Answers
Answer:
10.10 15.15
Step-by-step explanation:
25.30 15.12 25.13
Related Questions
2
M2|L23
Division Diver Duo
5,626 ÷ 62
How many times can 62 go into 562
Answers
The result of 5,626 divided by 62 is approximately 90 with a remainder of 48.
To calculate the division of 5,626 by 62, you can use long division. Here are the steps:
90
______________
62 | 5,626
- 4,96
-----
1,66
1,55
----
110
62
----
48
Therefore, the result of 5,626 divided by 62 is approximately 90 with a remainder of 48.
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I have a statistic that is normally distributed with a very large sample size. I add a single subject that is way above the median to the sample. What is likely to happen?
Answers
Adding a single subject that is way above the median to a sample with a very large sample size is likely to have a minimal impact on the overall distribution and statistics of the sample.
When the sample size is very large and the distribution of the statistic is approximately normal, the Central Limit Theorem states that the distribution of the sample mean approaches a normal distribution, regardless of the underlying population distribution. This means that the sample mean is less sensitive to individual extreme values.
If a single subject is added to the sample that is way above the median, it will have a relatively small effect on the overall sample mean. This is because the impact of a single extreme value diminishes as the sample size increases.
When adding a single subject that is way above the median to a sample with a very large sample size, the effect on the overall distribution and statistics of the sample is expected to be minimal. The large sample size ensures that the sample mean remains robust and less influenced by individual extreme values. Therefore, the addition of a single subject with a very high value is unlikely to significantly alter the characteristics of the sample distribution or the calculated statistics such as the mean or standard deviation.
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A one-sided significance test gives a P-value of .02. From this we can a) Reject the null hypothesis with 97% confidence. b) Reject the null hypothesis with 98% confidence. c) O Say that the probability that the null hypothesis is false is .02. d) Say that the probability that the null hypothesis is true is .02.
Answers
A one-sided significance test gives a P-value of .02. From this we can conclude that we can reject the null hypothesis with 98% confidence.
Here’s why: In statistical hypothesis testing, the p-value is the probability of obtaining a test statistic at least as extreme as the observed value, assuming that the null hypothesis is true. If the p-value is less than or equal to the significance level (α), the null hypothesis can be rejected. Conversely, if the p-value is greater than the significance level, there is insufficient evidence to reject the null hypothesis. Since a one-sided significance test was performed, we are only interested in the probability that the test statistic will fall in one tail of the distribution.
Thus, the p-value is the probability of obtaining a test statistic as extreme as the observed value in one tail of the distribution. If the p-value is .02, this means that there is a 2% chance of obtaining a test statistic as extreme or more extreme than the observed value if the null hypothesis is true. Since the p-value is less than the standard significance level of .05, we can reject the null hypothesis with 98% confidence. This is because we can be 98% confident that the true population parameter falls in the alternative hypothesis range.
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A swimmer swims 2 kilometers every 15 minutes. If he comes to swim at the same rate which graph best represents his swimming speed in kilometers per minute
Answers
Answer:
62
Step-by-step explanation:
divide lang yan.piste kasi bat kailangan 20 letters
Answer:
la respuesta es la D
Step-by-step explanation:
la velocidad es constante
PLEASE HELP! What is the ratio of the volumes of two spheres, if the ratio of their radii is 13: 9
Answers
Answer:
[tex] V_1 : V_2= 2197 : 729[/tex]
Step-by-step explanation:
Let the volumes of both the spheres be [tex] V_1, \:V_2[/tex] and their radii be [tex] r_1, \:r_2[/tex] respectively.
[tex] \huge r_1 : r_2= 13 : 9[/tex] (given)
[tex] \implies\huge \frac{r_1}{r_2}= \frac{13}{9}.....(1)[/tex]
[tex] \huge \frac{V_1}{V_2}=\frac{\cancel {\frac{4}{3} \pi} r_1^3}{\cancel {\frac{4}{3} \pi} r_2^3}[/tex]
[tex] \huge \frac{V_1}{V_2}=\frac{ r_1^3}{r_2^3}[/tex]
[tex]\huge \frac{V_1}{V_2}=\bigg(\frac{ r_1}{r_2}\bigg) ^3..... (2)[/tex]
From equations (1) & (2), we have:
[tex]\huge \frac{V_1}{V_2}=\bigg(\frac{13}{9}\bigg) ^3[/tex]
[tex] \huge \frac{V_1}{V_2}=\frac{2197}{729}[/tex]
[tex] \huge \therefore V_1 : V_2= 2197 : 729[/tex]
Thus, the ratio of the volumes of two spheres would be 2197 : 729.
