An eastern airport has recorded a monthly average of five near misses of landings and takeoffs in the past 5 years. We assume that the distribution of this number is Poisson. a. Find the probability that during a given month there are no near misses on landings and takeoffs at the airport. b. Find the probability that during a given month there are five near misses. c. Find the probability that there are at least five near misses during a particular month.
Answer:
The answer to this question can be defined as follows:
In option a "0.0067".
In option b "0.1755".
In option c "0.5595".
Step-by-step explanation:
It is about the distribution of Poisson:
[tex]\lambda = 5 (rate)[/tex]
t = 1
The formula for calculating Mean:
[tex]\to \mu = \lambda \times t[/tex]
[tex]\to P(X=x) = \frac{e^{-\mu} \mu^{x}}{x!}[/tex]
calculate the value of Mean:
[tex]\to \mu =5 \times 1\\\\ \to \mu= 5[/tex]
In point a:
When the value of x is equal to 0:
[tex]\to P(X = 0) = \frac{e^{-5} 5^{0}}{0!}[/tex]
[tex]= \frac{e^{-5} \times 1 }{0}\\\\ = 0.0067 \times 1 \\\\ = 0.0067[/tex]
In point b:
When the value of x is equal to 5:
[tex]\to P(X = 0) = \frac{e^{-5} 5^{5}}{5!}[/tex]
[tex]= \frac{e^{-5} \times 3125 }{120}\\\\ = \frac{0.0067 \times 3125}{120} \\\\ = \frac{21.0560}{120}\\\\ =0.1754 \\\\[/tex]
In point c:
When the value of x is equal to 5:
[tex]\to P(X \ge 5) = 1 - P(X < 5) \\\\ \to P(X \ge 5) = 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3) - P(X = 4) \\\\ \to P(X \ge 5) = 0.5595[/tex]
After a 90% reduction, you purchase a new soft drink machine on sale for $64. What was the original price of the soft drink machine?
Answer:
$640
Step-by-step explanation:
Let [tex]x[/tex] equal the original price of the machine.
We know that $64 is 10% of [tex]x[/tex] because $64 is left of [tex]x[/tex] after the 90% reduction.
Set up an equation:
[tex].10x=64[/tex]
Divide by the coefficient of [tex]x[/tex], which in this case is [tex].10[/tex]
[tex]x=640[/tex]
If m∠1= (7x –19)°, and m∠2 = (x + 5)°, find m∠2.
Given :
∠m1 = ( 7x - 19 )° .
∠m2 = ( x + 5 )° .
To Find :
The value of x .
Solution :
Since , relation between angle ∠m1 and ∠m2 is not given .
Let , us assume that sum of ∠m1 and ∠m2 is 180° .
So ,
[tex](7x-19)+(x+5)=180^{\circ}\\\\8x-14=180\\\\8x=194\\\\x=24.25^{o}[/tex]
Angle ∠m2 = (24.25 + 5 )° = 29.25° .
Therefore , ∠m2 = 29.25° .
Hence , this is the required solution .
Answer:
Given :
∠m1 = ( 7x - 19 )° .
∠m2 = ( x + 5 )° .
To Find :
The value of x .
Solution :
Since , relation between angle ∠m1 and ∠m2 is not given .
Let , us assume that sum of ∠m1 and ∠m2 is 180° .
So ,
Angle ∠m2 = (24.25 + 5 )° = 29.25° .
Therefore , ∠m2 = 29.25° .
Hence , this is the required solution .
Step-by-step explanation:
Let U = {English, French, History, Math, Physics, Chemistry, Psychology, Drama}, A = {Chemistry, Psychology, Math, History}, B = {Drama, English, French, Math, History}, and C = {Physics, Psychology, French}. Find the following. n(B ∪ C)
Drama, English, French, Math, History, Physics, Psychology
what is the value of x
Answer:
X=70
Step-by-step explanation:
Interior angles of parallel line sum up to be 180° so:
45+(2x-5)=180
45+2x=185
2x=140
x=70
A grid that represents 1 whole , what would you shade for 0.4 and 0.04? 100 squares in rows of 10.
