Answer:
The 90% confidence interval for the difference in mean breaking strength between the two types of yarn is (0.08N, 0.52N).
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem and subtraction of 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
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Subtraction of normal variables:
When we subtract two normal variables, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
A sample of 125 pieces of yarn had mean breaking strength 6.1 N and standard deviation 0.7 N.
This means that [tex]\mu_1 = 6.1, s_1 = \frac{0.7}{\sqrt{125}} = 0.0626[/tex]
In a sample of 75 pieces of yarn from the new batch, the mean breaking strength was 5.8 N and the standard deviation was 1.0 N.
This means that [tex]\mu_2 = 5.8, s_2 = \frac{1}{\sqrt{75}} = 0.1155[/tex]
Distribution of the difference:
[tex]\mu = \mu_1 - \mu_2 = 6.1 - 5.8 = 0.3[/tex]
[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.0626^2+0.1155^2} = 0.1314[/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 - 0.9}{2} = 0.05[/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 - 0.05 = 0.95[/tex], so Z = 1.645.
Now, find the margin of error M as such
[tex]M = zs[/tex]
[tex]M = 1.645*0.1314 = 0.22[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 0.3 - 0.22 = 0.08N
The upper end of the interval is the sample mean added to M. So it is 0.3 + 0.22 = 0.52N
The 90% confidence interval for the difference in mean breaking strength between the two types of yarn is (0.08N, 0.52N).
For which value of k does Limit as x approaches kf(x) = 4?
0
2
6
8
Answer:
2
Step-by-step explanation:
on Edge
Answer: 2
Step-by-step explanation:
have a great day!
pls help Graph the rectangle after a 90° clockwise rotation about the origin.
Answer:
can you post the graph so I can answer to the best o my ability
Will give brainliest
Answer: Because the question uses the word “distinct” meaning obvious, and clear, I would select AB, AC, CB. (If it’s asking for all the possible line segments, I would select AB, AC, CB, BA, CA, BC).
he first date went well. You are still dating the same person and still looking for a great person to spend your life with. You are cautiously moving forward with the relationship and know that if they are a great match, their likelihood of being kind to animals is 0.9 whereas their likelihood of being kind to animals if they are not a great match is 0.7. You see that your prospective spouse is kind to animals. What is the probability that they are a great match now?
Answer:
0.125 = 12.5% probability that they are a great match now.
Step-by-step explanation:
To solve this question, we need the probability of a person being a great match, which i will use 0.1.
This question is solved using conditional probability.
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Is kind to animals.
Event B: Is a great match.
Probability of being kind to animals:
0.9 of 0.1(Is a great match).
0.7 of 1 - 0.1 = 0.9(is not a great match). So
[tex]P(A) = 0.9*0.1 + 0.7*0.9 = 0.72[/tex]
Probability of being kind to animals and a great match:
0.9 of 0.1. So
[tex]P(A \cap B) = 0.9*0.1 = 0.09[/tex]
What is the probability that they are a great match now?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.09}{0.72} = 0.125[/tex]
0.125 = 12.5% probability that they are a great match now.
Male and female teachers were asked whether they preferred to use a whiteboard or a projector while teaching. The responses are summarized in the table. Projector Whiteboard Total Male 22 10 32 Female 28 15 Total 25 75 What is the approximate probability that a teacher prefers projectors and is female?
Answer: c is the answer
C: 0.560
Step-by-step explanation:
The probability that Joanne has eggs for breakfast and goes to school by car is 0.4. The probability that she goes to school by car on any day is 0.5. What is the probability that Joanne has had eggs for breakfast if she went to school by car?
A) .1
B) .2
C) .4
D) .5
E) .8
Answer:
A
Step-by-step explanation:
According to a report in USA Today (February 1, 2012), more and more parents are helping their young adult children get homes. Suppose 8 persons in a random sample of 40 young adults who recently purchased a home in Kentucky got help from their parents. You have been asked to construct a 95% confidence interval for the population proportion of all young adults in Kentucky who got help from their parents. You have been asked to construct a 95% confidence interval for the population proportion of all young adults in Kentucky who got help from their parents. What is the margin of error for a 95% confidence interval for the population proportion?
a.1.645(0.0040)
b.1.645(0.0632)
c.1.96(0.0040)
d.1.96(0.0632)
Answer:
d.1.96(0.0632)
Step-by-step explanation:
The margin of error for a 95% confidence interval for the population proportion calculated as below:
Given that x = 8
n = Size of the sample = 40 (Large sample)
Sample population: P=x/n = 8/40 = 0.2; q = 1-p = 0.8
Standard error = [tex]\sqrt{pq/n}[/tex] = [tex]\sqrt{0.2(0.8)}/40[/tex] = 0.0682
95% of confidence Z∝ = 1.96
Margin of Error = Z∝ .[tex]\sqrt{pq/n}[/tex]
Margin of Error = 1.96(0.0682)
So, therefore, option d is correct.
