The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation. Recently, Southwest Air had the best rate with 80 % of its flights arriving on time. A test is conducted by randomly selecting 15 Southwest flights and observing whether they arrive on time. (a) Find the probability that at least 2 flights arrive late.
Answers
Answer:
83.29% probability that at least 2 flights arrive late.
Step-by-step explanation:
For each flight, there are only two possible outcomes. Either they arrive late, or they do not. The probability of a flight arriving late is independent of other flights. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
And p is the probability of X happening.
80 % of its flights arriving on time.
This means that 100-80 = 20% arrive late, so \(p = 0.2\)
A test is conducted by randomly selecting 15 Southwest flights and observing whether they arrive on time.
This means that \(n = 15\)
Find the probability that at least 2 flights arrive late.
Either less than 2 arrive late, or at least 2 does. The sum of the probabilities of these events is decimal 1. So
\(P(X < 2) + P(X \geq 2) = 1\)
We want \(P(X \geq 2)\). Then
\(P(X \geq 2) = 1 - P(X < 2)\)
In which
\(P(X = 2) = P(X = 0) + P(X = 1)\)
So
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(P(X = 0) = C_{15,0}.(0.2)^{0}.(0.8)^{15} = 0.0352\)
\(P(X = 1) = C_{15,1}.(0.2)^{1}.(0.8)^{14} = 0.1319\)
\(P(X = 2) = P(X = 0) + P(X = 1) = 0.0352 + 0.1319 = 0.1671\)
\(P(X \geq 2) = 1 - P(X < 2) = 1 - 0.1671 = 0.8329\)
83.29% probability that at least 2 flights arrive late.
Related Questions
I have 28 seats in each row and 500 people plan to show up... How many rows will I have?
Answers
If we have 500 people, and all of them must take a seat, and in each row, we have 28 seats, then we need to divide the total of people by the total of seats by row. Then, we have the total number for rows:
\(R=\frac{500}{28}\Rightarrow R=17.8571\approx R=18\)Therefore, we will have 18 rows (of 28 seats each) to have the 500 people seated.
If we check the answer:
18 * 28 seats = 504 seats (we will have four more seats for people to get seated).
Jai: IITs are producing great engineers, who ultimately end up benefiting science and technology in India, but more important is the fact that they are greatly improving the image of India in the west Vijay: No, you're mistaken. Producing great engineers who benefit science and technology in India is the most important function of IITs. Without IITs, most of our software industry wouldn't have existed.
Answers
No, what they said is not fact.
The statement "producing great engineers who benefit science and technology in India is the most important function of IITs" and "IITs are greatly improving the image of India in the West" are both important functions of IITs, and the priority of these functions may depend on individual perspectives and goals.
Some people might argue that producing engineers is more crucial for the development of India's technology and economy, while others might argue that improving the image of India in the West is equally important for increasing its global recognition and competitiveness. Both functions play important roles and it is a matter of perspective which one is considered more important.
Correct Question :
Jai: IITs are producing great engineers, who ultimately end up benefiting science and technology in India, but more important is the fact that they are greatly improving the image of India in the west
Vijay: No, you're mistaken. Producing great engineers who benefit science and technology in India is the most important function of IITs. Without IITs, most of our software industry wouldn't have existed.
What they said is fact or not? Explain.
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Question 3
A group of 5 people went to the movies and spent $44 on food and drink. The total amount spent, including
tickets, was $98.50.
What was the price, in dollars, of one ticket?
Answers
Answer:
One ticket cost $10.90.
Step-by-step explanation:
The total spent was $98.50--food, drinks, admission--everything.
$44.00 was for food and drinks.
We can take the 44 away from the total.
98.50 - 44.00
= 54.50
They spent 54.50 on 5 tickets to get in. Divide to find the cost of one tickets. This assumes that all 5 tickets were the same price.
54.50 ÷ 5 = 10.90
The price of one ticket was $10.90
To make this look like algebra class...
let x = the price of one ticket
5x = the price of 5 tickets
5x + 44 = 98.50
subtract 44
5x = 54.50
divide by 5
x = 10.90
A parent teacher organization has six teachers and seven parents. How many four person committees can be formed if two people must be teachers and two people must be parents?
