Suppose that an airline overbooks seats on their flights. In particular, it sells 300 tickets for a flight when there are only 270 seats available. On average, we expect 15% of those with tickets to not show up. What is the probability that we will have enough seats for everyone who shows up
Answers
Using the normal approximation to the binomial, it is found that there is a 0.994 = 99.4% probability that we will have enough seats for everyone who shows up.
In a normal distribution with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X. The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with \(\mu = np, \sigma = \sqrt{np(1-p)}\).In this problem:
15% do not show up, so 100 - 15 = 85% show up, which means that \(p = 0.85\).300 tickets are sold, hence \(n = 300\).The mean and the standard deviation are given by:
\(\mu = np = 300(0.85) = 255\)
\(\sigma = \sqrt{np(1-p)} = \sqrt{300(0.85)(0.15)} = 6.185\)
The probability that we will have enough seats for everyone who shows up is the probability of at most 270 people showing up, which, using continuity correction, is \(P(X \leq 270 + 0.5) = P(X \leq 270.5)\), which is the p-value of Z when X = 270.5.
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{270.5 - 255}{6.185}\)
\(Z = 2.51\)
\(Z = 2.51\) has a p-value of 0.994.
0.994 = 99.4% probability that we will have enough seats for everyone who shows up.
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Related Questions
In the diagram, m∠1=45° and m∠3=57.5°.
What is m∠4?
Enter your answer as a decimal in the box.
Answers
Check the picture below.
Lesson 17: Use the Four Operations to Solve Problems Cool Down: Andre's Balloons Andre has 125 balloons. He and 4 friends hung up some balloons for a party at school and now there are 80 balloons left. If each person hung up the same number of balloons, how many balloons did each person hang up? 1. Write an equation with a letter for the unknown quantity to represent the situation. 2. Solve the problem. Explain or show your reasoning.
Answers
a) Using the four basic mathematical operations, the number of balloons that each person hang up is 9.
b) An equation representing the situation is x = (125 - 80)/5.
What are the mathematical operations?The four basic mathematical operations include addition, subtraction, division, and multiplication.
The mathematical operations provide solutions to mathematical problems using operands.
What is an equation?An equation is a mathematical statement showing that two or more mathematical expressions are equal or equivalent.
The total number of balloons that Andre has = 125
The number of balloons remaining after hanging some for the school party = 80
The difference (number of balloons used) = 45 (125 - 80)
The number of friends who hang the balloons = 5
The number of balloons hung by each friend of Andre = 9 (45/5)
Thus, we can conclude that each of the 4 friend and Andre hung 9 balloons, with 80 remaining.
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Figure the amount of concrete (in cubic yards) required to pour a floor slab of the following dimensions: 18′ × 24′ × 4′′. Show both exact and rounded figures in the blanks provided
Answers
The amount of concrete required to pour a floor slab of the following dimensions: 18′ × 24′ × 4′′ is 5.34 cu.yard.
What is a Cuboid ?A cuboid is a three dimensional shape , with 6 faces , each face is a rectangle.
The concrete can be considered as in the shape of a cuboid.
Length = 18
Breadth = 24'
Height = 4"
Volume of Cuboid = Length * Breadth * Height
Volume of the cuboid = 18 * 24 * 4 *12*12 *(0.0278)³
=5.34 cu.yard.
Therefore the amount of concrete required to pour a floor slab of the following dimensions: 18′ × 24′ × 4′′ is 5.34 cu.yard.
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A grocery store sold 250 pounds of fruit in May. This is 5 times more than it sold in January. How many pounds of fruit did the grocery store sell in January?
Answers
Answer:
50 pounds of fruits sold January
Step-by-step explanation:
5X = 250
divude both sides by 5 to get x
x = 50
Which equation has a solution of 4? Select all that apply. A 12x = 3 C10 + x = 14 B 6x = 24 DX-4 = 8
Answers
Answer:
C and B
Step-by-step explanation:
A. 12x = 3, x =1/4
C. 10 + x = 14, x = 4
B. 6x = 24, x =4
D. x -4 = 8, x =12
Only the expression mentioned in B and C gives the solution as 4. Options B and C are correct.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
A
12x = 3
Simplifying the above expression,
12x = 3
x = 3 / 12
x = 1 / 4
Similarly simplifying all the expressions gives,
B. x = 4
C. x = 4
D. x = 12
Thus, only the expression mentioned in B and C gives the solution as 4. Options B and C are correct.
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7.35 km = _______ mm
Answers
Answer: 7.35 km = 7350000 mm
Step-by-step explanation:
Multiply km by 1000000
7.35 * 1000000 = 7350000 mm
For the graph, name the parent function and write an equation of the graph.
