Answer:
- 24n
Step-by-step explanation:
- 3 × 8 × n
- 24 × n
- 24n
An investigator compares the durability of two different compounds used in the manufacture of a certain automobile brake lining. A sample of 243 brakes using Compound 1 yields an average brake life of 37,866 miles. A sample of 268 brakes using Compound 2 yields an average brake life of 45,789 miles. Assume that the population standard deviation for Compound 1 is 4414 miles, while the population standard deviation for Compound 2 is 2368 miles. Determine the 95% confidence interval for the true difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2. Step 2 of 3 : Calculate the margin of error of a confidence interval for the difference between the two population means. Round your answer to six decimal places.
Answer:
The margin of error is of 623.2016.
The 95% confidence interval for the true difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2 is (-8546.2016, -7299.7984).
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem, and subtraction between normal variables.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the subtraction of the means while the standard deviation is the square root of the sum of the variances.
A sample of 243 brakes using Compound 1 yields an average brake life of 37,866 miles. The population standard deviation for Compound 1 is 4414 miles.
This means that [tex]\mu_1 = 37866, s_1 = \frac{4414}{\sqrt{243}} = 283.16[/tex]
A sample of 268 brakes using Compound 2 yields an average brake life of 45,789 miles. The population standard deviation for Compound 2 is 2368 miles.
This means that [tex]\mu_2 = 45789, s_2 = \frac{2368}{\sqrt{268}} = 144.65[/tex]
Distribution of the difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2.
The mean is:
[tex]\mu = \mu_1 - \mu_2 = 37866 - 45789 = -7923[/tex]
The standard deviation is:
[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{283.16^2 + 144.64^2} = 317.96[/tex]
Confidence interval:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = zs[/tex]
[tex]M = 1.96*317.96 = 623.2016[/tex]
The margin of error is of 623.2016.
The lower end of the interval is the sample mean subtracted by M. So it is -7923 - 623.2016 = -8546.2016
The upper end of the interval is the sample mean added to M. So it is -7923 + 623.2016 = -7299.7984
The 95% confidence interval for the true difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2 is (-8546.2016, -7299.7984).
Use the picture below and determine which of the lines or line segments 20 points
is/are a diameter
mA
VE
Line m
Line Segment BC
Ο Ο Ο Ο Ο
Line Sesnent AB or AC
Line Segment DE
Line 1
can someone help, please :)
Find the geometric mean between each pair of numbers 8 and 12
Step-by-step explanation:
......................................................
expanded form :32,456
Answer:
30,000 + 2,000 + 400 + 50 + 6
Step-by-step explanation:
[tex]\text{The expanded form of 32,456 would be 30,000 + 2,000 + 4,000 + 50 + 6.}[/tex]
[tex]\text{We would have to identify what each number stands for.}[/tex]
[tex]\text{For example, 3 in 32,456 stands for 30,000.}[/tex]
[tex]\text{Hence, following this rule, we can conclude that the answer above is correct.}[/tex]
[tex]\text{I hope I helped you suceed!}[/tex]
Stock in Macy's costs $25.75 per share. Hector buys 200 shares of Macy's
through his broker who charges a commission of $25.75. How much did George
pay in total to purchase the stock?
Answer: $5175.75
Step-by-step explanation:
The amount that is paid in total to buy the stock will be gotten through the addition of the cost of the shares and the commission paid. This will be:
= (200 × $25.75) + $25.75
= $5150 + $25.75
= $5175.75
Therefore, the total amount that is paid to buy the stock will be $5175.75.
GIVING BRAINLIEST
Explain your reasoning.
3(n + 2) = 9(6 - n)
Answer: n = 4
Step-by-step explanation:
Divide both sides by 3
n+2=3(6−n)
Expand
n+2=18−3n
Subtract 2 from both sides
n=18−3n−2
Simplify 18−3n−2 to −3n+16.
n=−3n+16
Add 3n to both sides
n+3n=16
Simplify n+3n to 4n
4n=16
Divide both sides by 4
n= 4/16
Simplify 16/4 to4
n=4
Write an equation for the sum of x and 3 minus 2 is 12
Answer:
x + (3-2) = 12
Step-by-step explanation:
x + (3-2) = 12
or x + 1 = 12
so x = 11
the sum of the first four terms of an A.p is 62.if the difference between 4 terms and 2nd terms is 14. find the first term and common difference
Answer:
-2 -4 -6 -8
Step-by-step explanation:
I got the answer off of khan academy
Determine the median of the following numbers: 8, 11, 11, 12, 13, 15, 16, 16, 18, 21
Answer:
The median of the following numbers is 14
Step-by-step explanation:
Write an equation that you can use to find the value of x.
The perimeter of the triangle: 16 in.
Answer:
This question seems incomplete
Select the statement that correctly describes a normal distribution.
a. It is a negatively skewed distribution, as the extreme values are less than the median.
b. It is a symmetric distribution, as the mean and the median are the same.
c. It is a positively skewed distribution, as the extreme values are greater than the median.
d. It is a uniform distribution, as all of the values have equal frequency.
Answer:
b. It is a symmetric distribution, as the mean and the median are the same.
Step-by-step explanation:
Normal distribution:
The biggest characteristic of the normal distribution is that it's symmetric, that is, 50% of the values are below the mean and 50% are above, which means that the mean is the same as the median.
This means that the correct answer is given by option b.
Simplify 25a/8 x 2a/5
Answer:
If the slashes mean divisions and the x means multiplication, the answer would be 25a²/4/5
PLZ FULL ANSWER
Maria has the following scores on exams in her social studies class: 86, 75, 97, 58, 94, and 58. Find the mean, median, and mode of the scores. Should Maria’s social studies teacher use the mean, median, or mode of the exam scores to convince Maria that she needs to study more regularly for her exams?
