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Related Questions
Let A and B be disjoint compact subspaces of a Hausdorff space X. Show that there exist disjoint open sets U and V, with A⊂U and B⊂V.
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In Hausdorff-space "X", if A and B are disjoint "compact-subspaces", then there exist disjoint "open-sets" U and V such that A is contained in U and B is contained in V, because Hausdorff property ensures the existence of disjoint open neighborhoods for any two distinct points.
To prove existence of disjoint "open-sets" U and V with A⊂U and B⊂V, where A and B are "compact-subspaces" (disjoint) of "Hausdorff-space" X, we use the steps:
Step (1) : Since A and B are disjoint compact subspaces, we use the Hausdorff property to find open sets Uₐ and [tex]U_{b}[/tex] such that A⊂Uₐ and B⊂[tex]U_{b}[/tex], and Uₐ∩[tex]U_{b}[/tex] = ∅. This can be done for every pair of points in A and B, respectively, since X is Hausdorff.
Step (2) : Consider the set U = ⋃ Uₐ, where "union" is taken over all of Uₐ for each point in A. U is = union of "open-sets", hence open.
Step (3) : Consider the set V = ⋃ [tex]U_{b}[/tex], where union is taken over for all [tex]U_{b}[/tex] for "every-point" in B. V is also a union of open-sets and so, open.
Step (4) : We claim that U and V are disjoint. Suppose there exists a point x in U∩V. Then x must be in Uₐ for some point a in A and also in [tex]U_{b}[/tex] for some point b in B. Since A and B are disjoint, a and b are different points. However, this contradicts the fact that Uₐ and [tex]U_{b}[/tex] are disjoint open sets.
Therefore, U and V are disjoint open sets with A⊂U and B⊂V.
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You are a researcher studying the lifespan of a certain species of bacteria. A preliminary sample of 35 bacteria reveals a sample mean of = 66 hours with a standard deviation of 8 = 6.2 hours You would like to estimate the mean lifespan for this species of bacteria to within a margin of error of 0.5 hours at a 98% level of confidence. What sample size should you gather to achieve a 0.5 hour margin of error? Round your answer up to the nearest whole number. n= bacteria
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You should gather a sample of at least 29 bacteria to estimate the mean lifespan for this species of bacteria with a margin of error of 0.5 hours at a 98% level of confidence.
We are given a preliminary sample of 35 bacteria with a sample mean of 66 hours and a standard deviation of 6.2 hours. We need to calculate the sample size required to achieve the desired margin of error.
To calculate the sample size, we can use the formula:
n = (Z * σ / E)²
Where:
n is the required sample size
Z is the z-score corresponding to the desired confidence level (98% confidence corresponds to a z-score of 2.33)
σ is the standard deviation of the population
E is the desired margin of error
Plugging in the values, we have:
n = (2.33 * 6.2 / 0.5)²
Calculating the expression within parentheses:
2.33 * 6.2 / 0.5 ≈ 28.84
Rounding up to the nearest whole number, the required sample size is 29 bacteria.
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PLEASE HELP for a TEST EXPLAIN ANSWER pls give you brainlest!!!!
Answers
Answer:
B
Step-by-step explanation:
Answer:
a-4
Step-by-step explination:
hope this helps!
The population of a city and 2005 was 18,000. By 2010, the cities population has grown to 32,800. It’s a population grows flow a linear model, what is the projected population for 2015?
Answers
Answer:
47,600
Step-by-step explanation:
The rate is (32,800 - 18,000) = 14,800 per 5 years
therefore :
in 2015 = 2010 + 5 years
the pop. will be :
32,800 + 14,800 = 47,600
The answer is 47,600.
Hope this helped :)
PLEASE HELP I AM BEING TIMED I NEED THE RIGHT ANSWER AND A EXPLAINTION PLEASE I WILL HIVE YOU THE CROWN
Answers
Answer:
B
Step-by-step explanation:
Dependent values would be the numbers on the y axis
Let p, q, and r be the propositions You get an A on the final exam. You do every exercise in this book. You get an A in this class. p 9: r: (3 pts) Express as an English sentence: q-p b) (p) Express as an English sentence: ar - (-p A-q) Pe 2 c) (4 pts) Write the proposition below using the propositions p, q or r as well as logical connectors (including negation): "To get an A in this class or get an A on the final exam, you need to do every exercise in the book." 7. (pt) Use truth table to determine whether [-p Apv q)] →q is a tautology. (you may not need to use all the rows and columns available below.) 8. (4 pts) Use truth table to determine whether [(pv q) Apr)^(q→r)] →r (you may not need to use all the rows and columns available below.) is a tautology.