Answers
This is a transformation of the parent square root function, and it can be written as:
f(x) = √(-x + 4) - 2
Which is the parent function graphed?
It is ratter easy to identify the shape of the general square root function:
f(x) = √x
The only difference is that now it opens to the left, and it starts at the point (4, -2)
Then:
The sign of the x must be negative.
And with the known vertex we can write the equation:
f(x) = √(-x + 4) - 2
That is the graphed function.
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Find the volume of the cylinder to the nearest cubic foot. Use a calculator. A. 236 ft3 B. 942 ft3 C. 251 ft3 D. 75 ft3
Answers
\(\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=5\\ h=3 \end{cases}\implies V=\pi (5)^2(3)\implies V\approx 236~ft^3\)
Answer:
236 ft^3
Step-by-step explanation:
Base radius = 5 ft
Height = 3 ft
Volume = πr^2h
= π × 5^2 × 3
= 75π
= 235.61944901923 feet^3
Nearest Cubic Foot = 236 ft^3
Nearest Cubic Foot:
Hence Answer is:
236 ft^3
Hope this helps!
10h + 3y + 6 -4h -y -2 simplified
Answers
Answer:
6 h + 2 y + 4 is your answer
Step-by-step explanation:
Hope this helps! :)
Answer:
6h+2y+4
Step-by-step explanation:
so all you do is just subtract common factors so for 10h you just do 10h -4h and get 6h and do that for the rest
I am struggling to find domain and range please help thank you
Answers
Answer:
Domain: 0, 1, 2, 3, 4,
Range: 1, 2, 3, 4, 5,
Step-by-step explanation:
Based on the graph the domain of the function is 0, 1, 2, 3, 4, and the range is 1, 2, 3, 4, 5, therefore, the answer is:
a bag contains four types of coins. The probability of drawing a penny, nickel and dime is shown below. What is the probability of drawing a single coin that has a value of at least $.10?
Answers
Using probability we know that we have full probability or 1 that we will draw a coin that will have ethe value of at least $0.10.
What is probability?A probability is a numerical representation of the likelihood or chance that a specific occurrence will take place.
Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Simply put, probability is the likelihood that something will occur.
When we don't know how an occurrence will turn out, we can discuss the likelihood or likelihood of various outcomes.
So, we have the chart:
Penny = 2/5 = 0.4
Nickel = 1/5 = 0.2
Dime = 1/4 = 0.25
Then, the probability of getting a value of at least $0.10
P(E) = 3/3
P(E) = 1
Therefore, using probability we know that we have full probability or 1 that we will draw a coin that will have ethe value of at least $0.10.
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Examine the rotation. Which best describes point D?
Answers
X is carrying out a series of experiments which involve using increasing amounts of a chemical. In the first experiment he uses 6g of the chemical and in the second experiment he uses 7.8g of the chemical.
(i) Given that the amounts of the chemical used form an arithmetic progression, find the total amount of chemical used in the first 30 experiments. [4]
(ii) Instead it is given that the amounts of the chemical used form a geometric progression. X has a total of 1800g of the chemical available. Show that N, the greatest number of experiments possible, satisfies the inequality
1.3N ≤ 91.
and use logarithms to calculate the value of N.
Answers
Answer:
a) 963g
b) 17
Step-by-step explanation:
i) Now we must first find the common difference of the AP
d = 7.8 -6 = 1.8
Now the sum of the AP gives the total amount of chemical used for 30 experiments
Sn = n/2 [2a + (n-1)d]
n= 30, a = 6, d= 1.8
Sn = 30/2[2(6) + (30-1) (1.8)]
Sn = 15[12 + 52.2]
Sn = 963g
ii)For the G.P the common ration is (r)= 7.8/6 = 1.3
Since r>1, sum of GP = a (r^n -1)/r-1
If sum = 1800g
1800= 6(1.3^n -1)/1.3 - 1
1800 = 6(1.3^n -1)/0.3
1800 * 0.3 = 6(1.3^n -1)
540 = 6(1.3^n -1)
540/6 = (1.3^n -1)
90 = 1.3^n -1
90 + 1 = 1.3^n
1.3^n = 91
log 1.3^n = log 91
nlog1.3 = log 91
n = log91/log 1.3
n = 1.959/0.114
n = 17
Answer:
a) 963g
b) 17
Step-by-step explanation:
i) Now we must first find the common difference of the AP
d = 7.8 -6 = 1.8
Now the sum of the AP gives the total amount of chemical used for 30 experiments
Sn = n/2 [2a + (n-1)d]
n= 30, a = 6, d= 1.8
Sn = 30/2[2(6) + (30-1) (1.8)]
Sn = 15[12 + 52.2]
Sn = 963g
ii)For the G.P the common ration is (r)= 7.8/6 = 1.3
Since r>1, sum of GP = a (r^n -1)/r-1
If sum = 1800g
1800= 6(1.3^n -1)/1.3 - 1
1800 = 6(1.3^n -1)/0.3
1800 * 0.3 = 6(1.3^n -1)
540 = 6(1.3^n -1)
540/6 = (1.3^n -1)
90 = 1.3^n -1
90 + 1 = 1.3^n
1.3^n = 91
log 1.3^n = log 91
nlog1.3 = log 91
n = log91/log 1.3
n = 1.959/0.114
n = 17
55 - 3x7 + 8 divided by 4=?
