The Coalition for Airline Passengers Rights, Health, and Safety averages 400 calls a day to help stranded travelers deal with airlines. The hotline is staffed for 16 hours a day.
To calculate the average number of calls in different time intervals and the probability of different events related to these calls.
Part 1:
a. 60-minute interval average number of calls: 400/16 = 25 calls
30-minute interval average number of calls: 25/2 = 12.5 calls
15-minute interval average number of calls: 12.5/2 = 6.25 calls
Part 2:
b. To find the probability of exactly 6 calls in a 15-minute interval, we can use the Poisson distribution formula. Let's assume that the average number of calls in a 15-minute interval is 6.25. Then, the probability of exactly 6 calls in a 15-minute interval is:
P(6 calls) = (e^-6.25)*(6.25^6)/6! = 0.0686
c. To find the probability of no calls in a 15-minute interval, we can use the Poisson distribution formula. Let's assume that the average number of calls in a 15-minute interval is 6.25. Then, the probability of no calls in a 15-minute interval is:
P(0 calls) = e^-6.25 = 0.0047
d. To find the probability of at least two calls in a 15-minute interval, we can use the cumulative distribution function of the Poisson distribution. Let's assume that the average number of calls in a 15-minute interval is 6.25. Then, the probability of at least two calls in a 15-minute interval is:
P(X >= 2) = 1 - P(0 calls) - P(1 call) = 1 - 0.0047 - (e^-6.25)*(6.25^1)/1! = 0.9906
Thus, the average number of calls in a 60-minute interval is 25, in a 30-minute interval is 12.5, and in a 15-minute interval is 6.25. The probability of exactly 6 calls in a 15-minute interval is 0.0686, the probability of no calls in a 15-minute interval is 0.0047, and the probability of at least two calls in a 15-minute interval is 0.9906.
Learn more about Probability here brainly.com/question/11234923
#SPJ4
Suppose that Y1 and Y2 are independent, standard normal random variables. Find the density function of U = Y1^2 +Y2^2.
The cumulative distribution function (CDF) of U is also well known and is given by:
F(u) = 1 - [tex]e^{(-u/2)}[/tex] × γ(1/2, u/2)
where γ is the lower incomplete gamma function.
What is the chi-squared distribution?
The chi-squared distribution is a continuous probability distribution that is widely used in statistics and other fields.
The random variable U = Y1^2 + Y2^2 has a well-known distribution called the chi-squared distribution with two degrees of freedom. The density function of U is given by:
[tex]f(u) = (1 / (2 \times \pi)) \times e^{(-u/2)} \times (u/2)^{(1/2 - 1)}[/tex]
where e is the base of the natural logarithm and π is the mathematical constant pi. This distribution has a positive support on the interval [0, +∞).
The cumulative distribution function (CDF) of U is also well known and is given by:
F(u) = 1 - [tex]e^{(-u/2)}[/tex] × γ(1/2, u/2)
where γ is the lower incomplete gamma function.
To learn more about chi-squared distribution, Visit
https://brainly.com/question/1156490
#SPJ4
please help with finsing the lemgth of x
Answer:
x = 5
Step-by-step explanation:
You want the length of x in the figure showing similar triangles.
ProportionThe bottom edge of the triangle is 2/3 of the left edge.
The similar triangles have the same ratio of side lengths. That means x is 2/3 of (3+4.5):
(2/3)(7.5) = 5
The length x is 5 units.
PLS HELP me I am in need of help will mark brainiest
Answer:
Fourth option: √65/4
Step-by-step explanation:
Since the angles are similar, each of the angles of ΔEFG must be equal to each of the corresponding angles of ΔHIJ
Specifically, m ∠J in ΔHIJ = m∠G in Δ EFG
Let's first find ∠G
Since EFG is a right triangle,
tan(G) = EF/FG = √65/4
tan J must be the same as tan G = √65/4
This is the fourth option
The value of tanJ is in the right angled triangle HIJ√65 / 4
What is an equation?An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either be linear, quadratic, cubic, depending of the degree of the variable.
