overbooking flights is a common practice of most airlines. a particular airline, believing that 4% of passengers fail to show for flights, overbooks (sells more tickets than there are seats). suppose that for a particular flight involving a jumbo-jet with 267 seats, the airline sells 278 tickets. question 1. what is the expected number of ticket holders that will fail to show for the flight? (use 2 decimal place in your answer.) question 2. what is the probability that the airline will not have enough seats for all the ticket holders who show for the flight? (use 3 decimal places.)
1. 3.2673 is the expected number of ticket holders that will fail to show for the flight.
2. 0.425 is the probability that the airline will not have enough seats for all the ticket holders who show for the flight.
P(airline will not have enough seats for all the ticket holders who show for the flight) = P(more than 267 people show up for the flight)
p = P(will show for flight) = 1 - 0.04 = 0.96
n = 278
µ = n * p = 278 * 0.96 = 266.88
σ = [tex]\sqrt{ n*p* (1 - p)} = \sqrt{278 * 0.96 * 0.04} = 3.2673[/tex]
P(X > 267) = P(X > 267.5)
p(x- µ) / σ > 267.5- µ /σ
= P(Z> 267.5 – 266.88/ 3.2673 )
= P(Z > 0.19)
= 0.425.
What is probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. To understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.
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Which number line and equation show how to find the distance from -2 to 5? O O A. 1-2-(-5) 2 3 12-1-5) sing O c. 1-2-5 D. 2-5
To find the distance between two numbers on the number line, you have tu use absolute value
So, if I want to know the distance from -2 to 5, all I have to do is to substract 5 from -2 and then apply absolute value, like this:
[tex]\mleft|-2-5\mright|\text{ = }\mleft|-7\mright|\text{ = 7}[/tex]And the number line should look like this:
A pet boarder keeps a dog-to-cat ratio of 5:2. If the boarder has room for 98 animals, then how many of them can be dogs in a ratio
Answer:We have 70 dogs
Step-by-step explanation:
dogs: cats: total5 2 7We want 98 animals98/7 =14We need to multiply each number by 14dogs: cats: total…
hope this helps
Which of the following service providers may use credit reports and/or credit scores to decide whether a person can buy a service and/or what price he or she will pay?Group of answer choicesLandlordMortgage lenderCell phone companyAll of the aboveCredit card issuer
Answer:
All of the above
Explanation:
All the given options make use of credit scores and/or credit reports to decide whether a person can buy a service and/or to decide what price he or she will pay. landlords may use credit scores to decide if they will require a security deposit and, if so, how much it should be. Also, other service providers like Mortgage lender, Cell phone company and Credit card issuer makes use of credit scores and/or credit reports in making certain decisions.
The sum of three consecutive even integers is 20 less than four times the
first. What are the integers?
The most appropriate choice for linear equation will be given by -
The integers are 26, 28, 30
What is linear equation?
At first it is important to know about equation
Equation shows the equality between two algebraic expressions by connecting the two algerbraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Here,
Let the integers be x - 2, x, x + 2
Sum = x - 2 + x + x + 2 = 3x
20 less than Four times the first = 4(x - 2) - 20
By the problem,
[tex]3x = 4(x - 2) -20\\3x = 4x - 8 -20\\4x - 3x = 28\\x = 28[/tex]
The integers are 28 - 2, 28, 28 + 2
The integers are 26, 28, 30
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please help to find the value of x and explain how to get it in simple terms.
SOLUTION
From the image above
[tex]\begin{gathered} z^2=6^2+3^2\ldots\text{ by pythagora's rule } \\ z^2=36+9 \\ z^2=45 \\ z=\sqrt[]{45} \end{gathered}[/tex]Considering the bigger right angle triangle,
[tex](3+x)^2=y^2+45[/tex]We can obtain the expression of y from the smaller right angle triangle,
Using pythagora's rule, we have
[tex]y^2=6^2+x^2[/tex]Then, recall
[tex](3+x)^2=y^2+45[/tex]Substite the expression for y², we have
[tex](3+x)^2=6^2+x^2+45[/tex]Expand the paranthesis, we have
[tex]\begin{gathered} 9+6x+x^2=x^2+36+45 \\ \text{Subtract x}^2from\text{ both sides } \\ 9+6x=36+45 \\ \end{gathered}[/tex]subtract 9 from both sides, we have
[tex]\begin{gathered} 6x+9-9=81-9 \\ 6x=72 \end{gathered}[/tex]Divide both sides by 6, we obtain
[tex]\begin{gathered} \frac{6x}{6}=\frac{72}{6} \\ \text{Then} \\ x=12 \end{gathered}[/tex]Therefore
Answer: x= 12
Determine the relative frequency for the third class as a simplified fraction
GIVEN:
We are given a frequency distribution table showing different classes of hours of study and the frequency of each class of data.
