Answer:
(a) The probability that more than three arrive in one hour is approximately 0.018988
(b) The probability that no interval contains more than 3 arrivals in 30 separate one-hour intervals is approximately 0.56264
(c) The length of time such that the probability of no arrival is 0.1 is approximately 2.30259 hours
Step-by-step explanation:
The distribution of the arrival time of a small aircraft = Exponential distribution
The mean arrival time, μ = 1 hour
The pdf of a exponential distribution, f(x) = λ·e^(-λ·x)
The mean, μ = 1/λ
∴ 1 = 1/λ
λ = 1 hour
∴ For the exponential distribution, f(x) = 1·e^(-x)
(a) The Poisson probability is given as follows;
[tex]P(X = k) = \dfrac{\lambda^k \times e^{-k}}{k!}[/tex]
The probability for more than 3 is given as follows;
[tex]P(X > 3) = 1 - \dfrac{1^0 \times e^{-1}}{0!} - \dfrac{1^1 \times e^{-1}}{1!} - \dfrac{1^2 \times e^{-1}}{2!} - \dfrac{1^3 \times e^{-1}}{3!} \approx 0.018988[/tex]
(b) P(X ≤ 3) for 30 1 hour intervals = P(X ≤ 3)³⁰ = (1 - 0.018988)³⁰ ≈ 0.56264
(c) When the probability that no arrival occurs is 0.1, we have;
0.1 P(X > x) = f(x) = 1·e^(-x) = e^(-x)
-x·ln(e) = ln(0.1)
∴ x = -㏑(0.1) ≈ 2.30259
The length of time such that the probability that no arrival occur during the interval is 0.1, x ≈ 2.30259 hours.
HELP FAST!! IF RIGHT YOU WILL GET BRAINLIST! AND 5 STARS ⭐️
Solve for x.
x - 2(2 - 3/2x)= 2(4-x) + 10
A) -11/3
B) -3/11
C) 11/3
D) 3/11
Answer: The answer is C 11/3
Isolate the variable by dividing each sides by a factors that don't contain the variable.
Remove the brackets using the distributive law for the following: 5(4x - 3y) - 4(4x - 3y)
Answer:
4x - 3yStep-by-step explanation:
5(4x - 3y) - 4(4x - 3y)
= 5 × 4x - 5 × 3y - 4 × 4x + 4 × 3y
= 20x - 15y - 16x + 12y
= 20x - 16x - 15y + 12y
= 4x - 3y (Ans)
Add the following weights:
5 lb 9 oz
+ 1 lb 9 oz
Ib
OZ
Answer:
7 lbs 2 oz
Step-by-step explanation:
6 lbs 18oz
18 - 16 = 2oz
ANSWER THIS PLEASE ASAP
Candice and Chris run a relay race at recess. Candice runs 3/3 of a lap
around the track. Chris runs 1/3 of a lap around the track. How much farther does Candice run than Chris?
In 2016, the number of Internet users in the Middle East was about 1×108, and in Australia, it was about 3×107. Approximately how many times larger was the number of Internet users in the Middle East than in Australia in 2016?
0.03 times
0.3 times
3 times
30 times
Simplify the following question:
4
NEVAEH Last Saved: 11:16 AM
A vase in the shape of a cylinder has a radius of 4.3 centimeters and a volume of 1330.2 cubic centimeters, as
shown in the diagram.
What is the height of the vase in centimeters? Round your answer to the nearest tenth.
Answer:
h = 22.91 cm
Step-by-step explanation:
Given that,
The volume of a vase, A = 1330.2 cm³
Radius of the vase, r = 4.3 cm
We need to find the height of the vase. The formula for the volume of a cylinder is given by :
[tex]V=\pi r^2 h\\\\h=\dfrac{V}{\pi r^2}\\\\h=\dfrac{1330.2 }{3.14\times (4.3)^2}\\\\h=22.91\ cm[/tex]
or
h = 23 cm
So, the height of the vase is equal to 23 cm.
Here is some more
Find the value of x: 3x−7=8x+23
Answer: x=6
Step-by-step explanation:
Answer:
x = -6
Step-by-step explanation:
Subtract 3x from both sides to get -7=5x+23.
Subtract 23 from both sides to get -30=5x.
Divide 5 from both sides.
x = -6.
Solve by factoring
x^2-3x+16=7x
Find the area of the parallelogram
Answer:
18 x 16 = 288
Step-by-step explanation:
Formula of a parallelogram:
BH
(B x height) Your base times your height.
Identify the line segment that is a diameter.
Answer:
The line segment that is a diameter is BE.
hope it helps :)❤
Answer:
BE.