Answers
Answer
315 four-person committees can be formed if two people must be teachers and two people must be parents
Explanation
The number of teachers = 6
The number of parents = 7
The number of required teachers to be formed = 2
The number of required parents to be formed = 2
The number of four-person committees that can be formed =
⁶C₂ x ⁷C₂ = 15 x 21 = 315
∴ 315 four-person committees can be formed if two people must be teachers and two people must be parents
In a survey, the planning value for the population proportion is p*= 0.25. How large a sample should be taken to provide a 95% confidence interval with a margin of error of 0.06? Round your answer up to the next
whole number.
Answers
The sample should be taken to provide a 95% confidence interval is 200.
What is a confidence interval?A confidence interval is made up of the mean of your estimate plus and minus the estimate's range. This is the range of values you expect your estimate to fall within if you repeat the test, within a given level of confidence.
Confidence is another name for probability in statistics.
Given the planning value for the population proportion,
probability, p = 0.25
q = 1 - p = 1 - 0.25
q = 0.75
margin of error = E = 0.06
value of z at 95% confidence interval is 1.96,
the formula for a sample is,
n = (z/E)²pq
n = (1.96/0.06)²*0.25*0.75
n = 200.08
n = 200 approx
Hence sample size is 200.
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2 1/6* 2 5/6 IN SIMPLEST FORM
Answers
Answer:
6 5/36
Step-by-step explanation:
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the equation below represents the total price of Michigan State University per semester where c represents the number of classes and t represents the total cost for the semester including a one time fee for room and board
Answers
The equation that represents the total price of Michigan State University per semester is determined by the number of classes taken (c) and the total cost for the semester, which includes a one-time fee for room and board (t).
The equation captures the relationship between these variables and calculates the overall cost for a student attending the university. It is important to note that the equation provides a quantitative representation and does not take into account other factors such as scholarships, financial aid, or additional expenses. Therefore, the equation serves as a useful tool for estimating the total cost of attending Michigan State University, allowing students and their families to plan and budget accordingly for their education.For such more question on equation
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can someone help me please
Answers
Answer:
a) 1.2 seconds
b) 50 bpm
Step-by-step explanation:
a)The period is the value of t that makes the angle be 2π:
5πt/3 = 2π
t = 3(2π)/(5π) = 6/5
The period of the function is 6/5 = 1.2 seconds.
__
b)The number of beats per minute is ...
(1 beat)/(1.2 s) × (60 s)/(1 min) = 60/1.2 beats/min = 50 beats/min
2
Let g(x) = x + 4x-7.
What is g(x) in graphing form?
(x + 2) - 7 = 4
O g(x) = (x + 2)²-7
Onone of the answer choices
x² + 4x-7=0
O g(x) = (x + 2)² - 11
Answers
The graphing form of the function g(x) is: C) none of the answer choices.
The function g(x) = \(x^2 + 4x - 7\)is already in the standard form of a quadratic equation. In graphing form, a quadratic equation can be represented as y =\(ax^2 + bx + c,\) where a, b, and c are constants.
Comparing the given function g(x) =\(x^2 + 4x - 7\)with the standard form, we can identify the coefficients:
a = 1 (coefficient of x^2)
b = 4 (coefficient of x)
c = -7 (constant term)
Therefore, the graphing form of the function g(x) is:
C) none of the answer choices
None of the given answer choices (A, B, D, or E) accurately represents the graphing form of the function g(x) =\(x^2 + 4x - 7\). The function is already in the correct form, and there is no equivalent transformation provided in the answer choices. The given options either represent different equations or incorrect transformations of the original function.
In graphing form, the equation y = \(x^2 + 4x - 7\) represents a parabolic curve. The coefficient a determines the concavity of the curve, where a positive value (in this case, 1) indicates an upward-opening parabola.
The coefficients b and c affect the position of the vertex and the intercepts of the curve. To graph the function, one can plot points or use techniques such as completing the square or the quadratic formula to find the vertex and intercepts. Option C
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Write 27% as a fraction
Answers
Answer:
Step-by-step explanation:
27 is converted to 27/100 to change it to a fraction.