Which expression is equivalent to 4/9 × 7
key:
1. 9÷4×7
2. 4×7÷9
3. 4÷7×9
4. 7×9÷4
Thank you :)
Solve: 18^(x^(2)+4x+4)=18^(9x+18)
x = -2
x = 7
x = –2 and x = 7
no solution
Is this the problem?
[tex]18x^{2+4+4} = 18^{9x+18}[/tex]
Answer
The Answer is C
x=-2 and x=7
Find the measure of minor arc QN.
QN = 142°
A semicircle will always be equal to 180°, and we have two measures for semicircle QO.
[tex]QO = 180\\MN = 90\\NO = 38\\\\QM = QO - MN - NO\\QM = 180 - 90 - 38\\QM = 52\\\\QN = QM + MN\\QN = 52 + 90\\QN = 142\\[/tex]
Mr. Jackson earns $1,500 each week and his wife earns $850 a week. Each week they need to set aside $200 for food, $75 for gas, $625 for the mortgage, and $350 for savings. How much money will they have left each week?
Answer:
$1,100
Step-by-step explanation:
Given that
Earnings of Mr Jackson is $1,500
Earnings of his wife is $850
They need to set aside the following amounts
For foods, it would be $200
For gas, it would be $75
For Mortgage it would be $625
ANd, for savings, it would be $350
We need to find out the amount of money that they have left each week
So, the amount would be
= $1,500 + $850 - $200 - $75 - $625 - $350
= $1,100
Answer:
Step-by-step explanation:
The Hudson family is saving for a
family vacation to Disney World.
They determine that the trip will
cost $3,200. Mr. and Mrs.
Hudson have already set aside
$1,500 for the trip. If they leave
in 16 weeks, then how much
will they need to save
each week?
Tinisha is planning a birthday party. She can buy:
10 balloons, 8 cupcakes, and 8 hats for $50
5 balloons, 9 cupcakes, and 7 hats for $46, or
12 balloons, 7 cupcakes, and 9 hats for $51
Using b for the number of balloons, c for the number of cupcakes, and h for
the number of hats, write a system of equations to represent this situation.
Answer:
b+c+h=50
Step-by-step explanation:
Its the first one because you need to have the same amount of hats as cupcakes cause the hat really stands for people.
Please assist me with this two column proof. Part 1A
Answer:
Answer is in the step by step explanation
Step-by-step explanation:
Since we are given parallel lines, we know <BCA is congruent to <DAC because of alternate interior angles
Then AC is congruent to AC, that's reflexive prop
Now we have SAS, so Tri. ABC cong to tri. CDA,
Then you're done
Answer:
Step-by-step explanation:
BC = AD Given
<BCA = <CAD Alternate interior angles of parallel lines cut by a transversal.
AC = AC That's the reflexive property. A line is equal to itself
Triangle BCA = Triangle CAD SAS
Notice that the angle is included inside the two lines that define it (the angle). That's a very important consideration when using SAS. SAA doesn't always work. You can draw exceptions. SAS has no exceptions. It always works.
Rhianna has a spinner, which is divided into four equal parts. The parts are numbered 1, 2, 3, and 4. If Rhianna spins the spinner and tosses a coin, which table shows all the possible outcomes? 4 1 H1 H H 2 H2 H2 3. H3 H3 H4 4. O T T 1 11 T1 2 T2 T2 3 T3 T3 T4 1 4 H T 2 T2 T2 3 H3 H3 H1 4 0 T 1 T1 H1 2 T2 H2 3 T3 H3 H4
Answer:
The bottom table.
Step-by-step explanation:
It's the only one that shows options for heads and tails for every number.
Answer:
D the last one
saniyah collected a total of 9 seashells she gave 1/3 to her sis how many seashells did Saniyah have left?
Answer: The answer is 3.
Step-by-step explanation: You would multiply 9x1/3 which would give you 3. If you want to understand even better here's how to do so: Put 3(the answer that you got from multiplying 9x1/3) into the fraction 1/3 as 1. In other words, it would look something like this 3/3. Then, just multiply the two numbers 3x3 and that equals 9, the number you started with.
Hope that this helped!!:)
Considering the provided information in the given question, we have :
Total seashells Saniyah have = 9Number of seashells Saniyah gave to her sister = [tex]\sf \dfrac{1}{3} [/tex] of total.We need to find how many seashells did Saniyah have left.