Two triangles are similar if their corresponding angles are equal to each other.
Given that triangle EFG and triangle HIJ are similar, hence:
Angle G = Angle J
tanJ = tanG = √65 / 4
The value of tanJ is √65 / 4
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
If the public debt in 2006 was 6,783,231,062,743.62 and the budget for 2007 was in deficit by 595,821,633,586.70 what was the public debt in 2007?
Answer: The public debt in 2007 would be 6,783,231,062,743.62 + 595,821,633,586.70 = 7,379,052,696,330.32
Step-by-step explanation:
What is the answer to x in this equation 4x+4=12?
Answer:
x=2
Step-by-step explanation:
4x+4=12
-4 -4
_______
4x=8
_____
4 4
x=2
Three classes ordered lunch from a restaurant. In one class 5/6 of the children ordered hamburger, In the other class 2/4 ordered hot days. 1/2 of the other class ordered chicken wings. what is the total number of children that ordered Sandwiches ?
The total number of children that ordered Sandwiches is 1 5/6
What is the total number of children that ordered SandwichesFrom the question, we have the following parameters that can be used in our computation:
Class 1 = 5/6 Hamburger
Class 2 = 2/4 Hot days
Class 3 = 1/2 Chicken wings
So, the total number of children that ordered Sandwiches is
Total = 5/6 + 2/4 + 1/2
Evaluate
Total = 1 5/6
Hence, 1 5/6 of the three classes ordered sandwiches
Read more about fraction at
https://brainly.com/question/1622425
#SPJ1
given the parallelagram below, micheal writes triangle abc
Michael writes, "Triangle ABC is congruent to triangle CDA'',
if the segment AC ≅ AC.
What is congruent?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
Given the parallelogram below,
Michael writes, "Triangle ABC is congruent to triangle CDA''.
By the parallelogram property:
AB ≅ CD
BC ≅ AD.
If triangle ABC is congruent to triangle CDA,
then the segment AC ≅ AC.
Therefore, the segment AC ≅ AC.
To learn more about the congruent;
https://brainly.com/question/12413243
#SPJ1
Two houses are 1.5 inches apart on a map. The actual distance between the houses is 10.8 miles. What is the scale of the map?
Answer:
I inch = 7.2 miles
Step-by-step explanation:
Proportion method is applied:
1.5 inches on a map = 10.8 miles of actual distance
∴ 1 inches on the map = x miles of the actual distance
Cross-multiplication is applied:
(1.5 inches)(x miles) = (1 inch)(10.8 miles)
x needs to be isolated and made the subject of the equation:
x miles = [tex]\frac{(1 inch)(10.8 miles)}{1,5 inches}[/tex]
Inches in the numerator and denominator will cancel eachother out:
x miles = [tex]\frac{10.8 miles}{1.5}[/tex]
x miles = 7.2 miles
∴ Scale on the map:
1 inch = 7.2 miles
what is the geometric progression of; 1+3+6+9+12...
Answer:
Addition with the number 3.
Next numbers will be 15, 18, 21,...
Solve, for 0 ≤ x < 360°, the equation
5 sinx - 5 cosx = 2
In response to the query, x is equal to 60°, 120°, 240°, and 300°. These four options are the answer to the equation.
What does equation mean in its entirety?A mathematical equation is a statement that two amount or values are equal, such as 6 x 4 = 12 x 2. 2. A noun that counts. An equation is applied when several or more factors must be considered jointly in order to understand or explain the whole situation.