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q - p can be expressed as "If you do every exercise in this book, then you get an A on the final exam."
¬(p ∨ ¬q) can be expressed as "You need to do every exercise in this book and not get an A on the final exam."
The proposition "To get an A in this class or get an A on the final exam, you need to do every exercise in the book" can be written as "(r ∨ p) → q."
q - p: This proposition states that if you do every exercise in this book (q), then you get an A on the final exam (p).
¬(p ∨ ¬q): This proposition states that you need to do every exercise in this book (q) and not get an A on the final exam (¬p).
"(r ∨ p) → q": This proposition expresses that to get an A in this class (r) or get an A on the final exam (p), you need to do every exercise in the book (q). It is a conditional statement, where the antecedent is (r ∨ p) and the consequent is q.
For the truth table analysis:
[-p ∨ (p ∧ ¬q)] → q: The truth table should be constructed using the propositions p, q, and r, along with logical connectors. However, the given proposition doesn't involve the proposition r, so it cannot be analyzed using the truth table.
[(p ∨ q) ∧ r) ∧ (q → r)] → r: The truth table should be constructed using the propositions p, q, and r, along with logical connectors. However, the given proposition doesn't involve the proposition p, so it cannot be analyzed using the truth table.
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whats the answer to this?
Answers
Answer:
x=6
Step-by-step explanation:
The rent for an apartment was $6,600 per year in 2012. If the rent increased at a rate of 4% each year thereafter, use an exponential equation to find the rent for the apartment in 2021
Answers
Answer:
$9,393.78
Step-by-step explanation:
Using the equation:
A = P(1+r)^t
Where,
A = final amount
P = initial amount = $6,600
r = rate of increase = 4% = 0.04
t = time in years = 9 years (2012-2021)
A = 6,600(1 + 0.04)^9
= 6,600(1.04)^9
= 6,600(1.4233)
= 9,393.78
A = $9,393.78
How do you find the radius of a circle?
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Answer:
Divide the diameter by two
example if the diameter is 25 you divide 25 by 2 to get 12.5 as your radius .
please and this quickly and no links please
Answers
Answer:
11 months
Step-by-step explanation:
Since he has already read 14 books subtract them from the 80 books. you'll end up with 66. then diviid by 6 and you'll get 11 months
Joseph's front porch is rectangular. The length is 8 feet more than the width. The
perimeter of the porch is 52 feet. What is the width of the porch?
A. 9 feet
B. 14 feet
C. 17 feet
D. 22 feet
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A map has a scale of 1 inch : 40 miles. Use the given map distance to find the actual distance.
1.) 12 inches
2.) 1 foot
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Answer:
480 miles
Step-by-step explanation:
If one inch equals 40 miles, then 12 times that would be 4800 miles.
1 Inch 12 Inches
---------- = ------------------
40 Miles 480 Miles.
Billy made 2 gallons of juice for a picnic. He said that he made
2
4
quarts of juice.
Answers
Answer:
2/4 quarts of juice is 0.125 Gallons of juice for
Step-by-step explanation:
Please Give Brainliest
Answer:
He divided instead of using multiplication
Step-by-step explanation:
Consider a Markov chain with state space S = {1, 2, 3, 4, 5, 6} and transition probability matrix P = [ 0 0.5 0 0.1 0.4 0]
[ 0 1 0 0 0 0 ]
[ 0.3 0 0.2 0.1 0 0.4]
[0 0.7 0 0 0.3 0 ]
[0 0 0 0 1 0]
[0 0 0 0 0 1 ]
(a) Compute Pˣ. (b) If the process starts in state 3, what are the probabilities that it will be absorbed in state 2, state 5, and state 6, respectively?
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a)Pˣ = [tex]\begin{bmatrix}0.1 & 0.5 & 0.04 & 0.28 & 0.03 & 0.05\\0 & 1 & 0 & 0 & 0 & 0\\0.22 & 0 & 0.33 & 0.17 & 0.1 & 0.19\\0.7 & 0 & 0.43 & 0.3 & 0 & 0.57\\0 & 0 & 0 & 0 & 1 & 0\\0 & 0 & 0 & 0 & 0 & 1\end{bmatrix}[/tex] in matrix form, using eigen-values.
b)state 2 is 0.75; state 5 is 0 and ;state 6 is 0.25.
a)In order to calculate the value of Pˣ, follow the below-given steps:
Step 1: Compute the eigen-values of the matrix P.