Answer:
2197:729
hope it helps
please mark brainliest
Find the characteristic c using a 64-bit long real equivalent decimal number -147 with mantissa f = 0.1484375
Answers
Characteristic 'c' using a 64-bit long real equivalent decimal number -147 with mantissa 'f' = 0.1484375, the number can be expressed as -1.48 x 10^2. The characteristic 'c' is the exponent of the power of 10. Therefore, the characteristic 'c' is -2.
The scientific notation representation of a real number is given by 'm x 10^c', where 'm' is the mantissa and 'c' is the characteristic. In this case, we have a 64-bit long real equivalent decimal number -147 with mantissa 'f' = 0.1484375. The number can be written as -1.48 x 10^2.
To determine the characteristic 'c', we look at the exponent of the power of 10. In this case, the exponent is 2. However, since the number is negative, the characteristic is also negative. Therefore, the characteristic 'c' is -2.In summary, for the given number -147 with mantissa 0.1484375, the characteristic 'c' is -2.
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The marginal PMFs for two INDEPENDENT random variables are given as follows 1/8 x = -1 Px(x) 1/2 = 0 3/8 1 = X = X = - py(y) = Py = 5/16 y=-1 9/16 y=0 1/8 = y = 1 a) Find the joint PMF for X, Y
Answers
The joint PMF for X, Y is given by the following table:
x\y 5/128 9/128 1/64 5/32 9/32 1/16 15/128 27/128 3/64
The joint probability mass function (PMF) of two discrete random variables is a function that maps each pair of outcomes of the random variables to a probability. In particular, the joint PMF gives the probability that the random variables take a certain pair of values on each trial. Therefore, we have to find the probability that the random variables X and Y take each of the six possible values.
Therefore, the joint PMF for X, Y is given as follows:
For x = -1 and y = -1,P(X = -1, Y = -1)
= P(X = -1)P(Y = -1)
= (1/8)(5/16)
= 5/128
For x = -1 and y = 0,P(X = -1, Y = 0) = P(X = -1)P(Y = 0)
= (1/8)(9/16)
= 9/128
For x = -1 and y = 1,P(X = -1, Y = 1) = P(X = -1)P(Y = 1)
= (1/8)(1/8)
= 1/64
For x = 0 and y = -1,P(X = 0, Y = -1) = P(X = 0)P(Y = -1)
= (1/2)(5/16)
= 5/32
For x = 0 and y = 0,P(X = 0, Y = 0) = P(X = 0)P(Y = 0)
= (1/2)(9/16)
= 9/32
For x = 0 and y = 1,P(X = 0, Y = 1) = P(X = 0)P(Y = 1)
= (1/2)(1/8)
= 1/16
For x = 1 and y = -1,P(X = 1, Y = -1) = P(X = 1)P(Y = -1)
= (3/8)(5/16)
= 15/128
For x = 1 and y = 0, P(X = 1, Y = 0) = P(X = 1)P(Y = 0)= (3/8)(9/16)
= 27/128
For x = 1 and y = 1,P(X = 1, Y = 1) = P(X = 1)P(Y = 1)
= (3/8)(1/8)
= 3/64
Therefore, the joint PMF for X, Y is given by the following table:
x\y 5/128 9/128 1/64 5/32 9/32 1/16 15/128 27/128 3/64
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The height of a cylindrical vase is 11 inches as shown below. The base of the cylinder has a diameter of 4½ inches. Which measurement is closest to the volume of the cylinder in cubic inches? * 34 points 1,710.6 cubic inches 155.51 cubic inches 699.79 cubic inches 174.95 cubic inches
Answers
Answer:
174.95
Step-by-step explanation:
Volume=πr^2h
3.142 * (4.5÷2)^2 *11
=174.95
I need to know how much metal is needed to make the can
Answers
Answer:
we don't have any wasted metal and everything goes perfectly. In the real world, waste is inevitable.
A company needs to determine the optimum power and time settings for their new licorice-flavored microwaveable popcorn. They want to find a combination of power and time that delivers high-quality popcorn with less than 11% of the kernels left unpopped, on average-a value that their market research says is demanded by their customers. Their research department experiments with several settings and determines that power 9 at 4 minutes is optimum. Their tests confirm that this setting meets the less than 11% requirement. They change the instructions on the box and promote a new money back guarantee of less than 11% unpopped kernels. Complete parts a) and b) below.
a) If, in fact, the setting results in more than 11% kernels unpopped, what kind of error have they made? What will the consequence be for the company? What are the null and alternative hypotheses in this case?
