Answer:
a) 0.0065 = 0.65% probability of receiving no emails during an hour.
b) 0.1212 = 12.12% probability of receiving at least three emails during an hour
c) The expected number of emails received during 15 minutes is 1.2604.
d) 0.2835 = 28.35% probability that no emails are received during 15 minutes
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given time interval.
In this question.
121 emails per day.
A day has 24 hours, so per hour, 121/24 = 5.0417, which means that [tex]\mu = 5.0417n[/tex], in which n is the number of hours.
A. What is the probability of receiving no emails during an hour?
n = 1, so [tex]\mu = 5.0417[/tex]
This is P(X = 0).
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-5.0417}*(5.0417)^{0}}{(0)!} = 0.0065[/tex]
0.0065 = 0.65% probability of receiving no emails during an hour
B. What is the probability of receiving at least three emails during an hour?
Either you receive less than three emails during an hour, or you receive at least 3. The sum of the probabilities of these events is decimal 1. So
[tex]P(X < 3) + P(X \geq 3) = 1[/tex]
We want [tex]P(X \geq 3)[/tex]
Then
[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]
In which
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-5.0417}*(5.0417)^{0}}{(0)!} = 0.0065[/tex]
[tex]P(X = 1) = \frac{e^{-5.0417}*(5.0417)^{1}}{(1)!} = 0.0326[/tex]
[tex]P(X = 2) = \frac{e^{-5.0417}*(5.0417)^{2}}{(2)!} = 0.0821[/tex]
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0065 + 0.0326 + 0.0821 = 0.1212[/tex]
0.1212 = 12.12% probability of receiving at least three emails during an hour
C. What is the expected number of emails received during 15 minutes?
15 minutes is a fourth of an hour, so n = 1/4 and [tex]\mu = \frac{5.0417}{4} = 1.2604[/tex]
The expected number of emails received during 15 minutes is 1.2604.
D. What is the probability that no emails are received during 15 minutes?
[tex]P(X = 0) = \frac{e^{-1.2604}*(1.2604)^{0}}{(0)!} = 0.2835[/tex]
0.2835 = 28.35% probability that no emails are received during 15 minutes
simplify -5^5 ÷ -5^-6
Answer:
5^11
Step-by-step explanation:
-5^5 ÷ -5^-6
5^5 divide 5^-6
5^11
Which is not an example of a triangular prism?
Camping tents
Roofs
a shoebox
a skateboard ramp
Answer:
a shoe box
Step-by-step explanation:
i'm not 100% sure but isn't a shoe box rectangular?
Write an equation that best represents the line
The population of a city in the year 2000 was 500,000. Over the following decade the population
grew by 8%. What was the population of the city in 2010?
Answer:
The closest thing I could get was 540 000
The sum of four consecutive integers is -10. What are the integer
Answer:
see below
Step-by-step explanation:
Let x be the first integer
x+1 is the next integer
x+2 = next integer
x+3 = last integer
The sum of the 4 integers is -10
x+ x+1 + x+2 + x+3 = -10
Combine like terms
4x+6 = -10
Subtract 6 from each side
4x+6-6 = -10-6
4x = -16
Divide each side by 4
4x/4 = -16/4
x = -4
x+1 = -3
x+2 = -2
x+1 =-1
The integers are -4, -3, -2 ,-1
Least multiple of 5 and 25
Answer:
25
Step-by-step explanation:
25 is a multiple of 5, so is the least multiple of both 5 and 25.
Answer:
Hey there!
That would be 25.
Hope this helps :)
a man owned 75 shares of stock worth $50 each the corporation declared a dividend of 8% payable in stock how many shares did he then own
Answer:
81 shares
Step-by-step explanation:
Data provided in the question
Number of shares owned = 75 shares of stock
Per share value = $50
Dividend declared = 8%
Based on the above information. the number of shares owned is
[tex]= Number\ of \ shares\ owned \times dividend\ declared\ percentage + Number\ of \ shares\ owned[/tex][tex]= 75\shares \times 8\% + 75\shares[/tex]
= 81 shares
We simply added the number of shares owned and the number of shares owned after considered the dividend declared percentage so that the correct shares owned could arrive
Use the graph to estimate the solution of the system.
x + 2y = 5,
-x + 3y = 6
Which integers is the x-value between?