Answer:
The mean is 78
The Median is 80.5
And The Mode is 58.
Step-by-step explanation:
(Mean) 86,75,97,58,94, and 58 equal 468. Divide it by 6 (The Total Of All The Numbers) and it gives you 78.
(Mode) Find the number that occurs the most which would be 58.
(Median) Put the numbers in order. Order: 58,58,75,86,94,97. Next, your supposed to find the number in the middle, but since there are 2(75 and 86.)
Add them together and you get 161. After that, divide them by 2 and it'll give you 80.5
By the way, if the number of numbers in the problem add up to be an even number, divide it by 2 and find the average. If it's odd, divide it by 2 and round it up to get to the median.
So yes, the teacher should use the scores to convince Maria that she needs to study more regularly for her exams.
The mean, median, or mode of the exam scores is 78, 86 and 58
What is Mean, median and Mode?The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.
The median is the middle value when a data set is ordered from least to greatest.
The mode is the number that occurs most often in a data set.
Given data: 58, 58, 75, 86, 94, 97
1. Mean= sum of observation/ Total number observation
= 58+58+75+86+94+97/6
=468/6
=78
2. Median,
Since, n is even
median= (n/2)+ 1
= 6/2 + 1
= 3+1
=4 th term= 86
3. Mode: Mode is the repeating data
mode= 58
Learn more about mean , median and mode here:
https://brainly.com/question/15323584
#SPJ2
A student formed a pattern in which each term is represented by a sum. The first four terms of the pattern are shown below Which expression can be used to determine the value of the sum in any term, n
Answer:
n2
Step-by-step explanation:i did this last year
A bag contains 2 red, 4 blue, and 4 yellow marbles. What is the probability of pulling a red marble, putting the marble back, and then pulling a blue marble?\
Answer:
Di ko po alam sorry
Step-by-step explanation:
Di ko alam putaenamo
14. The Manilow family paid their electric bill using balanced billing all last year. The monthly
payment was m dollars. At the end of the year, the electric company told them they used more
electricity than they were billed for, and they owed d dollars. Express the value of the electricity
used by the Manilows last year algebraically.
Z
Answer:
12mx
Step-by-step explanation:
Given that
The monthly payment was m dollars
And, they used more electricity
We need to determine the value that should be expressed in algebraically
The Monthly payment is m dollars
Using balance billing, it would be mx dollars
So, the equation is
= mx × 12
= 12mx
hence, the same would be relevant and considered too
You determine that you can make 72 donuts in 2 hours. At that rate, how
many donuts can you make in 8 hours?
Answer:
576
Step-by-step explanation:
please help me here im begging you it won't let me just skip it
Answer:
ABCD in statement and the other in reasoning
Step-by-step explanation:
A triangle has side lengths 8, 7, 4. In a similar triangle the smallest side is represented by x + 5 and the longest side is represented by x - 3. What is the value of x?
Answer:
x = 11
Step-by-step explanation:
8/4 = (x+5)/(x-3)
cross-multiply:
8(x-3) = 4(x+5)
8x - 24 = 4x + 20
4x = 44
x = 11
Answer:
Step-by-step explanation:
X=11
The longest known is double than samallest known
2(x-3) = x+5
2x-6 = x+5
x= 11
11-3 = 8
11+5 = 16
Sides of the known triangle 8,7,4 (side 8 double than side 4)
Sides of the similar triangle 16,14,8 (side 16 double than side 8 )
(05.03 LC) What is the equation of a horizontal line passing through the point (2, 10)? (5 points)
Answer:
y=10
Step-by-step explanation: a horizontal line has no slope
Can someone here please help me out?
Answer:
hope you can now substitute and find y
What is the volume of a rectangular prism with a length of 2 1/2 inch width of 4 inches, and a height of 3 inches? * 21: 36 cu, in O 30 cu in 9.5 cu in 0 26 cu.in
Answer:
30 cubic inch
Step-by-step explanation:
What is 1/3 of $4.89 dollars
Answer:
im pretty sure its 1.63
Step-by-step explanation:
lmk if im wrong
Write equivalent fractions for 1 2/3 and 1 7/8 using 24 as the common denominator 2 24 7 1 0
Answer:
2×8=16
7×3=21
2/3 + 7/8 = 16/24 + 21/24
Should we take care of useless equipment and avoid the "trash pile" that is growing in space?
I personally think yes.
What is -13 decreased by 9
Answer:
-4
Step-by-step explanation:
Answer:
-22
Step-by-step explanation:
-13 - 9
When both the numbers have the same sign, we add them. After adding we put the same sign of the numbers to the answer
-13-9 = -22What are the answers
Answer:
3. 5cm
[tex]4. \: {a}^{2} + {b}^{2} = {c}^{2} [/tex]
Step-by-step explanation:
3. the hypotenuse C squared = side A squared + side B squared. So 3 × 3=9 and 4 × 4 =16 therefore 9 + 16 =25 and the square root of 25 = 5.
4. In mathematics, the Pythagorean theorem, or Pythagoras's theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle.
Hope it is helpful....Can I please get help with this math problem? Thanks in advance.
Answer:
answer: scale factor is 3
Hope this helps
Answer:
ans :; scale factor is 3
this is the correct ans.
Sandy is getting ready for the day. She can wear either a balck or white shirt and then either pants, shorts, or a skirt. Create a tree diagram or label all the combinations she can make. How many are there total?