Step-by-step explanation:
A diameter is any line segment which passes through the centre and has endpoints on the circle at opposite sides.
Simplify the expression.
1/2r – 2r + 6 – 3
Answer:
-3(r-2)/2
Step-by-step explanation:
r/ 2 − 2 r + 6 − 3
r /2 − 2 r⋅ 2/ 2+ 6 − 3
r/ 2 + − 2r ⋅ 2/ 2 + 6 − 3
r − 2 r ⋅ 2 /2 + 6 ⋅ 2/ 2 + − 3 ⋅ 2/ 2
r − 2 r ⋅2 + 6⋅ 2 − 3 ⋅ 2 /2
r − 4 r + 12 − 6 /2
−3 ( r − 2 ) /2
Hope that helps! Plz, mark brainiest! :D
Have a great day!
Help please thank you:) QUICKLY!!!!!!!!!
Answer:
y = -8
Step-by-step explanation:
2x2 - 12
4 - 12 = -8
hope this helps
need done soon! offering 20 points!!
Mrs. Roberts’ dog, Rover, loves to eat peanuts. A cylindrical can of peanuts has a diameter of 4 inches and a height of 9 inches. Which of the following equations can be used to find the volume of the can of peanuts? 8 points
Answer:
c
Step-by-step explanation:
cccccccccccc
Neal purchases a digital camera for his
family to use on their vacatlart. The model he
purchases is on sale for $129. The sales tax
rate for his city iş 7.5%.
How much sales tax does Neal pay on the
digital camera?
Answer:
101.91
Step-by-step explanation:
Could someone please give the answer to this question.?
Answer:
25
Step-by-step explanation:
v^2 - 10v + __ : what number when added to itself gives you -10 ? -5
what's -5 x -5 ? 25
(v-5)^2 is a perfect square
Maly is going to throw a fair coin 70 times. Write down an estimate for the number of times the coin will land on head
Answer:
there are 2 sides for a coin
so divide 70/2 = 35
estimate for heads - 35
Step-by-step explanation:
14.5 divided bye 9 please
Answer:
1.61111111
Step-by-step explanation:
calculator
Answer:
1.6111111111.... or 1 11/18
Step-by-step explanation:
Well you just divide
14.5/9
Which one would it be
Answer:
A or [tex]\frac{\sqrt{6} }{2}[/tex]
Step-by-step explanation:
*note- this method only works because the denominator values are being multiplied, if they were being added then there are extra steps to keep in mind but for now this is simple*
Start by dividing the root 12 in the numerator by the root 2 in the denominator
[tex]\frac{\sqrt{12} }{\sqrt{2} }=\sqrt{6}[/tex]
Then we simply substitute back in the 2 (from the denominator) that we ignored for a second to get our answer
[tex]\frac{\sqrt{6} }{2}[/tex]
*note- if you are allowed to use a calculator then you could also plug in your values to check each answer option but since this question isn't too complicated there should be no need to do so unless you forget how to solve it algebraically*
A swimming pool manager is making a schedule for his lifeguards next Monday. The pool policy states that there must be 2 lifeguards on duty for a pool attendance of up to 20, 3 lifeguards on duty for an attendance of 21-50, 4 lifeguards on duty for an attendance of 51-75, and 5 lifeguards on duty for an attendance of 76-100. Based on last Monday's pool attendance shown in the graph, how many lifeguards should be scheduled at 2:00?
A. 4 lifeguards
B. 5 lifeguards
C. 3 lifeguards
D. 2 lifeguards
Answer: A.4
Step-by-step explanation:
Suppose the population of a town is 17,400 and is growing 2% each year.
Predict the population after 9 years.
Answer: 20,532
Step-by-step explanation:
17,400(.02)=348
348(9)=3132
17,400+3132=20,532
Answer:
Step-by-step explanation:
This is an exponential growth function of the form:
[tex]y=ab^x[/tex] where a is the initial population and b is the growth rate. This could also be written as
[tex]y=a(1+r)^x[/tex] which is a bit more accurate. We'll use that one. r is the percent growth: 2% for us.