What is the x-value to the nearest tenth?
Which integers is the y-value between?
What is the y-value to the nearest tenth?
Answer:
x is between 0 and 1
x is almost 0.5
y is between 2 and 3
y is almost 0.2
Answer:
1st answer: 0 and 1
2nd answer: about 0.6
3rd answer: 2 and 3
4th answer: about 2.2
Step-by-step explanation:
I got it correct! Edge 2021:)
Mr. Suárez wants to paint his storage shed. He needs to calculate the lateral surface area of the shed so that he will know how much paint to buy. The shed is in the shape of a rectangular prism with the dimensions shown below. Including the doors, what is the lateral surface area of the storage shed in square feet? 784 ft2 266 ft2 532 ft2 336 ft2
Answer:
Lateral surface area of the storage shed = 336 ft²
Step-by-step explanation:
The picture is the complete question.
The shed is in the shape of a rectangular prism. The lateral surface area of the storage shed can be calculated below. The lateral area is the sides of the prism.
lateral area of a rectangular prism = 2h (l + w)
where
l = length
h = height
w = width
h = 8 ft
l = 14 ft
w = 7 ft
lateral area of a rectangular prism = 2h (l + w)
lateral area of a rectangular prism = 2 × 8 × (14 + 7)
lateral area of a rectangular prism = 16 (21)
lateral area of a rectangular prism = 336 ft²
Lateral surface area of the storage shed = 336 ft²
An experiment consists of spinning a spinner. Use the results in the table to find the experimental probability that the spinner does not land on yellow. Express your answer as a fraction in simplest form.
Red = 12
Blue = 10
Yellow = 6
A. 11/14
B. 3/7
C. 4/7
D. 3/14
Answer:
A. 11/14
Step-by-step explanation:
i hope this helps :)
The Probability of an Event P(E) is that the spinner does not land on yellow is 11/7.
An experiment consists of spinning a spinner.
Red = 12
Blue = 10
Yellow = 6
We have to determine,
The experimental probability is that the spinner does not land on yellow.
The total number of spinner= 12+10+6
The total number of spinner=28.
What is the formula for the experimental probability?Probability of an Event P(E) = Number of times an event occurs / Total number of trials.
The number of trials to not land on yellow is,
12+10=22
Therefore the Probability of an Event P(E) is given by,
[tex]P(E)=\frac{22}{28}[/tex]
[tex]P(E)=\frac{11}{14}[/tex]
Therefore option A is correct.
To learn more about the probability visit:
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Solve:
[tex]{2x}^{2} + x - 3 = [/tex]
Use the drop-down menus to answer the questions.
What is the probability that a randomly chosen tenth-grader is male?
Answer:
Step-by-step explanation:
The information given is not enough to determine the probability.
Given the number of male tenth-grader, and the number of all tenth-grader, the probability will then be: (number of male tentg-grader) divided by (the total number of students).
Answer:
What is the probability that a randomly chosen tenth-grader is male?
✔ 80/154
What is the probability that a randomly chosen tenth-grader is male given that the tenth-grader prefers geometry?
✔ 47/87
Are the events “male” and “geometry” independent?
✔ no, P(male) does not equal P(male | geometry)
Step-by-step explanation: These are the answers for edge 2020
This test is gonna be the end of me lol
Answer:
WC
Step-by-step explanation:
Noah paid off a loan with a simple interest rate of 9.7% in 4 months. What was the APR?
29.1%
3.23%
2.43
15.5%
9.7%
Answer:
9.7% for 4 months = 9.7 * 3 = 29.1% for the year.
Step-by-step explanation:
Let s be the solid obtained by rotating the region shown in the figure about the y-axis (Assume a = 5 and b = 2)
Sketch a typical approximating shell.