Required;
To determine the relative frequency for the third class
Step-by-step solution;
For a relative frequyency, we need to find the number of times an event occurs and express it as a fraction of the total events that occured in the survey/experiment.
The events in this case are hours of study and the occurrence is the total frequency for all classes of hours of study.
The total frequency is;
[tex]3+10+6+15+6=40[/tex]The relative frequency for the third class therefore would be;
[tex]\begin{gathered} Relative\text{ }Frequency_3=\frac{6}{40} \\ \\ Relative\text{ }Frequency=\frac{3}{20} \end{gathered}[/tex]ANSWER:
The relative frequency of the third class therefore is
[tex]\frac{3}{20}[/tex]1/2 (7/10-3/5) + -1.9
Answer: -1 17/20
Step-by-step explanation: use order of operations to solve, parenthesis, multiplication, addition/subtraction
Montraie drove 220 miles in 5 hours. If he continued at the same rate, how long would it take to travel 88 miles?
The time taken for Montraie to travel a distance of 88 miles is 2 hours.
How long would it take for Montraie to travel 88 miles?Speed is simply referred to as distance traveled per unit time.
It expressed mathematically as;
Speed = Distance ÷ time.
Given the data in the question;
Distance covered = 220 milesTime elapsed = 5 hoursSpeed = ?First, we determine the speed of Montraie.
Speed = Distance ÷ time.
Speed = 220 miles ÷ 5 hours
Speed = 44 miles per hour.
Now, time spent in traveling a distance of 88 miles will be;
Speed = Distance ÷ time
Time = Distance / Speed
Time = 88 miles / 44 miles per hour
Time = 2 hours
Therefore, the elapsed time is 2 hours.
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If Montraie drove 220 miles in 5 hours. If he continued at the same rate, then it takes 2 hours to travel 88 miles.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given that,
Montraie drove 220 miles in 5 hours.
We need to find how long it would take to reach 88 miles.
Let us form a equation based on given data.
Let x be the time to reach 88 miles.
We need to find value of x.
220/5=88/x
Apply cross multiplication
220x=440
x=440/220
x=2
Hence it takes 2 hours to travel 88 miles with same rate.
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can someone help me really quick
If the price of apples are proportional, the value of p is $6.75.
What is the value of p?If the relationship between the price of apples and the number of apples bought are proportional, it means that as the number of apples bought increases, the price paid would increase.
The function that represents the cost of purchasing apples is:
Total cost = cost per apple x number of apples bought
$4.50 = 6c
c = $4.50 / 6
c = $0.75
The price of 9 apples is p
p = 9 x $0.95
p = $6.75
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A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. price of 9 apples is $6.75.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
We need to find the value of p.
For 6 Apples the price is $4.5
We need to find for 9 apples.
For 9 apples the price is p, which we have to find
Let us form a equation to find it.
6/4.50=9/p
Apply cross multiplication
6p=4.5(9)
6p=40.5
Divide both sides by 6
p=6.75
Hence price of 9 apples is $6.75.
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The ratio between Siu's height and the height of her brother Tai is 5:6. If
Tai is 145 cm tall, how tall is Siu, to the nearest centimetre?
With the concepts of ratio, Siu's height is 121 cm tall.
What is a ratio?We can determine how much of one quantity is in the other by comparing two amounts of the same units and finding the ratio. Ratios can be divided into two groups. One is the part-to-whole ratio, and the other is the part to part ratio. The link between two distinct entities or groupings is depicted by the part-to-part ratio.
A ratio is a comparison between two amounts that often uses a fraction.
Considering that the fraction has been simplified,
Given that Siu's height is 5x
Tai's height is 6x.
Now, 6x= 145
Thus, x= 145/6
Now, Siu's height is 5x
Then, its height is (145 ×5)/6= 120.8 cm
Siu's height is 121 cm because it must be rounded to the closest centimeter.
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devon has 15 dollars to spend on snacks. the corner store has candy bars for $1 and sports drinks for $3. he only wants to purchase at most 10 items.
Devon can have 6 candy bars and 3 sports drinks when he has $15 to spend.
According to the question,
We have the following information:
Devon has $15.