A. H_o: μ< 11 vs. H_A: μ = 11
B. H_o: μ= 11 vs. H_A: μ> 11
C. H_o: μ= 11 vs. H_A: μ< 11
D. H_o: μ> 11 vs. H_A: μ = 11
b) To be sure that the method was successful, the research department popped 8 more bags of popcorn (selected at random) at this setting. All were of high quality, with the percentages of unpopped kernels being 6.7,12.9, 10.6, 7, 7.1, 3.1, 2.0, and 4.8. Does this provide evidence that they met their goal of an average of fewer than 11% unpopped kernels? Assume α=0.05.
c) Find T
d) Find P
Answers
A The null and alternative hypotheses in this case are:
Null hypothesis: H_o: μ ≥ 11
Alternative hypothesis: H_A: μ < 11
B We have statistically significant evidence to conclude that the setting results in less than 11% kernels unpopped.
C The t-statistic is -2.94.
d) The p-value is 0.004.
How to explain the informationa) In this case, the company has made a Type I error. This is when the null hypothesis is rejected, even though it is true. In this case, the company would be rejecting the hypothesis that the setting results in less than 11% kernels unpopped, even though it is actually true. The consequence of this would be that the company would be losing money on refunds for popcorn that is not actually defective.
b) In order to answer this question, we need to calculate the t-statistic and the p-value.
The t-statistic is calculated as follows:
t = (x - μ) / (s / √n)
Substituting these values into the formula for the t-statistic, we get:
t = (6.7 - 11) / (3.5 / √8)
= -2.94
The p-value is the probability of obtaining a t-statistic that is at least as extreme as the one we observed, assuming that the null hypothesis is true. In this case, the p-value is 0.004.
c) The t-statistic is -2.94.
d) The p-value is the probability of obtaining a t-statistic that is at least as extreme as the one we observed, assuming that the null hypothesis is true. In this case, the p-value is 0.004.The p-value is 0.004.
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Suppose that the average time a fully charged 6-volt laptop battery will operate a computer is 4.6 hours and follows the exponential probability distribution. Determine the following probabilities.
a) Determine the probability that the next charge will last less than 1.9 hours.
b) Determine the probability that the next charge will last between 2.9 and 4 hours.
c) Determine the probability that the next charge will last more than 5 hours.
(Round to four decimal places as needed.)
Answers
(a) 0.3694 is the probability that the next charge will last less than 1.9 hours. (b) 0.2344 is the probability that the next charge will last between 2.9 and 4 hours. (c) 0.3830 the probability that the next charge will last more than 5 hours.
To solve these probabilities, we need to use the exponential probability distribution formula. The formula for the exponential distribution is:
[tex]P(X \leq x) = 1 - e^{-\lambda x}[/tex]
where,
λ is the rate parameter, and
x is the variable representing the duration.
Given that the average time a fully charged 6-volt laptop battery will operate a computer is 4.6 hours, we can find the rate parameter (λ) by taking the reciprocal of the average:
λ = 1 / 4.6
Now let's calculate the probabilities:
a) Determine the probability that the next charge will last less than 1.9 hours.
Using the exponential distribution formula:
[tex]P(X \leq 1.9) = 1 - e^{(-\lambda \times 1.9)}[/tex]
[tex]P(X \leq 1.9) = 1 - e^{(-\frac{1}{4.6} \times 1.9)}[/tex]
[tex]P(X \leq 1.9) = 1 - e^{(-0.4130)}[/tex]
P(X ≤ 1.9) ≈ 0.3694 (rounded to four decimal places)
Therefore, the probability that the next charge will last less than 1.9 hours is approximately 0.3694.
b) Determine the probability that the next charge will last between 2.9 and 4 hours.
Using the exponential distribution formula:
P(2.9 ≤ X ≤ 4) = P(X ≤ 4) - P(X ≤ 2.9)
[tex]P(2.9 \leq X \leq 4) = [1 - e^{(-\lambda \times 4)}] - [1 - e^{(-\lambda \times 2.9)}][/tex]
[tex]P(2.9 \leq X \leq 4) = [1 - e^{(-\frac{1}{4.6} \times 4)}] - [1 - e^{(-\frac{1}{4.6} \times 2.9)}][/tex]
P(2.9 ≤ X ≤ 4) ≈ 0.2344 (rounded to four decimal places)
Therefore, the probability that the next charge will last between 2.9 and 4 hours is approximately 0.2344.