Answers
Answer:56 :)
Step-by-step explanation:
Answer:
36
Step-by-step explanation:
In a certain Algebra 2 class of 28 students, 7 of them play basketball and 5 of them play baseball. There are 18 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?
Answers
Answer:
2 students play both
Step-by-step explanation:n(u)=28
n(b)=7,n(b)=5,n(who play neither sport)=18
HERE,
n(u)=n(b)+n(b)-n(BnB)+n(who play neither sport)
28=7+5-n(BnB)+18
28=30-n(BnB)
n(BnB)=30-28
=2 answer
PLEASE I NEED HELP the question is,
In the diagram of triangle LAC and triangle DNC below, LA = DN, CA = CN, and DAC is perpendicular to LCN.
a) Prove that triangle LAC = triangle DNC.
b) Describe a sequence of rigid motions that will map triangle LAC onto triangle DNC.
Answers
Answer:
1244 DCD
Step-by-step explanation:
An investment website can tell what devices are used to access the site. The site managers wonder whether they should enhance the facilities for trading via "smart phones" therefore they want to estimate the proportion of users who access the site that way. They draw a random sample of 200 investors from their customers. Suppose that the true proportion of smart phone users in 36%. What is the probability that the sample proportion is between 0.30 and 0.40? Hint: You'll need to find one z-score for 0.30 and another for 0.40. Then find the area between the two z-scores.
Answers
Answer:
0.8418
Step-by-step explanation:
We have p = 0.36
Sample size = 200
We have to find the standard error of proportion
= √p(1-p)/n
= √0.36(1-0.36)/200
= 0.034
P(0.30<p^0.40)
= 0.30-0.36/0.034 = -1.76,
0.40-0.36/0.034 = 1.18
P(-1.76<z<1.18)
When we go to the standard normal distribution table
P(z<1.18) = 0.8810
P(z<-1.76) = 0.0392
0.8810 - 0.0392
= 0.8418
This is the probability of the sample proportion being between 0.30 and 0.40
restaurant owners say it is good for each customer to have about 300in2 of space at their table. how many customers would you seat at each table?
Answers
Based on unit conversions, the number of customers that would seat at each table is 12 persons.
How the number is determined?The number of customers per table can be determined using unit conversions, which involve multiplication and division.
In this situation, the total available space per table is converted to squared inches from squared feet, and divided by the required table space per customer.
Conversely, the required table space per customer can be converted to squared feet and the result used to divide the total available space per table.
The required table space per customer = 300 in²
The total available space (area) per table = 300 ft²
1 foot = 12 inches
300 ft² = 3,600 in² (12 x 300)
The number of customers per table = 12 (3,600 ÷ 300)
OR:
300 in² = 25 ft² (300 ÷ 12)
The number of customers per table = 12 (300 ÷ 25)
Thus, using unit conversions, we expect the restaurant owner to seat 12 customers per table.
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Question Completion:The area occupied by each table is 300 ft².
What are the domain and range of the function represented by the set of ordered pairs?
{(-6, 12), (-3, -2), (1, 0), (14, -4)}
A. Domain: {-6, -3, 1, 14}
Range: {-4, -2, 0, 12}
B. Domain: -6 ≤ x ≤ 14
Range: -4 ≤ y ≤ 12
C. Domain: {-4, -2, 0, 12}
Range: {-6, -3, 1, 14}
D. Domain: -4 ≤ x ≤ 12
Range: -6 ≤ y ≤ 14
Answers
Answer:
A
Step-by-step explanation:
the domain is the definition of the valid x (input) values.
the range is the definition of the valid y (result) values.
as the function is defined by listing the specific points, the function only consists of individual points and not of connecting lines.
therefore the domain and range cannot be continuous intervals (otherwise the function would suddenly also include points not in the original list).
so, B and D are wrong.
and A is right, because the domain contains the x values, and the range the y values.
6th grade math I mark as brainliest
Answers
Answer:
4 1/6
Step-by-step explanation:
If you divide 25 (Miles) by 6 (Days) then you get:
4.1666666666666666666666666666667.
But, when you make it a fraction you get 4 1/6.