Answer:
27%=27/100
Step-by-step explanation:
27% in fraction 27/100
17. Brendan works as a car salesman. He earns a salary of $1,000 per month, plus a commission of 3% on all sales. If he sold $250,000 worth of cars in May, what would his total earning be for the
month?
Answers
Answer:
His total earning for the month would be $8,500.
Step-by-step explanation:
In order to calculate the total earnings for the month, you have to find the 3% of the amount of the sales and add the monthly salary:
Monthly earnings=($250,000*3%)+$1,000
Monthly earnings=$7,500+$1,000
Monthly earnings=$8,500
According to this, the answer is that his total earning for the month would be $8,500.
Answer:
The Answer Is $8,500
Step-by-step explanation:
I just took the test
Determine each percentage by writing a proportion. Round to the nearest tenth if necessary.
What % of 6 is 5?
Answers
Answer:
Rounded: 83%
Step-by-step explanation:
5 ÷ 6 = 0.83 (3 repeating)
= 83%
Please mark me Brainliest :)
Answer:
83.3
Step-by-step explanation:
Set up your proportion. 5x100=500. 500/6= 83.3.
8. Higher Order Thinking In the diagram, m/1 = (125-y),
m2 = 24°, and m/3 = (x + 46)°. Solve for x and y and find
m21 and m23. Explain how you found the measure
of each angle and the value of each variable.
Answers
The measure of x and y of the angles are x = 20° and y = 35°
What are the angles formed by 2 intersecting lines?Two straight lines that intersect at the same location are said to be intersecting lines. The junction point is the place where two intersecting lines meet. Four angles are created when two lines cross. The four angles added together always equal 360 degrees.
Perpendicular lines are two straight lines that intersect and form right angles. When two perpendicular lines intersect, they form four right angles.
When lines intersect, two angle relationships are formed:
Opposite angles are congruent
Adjacent angles are supplementary
Given data ,
Let the measure of the first angle be m₁ = ( 125 - y )°
Let the measure of second angle m₂ = 24°
Let the measure of third angle m₃ = ( x + 46 )°
Now , from the diagram , m₁ = 90°
So , the measure of m₁ = ( 125 - y )° = 90°
On simplifying , we get
Adding y on both sides , we get
125 = 90 + y
Subtracting 90 on both sides , we get
y = 35°
Now , m₁ + m₂ + m₃ = 180° ( angles on a straight line )
So , 90° + 24° + ( x + 46 )° = 180°
x + 46 = 66
Subtracting 46 on both sides , we get
x = 20°
So , the measure of ₃ = 66°
Hence , the measures of angles are solved
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The tables represent the points earned in each game for a season by two football teams.
Panthers
14 10 10
10 17 3
28 13 17
32 16 10
14 7 21
Cowboys
10 3 8
6 24 12
21 3 10
28 28 7
7 13 3
Which team had the best overall record for the season? Determine the best measure of center to compare and explain your answer.
Panthers; they have a larger median value of 14 points
Cowboys; they have a larger median value of 10 points
Panthers; they have a larger mean value of about 14.8 points
Cowboys; they have a larger mean value of about 12.2 points
Answers
Answer:
Therefore, the Panthers had a better overall record for the season, with a total of 212 points earned compared to the Cowboys' total of 173 points.
Step-by-step explanation:
To compare the measures of center, we can calculate the mean and median points earned by each team:
Panthers: Mean = 212/15 = 14.13 points, Median = 14 points
Cowboys: Mean = 173/15 = 11.53 points, Median = 10 points
Based on these calculations, we can see that the Panthers have a larger mean value of about 14.13 points compared to the Cowboys' mean value of about 11.53 points. However, the median value for both teams is less useful for comparison since they are only one point apart. Therefore, we can conclude that the Panthers had the better overall record for the season based on both the total points earned and their larger mean value.
So, the answer is Panthers; they have a larger mean value of about 14.8 points (Option C is incorrect as the mean value of Panthers is approximately 14.13 and not 14.8).
Select the points that are solutions to the system of inequalities. Select all that apply. A(–2, 0)B (0, 10)C(–10, 10)D(1, 2)
Answers
Answer:
b and c
Step-by-step explanation:
i took the test
Which property can be used to show that if 3a = 4b, then 4b = 3a?