(c) Determine the probability that the next charge will last more than 5 hours.
Using the exponential distribution formula:
P(X > 5) = 1 - P(X ≤ 5)
[tex]P(X > 5) = 1 - [1 - e^{(-\lambda \times 5)}][/tex]
[tex]P(X > 5) = 1 - [1 - e^{(-\frac{1}{4.6} \times 5)}][/tex]
P(X > 5) ≈ 0.3830 (rounded to four decimal places)
Therefore, the probability that the next charge will last more than 5 hours is approximately 0.3830.
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Julio recibió $640.000: gastó las ⅜ partes para pagar sus estudios y la ¼ parte para reparar el auto, ¿cuánto dinero le queda?
Answers
Answer:
Resto= $240.000
Step-by-step explanation:
Dada la siguiente información:
Cantidad total de dinero= $640.000
Costo de estudio= 3/8= 0,375
Costo de auto= 1/4= 0,25
Primero debemos calcular la cantidad total gastada, y después la diferencia:
Costo de estudio= 0,375*640.000= 240.000
Costo de auto= 0,25*640.000= 160.000
Gasto total= $400.000
Resto= 640.000 - 400.000
Resto= $240.000
help
------
me
------
plsss
--------
Answers
Answer:
1 is E 2 is C
Step-by-step explanation:
15 is equal to or less than 6x
Use the consumption function C = C₁ + bY and the income function Y=C+ S. to derive expressions for the MPC, APC, MPS. and APS. 7 marks 5. Given the consumption functions C= 50+ 0.5Y, Deduce expressions for the marginal propensity to save and the average propensity to save. Show that the MPS>APS. Confirm this statement by evaluating APS and MPS at Y = 20. 6 marks 6. Find the derivatives of the following functions. AC = + QI(Q) 3 marks Page 2 y=(√2+1)(√2-3) 3 marks 7. Determine the intervals along which each of the following curves is increasing or decreasing (consider the positive half of the plane, z>0) 5 marks (a) AC=Q²-20Q+120 (b) TR=50Q-Q²
Answers
In the given problem, we start by deriving expressions for the marginal propensity to consume (MPC), average propensity to consume (APC), marginal propensity to save (MPS), and average propensity to save (APS) using the consumption function and income function.
Deriving expressions for MPC, APC, MPS, and APS:
Using the consumption function C = C₁ + bY and the income function Y = C + S, we can derive the following expressions:
MPC (Marginal Propensity to Consume) = ΔC / ΔY
APC (Average Propensity to Consume) = C / Y
MPS (Marginal Propensity to Save) = ΔS / ΔY
APS (Average Propensity to Save) = S / Y
Deducing expressions for MPS and APS:
Given the consumption function C = 50 + 0.5Y, we can deduce the expressions for MPS and APS as follows:
MPS = ΔS / ΔY = Δ(Y - C) / ΔY = 1 - MPC
APC = C / Y = (50 + 0.5Y) / Y
APS = S / Y = (Y - C) / Y = 1 - APC
Confirming MPS > APS:
To confirm that MPS is greater than APS, we evaluate them at Y = 20:
MPS = 1 - MPC = 1 - 0.5 = 0.5
APC = C / Y = (50 + 0.5 * 20) / 20 = 52.5 / 20 = 2.625
APS = 1 - APC = 1 - 2.625 = -1.625
Since APS is negative and MPS is positive, it is evident that MPS > APS.
Derivatives of the given functions:
a) AC = Q² - 20Q + 120
The derivative of AC with respect to Q is: d(AC)/dQ = 2Q - 20
b) TR = 50Q - Q²
The derivative of TR with respect to Q is: d(TR)/dQ = 50 - 2Q
Determining intervals of increase or decrease:
a) AC = Q² - 20Q + 120
The quadratic function AC has a positive coefficient for the quadratic term (Q²), indicating a U-shaped curve. It opens upward, which means it is increasing for Q values less than the vertex of the parabola (Q = 10) and decreasing for Q values greater than the vertex.
b) TR = 50Q - Q²
The quadratic function TR has a negative coefficient for the quadratic term (Q²), indicating a downward-opening parabola. It is decreasing for all values of Q.
In summary, we derived expressions for MPC, APC, MPS, and APS using the consumption function and income function. We confirmed that MPS > APS by evaluating them at a given income level.