Filling in the formula:
[tex]y=17400(1+.02)^x[/tex] and then simplifying:
[tex]y=17400(1.02)^x[/tex]
That's the model for this population. Filling in any number of years for x will give you the population y. Our time is 9 years:
[tex]y=17400(1.02)^9[/tex]
Take care of the exponents first, giving us:
[tex]y=17400(1.195092569)[/tex] and then multiply to get
y = 20,794.6 or 20,794 people (since you can't have 6/10 of a person)
what is 23 – 7x + 6 + 8x = 26
Answer: x = -3
Step-by-step explanation: hope this helps
23 – 7x + 6 + 8x = 26
x + 29 = 26
x + 29 - 29 = 26 - 29
x = 26 - 29
x = -3
Answer:
x=-3
Step-by-step explanation:
23 – 7x + 6 + 8x = 26
Add the numbers to get,
29-7x+8x=26
Move the constant to the right,
29+x=26
Add the numbers to get,
x=26=29
Calculate the difference
x=26-29
Calculate,
x=-3
-7y-4 = 4y×(8-6)-64 answer fast
Answer: y=4
Step-by-step explanation:
-7y-4=8y-64
-7y-4+4=8y-64+4
-7y=8y-60
-7y-8y=8y-60-8y
-15y= -60
[tex]\frac{-15y}{-15}[/tex] =[tex]\frac{-60}{-15}[/tex]
y=4
IM NOT SMART SUBSTITUTION METHOD AGAIN
Answer:
x = 6
y = -3
Step-by-step explanation:
15x + 31y = -3
we are given that x =( - y + 3 )
so in the equation 15x + 31y = -3 we substitute "x" for ( -y + 3 ) and we solve for y
so 15 ( -y + 3 ) + 31y = -3
now we use basic algebra to solve for y
step 1 distribute the 15
15 * -y = -15y
15 * 3 = 45
now we have 45 - 15y + 31y = -3
step 2 combine like terms
-15 + 31y = 16y
now we have 45 + 16y = -3
step 3 subtract 45 from each side
-3 - 45 = -48
45 - 45 cancels out
now we have 16y = -48
step 4 divide each side by 16
16y/16=y
-48/16=-3
we're left with y = -3
Now to find x we substitute -3 for y in x = -y + 3
* substitute *
x = - ( -3) + 3
the two negative signs cancel out and we get x = 3 + 3
3 + 3 = 6
we're left with x = 6
Convert 0.9 cm into m
Answer is 0.009
0.9 ( 0.01 m / cm ) = 0.009
For her science fair project, Emily
conducted an experiment to investigate
the effects of watering on tomato plants.
She varied the amount of water given to
the plants and measured each plant's
height after two weeks. Emily
hypothesized that the more water she
added, the taller her tomato plants would
be.
1. Was Emily's hypothesis correct? Explain
your answer.
2. According to Emily's data, what is the
optimal weekly amount of water for
tomato plant growth? Explain your answer.
Answer:1 yes it is correct because the more water you give a plant the helter it is
2 about 2 times a day
Step-by-step explanation:
At a car dealership yesterday, the ratio of trucks sold to cars sold was 5.6. If the dealership sold 30 cars, how many trucks were sold?
Answer:
25
Step-by-step explanation:
ratio 5:6
[tex]\frac{5}{6} = \frac{x}{30}[/tex]
6x = 5(30)
6x = 150
x = 25
A recipe calls for 3 cups of sugar and 9 cups of water. How many cups of water should
be used with 2 cups of sugar?
3 cups
B
8 cups
4 cups
D
6 cups
ANZWER QUICK PlZZ
Answer:
Step-by-step explanation:
3/9 = 2/w
Cross multiply.
3w = 18
w = 6 cups
how much is a a $479.00 purchase with 7.5% sales tax
Answer:
$514.93
Step-by-step explanation:
Before Tax Price: $479.00
Sale Tax: 7.50% or $35.93
After Tax Price: $514.93
Which plot correctly displays the data set with maximum of 48, a minimum of 27, a median of 36, an upper quartile of 45, and a lower quartile of 32?
Options :
A box-and-whisker plot. The number line goes from 25 to 50. The whiskers range from 27 to 48, and the box ranges from 32 to 45. A line divides the box at 36.
A box-and-whisker plot. The number line goes from 25 to 50. The whiskers range from 27 to 46, and the box ranges from 32 to 45. A line divides the box at 36.
A box-and-whisker plot. The number line goes from 25 to 50. The whiskers range from 27 to 48, and the box ranges from 31 to 39. A line divides the box at 36.
A box-and-whisker plot. The number line goes from 25 to 50. The whiskers range from 27 to 46, and the box ranges from 31 to 39. A line divides the box at 36.
Answer:
A box-and-whisker plot. The number line goes from 25 to 50. The whiskers range from 27 to 48, and the box ranges from 32 to 45. A line divides the box at 36.
Step-by-step explanation:
Given the five number summary which are all displayed on a box and whisker plot :
Maximum = 48
Minimum = 27
Median = 36
Upper Quartile = 45
Lower quartile = 32
Maximum and minimum values are displayed by the whiskers :
Starting point of whisker = minimum value
End point of whisker = maximum value
The quartiles are displayed by the box :
Starting point of the box = lower quartile
End point of the box = upper quartile
Line in between the box = Median