Answer:
40/4 shaded in squares
Step-by-step explanation:
for 0.4, since 100 is a whole, multiply by 100.
0.4*100=40
shade in 40 squares
for 0.04, multiply by 100
0.04*100=4
shade in 4 squares
Help me ASAP plssssssssssssssss
Answer: it’s B
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
find the probability that there are no H when a fair coin is flipped three times.
(round the answer to 4 decimal points)
Step-by-step explanation:
Probability of heads is 1/2, and the probability of tails is 1/2. The probability of getting no heads (3 tails) is:
P = (1/2)³
P = 1/8
P = 0.1250
Which choice correctly expresses the number below in scientific notation?
Answer:
I think 2nd option is correct
the square root of a number, less than nine (write into a verbal expression)
Answer: 9 - [tex]\sqrt{x}[/tex]
Step-by-step explanation:
Let say the number is x.
So the square root of x will be [tex]\sqrt{x}[/tex] and is less than 9 so we will subtract that from 9.
[tex]9-\sqrt{x}[/tex]
Ava is 23cm taller than Olivia, and Olivia is half the height of Lucas. If Lucas is is 1.78m tall, how tall is Ava and Olivia?
Answer:
Ava = 1.12 m tall
Olivia = 0.89 m tall
Step-by-step explanation:
given;
Ava is 23cm taller then Olivia,
Olivia is half the height of Lucas.
If Lucas is 1.78m tall
find:
how tall are Ava and Olivia
-------------------------------------
Ava = Olivia + 0.23
Olivia = Lucas / 2
Lucas = 1.78
plugin values into the equation above
Olivia = 1.78 / 2
Olivia = 0.89 m tall
Ava = 0.89 + 0.23
Ava = 1.12 m tall
Will mark Brainliest!!!!! Suppose A, R, and B are collinear on AB, and
AR: AB = 1/4 What are the coordinates of R?
Please give explanation
Answer:
[tex]R(x,y) = (\frac{7}{4},\frac{1}{4})[/tex]
Step-by-step explanation:
Given
[tex]A = (1,-1)[/tex]
[tex]B = (4,4)[/tex]
[tex]AR:AB = 1:4[/tex]
Required
Determine R
This question will be solved using line ratio formula
[tex]R(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2+ny_1}{m + n})[/tex]
Where
[tex]A = (1,-1)[/tex]
[tex]B = (4,4)[/tex]
[tex]m:n = AR : RB[/tex]
Since R is on A and B;
[tex]AB = AR + RB[/tex]
[tex]4 = 1 + RB[/tex]
[tex]RB = 3[/tex]
Hence;
[tex]m:n = 1 : 3[/tex]
[tex]A = (1,-1)[/tex]
[tex]B = (4,4)[/tex]
[tex]R(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2+ny_1}{m + n})[/tex] becomes
[tex]R(x,y) = (\frac{1 * 4 + 3 * 1}{1+3},\frac{1 * 4 + 3 * -1}{1 + 3})[/tex]
[tex]R(x,y) = (\frac{4 + 3}{4},\frac{4 - 3}{4})[/tex]
[tex]R(x,y) = (\frac{7}{4},\frac{1}{4})[/tex]
Evaluate –32 + (2 – 6)(10
Steps to solve:
-32 + (2 - 6)(10)
~Simplify
-32 + (-4)(10)
~Multiply
-32 - 40
~Subtract
-72
Best of Luck!
Answer:
The answer is -49Step-by-step explanation:
The equation is: –32 + (2 – 6)(10).
Then u have to do PEMDAS
P=Parentheses
E=Exponents
M=Multiplication
D=Division
A=Addition
S=Subtraction
you follow the steps to get -49
In a paint store you’re mixing paint for a larger order. Paint requires mixture of 75% base 25% color. How many gallons of base should you mix for 4 gallons of color ?
