If B = (8, 145, 287, 7005). Find the outer measure of B, i.e µ*(B).
Answers
Answer:
Step-by-step explanation:To find the outer measure of B, denoted as µ*(B), we need to take the infimum of the sums of the lengths of the intervals that cover B.
We start by considering a cover of B by intervals. Since B is a set of four points, we can construct a cover of B with four intervals, each containing one of the points. Specifically, we define:
I1 = (8 - ε, 8 + ε)
I2 = (145 - ε, 145 + ε)
I3 = (287 - ε, 287 + ε)
I4 = (7005 - ε, 7005 + ε)
where ε is a small positive number.
Then, the lengths of these intervals are:
|I1| = 2ε
|I2| = 2ε
|I3| = 2ε
|I4| = 2ε
The sum of the lengths of these intervals is:
|I1| + |I2| + |I3| + |I4| = 8ε
Since ε can be made arbitrarily small, we can take the infimum of the sum of the lengths of the intervals over all covers of B by intervals. Therefore, we have:
µ*(B) = inf{|I1| + |I2| + |I3| + |I4|} = inf{8ε} = 0
Hence, the outer measure of B is 0.
Related Questions
In the equation (x-3)²+(y-2)2=16, the radius of the circle is...
16
3
32
4
Answers
Step-by-step explanation:
This is of the form
(x-h)^2 + ( y-k)^2 = r^2 so r^2 = 16 means r = 4 units
Please answer this correctly without making mistakes
Answers
Answer:
293inch
Step-by-step explanation:
All students are classified as either full-time or part-time. Kenneth conducted a survey in which he collected data on the percentage of students that are full-time and the percentage of students that are part-time. Which of the following could sufficiently display the data if only the two given categories are to be included?
a. pie chartb. bar graphc. neither a pie chart nor a bar graphd. either a pie chart or a bar graph
Answers
Answer:
A
Step-by-step explanation:
I need help filling out the definition for these
PLEASE HELP !!!!!!!
Answers
Integers are positive or negative whole numbers.
Integers are the number which starts from 0 and goes both sides of the number line.Its infinite at both ends of the numbers.Hence
\(\\ \sf\bull\dashrightarrow R_f=\{-\infty,\infty\}\)
What’s the equation of a line that is perpendicular to -x +2y =4 and passes through the point (-2,1)
Answers
Answer:
y = -2x - 3
Step-by-step explanation:
Given:
Equation of -x +2y =4
Point of (-2,1)
-x + 2y = 4
y = x/2 + 2 or y = 1/2x + 2
Which means the equation's slope is m = 1/2.
The slope of the perpendicular line is negative inverse which is m = -2.
Now we have an equation of y = -2x + a.
Use (-2, 1) to find a:
1 = (-2)(-2) + a
a = -3
y = - 2x - 3
Step be step
(+1 point) Write the equation of the line in slope-intercept form given the following information.
18. slope = -2 and y-intercept (0,6)
(+3 points) Write the equation of the line given the following information in point-slope form
then rewrite in slope-intercept form.
19. Slope =
contains (-4, 3)
Answers
Answer:
18. y = -2x + 6
19. y = -1/2x -1/2
Step-by-step explanation:
y = mx + b
18. The point (0,6) 0 is the x-intercept and 6 is the y-intercept
For now, all we care about is 6
-2 is the slope which means the line will go down 2 and right 1
m = slope
b = y-intercept
y = -2x + 6
19.
-1/2 is the slope which means the line will go down 1 and right 2
For the y-intersept, I just played with it on a graphing calculater until I got it right.
m = slope
b = y-intercept
y = -1/2x -1/2
Assume that a simple random sample has been selected and test the given claim.Claim: The average age of actresses when they win an acting award is more than 34 years oldTo test this claim a simple random sample (SRS) of 27 actresses is used. This sample of 27 actresses had a sample mean of 31.4 years and a standard deviation = 11.2 years. Assume the the distribution of actresses ages is approximately normal.Select all TRUE statements from those given below..For this hypothesis test; H0: ? 34 H1: ?>342. The correct decision is to "support" (fail to reject) the null hypothesis H0.3. We decide to reject the claim that the average age of actresses when they win an acting award is more than 34 years old.4. For this hypothesis test, the P-value = .8815. For this hypothesis test, the test statistic is t = -1.21
Answers
Answer:
how big is your noodle
Step-by-step explanation:
If AB is 126, what does x equal? HELPPP
Answers
Reason
126/2= 63
9x+18=63
9x=45
x=5
A tiny cube shaped space inside a computer chip has been measured to be 0.0000254m wide, 0.0000035m long and 0.000255m high. What is its volume? Write your answer in scientific notation.The volume is _______ \(m^{3}\)For example, if you want to enter the number 4.578×10−3, you would type 4.578 * 10^-3.