Cost of 1 candy bar = $1
Cost of 1 sports drink = $3
Devon wants to purchase at most 10 items.
It means that the total items should be less than or equal to 10.
Now, we have to spend $15 in such a way that number of items should be less than or equal to 10.
Now, we will look for the number of items for sports drink and change the number of candy bars accordingly.
Let's take 1 sports drink:
$3
We are left with $12. Now, there will be 12 candy bars.
So, this can not satisfy our conditions.
Let's take 2 sports drink:
$6
We are left $9. Now, there will be 9 candy bars. And the number of items is 11.
(This is not satisfying our condition.)
Let's take 3 sports drink:
$9
We are left with $6. Now, there will be 6 candy bars. And the number of items is 9.
This is satisfying all the conditions.
Hence, Devon can have 6 candy bars and 3 sports drinks when he has $15 to spend on snacks.
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this sentence is false
Answer: what sentence ?
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
The sentence is true because if it is true, then the sentence is false.
You are asking if the sentence is false, and it is false, so the question you asked is true.
This is so confusing though...
Order of Operations
If you do not use the proper order of operations, you will not get
the correct answer.
Write which operation should be done first.
1.6 + 3 × 2
2.13 – 1 + 4 ÷ 2
3.5 × (7 – 2) + 1
4.(19 + 23) – (4 × 5)
For questions 5 through 8, evaluate the expression for x = 6 and y = 17.
5.4x + 5y
6.12x + (20 – y)
7.x ÷ 3 + y
8.4y ÷ 2 + (8x + 10)
9.Patty made $34 baby sitting on each of 3 weekends. If she spent $50 on gifts
for her family, how much money does she have left?
10.Carlos solved 20 – (2 × 6) + 8 ÷ 4 = 29. Is this the correct answer?
To answer this question, we need to apply the rules of "PEMDAS".
Thus:
- we first deal with the numbers in the "Parentheses" or brackets
- then we perform the "Multiplication" operation
- and then we perform the "Subtraction" operation
This is done as follows:
[tex]6\times14-(9+8)\times2[/tex]- by dealing with the numbers in the parentheses, we get:
[tex]6\times14-(17)\times2[/tex]- now, by dealing with the multiplication, we have:
[tex]84-34[/tex]- finally, we deal with the subtraction, as follows:
[tex]50[/tex]With the exception of column one, all amounts are in dollars. What is starting principal of the loan? Give your answer in dollars to the nearest dollar. Do not include commas or the dollar sign in your answer.
SOLUTION
First let us get the monthly rate
This can be gotten using the formula
[tex]P\times\frac{r}{12}=i[/tex]Where P is principal,
r is the percent interet rate per year, so to get monthly interest is divide by 12
i is the monthly interet.
Using column 1 to determine the rate, we have
[tex]\begin{gathered} P\times\frac{r}{12}=i \\ 149,783.55\times\frac{r}{12\times100}=748.92 \\ \frac{149,783.55r}{1200}=748.92 \\ r=\frac{1200\times748.92}{149,783.55} \\ r=6\text{ percent} \end{gathered}[/tex]Now, the interest rate r = 6%
The starting principal becomes
[tex]\begin{gathered} P\times\frac{6}{12\times100}=750 \\ \frac{6P}{1200}=750 \\ P=\frac{750\times1200}{6} \\ P=150000\text{ dollars } \end{gathered}[/tex]Therfore, the answer is 150000 dollars
The headlights of an automobile are set such that the beam drops 2.00 in. for each 28.0 ft in front of the car. What is the angle between the beam and the
Road?
The most appropriate choice for trigonometry will be given by -
Angle between beam and road is 0.33°
What is Trigonometry?
Trigonometry shows the relationship between sides and angles of a right angled triangle.
There are six trigonometrical functions. They are [tex]sin\theta, cos\theta, tan\theta, cos\theta, sec\theta, cosec\theta[/tex]
[tex]sin\theta = \frac{perpendicular}{hypotenuse}\\\\cos\theta = \frac{base}{hypotenuse}\\\\tan\theta = \frac{perpendicular}{base}\\\\cot\theta = \frac{base}{perpendicular}\\\\sec\theta = \frac{hypotenuse}{base}\\\\cosec\theta = \frac{hypotenuse}{perpendicular}\\[/tex]
Trigonometry is a very important tool in mathematics.
Here,
The headlights of an automobile are set such that the beam drops 2.00 in. for each 28.0 ft in front of the car.