This equation can be solved using the trigonometric identity:
[tex]sinx = \sqrt{ (1 - cos^2x)}[/tex]
This identity can be used as a substitution in the equation:
5 sinx - 5 cosx = 2
5 [tex]\sqrt{(1 - cos^2x) }[/tex] - 5 cosx = 2
5 sqrt[tex](1 - cos^2x)[/tex]) = 7 + 5 cosx
Squaring both sides:
25([tex]1 - cos^2x[/tex]) = 49 + 70 cosx + 25 [tex]cos^2x[/tex]
25 - 25 [tex]cos^2x[/tex] = 49 + 70 cosx + 25 [tex]cos^2x[/tex]
0 = 74 + 45 cosx
45 cosx = -74
cosx = -74/45 = -2/3
The inverted cosine function can be used to determine that x = cos-1(-2/3). x must be within the range of 0° to 360°, hence x must be 300°.
5 sin - 5 cos - 5(-1/2) = 5 sqrt(3)/2 + 5/2 = 2 + 2.5 = 2.5
Since the left side of the equation is not equal to 2, x = 300° is not a solution to the equation.
We can repeat this process for the other solutions to the equation:
x = 60°, x = 120°, x = 240°, and x = 300°
These are the four solutions to the equation for 0° <= x < 360°.
To know more about Equation visit :
https://brainly.com/question/10413253
#SPJ1
I really need help with these questions pls?
Answer:
Top one is 3/8
Middle is 4/7
Bottom is 1/3
Step-by-step explanation:
All things algebra unit 5 homework 10 systems of inequalities
Note that a system of two linear inequalities in two variables is made up of at least two inequalities in the same variables.
What are systems of inequalities used for?Consider the following scenarios: highway speed restrictions, minimum credit card payments, the quantity of text messages you may send each month from your cell phone, and the time it will take to commute from home to school.
All of these may be expressed mathematically as inequalities. A linear inequality's solution is the ordered pair that is a resolution to all inequalities in the system, and the graph of the linear inequality is the graph of all system solutions.
Learn more about systems of inequalities:
https://brainly.com/question/16339562
#SPJ1
suppose that x is a discrete random variable that takes integer values from 1 to 100 (both inclusive), and has cumulative distribution function (cdf)
The probability that the discrete random variable x takes a value less than or equal to 50 is 0.50, since F(50) = 50/100 = 0.50.
F(x) = x/100
Then, the probability that x takes a value less than or equal to 50 is 0.50, since
F(50) = 50/100 = 0.50
The cumulative distribution function (CDF) of a random variable is a function that gives the probability that the random variable is less than or equal to a certain value. In this case, the CDF of the random variable x is given by F(x) = x/100.
Therefore, to find the probability that x takes a value less than or equal to 50, we simply need to evaluate the CDF at x = 50. This is done by substituting 50 into the CDF, which gives us F(50) = 50/100 = 0.50. This means that the probability that x takes a value less than or equal to 50 is 0.50.
Learn more about probability here
https://brainly.com/question/11234923
#SPJ4
Cavalleria Pizza sells only pizza. They offer five types of crust, two types of cheese, four meat toppings and
four vegetable toppings. If you must order exactly one type of cheese, one meat topping and one vegetable
topping on your pizza, how many different pizzas can you order at Cavalleria Pizza?
Answer:
3?
Step-by-step explanation:
im not sure sorry
a negative x a negative =
An emergency plumber charges $65 as a call out few plus an additional $75 per hour. He arrives at the house at 9:30 and works to repair a water tank. The total repair bill is $196.25. Use the variable t for the number of hours.
Answer:
Step-by-step explanation:
Answer:
Around 11:15 am
Step-by-step explanation:
Let h represents the number of hours the plumber works
Since the plumber charges $65 fee plus $75 per hour, the bill can be calculated by:
→ bill = 65 + 75h
Since the bill is $195.25
→ 195.25 = 65 + 75h
→ 75h = 130.25
→ h = 1.74
1.74 implies that the plumber worked almost 1 hour and 45 minutes. Since the plumber started at 9:30, the repair was completed around 11:15 am.
Simplify expression[5-6+1]
Answer: 0
Step-by-step explanation:
Using GEMDAS
- Grouping
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
[5-6+1]
= [-1+1] because you add/subtract from left to right
= [0] because -1+1=0.
