
Factor the following polynomial completely. -x^2y^2+x^4+4y^2-4c^2
Answers
Answer: -(x - 2)(x + 2)(y - x)(y + x)
Step-by-step explanation:
Factor the following polynomial completely.
-x2y2 + x4 + 4y2 - 4x2
I assume the polynomial is as follows:
-x^2y^2 + x^4 + 4y^2 - 4x^2
Therefore:
-(x - 2)(x + 2)(y - x)(y + x)
Which of the following equations could be the function pictured in the graph?
A. y = ( x - 1 ) ( x + 3 )
B. y = ( x + 1 ) ( x - 3)
C. y = ( x + 1 ) (x + 3)
D. y = ( x + 1 ) ( x - 1 )
Answers
Answer: B
Step-by-step explanation:
We can find the correct equation by finding the x-intercepts, or the zeroes.
To find the x-intercept, you have to make the y's value = 0. If y on the graph is zero, the x-intercept is (-1,0) and (3,0).
Then look at the equations and see which one has -1 and 3 as the values of x.
The answer is B.
Please help I will give you BRAINLIEST
Answers
============================================================
Explanation:
Starting at (4, -1) and moving four units up will have us arrive at (4, 3). We add 4 to the y coordinate and keep the x coordinate the same. The algebraic rule is stated as \((x,y) \to (x,y+4)\).
Next, we reflect over the y axis. This will have us flip the sign of the x coordinate while keeping the y coordinate the same. The algebraic rule for this kind of reflection is \((x,y) \to (-x,y)\). The point (4,3) reflects over the y axis to get to (-4,3)
So we started at (4, -1), then moved four units up to get to (4,3) and then reflected over the y axis to get to (-4, 3) which is the final stop.
This is all shown in the diagram below.
With the airplane loaded as follows, what action can be taken to balance the airplane? front seat occupants = 411 lb rear seat occupants = 100 lb main wing tanks = 44 gal
Answers
The airplane will become balanced if we add a 100- pound weight to the baggage compartment.
Why should the weight on the airplane be balanced?An airplane is used to convey people and goods from one point to another by air. The airplane must be airlifted. This means that the airplane must be balanced while on air. If the airplane is not balanced, it may be difficult to control.
Looking at the situation of this airplane, the airplane will become balanced if we add a 100- pound weight to the baggage compartment.
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Identify the sampling technique used in the given scenario. The English department is interested in overall performance in its entry-level 101 course. The department chair selects every tenth student's final grade from a list of all students enrolled in the course and calculates the average final grade.
Answers
The sampling technique used in the given scenario is Systematic sampling technique.
Systematic sampling technique
Systematic sampling is a probability sampling technique in which researchers randomly choose individuals of a population at regular intervals. The sampling interval, or fixed periodic interval, is calculated by dividing the population size by the required sample size.
Types of Systematic sampling technique
A systematic sample can be generated in three ways:
Systematic random sampling: The most common type of systematic sampling in which the subject is chosen at a predefined interval.
Linear systematic sampling: Instead of picking the sample interval at random, a skip pattern is constructed by following a linear path.
Circular systematic sampling: It occurs when a sample begins from the same spot where it ends.
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Select the instances in which the variable described is binomial.1) A coin flip has two outcomes: heads or tails. The probability of each outcome is 0.50. The random variable represents the total number of flips required to get tails.2) A quality check on a particular product must meet five guidelines. All products are made in the same factory under the same conditions. The random variable represents the total number of products out of 35 tested that pass inspection.3) There are two choices of burritos at a restaurant, vegetarian or beef. The random variable represents the total number out of 254 customers who ordered beef.4) Based on the parents' genetics, each of 6 children from a particular pair of parents has a 0.30 probability of having blue eyes. The random variable represents the total number of children from this pair of parents with blue eyes.5) The probability of drawing a king in a standard deck of cards is 0.08. Seven cards are drawn without replacement. The random variable represents the total number of king cards observed.
Answers
Answer: 2) A quality check on a particular product must meet five guidelines. All products are made in the same factory under the same conditions. The random variable represents the total number of products out of 35 tested that pass inspection.
• 3) There are two choices of burritos at a restaurant, vegetarian or beef. The random variable represents the total number out of 254 customers who ordered beef.
• 4) Based on the parents' genetics, each of 6 children from a particular pair of parents has a 0.30 probability of having blue eyes. The random variable represents the total number of children from this pair of parents with blue eyes
Step-by-step explanation:
The binomial distribution simply means the probability of success or failure in an experiment. The instances in which the variable described is binomial are given below:
• 2) A quality check on a particular product must meet five guidelines. All products are made in the same factory under the same conditions. The random variable represents the total number of products out of 35 tested that pass inspection.
• 3) There are two choices of burritos at a restaurant, vegetarian or beef. The random variable represents the total number out of 254 customers who ordered beef.
• 4) Based on the parents' genetics, each of 6 children from a particular pair of parents has a 0.30 probability of having blue eyes. The random variable represents the total number of children from this pair of parents with blue eyes.
Option 1 isn't binomial since the number of trails that are given isn't fixed. Option 5 isn't binomial as well
Therefore, the correct options are 2,3 and 4.
Find the Present Value of Perpetuity that pays you $1,800 per
year forever assuming your money is worth 5%?
* Please be very detailed in your answer.
