Answer:
a) The 99% confidence interval on the proportion of aircraft that have such wiring errors is (0.0005, 0.0095).
b) A sample of 408 is required.
c) A sample of 20465 is required.
Step-by-step explanation:
Question a:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
Of 1600 randomly selected aircraft, eight were found to have wiring errors that could display incorrect information to the flight crew.
This means that [tex]n = 1600, \pi = \frac{8}{1600} = 0.005[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.005 - 2.575\sqrt{\frac{0.005*0.995}{1600}} = 0.0005[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.005 + 2.575\sqrt{\frac{0.005*0.995}{1600}} = 0.0095[/tex]
The 99% confidence interval on the proportion of aircraft that have such wiring errors is (0.0005, 0.0095).
b. Suppose we use the information in this example to provide a preliminary estimate of p. How large a sample would be required to produce an estimate of p that we are 99% confident differs from the true value by at most 0.009?
The margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
A sample of n is required, and n is found for M = 0.009. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.009 = 2.575\sqrt{\frac{0.005*0.995}{n}}[/tex]
[tex]0.009\sqrt{n} = 2.575\sqrt{0.005*0.995}[/tex]
[tex]\sqrt{n} = \frac{2.575\sqrt{0.005*0.995}}{0.009}[/tex]
[tex](\sqrt{n})^2 = (\frac{2.575\sqrt{0.005*0.995}}{0.009})^2[/tex]
[tex]n = 407.3[/tex]
Rounding up:
A sample of 408 is required.
c. Suppose we did not have a preliminary estimate of p. How large a sample would be required if we wanted to be at least 99% confident that the sample proportion differs from the true proportion by at most 0.009 regardless of the true value of p?
Since we have no estimate, we use [tex]\pi = 0.5[/tex]
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.009 = 2.575\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.009\sqrt{n} = 2.575*0.5[/tex]
[tex]\sqrt{n} = \frac{2.575*0.5}{0.009}[/tex]
[tex](\sqrt{n})^2 = (\frac{2.575*0.5}{0.009})^2[/tex]
[tex]n = 20464.9[/tex]
Rounding up:
A sample of 20465 is required.
A graphic designer creates a logo in the shape of an ellipse. The equation x^2/64 + y^2/14.44 = 1, with units in centimeters,
represents the outer edge of the logo. How tall is the logo?
a. 3.8 cm
b. 7.6 cm
c. 8 cm
d. 16 cm
Using the equation of ellipse, the height of the logo is 7.6cm
What is equation for ellipse?The equation of ellipse having a center (h, k) is given as;
[tex]\frac{(x - h)^2}{a^2} + \frac{(y - k)^2}{b^2} = 1[/tex]
where a is the semi-major axis and b is the semi-minor axis. The major axis is the longer of the two axes, and the minor axis is the shorter of the two axes. The center of the ellipse is the point (h, k).
The graph of an ellipse is a closed curve that is similar to a circle, but it is not a circle. The ellipse is wider than it is tall if a > b, and it is taller than it is wide if a < b.
In the given problem;
The equation for an ellipse is
[tex]\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1,[/tex] where a is the semi-major axis and b is the semi-minor axis. In this case, a = √64 = 8 and b = √14.44 = 3.8
Since b = 3.8, the height of the logo = 2b = 2 * 3.8 = 7.6cm
Learn more on equation of ellipse here;
https://brainly.com/question/30995389
#SPJ1
You come across a box of perfume what should you do Amazon
(Algebra 2) help me please:( no links I will report please help me out )!!!
Answer:
The answer should be $57000(1.025)²⁰ = $93,401
Step-by-step explanation:
Two circles are concentric. Two arcs are formed by the same central angle, with arc lengths of 54 and 81 respectively. Which of the following are possible radii for the circles? Select the two correct answers.
23 and 32
12 and 18
32 and 64
40 and 60
14 and 41
Answer:
i think the answer is 12 and 18
Find the measure of x.
SOMEONE PLEASE HELP
Which of the following is TRUE?
A. 8<-7
B -1 > 1
C. 6> 3
D. 4 <-2
9514 1404 393
Answer:
C. 6 > 3
Step-by-step explanation:
It is true that 6 is greater than 3.
__
All negative numbers are less than any positive numbers.
We hope you are sufficiently familiar with numbers and counting to be able to tell which positive numbers are more or less than any other positive number.
Please help I would be really happy:)
To compute the necessary sample size for an interval estimate of a population proportion, all of the following procedures are recommended when p is unknown except :____________
a. use the sample proportion from a previous study.
b. use the sample proportion from a preliminary sample.
c. use 1.0 as an estimate.
d. use judgment or a best guess.
Answer:
c- use 1.0 as an estimate
Step-by-step explanation:
Factorise: x^2/y^2+1+y^2/X^2
Answer:
[tex]( \frac{x}{y} + \frac{y}{x} + 1)( \frac{x}{y} + \frac{y}{x} - 1)[/tex]Step-by-step explanation:
Hope it is helpful.....