Answer is 0
Use the general slicing mothod to find the volume of the following solid. The solid with a semicircular base of radius 16 whose cross section is perpendicular to the base and parallel to the diameter are squares. Place the semicircle on the xy-plane so that its diameter is on the x-axis and it is centered on the y-axis. Set up the integral that gives the volume of the solid. Use increasing limits of integration.
[tex]V= [0,16] \int\limits {4y^2 \sqrt{(256 - y^2)} } \, dy[/tex] would be the integral that gives the volume of the solid.
What is Disk method of integration?
Disc integration is a method for estimating the volume of a solid of revolution of a solid-state material when integrating along an axis "parallel" to the axis of revolution in integral calculus.
The volume of the solid can be found using the disk method of integration. In this method, we consider thin slices of the solid perpendicular to the x-axis, each of which is a disk with a square cross-section.
The volume of each slice is equal to the product of the area of its cross-section and its thickness, which is equal to the difference in x-coordinates between the top and bottom of the slice.
Let's call the top-right corner of the square cross-section (x, y, z). We k[tex]x^2 + y^2 = 256[/tex]
And we also know that the side length of the square is equal to 2y. So, the area of the cross-section is equal to [tex](2y)^2 = 4y^2.[/tex] The volume of the slice is equal to [tex]4y^2 dx.[/tex]
Since the semicircle is centered at the origin, the value of y ranges from 0 to 16.
The value of x ranges from 0 to the square root of [tex]256 - y^2.[/tex]Using these ranges, the volume of the solid can be calculated as follows:
[tex]V=\int\limits {[0,16] 4y^2 \sqrt{(256 - y^2)} } \, dy\\V= [0,16] \int\limits {4y^2 \sqrt{(256 - y^2)} } \, dy[/tex]
This is the integral that gives the volume of the solid.
Therefore, [tex]V= [0,16] \int\limits {4y^2 \sqrt{(256 - y^2)} } \, dy[/tex] would be the integral that gives the volume of the solid.
To know more about Disk method of integration visit,
https://brainly.com/question/24097452
#SPJ4
Shannon put some money in her savings account. After 6 months, she earned $10.50 in interest. If the interest rate was 7%, how much money did Shannon put in her account?
The amount of money put by Shannon in her account is $300.
What is simple interest?Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific amount of time.
Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to calculate interest, the principal amount in simple interest remains constant.
Given that Shannon put some money in her savings account. After 6 months, she earned $10.50 in interest. If the interest rate was 7%,
The amount will be calculated as:-
SI = ( P x R x T ) / 100
10.50 = ( P x 7 x 1 ) ( 2 x 100 )
P = ( 10.50 x 2 x 100 ) / ( 7 )
P = $300
Therefore, $300 has been deposited into Shannon's account.
To know more about simple interests follow
https://brainly.com/question/13789484
#SPJ1
In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse.
If a = 5.7 meters and c = 9.6 meters, what is b? If necessary, round to the nearest tenth.
Solving the provided question, we can say by Pythagorean theorem b = [tex]\sqrt{a^2 + b^2}[/tex] = [tex]\sqrt{32.49 + 92.16}[/tex] = 11.231meters
what is Pythagorean theorem?The Pythagorean Theorem, sometimes known as the Pythagorean Theorem, is the basic Euclidean geometry relationship between a right triangle's three sides. According to this rule, the area of a square with the hypotenuse side equals the sum of the areas of squares with the other two sides. The Pythagorean Theorem, often known as the generic algebraic notation a2 + b2 = c2, states that the square that crosses the hypotenuse of a right triangle opposite the right angle equals the sum of the squares that span the sides of a right triangle.