Multiple choice question.
A)
Symmetric Property of Equality
B)
Reflexive Property of Equality
C)
Substitution Property of Equality
D)
Transitive Property of Equality
Answers
Answer:
Hello your answer should be A symmetric property
Step-by-step explanation:
hope this helps
Symmetric property of equality to show that 3a = 4b, then 4b = 3a?
What is symmetric property of equality?The symmetric property of equality is a simple property that says we can interchange the sides of an equation without changing the truth-value of the equation. That is, if a = b, then b = a. Each side of the equation can be thought of as the mirror image of the other
We have the following information available from the question is:
We have to determine the which property can be used to show that if 3a = 4b, then 4b = 3a
Now, According to the question:
3a = 4b
4b = 3a (both are equal)
This property is used to simplify the equations, to reverse the equations, and also for proofs in numerical and non-numerical logic.
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A man is 4 times as old as his son. In 5 years time he will be 3 times as old as his son. What is the present age of the son in years.
Answers
Answer: 40 years old.
Step-by-step explanation:
Let man's age = a
Let son's age = b
Since a man is 4 times as old as his son, therefore
a= 4b
In 5 years, he will only be 3 times as old as his son, therefore
a+5=3(b+5)
Apply substitution method :
4b+5=3b+15
b=10
a=40
Danielle poured 3/4 gallon of water from a 7/8 gallon bucket.How much water is left in the bucket?
Answers
Answer:
1/8
Step-by-step explanation:
3/4 = 6/8 after you multiply top and bottom by 2
Subtract 3/4 from 7/8 and we get
7/8 - 3/4 = 7/8 - 6/8 = (7-6)/8 = 1/8
There is 1/8 of a gallon left
Kellen is having friends over for dinner and needs to buy chicken. He is looking for the best deal. There are three package options for the chicken.
3 lbs. for $15.39
2 lbs. for $9.19
1 lb. for $7.05
Answers
Answer:
But the 2lbs.
Step-by-step explanation:
Divide $9.19 by 2 and you get 4.595 which would be the cheapest option out of the 3 because the 1lb is $7.05 and the 3lb is $5.13.
You're welcome.
HELP ASAP!!!
Which of the following statements are true? Chose the two correct answers.
A.
The seal is a carnivore.
B.
The polar bear is an herbivore.
C.
The fish are producers.
D.
The polar bear is a top predator.
E.
The seal is an herbivore.
Answers
Answer below
Brainliest
Answers
Answer:
25 remainder of 4
Step-by-step explanation:
Answer:
here hope this will be you ^^"
▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃
3.55. Постройте график линейной функции:
1) у = 2/3х – 4;
2) y = 2x + 6;
3) у = -1,5х – 3;
4) y = -1/2x + 1;
5) y = 5/3x - 2;
6) y = -4/3x + 2;
Answers
Answer:
4) y = -1/2x + 1;
Step-by-step explanation:
maybe
or maybe not
tosta las siguientes preguntas
a) ¿Qué fracción de la barra completa me quiere regalar Memo?
b) ¿Qué fracción de la barra completa me regalaria si decide darme solo la tercera parte de lo que tiene
c) ¿Qué fracción seria si decide darme 275 partes de lo que le queda?
do queremos calcular ura fracción de una fracción, en realidad se traduce en una multiplicacion
one
La cuarta parte de la mitad
Answers
Question The population of North Dakota was about 672,000 in 2010. The population is projected to be about 630,000 in 2020. Find the percent decrease of the population of North Dakota. (Round to the nearest tenth of a percent.)
Answers
Answer: 6.25%
Step-by-step explanation:
Percent Decrease = ( ( Starting Value - Final Value ) / Starting Value ) * 100
So 672,000-630000 = 42,000
42,000 / 672,00 = 0.0625
Finally multiply by 100 soooooo 0.0625 * 100 = 6.25%
206) A recipe for cupcakes calls for 3-
3
10
200
7
sugar. Julio accidentally put in 4-
10
How many extra cups did he put in?
cups of
cups.