Answers
Given:
\(\begin{gathered} w=0.0000254m \\ l=0.0000035m \\ h=0.000255m \end{gathered}\)Required:
To find the volume.
Explanation:
The volume formula is
\(V=lwh\)Here
\(\begin{gathered} V=0.0000254\times0.0000035\times0.000255 \\ =2.2669\times10^{-14}m^3 \end{gathered}\)Final Answer:
\(v=2.2669\times10^{-14}m^3\)What is the slope and equation, how much battery does she lose an hour
Answers
Answer:
The slope is y=-5x+100 and she loses 5% per hour
Step-by-step explanation:
hope it helps and can you pls give me brainliest im desperate
Graph the image of this figure after a dilation with a scale factor of 12centered at the origin.
Use the polygon tool to graph the dilated figure.
Answers
Answer:
1.(-4,2)
2.(2,4)
3.(-2,8)
Answer:
(1,2) (0,4) (-4,2)
Step-by-step explanation:
took the quiz and got it right.
Twenty standard cartons of octal boxes weigh a total of 1,100 pounds. Find the weight per carton.
Answers
Twenty standard cartons of octal boxes weigh a total of 1,100 pounds. The weight per carton is 55 pounds.
Given that twenty standard cartons of octal boxes weigh a total of 1,100 pounds. We need to find the weight per carton.
How to find the weight per carton? To find the weight per carton, we need to divide the total weight of twenty standard cartons of octal boxes by 20.Let's assume the weight of each carton be x.
Therefore, the equation can be formed asx * 20 = 1,100 Solving the above equation for x, x = 1,100/20 Therefore, the weight per carton is 55 pounds. So, twenty standard cartons of octal boxes weigh a total of 1,100 pounds.
The weight per carton is 55 pounds.
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-6(y+15)=-3y+6
what value of y makes the equation true
Answers
Answer:
y = -32
Step-by-step explanation:
-6(y+15)=-3y+6
Distribute
-6y - 90 = -3y +6
Add 6y to each side
-6y -90+6y = -3y+6y +6
-90 = 3y+6
Subtract 6 from each side
-90 -6 = 3y +6-6
-96 = 3y
Divide by 3
-96/3 = 3y/3
-32 = y
Answer:
-32 !!!!
Step-by-step explanation:
The length and the width of a mobile phone are 13 cm and 7 cm respectively.
It has a screen PQRS as shown in the figure.
What is the area of the screen?
Answers
Answer:
91 Will be the answer
length × breadth.
13 × 7
= 91
Step-by-step explanation: Hope this helps u have a good day!!
In ΔHIJ, the measure of ∠J=90°, JH = 81 feet, and HI = 91 feet. Find the measure of ∠I to the nearest degree.
Answers
Answer:
63°
Step-by-step explanation:
\(Sin0=\frac{81}{91}\)\(x=sin^{-1}(81/91)\\\\\)\(= 62.887\)≈ 63°༻﹡﹡﹡﹡﹡﹡﹡༺
hope it helps...
have a great day!!
16 emails to 6 text messages- 10 emails to 4 text messages proportional or not
Answers
Given:
16 emails to 6 text messages- 10 emails to 4 text messages
To find:
Whether 16 emails to 6 text messages- 10 emails to 4 text messages proportional or not.
Solution:
Check the ratio of emails to text. If the ratios are equal then the relation is proportional.
16 emails to 6 text messages.
\(\dfrac{Emails}{Text}=\dfrac{16}{6}\)
\(\dfrac{Emails}{Text}=\dfrac{8}{3}\)
\(\dfrac{Emails}{Text}=8:3\)
10 emails to 4 text messages.
\(\dfrac{Emails}{Text}=\dfrac{10}{4}\)
\(\dfrac{Emails}{Text}=\dfrac{5}{2}\)
\(\dfrac{Emails}{Text}=5:2\)
Since \(\dfrac{8}{3}\neq \dfrac{5}{2}\) or \(8:3\neq 5:2\), therefore, it is not proportional.