Which description is correct for the polynomial 4x2+3x−2?
quartic trinomial
cubic binomial
quadratic trinomial
cubic trinomial
Answer:
Step-by-step explanation:
quadratic trinomial, because the highest degree of x is 2 and the expression has 3 terms.
A box contains 8 white balls, 7 black balls, & 2 red balls.
a) how many red balls must be added to the box so that the probability of drawing a red ball is 8/9
b)how many black balls must be added to the original box so that the probability of drawing a white ball is 1/9?
Answer:
a) 118
b) 55
Step-by-step explanation:
a) Originally, there are 2 red balls and a total of 17 balls.
8/9 = (2 + x) / (17 + x)
8 (17 + x) = 9 (2 + x)
136 + 8x = 18 + 9x
x = 118
b) Originally, there are 8 white balls and a total of 17 balls.
1/9 = 8 / (17 + x)
17 + x = 72
x = 55
how do i math? plssssssssssssssssss answer
Answer:
you just math you know pretty easy when you know what to do
Step-by-step explanation:
just practice
If Ben invests $3000 at 4% interest per year, how much additional money must he invest at 5.5 % annual interest to ensure that the interest he receives each year is 4.5 % of the total amount invested?
Answer:
$1500
Step-by-step explanation:
Investment 1 = $3000Interest 1 = 4%Investment 2 = xInterest 2 = 5.5%Total interest = 4.5%Total interest:
3000*0.04 + x*0.055 = (3000+ x)*0.045 ⇒ multiply by 100 both sides3000*4 + 5.5x = 3000*4.5 + 4.5x ⇒ parenthesis5.5x - 4.5x = 3000(4.5-4) ⇒ collect like termsx = 3000*0.5 ⇒ simplifyx = 1500 ⇒ answerAdditional money is $1500
I WILL MARK BRAINLIEST!!!
What is 178.80 as a fraction?
Answer: 178 4/5 or as an improper fraction 894/5
Hope this helps!
Please mark Brainliest!
Which equation must be true for m(x) and n(x) to be inverse?
Answer:
see below
Step-by-step explanation:
When the functions are inverses of each other, it will be true that ...
m(n(x)) = n(m(x)) = x
The expanded form of this equation is shown below.
HELP PLZ AND.... HIIIII!
Answer:
0.002 meters per second
Answer: 0.0002 meters per second
(c) Given that the system has at least one type of defect, what is the probability that it has exactly one type of defect
Answer:
The probability is 0.357
Step-by-step explanation:
Given that,
The system has at least one type of defect,
Suppose, A certain system can experience three different types of defects.
Let [tex]A_{i}[/tex] (i = 1,2,3) denote the event that the system has a defect of type i.