Use substitution. What is the solution to the system of equations? Use the drop-down menus to explain your answer.
y = 12x + 2
2y = x + 4
choose
The system of equations has no solution,infinitely many solutions, one solution The two equations represent parallel lines, the same lines, intersecting lines.
Answer:
The system of equations has one solution. The two equations are intersecting lines.
Step-by-step explanation:
if you want to use the substitution method, you would have to plug in y for 12x+2 in the second equation.
2(12x+2)=x+4
next, you have to distribute
24x+4=x+4
subtract 24x from each side
4=-23x+4
subtract 4 from each side
0=23x
divide each side by 23
x=0
now, plug in 0 to one equation.
y=12(0)+2
y=2
the lines intersect at one point, (0,2)
Determine the radius of a cone that has a volume of 230 ft' and a height of 15 ft.
Round the answer to the nearest tenth.
Answer:
the formula for finding cone volume is V=πr²× 1/3
Step-by-step explanation:
230=3.14×x²×1/3
we have to solve for X that is our radius
14.8
Using property simplify 472x96+472x4
Answer:
183136 is the correct answer
What is the value of the expression 1/7 divided by 5 ?
Answer:
It would be 1/35.
Step-by-step explanation:
You turn 5 into 1/5 and then multiply 1/7 with 1/5, which is 1/35.
The value of the expression 1/7 divided by 5 is,
⇒ 1 / 35
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
We have to given that;
The expression is,
⇒ 1/7 divided by 5
Now, We can simplify as;
⇒ 1/7 divided by 5
⇒ 1 / 7 ÷ 5
⇒ 1 / 7×5
⇒ 1 / 35
Thus, The value of the expression 1/7 divided by 5 is,
⇒ 1 / 35
Learn more about the divide visit:
https://brainly.com/question/28119824
#SPJ3
It takes 3 pieces of wood to make a bird house. Marina has 21 pleces of wood. She uses this problem to find out how many bird houses she can
make.
21 +3
Which other problem could Marina use to find the number of bird houses she can make
She can find out answer by dividing 21÷3 and the answer is 7
She can make 7 bird house
7 is the answer of the question
21÷ 3
=7
Step-by-step explanation:
hope it is helpful to you
a. Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases.
b. Eliminate the parameter to find a Cartesian equation of the curve.
x=1 + 3t, y= 2-t^2
Answer:
y = 2 - ( x - 1)²/9
Step-by-step explanation: See Annex
As the parameter t increases, the value of x increases and the value of y decreases, we get the figure of the annex ( the arrow in the Annex indicates the way of the curve with t increasing.
b) to eliminate the parameter:
x = 1 + 3*t (1) y = 2 - t² (2)
Then from equation (1) t = ( x - 1 ) / 3
plugging that value in equation (2)
y = 2 - [ ( x - 1 ) / 3 ]²
y = 2 - ( x² + 1 - 2*x)/9
9*y = 18 - x² + 1 - 2*x or y = 2 - ( x - 1)²/9
The curve is a parabol
The final exam grade distribution for all students in the introductory statistics class at a local community college is displayed in the table, with A = 4, B = 3, C = 2, D = 1, and F = 0. Let X represent the grade for a randomly selected student from the class.
What is the standard deviation of the distribution?
A) 1.16
B) 1.08
C) 1.41
D) 2.98
The standard deviation of the distribution is 1.08.
Option B is the correct answer.
What is a standard deviation?The standard deviation measures how spread out the data is from the mean, and it is a measure of the average distance of the data points from the mean.
We have,
To find the standard deviation of the distribution, we first need to calculate the expected value (mean) of X.
The expected value of X is:
E(X) = (4)(0.4) + (3)(0.32) + (2)(0.17) + (1)(0.08) + (0)(0.03)
= 1.6 + 0.96 + 0.34 + 0.08 + 0
= 2.98
Next, we need to calculate the variance of X:
Var(X) = (4 - 2.98)²(0.4) + (3 - 2.98)²(0.32)
+ (2 - 2.98)²(0.17) + (1 - 2.98)²(0.08) + (0 - 2.98)²(0.03)
= 0.64(0.4) + 0.0004(0.32) + 0.7921(0.17) + 5.4084(0.08) + 8.6404(0.03)
= 0.256 + 0.000128 + 0.134257 + 0.432672 + 0.259212
= 1.082
The standard deviation of X is the square root of the variance:
So,
SD(X) = √(Var(X))
= √(1.082)
= 1.04 (approximately)
Thus,
The standard deviation of the distribution is 1.08.
Learn more about standard deviation here:
brainly.com/question/23907081
#SPJ7
Use a ratio box to solve this problem. The price of one model of car increased 10 percent in one year. If the price this year is $17,600,
what was the price last year
Answer:
$15,840
Step-by-step explanation:
10% of 17600 = 1760
17600 - 1760 = 15840
a boy is 20 years old at present. How old was he 3 years ago?
Answer: seven-teen
Step-by-step explanation:twenty minus three
The age of the boy three years ago is A = 17 years
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
The present age of the boy = 20 years
Three years ago, the boy's age would have been:
20 - 3 = 17
Hence , the boy was 17 years old three years ago.