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as of today, the team has played seven games, and _____________ has won them all.
Answers
As of today, the team has played seven games, and "the team" has won them all.
This statement indicates that the team, whose specific name or identity is not provided, has achieved a perfect winning record by emerging victorious in all seven games they have participated in. The emphasis is on the collective success of the team rather than attributing the wins to any particular individual or naming the team itself. The phrase "has won them all" highlights the team's unbeaten streak and implies their dominance in the competition.
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A pizza cut into 8 pieces cost $10.00.
What is the cost per piece?
Answers
Answer:
$1.25
Step-by-step explanation:
10/8 =1.25
Answer:
$1.25
Step-by-step explanation:
just divided 10 with 8
asfjpasjfaafdad adsafdshfd
Answers
4020
you're supposed to multiply the length value by 1760
:P
Callum is walking 270 miles to raise money for cancer research. He plans to walk 1/9 of the distance each day. After 7 days, how much farther does he have to walk to reach his goal?
Answers
Lin opened a savings account that pays 5.25% interest and deposited $5000. If she makes no deposits and no withdrawals for 3 years, how much money will be in her account?
Answers
Answer:
$5829.57
Step-by-step explanation:
Annually compounding interest formula: [tex]PV(1+i)^t[/tex]
5000(1+.0525)^3
5829.567266
which rounds to: 5829.57
A Gallup poll conducted in November 2010 found that 493 of 1050 adult Americans believe it is the responsibility of the federal government to make sure all Americans have healthcare coverage.
Use Minitab Express to construct the following confidence intervals. Report your answers as decimals (not percents) rounded to three decimal places, where applicable.
a) We are 95% confident that the proportion of all adult Americans who believe it is the responsibility of the federal government to make sure all Americans have healthcare coverage is between ____ and ____
b) We are 99% confident that the proportion of all adult Americans who believe it is the responsibility of the federal government to make sure all Americans have healthcare coverage is between _____ and ____
Answers
The sample proportion is calculated by dividing the number of individuals who believe it is the responsibility of the federal government (493) by the total number of adult Americans surveyed (1050).
a) For the 95% confidence interval, we use the formula: Sample proportion ± Z * (Standard error). The value of Z is determined by the desired confidence level. In this case, for a 95% confidence level, Z is the critical value corresponding to a two-tailed test. By plugging in the values, we can calculate the lower and upper limits of the interval.
b) Similarly, for the 99% confidence interval, we use the same formula but with the appropriate critical value for a 99% confidence level.
Using Minitab Express or statistical tables, we can find the critical values and compute the confidence intervals.
Hence, the 95% confidence interval represents our level of confidence that the true proportion of adult Americans who believe it is the responsibility of the federal government to provide healthcare coverage lies within the reported interval. Similarly, the 99% confidence interval provides a higher level of confidence in capturing the true proportion.
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Which value below represents the solution to 64 = 4u
Answers
Answer:
You didnt write the options
Answer:
u=16
Step-by-step explanation:
64=4u
divide both sides by 4
16=u
on number 6 what should i color in
Answers
Answer:
For 5/11 shade in the third bubble (0.45 repeating)
You must exert a force of 4.5 N on a book to slide it across a table. If you moved it 5 meters. How much work was done on the book?
Answers
Answer:
22.5 JStep-by-step explanation:
The work done by an object can be found by using the formula
workdone = force × distance
From the question we have
workdone = 4.5 × 5
We have the final answer as
22.5 JHope this helps you
p is a plane in r3. its equation is: x 4y − 3z = 0. this plane is the nullspace of what matrix a ? find the basis for the nullspace of a. find the basis for the line p⊥ that is perpendicular to p.
Answers
The vector [1, 1, 1]ᵀ as it is symmetrical to the ordinary vector. Thus, "[1, 1, 1]T" serves as the foundation for the line p.
We can rewrite the plane's equation as a matrix equation to find the matrix A whose nullspace matches the given plane. The plane's equation is as follows:
x - 4y + 3z = 0
We can revise it in lattice structure as:
Where [A] is a 1x3 matrix and [x, y, z]T is a column vector, [A] = [0]. The rows of the matrix [A] will serve as the equation's coefficients for x, y, and z due to the equation's homogeneity and linearity.