Suppose that the following probabilities are,
[tex]P(A_{1})=0.11[/tex]
[tex]P(A_{2})=0.08[/tex]
[tex]P(A_{3})=0.05[/tex]
[tex]P(A_{1}\cup A_{2})=0.13[/tex]
[tex]P(A_{1}\cup A_{3})=0.13[/tex]
[tex]P(A_{2}\cup A_{3})=0.11[/tex]
[tex]P(A_{1}\cap A_{2}\cap A_{3})=0.01[/tex]
[tex]P(A_{1}\cap A_{2})=0.06[/tex]
[tex]P(A_{1}\cap A_{3})=0.03[/tex]
[tex]P(A_{2}\cap A_{3})=0.02[/tex]
[tex]P(A_{1}\cup A_{2}\cup A_{3})=0.14[/tex]
We need to calculate the probability that it has exactly one type of defect
Using given data
[tex]P=\dfrac{P(A_{1}\cap A_{2}'\cap A_{3}')}{P(A_{1}\cup A_{2}\cup A_{3})}+\dfrac{P(A_{1}'\cap A_{2}\cap A_{3}')}{P(A_{1}\cup A_{2}\cup A_{3})}+\dfrac{P(A_{1}'\cap A_{2}'\cap A_{3})}{P(A_{1}\cup A_{2}\cup A_{3})}[/tex]
[tex]P=\dfrac{P(A_{1})-P(A_{1}\cap A_{2})-P(A_{1}\cap A_{3})+P(A_{1}\cap A_{2}\cap A_{3})}{P(A_{1}\cup A_{2}\cup A_{3})}[/tex] + [tex]\dfrac{P(A_{2})-P(A_{1}\cap A_{2})-P(A_{2}\cap A_{3})+P(A_{1}\cap A_{2}\cap A_{3})}{P(A_{1}\cup A_{2}\cup A_{3})}[/tex]+ [tex]\dfrac{P(A_{3})-P(A_{1}\cap A_{3})-P(A_{2}\cap A_{3})+P(A_{1}\cap A_{2}\cap A_{3})}{P(A_{1}\cup A_{2}\cup A_{3})}[/tex]
P = [tex]\dfrac{P(A_{1})+P(A_{2})+P(A_{3})-2P(A_{1}\cap A_{2})-2P(A_{1}\cap A_{3})-2P(A_{2}\cap A_{3})+3P(A_{1}\cap A_{2}\cap A_{3})}{P(A_{1}\cup A_{2}\cup A_{3})}[/tex]
Put the value into the formula
[tex]P=\dfrac{0.11+0.08+0.05-2(0.06)-2(0.03)-2(0.02)+3(0.01)}{0.14}[/tex]
[tex]P=0.357[/tex]
Hence, The probability is 0.357
Find the unit rate of 90 miles/2 hours, IN FEET PER SECOND! can you please do it step by step plz?
Answer:
45, 90/2 equals 45. everytime you need to find it you do miles/hours
Convert 30 pages/hour to pages/day.
Is this relation a function?
Heidi Muir, a sporting goods wholesaler, purchased goods from a supplier for $3,400. The
supplier offers a 3% discount if the invoice is paid within 10 days; if not paid within 10 days, the
full amount must be paid within 30 days of the invoice date. Use the formula to find the annual
rate Heidi, in effect, is paying the supplier if she fails to pay the invoice at the end of the discount
period
Answer:
56.44%
Step-by-step explanation:
From the question, we have the following values
% Discount = 3%
Full allowed payment days = 30 days
Discount days = 10 days
1 year = 365 days
The formula for Effective Annual rate or Annual rate in effect =
Discount %/(1-Discount %) x (365 days/(Full allowed payment days - Discount days))
= 3%/(1 - 3%) × (365 days/30 days - 10 days)
= 0.03/(1 - 0.03) × (365/20)
= 0.03/0.97 × (365/20)
= 0.5644329897
Converting to percentage
0.5644329897 × 100
= 56.44329897%
Approximately = 56.44%
Therefore, the annual rate Heidi, in effect, is paying the supplier if she fails to pay the invoice at the end of the discount period is 56.44%
What percent of 86 is 50 to the nearest whole percent
Answer:
58%
Step-by-step explanation:
50/86 is approximately equal to 0.58, and when you convert that into percentage you get 58%
1. Simplify (–6x2 + x – 5) + (9x2 – 3x+6).
Answer:
= 7-2x. is the answer :p
What is the value of the 3 in 513
Answer:
3
Step-by-step explanation:
513 = 500 + 10 + 3
The 5 is worth 500.
The 1 is worth 10.
And the 3 is worth 3 !
Answer:
The value of 3 in 513 is the ones place.
Step-by-step explanation:
If you used the input value 12 in the function y=2x,what would be the output value
Answer:
24
Step-by-step explanation:
If you put 12 in for x, you would get y=2*12 and 2 times 12 is 24. I hope this helps :)