Here, we get λ = 1, λ = 0.6, λ = 0.4, λ = 0.1, λ = 0, λ = 0.
Step 2: Compute the eigen-vectors corresponding to each eigenvalue of the matrix P.
Step 3: Compute the diagonal matrix D and the transition matrix T. [tex]\begin{matrix}1 & 0 & 0 & 0 & 0 & 0\end{matrix}0.6[/tex]
[tex]\begin{matrix}0.58 & 0.25 & 0.72 & 0 & 0 & 0\end{matrix}0.4.[/tex]
[tex]\begin{matrix}0.07 & 0 & 0.04 & 0.7 & 0 & 0\end{matrix}0.1.[/tex]
[tex]\begin{matrix}0.35 & 0.75 & 0.56 & 0 & 1 & 0\end{matrix}0.[/tex]
[tex]\begin{matrix}0 & 0 & 0 & 0.3 & 0 & 1\end{matrix}[/tex]
Pˣ = T . Dˣ . T⁻¹
We get the following matrix as a result.
Pˣ = [tex]\begin{bmatrix}0.1 & 0.5 & 0.04 & 0.28 & 0.03 & 0.05\\0 & 1 & 0 & 0 & 0 & 0\\0.22 & 0 & 0.33 & 0.17 & 0.1 & 0.19\\0.7 & 0 & 0.43 & 0.3 & 0 & 0.57\\0 & 0 & 0 & 0 & 1 & 0\\0 & 0 & 0 & 0 & 0 & 1\end{bmatrix}[/tex]
b)If the process starts in state 3,
the probability that it will be absorbed in state 2 is 0.75,
the probability that it will be absorbed in state 5 is 0, and
the probability that it will be absorbed in state 6 is 0.25.
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The top of a tall building has four triangular faces that slope toward a single point. What shape best models the top
of the building?
А cube
c. triangular pyramid
B cone
Dsquare pyramid
Choose
Answers
Answer:
Option D, square pyramid
Step-by-step explanation:
The base of a square pyramid is a square of side of length "A"
and the height of the pyramid is "h"
From the four sides of base of pyramid, four surfaces arises that are slanting and meet at a point at the top at height "h"
Hence, option D is correct
If Lin runs 21 laps at the same rate, how long does it take her?
minutes
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LOOK RIGHT HERE! HELP FASSST EMERGENCY! Don't go past go to this question right here and no Decimal answers plz. Thanks the answer is not 144 BTW. Thank you.
Answers
Answer: 140cm^3
Step-by-step explanation:
Consider the following argument by analogy.
Some doctors recommend that people over the age of 40 should get a physical every year. As one physician argued, "People take their car in for servicing every few months without complaint. Why shouldn’t they take similar care of their bodies?" [U.S. News & World Report, Aug. 11, 1986]
Analyze and evaluate this argument by doing the following: 1) Identify the two things being compared (A and B) and the property P attributed to B in the conclusion. 2) Identify the (unstated) properties (S) that are supposed to make A and B similar. 3) Analyze the argument into its inductive and deductive elements. The deductive step with be a valid syllogism with a universal major premise. 4) Evaluate the inductive generalization in the inductive step: a) Consider its initial plausibility given our other knowledge; b) Look for additional positive instances besides the one stated; c) Look for counterexamples.
Answers
The argument draws an analogy between car servicing and regular physicals for people over 40, highlighting the need for preventive care and maintenance. The deductive step is a valid syllogism with a universal major premise, and the inductive generalization is plausible given the potential benefits of regular check-ups, although individual circumstances may vary.
1) In this argument by analogy, two things are being compared: A) taking a car in for servicing every few months, and B) getting a physical every year for people over the age of 40. The property P attributed to B in the conclusion is the need for regular care or check-ups.
2) The unstated properties (S) that are supposed to make A and B similar include the idea that both cars and bodies require regular maintenance to ensure proper functioning and longevity. The argument assumes that just as neglecting car maintenance can lead to breakdowns and costly repairs, neglecting regular physical check-ups can lead to health problems and potential medical issues.
3) The deductive step of the argument can be formulated as follows:
Major premise: Cars need regular servicing to prevent breakdowns and maintain optimal performance.
Minor premise: Bodies are similar to cars in the sense that they require regular check-ups to prevent health issues and maintain optimal well-being.
Conclusion: People over the age of 40 should get a physical every year.