A. Saving money at the grocery store by using unit pricing.
a. Toilet paper A is 6 mega rolls for $4.59.
Toilet paper B is 12 mega rolls for $9.02
How to I find which one is the better deal?
Answers
Based on the calculations using unit pricing, Toilet paper B has a lower unit price and is the better deal between the two. Customers will save more money if they purchase toilet paper B rather than toilet paper A because the price per mega roll is lower. (option b)
Saving money while shopping is one of the best ways to reduce your expenses and have more disposable income for other things. Unit pricing is a pricing system that displays prices in standard units, allowing customers to compare prices across different brands and package sizes and save money. To determine which toilet paper deal is better, we can use the unit price method, which divides the price by the number of units in the package. The toilet paper with the lower unit price is the better deal.
The formula for unit pricing is as follows:
Unit price = total price ÷ number of units
Using the above formula, we can calculate the unit price of toilet paper A and toilet paper B as follows:
For Toilet paper A:
Unit price = $4.59 ÷ 6 mega rolls
Unit price = $0.765 per mega roll
For Toilet paper B:
Unit price = $9.02 ÷ 12 mega rolls
Unit price = $0.751 per mega roll
Therefore, based on the calculations, Toilet paper B has a lower unit price and is the better deal between the two. Customers will save more money if they purchase toilet paper B rather than toilet paper A because the price per mega roll is lower. (option b)
Unit pricing is a great way to compare prices, and consumers should always use it to determine the better deal between two products, as this will help them save money and stick to their budget.
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1) A sample of 49 observations is taken from a normal population. The sample mean is 55 and the sample standard deviation is 10. Determine the 99% confidence interval for the population mean.
2) The Fox TV network is considering replacing one of its primetime crime investigation shows with a new family-oriented comedy show. Before a final decision is made, network executives commission a sample of 400 viewers. After viewing the comedy, 250 indicated they would watch the new show and suggested it replace the crime investigation show.
A) Estimate the value of the population proportion.
B) Compute the standard error of the proportion.
C) Develop a 99% CI for the population proportion.
D) Interpret your findings.
Answers
1) The 99% confidence interval for the population mean is;
CI = (51.32, 58.68)
2)(a) The value of the population proportion is; 0.625
b) The standard error of the proportion is; 0.0624
c) A 99% CI for the population proportion is; CI = (0.5626, 0.6874)
d) The interpretation is that the proportion of those who watched the new show and suggested it replace the crime investigation show is between 0.5626 and 0.6874
How to find the confidence interval?1) We are given;
Sample size; n = 49
Sample Mean; x' = 55
Standard deviation; s = 10
Confidence level = 99%
Formula for confidence level is;
CI = x' ± z(s/√n)
z at 99% is; 2.576
Thus;
CI = 55 ± 2.576(10/√49)
CI = (51.32, 58.68)
2) The formula for confidence interval for proportion is;
CI = p ± z√(p(1 - p)/n)
We are given;
Sample size; n = 400
X = 250
a) Thus, population proportion = 250/400 = 0.625
b) Standard error is given by the formula;
SE = z√(p(1 - p)/n)
SE = 2.576√(0.625(1 - 0.625)/400)
SE = 0.0624
c) The 99% CI for the population proportion is;
CI = 0.625 ± 0.0624
CI = (0.5626, 0.6874)
D) The interpretation is that the proportion of those who watched the new show and suggested it replace the crime investigation show is between 0.5626 and 0.6874
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you have housing and fixed expenses of $813.52 a month you want to have a 6 month emergency fund and you want to have it funded in 18 months how much must you save per month?
Answers
Answer:
271.17 is the answer
Step-by-step explanation:
we know that the housing and fixed expenses of $813.52/month.
6 months emergency funds
= 813.52 × 6 = 4881.82
We know that you want to have it funded in 18 months
put it fraction will solve the problem:
\(\frac{4881.12}{18}\) = 271.17
271.71 being the answer
Simplify -2y + 14 - 9y + 5
Answers
Answer:
y= 11/19
Step-by-step explanation:
Which expression can be used to find the surface area of the following square pyramid?
Answers
Answer:
C
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
What is the additive inverse of the polynomial? -7y^2+x^2y-3xy-7x^2
Answers
The additive inverse of the polynomial is +7y²-x²y+3xy+7x².
What is Additive inverse?The additive inverse can be defined as when we add a number to some number and get result as zero.