⇒ Number of seashells Saniyah have left = Total seashells – Number of seashells she gave to her sister
⇒ [tex] \sf {Left \: seashells = 9 - \Bigg \lgroup \dfrac{1}{3} \times 9 \Bigg \rgroup } [/tex]
⇒ [tex] \sf {Left \: seashells = 9 - \Bigg \lgroup 1 \times 3 \Bigg \rgroup } [/tex]
⇒ Left seashells = 9 – 3
⇒ Left seashells = 6
Therefore, Saniyah have left [tex] \bf {6 \: seashells } [/tex].
Which equation best represents the relationship
between x and y in the graph?
FOR BRAINLSIT!!
Answer:
I've never had to deal with this before but I would say C
Answer:
The best option is C ( y=(1/4) x +3)
betty closes the nozzle and fills it completely with a liquid. She then opens the nozzle. If the liquid drips at the rate of 14 cubic inches per minute, how long will it take for all the liquid in the nozzle to pass through(Use Pi = 3.14
Answer:
4.71 minutes
Step-by-step explanation:
Incomplete question [See comment for complete question]
Given
Shape: Cone
[tex]r = 3[/tex] -- radius
[tex]h = 7[/tex] --- height
[tex]Rate = 14in^3/min[/tex]
Required
Time to pass out all liquid
First, calculate the volume of the cone.
This is calculated as:
[tex]V = \frac{1}{3} \pi r^2h[/tex]
This gives:
[tex]V = \frac{1}{3} * 3.14 * 3^2 * 7[/tex]
[tex]V = \frac{1}{3} * 197.82[/tex]
[tex]V = 65.94in^3[/tex]
To calculate the time, we make use of the following rate formula.
[tex]Rate = \frac{Volume}{Time}[/tex]
Make Time the subject
[tex]Time= \frac{Volume}{Rate }[/tex]
This gives:
[tex]Time= \frac{65.94in^3}{14in^3/min}[/tex]
[tex]Time= \frac{65.94in^3}{14in^3}min[/tex]
Cancel out the units
[tex]Time= \frac{65.94}{14} min[/tex]
[tex]Time= 4.71 min\\[/tex]
Answer:
The time it will take for all the liquid to pass through is 4.71 minutes.
-Don't worry it's been already verified by myself .
Joe ran 3 miles yesterday and wants to run at least 15 miles this week. Write an inequality that can be used to determine the additional number of days Joe must run this week if each run is 3 miles. Then solve the inequality.
9514 1404 393
Answer:
3 +3d ≥ 15
d ≥ 4
Step-by-step explanation:
Since Joe runs 3 miles for each day he runs, the number of miles he runs in d days is 3d. That, added to the distance he has already run, will total the amount for the week. He wants that to be at least (greater than or equal to) 15 miles:
3 + 3d ≥ 15
__
We can divide by 3 to get ...
1 + d ≥ 5
d ≥ 4 . . . . . . . subtract 1
Joe must run at least 4 additional days this week to run at least 15 miles.
Scenario: The Cannon Instructions: View the video found on page 1 of this Journal activity. Using the information provided in the video, answer the questions below. Show your work for all calculations. The Cannon: Ernest's friend Nik is about to be shot out of a cannon. The path he will travel follows a parabolic arch that can be described by this polynomial. f(x) = –0.05(x2 – 26x – 120) He is supposed to land on a safety net 30 feet away. Does the function give you enough information to tell you where he will land? If so, how far from the cannon will he land?
Answer:
Part A
Yes
Part B
He will land at a point 30 meters from Cannon
Step-by-step explanation:
Part A
The given function that represent the path of the Cannon, which is the path of a parabolic arc, is presented as follows;
f(x) = -0.05·(x² - 26·x - 120)
We note that the height, 'h', of the path of a parabola at a horizontal distance, 'x' from the origin is equal to f(x)
Therefore, given that at the ground level, at the start and end of the flight, the f(x) = 0, we can write;
-0.05·(x² - 26·x - 120) = 0
∴ x² - 26·x - 120 = 0
x = (26 ± √((-26)² - 4 × 1 × (-120)))/(2 × 1)
Which gives;
x = 30 or x = -4
Therefore, he lands at a point 30 meters from the starting point
Therefore, the function gives enough information to tell where he will land
Part B
He lands at the point, x = 30 from the point the cannon was fired.
A sound wave with amplitude xo is measured by an observer to have an intensity of I0 when the observer is standing 4.0 meters from the source. Which best describes the amplitude of a sound wave and distance from the source where it will be measured with an intensity of 16Io?
Answer:
C) Increase the amplitude to 2xo and stand 2 meters from the source.