4) The inductive generalization in the argument relies on the plausibility of the comparison between car maintenance and physical check-ups. To evaluate its validity, we can consider the following:
a) The initial plausibility of the generalization: Given our knowledge that regular check-ups can help detect health problems early and promote overall well-being, it is reasonable to argue that regular physicals are beneficial, similar to regular car servicing.
b) Additional positive instances: We can find support for the generalization by examining medical recommendations and practices that emphasize the importance of regular check-ups for preventive care.
c) Counterexamples: While some individuals may not experience health issues or see the need for frequent physicals, the argument assumes that the general population will benefit from regular check-ups.
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f left parenthesis x right parenthesis equals 3 over 4 x squared .
Answers
Answer:
Step-by-step explanation: try your best
Which of the following number lines best represents the value, 144/2
Answers
Answer:
C
Step-by-step explanation:
sqrt of 144 is 12
then 12 divided by 2 is 5
C has the point of 6
What is the value of f(x) = 4x -9
Answers
Answer:
i believe its ()=4−9
Step-by-step explanation:
Answer:
f=4x-9
Step-by-step explanation:
f(x) = 4x-9
f(x)= 4x-9
x x
f=4x-9
Suppose the random variables X and Y have the following joint PDF: fxy(x, y) = cxy ,0 < x < b < 1 Determine the value of c.
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The random variables X and Y have the value of c is 2/b².
Considering that the joint PDF of X and Y as fxy(x, y) = cxy ,0 < x < b < 1. Integrating the given PDF over its domain is necessary in order to determine the value of c. To find the worth of c, we utilize the accompanying integral:∫∫fxy(x, y)dxdy = 1,where the mix is done over the whole area of x and y. Therefore, cxy dxdy = 1. (1) For x, the integration limits are (0 to b) and for y, they are (0 to 1).
Therefore, by substituting these limits into equation (1), we obtain: 01 0b cxy dxdy = 1 c * [x2/2]0r1[y2/2]0rb = 1 c = 2 / b2 The value of c is therefore 2/b².
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A line passes through the points (-1, 10) and (3, 2). Which shows the graph of this line?
8
8
4
2
- 108
2
46
8 10
X
12
-8
-10
10
6
Answers
Answer:
C
Step-by-step explanation:
EDGE 2021
A sprinkler waters a circular area. The sprinkler sprays 30 gallons of water per minute.
Select as few quadrants as possible that would allow you to create a graph of the total number of gallons of water,
y, sprayed by the sprinkler after x minutes.
Quadrant 1
Quadrant 2
Quadrant 3
Quadrant 4
Answers
Answer:
Quadrant 1
Step-by-step explanation:
The number of gallons of water sprayed after x minutes would never be negative, nor would time be negative, so the first quadrant would be all that you need
Jeremy wants to determine the number of solutions for the equation below without actually solving the equation. -3(x+1)+3x=-3(x-1)+3 Which method should Jeremy use? Determine whether the equation has the form a = a, and if it does, the equation has infinitely many solutions. Determine whether the equation has the form a = b, and if it does, the equation has no solution. Determine whether the equation has the form x = a, and if it does, the equation has one solution. Determine whether the equation has the form x = 0, and if it does, the equation has no solution.
Answers
Answer:C
Step-by-step explanation:
I have taken a test and it was right sorry if it isn’t right
Answer:
C
Step-by-step explanation:
determine whether the equation has the form x=a, and if it does, the equation has one solution
8-2(4×3-5)
does this equal -4?
Answers
Answer:
-6
Step-by-step explanation:
Answer:
No -6
Step-by-step explanation:
Can someone please respond to this
Answers
Answer:
that's easy, use the 6969 equation, with a some 420's and that will do it
yo i need help please i need the correct answer i will give u a brainliest to please just help me
Answers
Answer:
a
Step-by-step explanation:
What method did you use? Why? Solve. for x: 47° 13
Answers
Answer:
Step-by-step explanation:
Givens
You have the hypotenuse: 13
You seek the adjacent side: x
You have the angle enclosing the 2: 47 degrees.
The relationship is the Cosine
Solution
Cos(47) = opposite / hypotenuse
Cos(47) = 0.6820 From your calculator
Cos(47) = x / 13 Multiply both sides by 13
13*cos(47) = x
x=8.866
Leo flips a paper cup 50 times and records how the cup landed each time. The table below shows the results.
RESULTS OF FLIPPING PAPER CUP
Outcome Right-side UP Upside Down On its Side
Frequency
10
18
22
Based on the results, how many times can he expect the cup to land on its side if it is flipped 1,000 times?
333
440
550
786
N
Previous
Answers
Answer:
440
Step-by-step explanation:
i did the test already