Answers
Julio accidentally put in an extra 1/10 cup of sugar.
To calculate the number of extra cups of sugar that Julio put in, we need to find the difference between what the recipe called for (3/10 cups) and what he actually added (4/10 cups).
The difference can be calculated as follows:
Actual amount - Required amount = Extra amount
= 4/10 - 3/10
= 1/10
Therefore, Julio accidentally put in an extra 1/10 cup of sugar.
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From the figure which is greater between a and Q
Answers
Answer:
a
Step-by-step explanation:
the horizontal distance is shorter so the angle will be greater.
added:
tan a = AD/2a
tan Q - AD/3a
Just looking at the fractions AD/2a and AD/3a, the denominator of AD/2a is smaller so the resulting calculation will be greater, hence a is the larger angle.
Simplify the expression.
4f8 +39) + 5g
Answers
Answer:4f^8+5g+39
Step-by-step explanation:
Help. This is graded lol. Also due in 1 hour soooooo pls go quick. Also explain, since I actually wanna know how to do this.
40 POINTS ON THE LINE (idk if that's a lot)
Answers
1. 47
2. 119
3. 97
4. 62
explanation:
1. 180-133= 47
2. they’re vertical angles, so they’re equal
3. 180-83= 97
4. set the two expressions equal to each other and solve
8x-34 = 5x+2
x= 12
plug in 12 for x
5(12)+2
to get
62
Answer:
\(m\angle1 =47^o\)
\(m\angle2 =119^o\)
\(m\angle ABC =97^o\)
\(m \angle FED = 62^o\)
Step-by-step explanation:
angle 1 and the angle 133 degrees are supplementary angles, then added should give 180 degrees.
angle1 + 133 = 180 then angle1 = 180-133 = 47 degrees
\(m\angle1 = 180^o - 133^o=47^o\)
Angle 2 is of the same measure as the angle marked as 119 degrees since they are what is called "corresponding angles between parallel lines."
Angle ABC plus angle that measures 83 degrees should add to 180 since their sum gives a straight line, then:
ABC + 83 = 180
ABC = 180 - 83 = 97 degrees
Last image:
The two angles with algebraic denomination should be equal because they are alternate internal angles, Then this equality can be written as:
8 x - 34 = 5 x + 2
solve for x by subtracting 5 x from both sides:
3 x - 34 = 2
add 34 to both sides:
3 x = 2 + 34
3 x = 36
x = 36/3
x = 12
and now knowing x we can find angle DEF
DEF = 5 x + 2 = 5 (12) + 2 = 60 + 2 = 62 degrees
Pythagorean triples are given by these formulas:
(2²-37, 2zy, z²+37²)
The hypotenuse of a right triangle is 29. The lengths of the legs are whole numbers. List your answers in increasing
order.
The lengths of the two legs are
and
Answers
The lengths of the two legs of the right triangle are 58 and 839, in increasing order.
We have,
The formula given is incorrect.
The correct formula for Pythagorean triples with a given integer z is:
(z² - 1², 2z, z² + 1²)
Using this formula, we can find the two legs of the right triangle with hypotenuse 29 as follows:
z² + 1² = 29²
z² + 1 = 29²
z² = 29² - 1
z² = 840
z = √840
z = 28.98
Since z must be an integer, we can try integer values close to 28.98 to find one that works.
Trying z = 29,
a = z² - 1² = 840 - 1 = 839
b = 2z = 58
c = z² + 1² = 840 + 1 = 841
Therefore,
The lengths of the two legs of the right triangle are 58 and 839, in increasing order.
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A number is 9 more than another number. Twice the sum of the two numbers is 46. Find the two numbers.
Answers
Answer:
7 and 16
Step-by-step explanation:
let the 2 numbers be x and y , then
y = x + 9 → (1)
2(x + y) = 46 ( divide both sides by 2 )
x + y = 23 → (2)
substitute y = x + 9 into (2)
x + x + 9 = 23
2x + 9 = 23 ( subtract 9 from both sides )
2x = 14 ( divide both sides by 2 )
x = 7
and y = x + 9 = 7 + 9 = 16
The 2 numbers are 7 and 16