Step-by-step explanation:
Correct on Edge
A. 93
B. 57
C. 132
D. 123
Answer:
B
Step-by-step explanation:
The interior angles of a triangle always add up to 180 degrees.
We have two angles already and they add up to 60+63=123 degrees
180-123=57
so the remaining angle is 57 degrees
9514 1404 393
Answer:
D. 123°
Step-by-step explanation:
The external angle is equal to the sum of the remote internal angles.
m∠1 = 60° +63°
m∠1 = 123°
20 POINTS!!!!!!!The monthly salary of an employee with 33 hours of training can be written as
D-Salary(33) or S(33)
D is correct hope this helps
2 x - 3 / 5 = - 1 / 10
Answer:
1/4
Step-by-step explanation:
2x=-1/10 + 3/5
2x=1/2
x=1/4
A cylinder has a volume of 308 cubic inches and a height of 8 inches.What is the radius of the cylinder?Usr 3.14 for pie round to the nearest tenth of a unit
Answer: 3.5 inches
Step-by-step explanation:
Johnson Electronics makes calculators. Consumer satisfaction is one of the top
priorities of the company’s management. The company guarantees the refund of
money or a replacement for any calculator that malfunctions within two years from
the date of purchase. It is known from past data that despite all efforts, 12% of the
calculators manufactured by this company malfunction within a 2-year period. The
company recently mailed 550 such calculators to its customers.
a. Find the probability that exactly 32 of the 550 calculators will be returned for
refund or replacement within a 2-year period.
b. What is the probability that 30 or more of the 550 calculators will be returned for
refund or replacement within a 2-year period?
a. What is the probability that 15 to 35 of the 550 calculators will be returned for
refund or replacement within a 2-year period?
Answer:
later ill answer this .. read and understand
At the candy store, Sophie filled a bag with 2 2/3 kilograms of candy. 1/4 of the weight of the candy was from chocolate covered pretzels. How much did the chocolate covered pretzels in Sophie's bag weigh?
Answer:
The chocolate covered pretzels in Sophie's bag weighed [tex]\frac{2}{3} = 0.6667[/tex] kilograms.
Step-by-step explanation:
Sophie filled a bag with 2 2/3 kilograms of candy.
This means that the total weight is of:
[tex]2\frac{2}{3} = 2 + \frac{2}{3} = \frac{6}{3} + \frac{2}{3} = \frac{8}{3}[/tex]
The total weight is of 8/3 kilograms.
1/4 of the weight of the candy was from chocolate covered pretzels. How much did the chocolate covered pretzels in Sophie's bag weigh?
1/4 of 8/3. So
[tex]\frac{1}{4} \times \frac{8}{3} = \frac{1*8}{4*3} = \frac{2}{3} = 0.6667[/tex]
The chocolate covered pretzels in Sophie's bag weighed [tex]\frac{2}{3} = 0.6667[/tex] kilograms.
Victor drew trapezoid PQRS on a
coordinate plane. The coordinates of each
vertex are:
P(8,4) Q(10, 4) R(13, -1) S(8, -1)
tion
What is the length, in units, of side PS?
A. 2
B. 3
C. 4
D. 5
Answer:
Step-by-step explanation:
b
Answer:
b hope it helps make brainlliest ty
Step-by-step explanation:
can you make me brainlliest
Check the pic
please explain
Answer:
Option C
Step-by-step explanation:
From the picture attached,
In ΔABC,
m∠BAC + y° = 180° [Linear pair of angles are supplementary]
m∠BAC = 180° - y°
m∠ABC = x° [Vertically opposite angles]
m∠ACB = z° [Vertically opposite angles]
By triangle sum theorem,
m∠BAC + m∠ABC + m∠ACB = 180°
(180 - y)° + x° + z° = 180°
x - y + z = 180 - 180
x - y + z = 0
Option C will be the answer.
Choose the equation where b=6 is a solution. 11- b = 6 b + 4 = 9 8b = 48 63 b = 9
Answer:
8b = 48
Step-by-step explanation:
this is because you would substitute the b for the 6 and then multiply straight across giving you a total of 48.
Answer:
8b = 48
Step-by-step explanation:
8 x 6 = 48
20 POINTS HELP!!
What value of x and y make the polygon below a parallelogram
Answer:
Step-by-step explanation:
3x = 12
x=4
x+y =5y
4+y = 5y
4 = 4y
1=y
Answer:
x-5 = y
72 -5 = 67
y=67
x = 72
Step-by-step explanation:
In a parallelogram, the diagonals bisect each other.
That being the case,
6x = 72
x = 12 In a parallelogram, the diagonals bisect each other.
That being the case,
6x = 72
x = 12 and the diagonals measure
144 and 134
i hope this helps!! ^_^