Given polynomial:
-7y²+x²y-3xy-7x²
As, the value of additive inverse is same as of the number but the sign of the additive inverse is opposite.
So,
= +7y²-x²y+3xy+7x²
Check:
-7y²+x²y-3xy-7x² + 7y²-x²y+3xy+7x²
= -7y²+ 7y² +x²y -x²y -3xy +3xy -7x² +7x²
=0
Hence, the additive inverse of the polynomial is +7y²-x²y+3xy+7x².
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the day time temperatures recorded over 5 consecutive days in october were 14.6,15.2,15.8,16.1 . find the average temperature
Answers
Answer: 15.54 degrees.
Step-by-step explanation:
To find the average temperature, we need to add up all the temperatures and then divide by the number of days:
Average temperature = (14.6 + 15.2 + 15.8 + 16.1) / 5
= 77.7 / 5
= 15.54
Therefore, the average temperature over the 5 consecutive days in October is approximately 15.54 degrees.
C(t)=26(0.87)^(t) answer
Answers
please give brainliest
C(T) = 26(0.87)^(T)
open the pdf, it gives the answer
you're welcome! ^-^
Which choice is equivalent to the quotient shown here for acceptable
values of X?
√25(x-1) + √5(x-1)²
OA. √25(x-1)-5(x-1)²
OB.
5
1(x-1)
OC. √125(x-1)3³
OD. √5(x-1)
Answers
The equivalent to the quotient shown in the task content for acceptable values of x is; √(5/(x-1)).
What is the equivalent of the quotient?It follows from the task content that the expression given is; √(25(x-1)) ÷ √(5(x-1)²).
It therefore follows from the the laws of indices that the evaluation is thus;
= √{(25/5) ×(x-1)/(x-1)²}.
Ultimately, upon evaluation we have;
= √(5/(x-1))
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the 7th-grade class wants to collect empty soda pop cans to earn $50.00. If pop cans earn $0.25 per pound how many cans will they need to collect to earn the $50.00?
Answers
200 pounds need to collect to earn the $50.00. Divide the cost per pound from the total amount needed, \(\frac{50.00}{0.25}\)= 200 pounds.
Is the British pound?The official money of the U.k. and its regions is the GBP, or British pound sterling. The Pound is the earliest currency that is still accepted as legal tender in the entire world. The GBP, represented by pound sign (£), has one of the greatest trade volumes worldwide.
What makes something a "pound"?The development of the pounds sterling -The Latin word "libra," which means balance and weight, is where the name "pound sterling" comes from. During the years, the pound banknotes underwent various revisions before being initially printed by the Bank of England and over 300 years ago.
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these are the first five terms in a Fibonacci sequence.
1 5 6 11 17
Write down the next two terms in the sequence.
Answers
Answer: 28 and 45
Step-by-step explanation: you add 11 and 17 to get 28 and then add 28 and 17 to get 45
You are using a magnifying glass that shows the image of an object that is six tin image of the termite seen through the magnifying glass. 9.5 mm The image length through the magnifying glass is millimeters.
Answers
When viewed through the magnifying glass, the termite appears to be approximately 1.58 mm in length.
When using a magnifying glass, the image of an object appears larger. In this case, the termite is being viewed through a magnifying glass that magnifies the image by a factor of six. The actual length of the termite is not mentioned in the given information. However, it is stated that the length of the image seen through the magnifying glass is 9.5 mm.To determine the actual length of the termite, we can divide the length of the image by the magnification factor. Therefore, the actual length of the termite would be 9.5 mm divided by 6, which is approximately 1.58 mm.Therefore, when viewed through the magnifying glass, the termite appears to be approximately 1.58 mm in length.For more questions on magnifying glass
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Please help me with this I will give brainliest. Find the value of x. Round to the nearest tenth
Answers
Answer:
the second option
Step-by-step explanation:
\( \sin(20) = \frac{x}{18} \\ x = 6.15 = 6.2\)
Andrea is enjoying the novel she is reading. She had read 431 pages when she checked yesterday. She read more this afternoon and has now read a total of 487 pages. Write and solve an equation to find how many pages Andrea read today.
Answers
The number of pages Andrea read today is 56 pages.
Given that, Andrea is enjoying the novel she is reading. She had read 431 pages when she checked yesterday.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the number of pages Andrea read today be x.
She read more this afternoon and has now read a total of 487 pages.
Now, x=487-431
⇒ x=56
Hence, the number of pages Andrea read today is 56 pages.
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