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ2
MATH MATH MATH MATHHHHHHHHHHHHHH
Answer:
1. Obtuse angle
2. 5
3. 117
Step-by-step explanation:
1. Any angle that is wider than 90 degrees is obtuse.
2. 180 = straight angle so, 180-140=40 8x5=40 so x=5
3. Supplementary angles are one angle that is 180 so, 180-63= 117
Probability distribution
Answer:
a) The value of q is 0.2.
b) E(X) = 1.85.
Step-by-step explanation:
Question a:
The sum of all the probabilities must be 1. So
[tex]0.3 + x + 0.1 + 0.15 + 0.25 = 1[/tex]
[tex]x + 0.8 = 1[/tex]
[tex]x = 0.2[/tex]
The value of q is 0.2.
Question b:
Multiplication of each value of x by its probability. So
[tex]E(X) = 0*0.3 + 1*0.2 + 2*0.1 + 3*0.15 + 4*0.25 = 1.85[/tex]
So the answer is E(X) = 1.85.
the parent cosine function is transformed to create the function m(x) =-2cos(x+π). which graphed function has the same amplitude as function m
Answer: Graph D
Step-by-step explanation: Got it right on plato
The graph of a function with the same amplitude as m(x) is graph D.
Which graphed function has the same amplitude as m(x)?
The general cosine function is written as:
f(x) = A*cos(kx) + M
Where A is the amplitude, k is the angular frequency, and M is the midline.
In our case:
m(x) = -2*cos(x+π).
The amplitude is -2, which means that the distance between a peak and a trough must be twice the absolute value of the amplitude:
2*|-2| = 4
With this in mind, the only graph that meets this requirement is the graph D.
If you want to learn more about cosine functions, you can read:
https://brainly.com/question/7872492
sum of two numbers is 5 while the difference of the two numbers is 6 find the two numbers
Answer:
Suppose the one number be x
And the other number be 6x
The sum of two numbers is 5
x+6x=5
7x=5
X=5/7
Therefore
One number be 5/7
And other number be 6 * 5/7=30/7
If you are helped with my answer pls tag me brianliest I really want it
THANK YOU...............
What is the measure of angle AXG
Answer:
180°
Step-by-step explanation:
it's half of a circle
The angle AXG is a straight line. The measure of a straight line would be 180
The measure is 180
Does this graph below represent a function? (Yes or no)
Answer:yes
Step-by-step explanation: it represents a function
539,904 nearest 10 for my homwork
Answer:
539,900 if thats what you're looking for.
Step-by-step explanation:
Answer:
539900
Step-by-step explanation:
what is the sum of the first 10 terms of the geometric sequence 1 , -2, 4, -8, 16, 32...
Answer:
S10= -341
Step-by-step explanation:
1,-2,4,-8,16,.......
Sum of first 10 terms of geometric sequence
Sn=a(r^n-1)/r-1
where, a= first term
n= number of terms
r=common ratio
common ratio (r)= second term/first term
r=-2/1
r=-2
a=first term
a=1
n= number of terms
n=10
S10=1[(-2)^10-1]/-2-1
S10=(1024-1)/-3
S10=1023/-3
S10= -341
therefore, the sum of the first 10 terms is -342
can someone help me pls
Answer:
[tex]x = 55°[/tex]
Step-by-step explanation:
L1 and L2 are parallel, so that the 2 interior angles are equal to 180°.
[tex](2x + 10) + (x + 5) = 180° \\ 2x + x + 10 + 5 = 180° \\ 3x = 165° \\ x = 55°[/tex]
Easton is deciding between two landscaping companies for his place of business.
Company A charges $25 per hour and a $150 equipment fee. Com piny B charges $35
per hour and a $100 equipment fee. Let A represent the amount Company A would
charge for t hours of landscaping, and let B represent the amount Company B would
charge fort hours of landscaping. Write an equation for each situation, in terms oft,
and determine the number hours, t, that would make the cost of each company the
same.
Answer:
i. A = $25 t + $150
ii. B = $35 t + $100
iii. Number of hours = 5
Step-by-step explanation:
For company A:
A = $25 t + $150
where A is the amount charged and t is the number of hours of landscaping.
For company B:
B = $35 t + $100
where B is the amount charged and t is the number of hours of landscaping.
When the time is 5 hours, then:
i. A = $25 t + $150
= $25 (5) + $150
= $125 + $150
A = $275
ii. B = $35 t + $100
= $35(5) + $100
= $175 + $100
B = $275
Therefore, the number of hours that would make the cost of each company to be the same is 5 hours.
thor peeled 14 oranges every 21 hours. at this rate, how many would he peel in 9 hours?
Answer:
13.5
Step-by-step explanation:
14 oranges in 21 hour translates to:
3/2 oranges per hour.
So, in 9 hours thor can peel 13.5 oranges.
What is the missing number in the synthetic division problem below?
A. 9
B. 8
C. -7
D. 2