Answers
Therefore, the present value of the perpetuity that pays $1,800 per year forever, assuming a 5% interest rate, is $36,000. To find the present value of a perpetuity that pays $1,800 per year forever, we can use the formula:
Present Value = Cash Flow / Interest Rate
In this case, the cash flow is $1,800 and the interest rate is 5%. Plugging these values into the formula, we get:
Present Value = $1,800 / 0.05. Simplifying this equation, we find that:
Present Value = $36,000
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A ranger at the top of a fire tower observes the angle of depression to a fire on level ground to be 6.0°. If the tower is 260 ft tall, what is the ground distance from the base of the tower to the fire? (Round your answer to 3 significant digits.)
Answers
To find the ground distance from the base of the tower to the fire, we can use trigonometry and the angle of depression. Let's denote the ground distance as "d."
We have a right triangle formed by the height of the tower (260 ft), the ground distance (d), and the angle of depression (6.0°). The height of the tower is the opposite side of the right angle, and the ground distance is the adjacent side.
Using the trigonometric ratio for tangent (tan), we can set up the following equation:
tan(6.0°) = opposite/adjacent
tan(6.0°) = 260/d
Now, we can solve for "d" by rearranging the equation:
d = 260 / tan(6.0°)
Using a calculator, we find that tan(6.0°) is approximately 0.1051. Therefore: d = 260 / 0.1051 ≈ 2473.102 ft
Rounding to three significant digits, the ground distance from the base of the tower to the fire is approximately 2473 ft.
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Express the radical using the imaginary unit, i. Express your answer in simplified form. EV -49 = =
Answers
You have the following expression:
\(\pm\sqrt[]{-49}\)In order to express the previous number as an expression with the imaginary unit, you consider the following:
\(\begin{gathered} 49=7^2 \\ \sqrt[]{-1}=i \end{gathered}\)where the square root of -1 is the imaginary unit i by definition. Thus, by replacing you obtain:
\(\pm\sqrt[]{-49}=\pm\sqrt[]{(-1)(49)}=\pm\sqrt[]{(-1)(7^2)}=\pm7\sqrt[]{-1}=\pm7i\)Hence, the given expression in terms of the imaginary unit is :
\(\pm7i\)Please help me caramel find the value of X.. The Diagram is not to scale
Answers
The value of x in the given diagram is 48
How to determine the value of x in the diagram?A scale factor is the size by which a shape is enlarged or reduced. It is used in increasing or reducing the size of a 2D shape, such as triangle, square, rectangle, etc.
In the given diagram, the scale factor is:
Scale factor = bigger side/smaller side= (45+45)/45 = 90/45 = 2/1
To find x, use the scale factor and the corresponding sides. Thus:
bigger side/smaller side = 2/1
x/24 = 2/1
x = 2 ×24 = 48
Note: You can simply multiply any of the smaller sides by 2 to get the corresponding bigger sides
Therefore, the value of x is 48
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using PEMDAS solve: 36+10×0.5-18÷6
Answers
A rectangular paperboard measuring long and wide has a semicircle cut out of it, as shown below. What is the perimeter of the paperboard that remains after the semicircle is removed? (Use the value for , and do not round your answer. Be sure to include the correct unit in your answer.)
Answers
Perimeter of the paperboard that remains after the semicircle is removed = 37. 74 in
How to determine the perimeterFrom the information shown in the diagram, we have that the semi circle is cut out of the rectangular paperboard.
The perimeter of a rectangle is expressed as;
Perimeter = 2(l + w)
Given that;
Length = 24 in
Width = 18 in
Radius of the semi circle = width of the paperboard = 9 in
1Circumference of the semi circle = πr + 2r
Substitute the values
= 3.14(9) + 2(9)
Expand the bracket
= 46. 26 in
Perimeter of the paperboard that remains after the semicircle is removed
= 2(l + w) - circumference of semicircle
= 2(24+ 18) - 46. 26
= 84 - 46. 26
= 37. 74 in
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One third of a number is 12 less than the number itself
Answers
Answer:
18
Step-by-step explanation:
1/3 n = n - 12 Cross multiply
n = 3(n - 12)
n = 3n -36
2n = 36
n = 36/2
n = 18
(1/3)n=n-12
(3)(1/3)n=(3)n-12
n=3n-36
-2n=-36
n=18
when using a graduated pipet, at which point do you measure the volume?
Answers
The volume is measured at the bottom of the meniscus when the liquid level is between the two etched marks on the pipet.
1. Place the graduated pipet on a flat surface and make sure it is level
2. Draw the liquid up until the meniscus is level with the etched line that corresponds to the desired volume
3. Make sure the liquid is not touching the etched line above it
4. Observe the bottom of the meniscus and take the reading at the point where the liquid level is between the two etched lines
The volume is measured at the bottom of the meniscus when the liquid level is between the two etched marks on the pipet.
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the mean retirement age for all employees at a major company was 67 with a standard deviation of 6 years. suppose we wanted to create a sampling distribution out of this data using a sample size of 36. report all answers below to the nearest whole number. the mean of the sampling distribution would be . the standard error (standard deviation) of the sampling distribution would be
Answers
The sample distribution would have a mean of 67
The sample distribution's standard deviation would equal its standard error = 1
μ = 67
σ = 6
n = 36
Approximately normal sampling distribution for the sample mean with mean and standard deviation = σ / √n
The sample distribution's mean would be, μ = 67
The sample distribution's standard error (standard deviation) would be = σ / √n = 6 / √36 = 1
According to the central limit theorem, if the population distribution is normal, the sampling distribution of the sample mean will be roughly normal for any sample size, or if the sample size is large enough to be n>30, the sampling distribution will be roughly normal with mean and standard deviation for any population distribution = σ / √n
Therefore, The sample distribution's mean would be = 67
and the sample distribution's standard error (standard deviation) would be = 1
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