By Pythagorean theorem
a = 5.7 meters and c = 9.6
b = [tex]\sqrt{a^2 + b^2}[/tex]
b = [tex]\sqrt{32.49 + 92.16}[/tex]
b = [tex]\sqrt{124.65}[/tex]
b = 11.231meters
To know more about Pythagorean theorem visit:
https://brainly.com/question/14930619
#SPJ1
A scientist evaluated the local deer population. The scientist found that there were 110 juveniles and 90 adults in the local population. What percentage of the deer were juveniles?
Answer:
55%
Step-by-step explanation:
To find the percentage of juveniles in the local deer population, we need to calculate the proportion of juveniles in the total population and convert it to a percentage.
First, find the total number of deer in the population by adding the number of juveniles and adults:
110 juveniles + 90 adults = 200 deer
Next, divide the number of juveniles by the total number of deer and multiply by 100 to convert to a percentage:
110 juveniles / 200 deer * 100 = 55%
Therefore, 55% of the local deer population were juveniles.
A teacher randomly chooses a two-person leadership team from a group of four qualified students. Three of the students, Sandra, Marta, and Jane, are girls. The fourth student, Franklin, is a boy.
Using the sample space of possible outcomes listed below, where each student is represented by the first letter of his or her name, answer each of the following questions.
What is P(A)P, left parenthesis, A, right parenthesis, the probability that the first student is a boy?
Answer: The sample space of possible outcomes is:
{SM, SJ, MJ, MS, JS, JM}.
There are 6 possible outcomes in the sample space, and 1 of these outcomes results in the first student being a boy (Franklin, represented by "F").
Therefore, the probability of the first student being a boy is P(A) = 1/6.
Step-by-step explanation:
Let P(x) = 3x³ - 7x² + 3x-4 and Q(x) = 2x³ - 6x² - 15. Add the polynomials functions, as indicated below.
(P+Q)(x)
(P+Q)(x) = (Simplify your answer. Do not factor.)
K
The addition of the polynomial P(x) and Q(x) is 5x³ - 13 x² + 3x - 19.
What is Polynomial?A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminates in mathematics.
Given:
P(x) = 3x³ - 7x² + 3x-4 and Q(x) = 2x³ - 6x² - 15.
Now, adding the both Polynomials
P(x) + Q(x)
= 3x³ - 7x² + 3x-4 + 2x³ - 6x² - 15.
Now, solving the like terms
= 3x³ + 2x³ - 7x² - 6x² +3x -4 -15
= (3+ 2) x³ + (-7-6) x² +3x -4 - 15
= 5x³ - 13 x² + 3x - 19
Learn more about Polynomial here:
https://brainly.com/question/11536910
#SPJ9
hey thank for helping me
Answer: -1
Step-by-step explanation:
When the graph g hits g=2, the y is -1
Jessie is baking a cake and uses 1/2 of the 4
pound bag of flour. How many pounds of
flour did Jessie use to bake her cake?
Answer: 2 pounds of flour
Step-by-step explanation:
1/2 of four is two,
4 * 1/2 = 2
Answer:
Jessie used 1/2 of the 4-pound bag of flour, so she used 1/2 * 4 pounds = 2 pounds of flour to bake her cake.
An automobile manufacturer can produce up to 300 cars per day. The profit made from the sale of these vehicles can be modelled by the function p(x) = -x²+ 350x-6600 where p(x) is the profit in thousand Rupees and x is the number of automobiles made and sold. Answer the following questions based on this
model:
(i) When no cars are produce what is a profit/loss?
(ii) What is the break even point? (Zero profit point is called break even)?
(iii) What is the profit/loss if 400 cars are produced?
i) The profit/loss when no cars are produced is a loss of 6600 Rupees.
II) The break even point is at 20 cars
III) The profit/loss if 400 cars are produced is; a loss of 13400Rupees.
How to solve Profit functions?(i) When no cars are produced, x = 0.
Thus, plugging this value into the function p(x) = -x² + 350x - 6600, we have;
p(0) = -0² + 350(0) - 6600 = -6600.
Therefore, the profit/loss when no cars are produced is a loss of 6600 thousand Rupees.