As a result, matrix A is:
[A] = [1, -4, 3] We must solve the equation A * x = 0, where x is a column vector, in order to determine the nullspace's basis. For this situation, we really want to address:
We can represent it as a system of equations: [1, -4, 3,] [x, y, z]T = [0].
x - 4y + 3z = 0
To track down the reason for the nullspace, we settle the arrangement of conditions and express the arrangement concerning boundaries. Let's figure out the system:
x = 4y - 3z
Picking y = t (a boundary), we can revamp the arrangement as:
The nullspace of matrix A is spanned by the vector [4, 1, 1]T, so "[4, 1, 1]T" serves as the foundation for the nullspace of A. Since x = 4t, y = t, and z = t,
Presently, to find the reason for the line p⊥ that is opposite to p, we know that any vector in p⊥ is symmetrical to any vector in p. Hence, the reason for p⊥ can be found by finding a vector that is symmetrical to the ordinary vector of p (which is [1, - 4, 3]ᵀ).
We can pick the vector [1, 1, 1]ᵀ as it is symmetrical to the ordinary vector. Thus, "[1, 1, 1]T" serves as the foundation for the line p.
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Here is my question.
Answers
Answer: True False True true
Step-by-step explanation:
Answer:
true
false
true
true
Step-by-step explanation:
Help me please thanks
Answers
Answer:
64 square cm
Step-by-step explanation:
(I pulled this out of the comments in case someone else needs this answer. Easier to see as an answer than as comments in the app)
Area 2 is easier, so we’ll start with that one. Area of a rectangle is length x width.
8 x 6 = 48 square cm
Area 1 is a triangle, so the formula is 1/2(base)(height). The height of the triangle is 8, because it’s the same as the base of the rectangle. The base of the triangle is 4, because we can subtract the 6 from the rectangle from the total side length of 10. Does that make sense?
So 1/2 (4)(8)= 1/2(32) = 16 square cm
Then we add 16 + 48 = 64 square cm
Rosalind Franklin played an important role in the discovery of DNA's structure. Her data was used to support Watson's and Crick's hypothesis that DNA had the structure of a double helix. Even with this data and support from other scientists, the structure of DNA was not a widely accepted theory. Select all of the reasons why was their discovery was not considered a theory at the time of the paper's publication? 1. A newly released hypothesis must wait a least a year before the scientific community can vote for it to become a theory. 2. Theories are never developed by three people. 3. Theories need to undergo peer-review. 4.The hypothesis wasn't supported by their own data.
Answers
Answer:
The correct option is;
3. Theories need to undergo peer-review
Step-by-step explanation:
Within the scientific community, a theory has to be peer-reviewed by subject matter experts before it can be normally considered a valid theory. The peer-review process is one in which another scientific expert on the subject analyze, study, and repeat the experiments in the same conditions as stated in a publication submitted to a journal as a theory. The peer-review process aims to confirm the theory. A discovery which survives the peer review process will be considered a scientific theory and can then be expanded upon.
| 50 Points | Please give explanation | Reporting false answers | Giving correct brainliest
Answers
Answer: answer is D
Step-by-step explanation:
because science is more important than life
Let X be a topological space and A ⊂ X. The closure of A, denoted
A¯, is the intersection of all closed sets containing A.
(a) Show that A¯ is the smallest closed subset of X containing A, in
the following sense: if A ⊂ F ⊂ X and F is closed, then A¯ ⊂ F.
Answers
The "closure(A⁻)" of "subset-A" in a topological-space X is the intersection of all "closed-sets" containing A. It is smallest closed subset of X that contains A, means that if A⊂F⊂X and F is closed, then A⁻ is a subset of F.
In order to show that the closure(A⁻) is the smallest closed subset of X which contains "A", we need to prove that if A ⊂ F ⊂ X and F is closed, then A⁻ ⊂ F,
We know that, A⁻ is intersection of all "closed-sets" containing A. Since F is "closed-set" which contains "A", it is one of the sets in the intersection defining A⁻. So, A⁻ is contained in F.
To show that A⁻ ⊂ F, we consider an arbitrary point x ∈ A⁻, which means that x is in the intersection of all closed sets containing A. Since, F is one such "closed-set" containing A, x must be in F as well.
Since x was an "arbitrary-point" in A⁻, we have shown that every point in A⁻ is also in F, So, A⁻ ⊂ F.
Therefore, we have proved that if A ⊂ F ⊂ X and F is closed, then A¯ ⊂ F.
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Jennifer painted a tabletop that is shaped like a circle. the circumference of the tabletop is 6π. Which measurement is closest to the area of the tabletop in square feet?
Answers
28.26 sq. Ft is the area of the table top