According to the figure attached here, 2.0 inch forms the height of the triangle and 28.0 ft forms the base of the triangle
Let the angle be [tex]\theta[/tex]. Now trigonometry is applied here
[tex]tan\theta = \frac{\frac{2}{12}}{28}\\tan\theta = \frac{1}{6 \times 28}\\tan\theta = \frac{1}{168}\\\theta = tan^{-1}\frac{1}{168}\\\theta = 0.33^{\circ}[/tex]
Angle between beam and road is 0.33°
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is there a right triangle in which two side lengths are simple fractions (ratios of integers such as 2/7 or 2/3), and the other side length is an integer?
Yes , there can be a Right triangle with two side lengths as simple fraction and other side length as an integer .
In the question ,
we have to find , whether a Right Triangle can be made by two fractions and an integer length .
yes, we can make a Right Triangle with two lengths as fractions and other length as integer .
let us prove it with the help of an example .
Consider the triplet 7 , 24 , 25 .
let the two fractions side be 7/25 and 24/25 , and the hypotnuse of the right triangle be 1 .
We know that for the Right Triangle
(side1)² + (side2)² = hypotnuse²
(7/25)² + (24/25)² = 1²
49/625 + 576/625 = 1
(49+576) / 625 =1
625/625 = 1
1 = 1
hence ,it is a Right Triangle .
Therefore , Yes , there can be a Right triangle with two side lengths as simple fraction s and other side length as an integer .
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due wensday but prefered be done now
The correct statement about the function is the y-intercept is (0.71), and 71 represents the starting temperature.
What is the y-intercept?
A graph can be described as a pictorial representation of data. A graph has a y-axis and a x-axis. The x-axis in this question represents time and the y-axis is the temperature.
The function shown in the graph is a linear function. This is because the curve is a straight line. The y-intercept is the point where the line crosses the y-axis. The y-intercept is the value of the data set when x is zero. The y-intercept represents the initial temperature or the starting temperature.
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Assuming a direct proportion between the distance and time, how far would they travel in 5 hours?
A family taking a road trip vacation travels 126 miles in 3 hours.
We can calculate the constant of proportionality as:
[tex]\frac{126\text{ miles}}{3\text{ hours}}=42\text{ miles/hour}[/tex]Then, in 5 hours they would travel:
[tex]d=5\text{ hours}\cdot\frac{42\text{ miles}}{1\text{ hour}}=210\text{ miles}[/tex]In 5 hours they would travel 210 miles.
Before a piece of steel can be sold for its maximum price, it must be 35 feet long with an absolute error of 1 foot. Find the range of acceptable heights for steels that are to be sold at full price by writing an absolute value inequality to represent this situation then solving it.
Let's call x to the height. The inequality that represents an acceptable range is:
|x - 35| ≤ 1
Solving it, we get:
x - 35 ≤ 1 or x - 35 ≥ -1
x ≤ 1 + 35 x ≥ -1 + 35
x ≤ 36 x ≥ 34
which is equivalent to 34 ft ≤ x ≤ 36 ft
How much time will it take for these two vehicles to meet?
34 miles, 55mph, 30mph
The time for the two vehicle will meet is 0.4 hours .
How to find the time the two vehicles will meet?According to the diagram, the first car drive at a speed of 55 miles per hour and the second vehicles drives at a speed of 30 miles per hour.
The distance apart of the cars is 34 miles.
Speed is measured as the ratio of distance to the time in which the distance was covered.
In other words, speed is the distance travelled per unit of time.
speed = distance / time
Therefore,
distance = speed × time
Hence,
let
x = time use by the car
Therefore, the total distance can be express as follows:
55x + 30x = 34
85x = 34
divide both sides by 85
85x / 85 = 34 / 85
x = 0.4 hours.
Therefore, it will take 0.4 hours for the cars to meet.
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2x+y = -7
-4x -5y =23
Answer:
x = -2
y = -3
Step-by-step explanation:
If it is a simultaneous equation.
2x+y = -7-----equation 1
-4x -5y =23-----equation 2
5(2x+y = -7)
-4x -5y =23
10x+5y = -35
-4x -5y =23 +5y cancel -5y
10x= -35
-4x=23
6x = -12
x = -2
Solving for Y
Substitute the value of x in equation one or two.
equation two = -4x -5y =23
-4x -5y =23
-4(-2) -5y =23
8-5y=23
-5y = 23-8
-5y = 15
y = -3
How is 6 divided by (-3) equals -2
Since a positive number divide or multiplies a negative number
Then the answer will be a negative number
So:
6 / -3 = -2
6 is a positive number and it's being divide by -3 which is a negative number
So the answer is -2
Describe the end behavior of the graph of the following polynomial function:
We will have the following:
From the polynomial we will have that:
*It falls to the left and rises to the right.