(ii) The break-even point is the point at which the profit is zero, i.e., p(x) = 0. Setting p(x) = 0 and solving for x, we find that;
-x² + 350x - 6600 = 0
x = 20
Therefore, the break-even point is x = 20 cars. T
(iii) If 400 cars are produced, the profit can be found by plugging this value into the function p(x) = -x² + 350x - 6600.
We find that p(400) = -400² + 350(400) - 6600
= -160000 + 140000 + 6600 = -13400. Therefore, the profit/loss if 400 cars are produced is a loss of 13400 Rupees.
Read more about Profit Functions at; https://brainly.com/question/25638609
#SPJ1
what are some services offered by the banks and credit unions
Step-by-step explanation:
mortgages, lines of credit, checking and savings accounts, auto loans and the convenience of electronic banking and Automated Teller Machines (ATMs)
Step-by-step explanation:
Banks and credit unions offer a variety of financial services, including:
Checking and savings accounts
Personal loans
Mortgages
Credit cards
Investment products (e.g. mutual funds, individual retirement accounts (IRAs))
Foreign currency exchange
Online and mobile banking
Wire transfers
Automated teller machines (ATMs)
Insurance products (e.g. life, auto, homeowners)
Wealth management services
Small business banking services.
Note that the exact services offered may vary depending on the institution.
Solve the equation for the specified variable.
M = F/a
a=
Answer:
A=F/M
Step-by-step explanation:
m=f/a ......,,, cross product
f= ma......,..., both sides divided by m
then the answer is a=f/m
Find the values of a and b that make the following piecewise defined function both continuous and differentiable everywhere. - 6 x <5 f(x) = { -27 *"ax + b, 125
The values of a = 17 and b = - 56
that make the following piece wise defined function both continuous and differentiable everywhere.
What is continuous function?A continuous function in mathematics is one that doesn't change value unexpectedly due to discontinuities, or breaks in the function's continuity. A continuous function in mathematics is a function that causes the value of the function to continuously vary as a result of a continuous variation of the argument, or a change without a leap. Thus, there aren't any discontinuities—rapid changes in value.
conditions are:
1.
f(x) is continuous if,
[tex]\lim_{x \to \ 5^{-}}f(x)[/tex] = [tex]\lim_{x \to \ 5^{+}}f(x)[/tex] = f(5)
2.
differentiable if,
[tex]\lim_{x \to \ 5^{-}}f^'(x)[/tex] = [tex]\lim_{x \to \ 5^{+}}f^'(x)[/tex]
for 1st condition:
⇒ [tex]\lim_{x \to \ 5^{-}}f(x) = \lim_{x \to \ 5^{+}}f(x)[/tex]
⇒ [tex]\lim_{x \to \ 5^{-}}(-3x -6) = \lim_{x \to \ 5^{+}}(-2x^2+ax+b)[/tex]
⇒ (-3 × (-5) - 6) = - 2(5)² + a(5) + b
⇒ - 21 = - 50 + 5a + b
⇒ 5a + b = 29 ................... (1)
For 2nd condition:
⇒ [tex]\lim_{x \to \ 5^{-}}f^'(x) = \lim_{x \to \ 5^{+}}f^'(x)[/tex]
⇒ [tex]\lim_{x \to \ 5^{-}} \frac{d}{dx} (-3x - 6) = \lim_{x \to \ 5^{+}} \frac{d}{dx}(-2x^2 + ax + b)[/tex]
⇒ - 3 = - 4x + a
⇒ - 3 = - 4 (5) + a
⇒ a = 17
Substitute a = 17 in equation (1) we get:
5(17) + b = 29
or, b = - 56
To know more about continuous function refer to:
https://brainly.com/question/18102431
#SPJ4
The complete question is as follows:
Math 5th grade
Roshaun walks around the city park. The square park measures 61 1/4 yards on each side. How far does Roshaun walk?
Answer: 245 yds
Step-by-step explanation:
61 1/4 times 4 = 245