Answer:
4 1/6
Step-by-step explanation:
25/6
Hope this helps! Good Luck!
Is 2x - 3 = -7 x + 2 > y a true or false statement?
Answers
What does please put it in simplest radical form and rationalize the denominators
N=
M=
Answers
Answer:
n = 6
m = 6√3
Step-by-step explanation:
Reference angle = 30°
Opposite = n
Adjacent = m
Hypotenuse = 12
✔️To find n, apply the trigonometric ratio, SOH:
Sin 30° = Opp/Hyp
Sin 30° = n/12
n = Sin 30° × 12
n = ½ × 12 = 6
✔️To find m, apply the trigonometric ratio, CAH:
Cos 30° = Adj/Hyp
Cos 30° = m/12
m = Cos 30° × 12
m = √3/2 × 12 (cos 30 = √3/2)
m = √3 × 6
m = 6√3
What’s the difference between -70 in -30 on the number line
Answers
Answer:
If the distance is meant instead of a difference the answer is 40
Step-by-step explanation:
You would subtract the absolute value of
|-70-(-30)|
|-70+30|
|-40|
The absolute value of -40 is 40
for the function
please help
Answers
Answer: B
Step-by-step explanation:
In order to find out if the functions are continuous at 0, you must plug in 0 into both of the piecewise equations. If the answers are the same then they are continuous at 0 if they are different then it is not continuous.
e× + 1
e⁰ + 1
1 +1
2
2 + sin x
2 + sin 0
2 + 0
2
Since the first part equation =2 when x=0 and the second part equation =0 when x=0, the functions would be continuous because they are the same. But because there is no ≤ or ≥ there is no value for x=0. It's been removed.
Your answer is B
Answer: Choice B
The function f is continuous on \((-\infty,0) \cup (0,\infty)\)
There is a removable discontinuity at x = 0.
====================================================
Explanation:
Let
\(g(\text{x}) = e^{\text{x}}+1\\h(\text{x}) = 2+\sin({\text{x}})\\\)
The f(x) function changes its identity based on what the input x would be.
If x < 0, then f(x) = g(x)
If x > 0, then f(x) = h(x)
Plug x = 0 into g(x)
\(g(\text{x}) = e^{\text{x}}+1\\g(0) = e^{0}+1\\g(0) = 1+1\\g(0) = 2\\\)
Do the same for h(x)
\(h(\text{x}) = 2+\sin({\text{x}})\\h(0) = 2+\sin(0)\\h(0) = 2+0\\h(0) = 2\\\)
Both functions produce the same output (2) when x = 0. Therefore, the two pieces are connected. Both pieces approach y = 2 when x gets closer and closer to zero. But we'll have an open hole at x = 0 since neither piece is defined when x = 0. This makes f(0) undefined. We have a removable discontinuity at x = 0. This is in contrast to a jump discontinuity where the two pieces do not approach the same y value.
To express this in interval notation, start with the set of real numbers \((-\infty,\infty)\) and poke a hole at x = 0 to remove it.
We'll end up with \((-\infty,0) \cup (0,\infty)\) as the domain and where f(x) is continuous.
Refer to the graph below.
Steve wants to buy 40 markers for school. Markers come in packages of 10. How many packages of markers will Steve need to buy?
Answers
Answer:
steve need to buy 4 packages.
Step-by-step explanation:
1 package=10markers. 40 marker= 40/10=4
Answer:
4
Step-by-step explanation:
40/10 = 4/1 = 4
Carter plans to read 4 books during summer break: Charlottes web, Grasshopper summer, Diary of a Wimpy Kid, and Diary of a Wimpy kid 2. He wants to read diary of a wimpy kid 2 after diary of a wimpy kid. How many different orders can he read his books in?
Answers
Answer: 32
Step-by-step explanation:
4 x 4 x 4
Answer:12
Step-by-step explanation:
Just got it from the practice Test.
GIVING OUT BRAINLIEST ANSWER !! PLS HELP ME OUT !! (last minute)
Answers
Answer:
1:\(\sqrt{3}\);2
Step-by-step explanation:
those are the side length ratios
Answer:
1:√3:2
Step-by-step explanation:
Brainliest please
Thank you for taking the time out of your day to help me. Appreciate it.
Answers
Answer:
calculator gave me 6.5732
Step-by-step explanation:
Find the sum of 31 + 32 +33 + ... + 230.
Answers
Answer:
134
Step-by-step explanation:
A ladder 14 feet long rests against the side of a building. The base of the ladder rests on level ground 2 feet from the side of the building. What angle does the ladder form with the ground?
Answers
A ladder 14 feet long rests against the side of a building. The base of the ladder rests on level ground 2 feet from the side of the building. What angle does the ladder form with the ground?
see the attached figure to better understand the problem