This can be seeing as follows:
Sal elrove 3000 miles in 75 hours. At this rate how long will it take to drive 4000 miles
Answer:
Step-by-step explanation:
First, we need to find the rate. miles/hours. 3000/75 = 40mph (miles per hour). to find the answer we need to divide the rate by the distance they want us to find. to see a deeper explanation of why scroll past the answer. 4000/40 = 100 hours.
deeper explanation:
we can set the numbers given to us equal to what we are looking for.
miles/hour
3000/75 = 4000/x x being the time we are looking for
cross multiply 3000x=300000
divide by 3000 x=100 hours
juan went out to eat dnner,and the meal cost $60.00.If juan recived a 18% discount,what was the total value of the discount
Multiply by the decimal form of the percentage,
60 * 0.18 = 1.08
So the discount is for $1.08 off,
60 - 1.08 = 58.92
Giving a total of $58.92 after the discount is applied
What is x and y and how do I solve for it in the future?
The values of x and y in the triangle are 15 and 88 degrees.
How to find the angles of a triangle?A triangle is a polygon with 3 sides. The sum of angles in a triangle is 180 degrees.
A triangle can be classified base on its sides and angles as equilateral triangle, isosceles triangle and scalene triangles.
An equilateral triangle has three of its sides and angles equal to each other.
An isosceles triangle has 2 sides and angles equal to each other.
A scalene triangle has no sides equal to each other.
Therefore,
The other triangle on the left side is an equilateral triangle.
Therefore, all it sides and angles are equal.
Hence, each angle of the triangle is 60 degrees.
A traversal line cut across the sides of the parallel lines of the triangles formed.
Therefore,
60° = 4x
x = 60 / 4
x = 15
Therefore,
60 + y + 32 = 180(sum of angles in a triangle)
y = 180 - 92
y = 88°
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The monthly cost (in dollars) of water use is a linear function of the amount of water used (in hundreds of cubic feet, hcf). the cost for using 18 hcf of water is $39.67, and the cost for using 37 hcf is $69.12. what is the cost for using 21 hcf of water?
The monthly cost of water use can be represented using a linear equation y = 1.55 x + 11.77 and the cost of using 21 hcf is $44.32.
A linear equation can be represented by a line equation:
y = mx + c
Where:
m = slope
c = constant
From the problem, we have 2 equations:
39.67 = 18 m +c
69.12 = 37 m + c _
29.45 = 19 m
m = 1.55
Substitute m = 1.55
39.67 = 18 . (1.55) + c
c = 11.77
Hence, the linear equation is:
y = 1.55 x + 11.77
Substitute x = 21
y = 1.55 . (21) + 11.77 = 44.32
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giving brainliest to first person who answers!
Evaluate.
7 x 5 + 4² − 2³ / 4
Write an equation (a) in slope-intercept form and (b) in standard form for the line passing through (1,6) and perpendicular to 3 x + 7y = 1.a) The equation of the line in slope-intercept form is enter your response here
The equation
[tex]3x+7y=1[/tex][tex]7y=-3x+1[/tex][tex]y=\frac{-3x}{7}+\frac{1}{7}[/tex]has slope -3/7.
The product of perpendicular lines must be -1, so the slope of the new equation must be:
[tex]m\cdot-\frac{3}{7}=-1[/tex][tex]m=\frac{-1\cdot7}{-3}=\frac{7}{3}[/tex]The line with that slope and that passes throught (1,6) is:
[tex](y-6)=m(x-1)[/tex][tex](y-6)=\frac{7}{3}(x-1)[/tex][tex]y-6=\frac{7}{3}x-\frac{7}{3}[/tex][tex]y=\frac{7}{3}x-\frac{7}{3}+6[/tex][tex]y=\frac{7}{3}x-\frac{7}{3}+\frac{18}{3}[/tex][tex]y=\frac{7}{3}x+\frac{11}{3}[/tex]The following graph shows both equations:
[tex]y=\frac{7}{3}x+\frac{11}{3}[/tex][tex]3\cdot y=(\frac{7}{3}x+\frac{11}{3})\cdot3[/tex][tex]3y=7x+11[/tex][tex]-7x+3y=11[/tex]