What are its circumference c and height h?
c(x) =
h(x) =
Use shells to find the volume V of S.
V =
Answer:
see attached for a figurec(x) = 2πxh(x) = 5x(x -2)^2V = 32π/3Step-by-step explanation:
The volume is the summation of the volumes of the shells. The volume of a shell is its circumference ...
c(x) = 2πx
multiplied by its height ...
h(x) = 5x(x -2)^2
and its thickness, dx.
That summation is the integral ...
[tex]\displaystyle V=\int^2_0 {2\pi x(5x)(x-2)^2} \, dx=10\pi\int^2_0 {(x^2-2x)^2} \, dx=10\pi\left(\dfrac{2^5}{5}-\dfrac{4(2^4)}{4}+\dfrac{4(2^3)}{3}\right)\\\\\boxed{V=\dfrac{32\pi}{3}}[/tex]
The circumference of the shell is c(x) = 2πx
The height of the shell is [tex]h(x) = 5x(x-2)^{2}[/tex]
The required volume of the shell is [tex]\frac{32\pi}{3}[/tex].
Given that,
S be the solid obtained by rotating the region,
Where, a = 5 and b =2
We have to determine ,
What are its circumference c and height h.
According to the question,
The volume is the summation of the volumes of the shells. The volume of a shell is its circumference ,c(x) = 2πx
And the height of the shell.
[tex]h(x) = 5x(x-2)^{2}[/tex]
The volume of the shell is given by,[tex]V = \int (circumference) \ )(height )\ . dx\\\\[/tex]
Where dx thickness of the shell.
Substitute the value in the equation,
[tex]v = \int\limits^2_0 {2\pi x .(5x) (x-2)^{2} }\, dx\\\\v = \int\limits^2_0 {10\pi x^{2} (x-2)^{^{2}} \ d x\\\\\\v =10\pi \int\limits^2_0 {x^{2}.(x^2+4-4x)} \, dx \\\\V = 10\pi \int\limits^2_0( {x^{4} + 4x^{2} - 4x^{3}) \, dx[/tex]
[tex]v = 10\pi \ [ \dfrac{x^{5}}{5} + \dfrac{4x^{3}}{3} - x^{4}]^{2}_0\\\\v = 10\pi [ \dfrac{2^{5}}{5} + \dfrac{4.2^{3}}{3} - 2^{4} - \dfrac{0^{5}}{5} -\dfrac{4.0^{3}}{3} + 0^{4}]}\\\\v = 10\pi \ [ \dfrac{32}{5} + \dfrac{32}{3} - 16 -0-0+0]\\\\v = 10\pi [\dfrac{96+160-240}{15}]\\\\v = 10\pi [\dfrac{16}{15}]\\\\v = \dfrac{32\pi }{3}[/tex]
Hence, The required volume of the shell is [tex]\dfrac{32\pi}{3}[/tex].
To know more about Integration click the link given below.
https://brainly.com/question/16649904
What is the median number of carrots in a one-pound bag?
Answer:
To find the medium order the numbers from least to greatest. Then each time cross off one number from the left side and the right. When you get down to 1 or you have 2 left those are your medians. If you have 2 numbers add them up and divide them by 2. If you have 1 that is your medium. Hope this helps. The median is 70.
Step-by-step explanation:
What is the volume of a box with length
1 m, width 8 m, and depth 6 m?
Answer:
Here is the answer mate. Hope it helps. Please rate my answer and mark as brainlist if you find it helpful.
Answer:
[tex] = 48 {m}^{3} [/tex]
Step-by-step explanation:
[tex]volume = l \times w \times b \\ = 1 \times 8 \times 6 \\ = 48 {m}^{3} [/tex]
Convert the angle θ = 3 π 5 θ= 5 3π theta, equals, start fraction, 3, pi, divided by, 5, end fraction radians to degrees.
Answer: 3pi/5 and 5/3pi?
Step-by-step explanation:
Answer:
Step-by-step explanation:
3pi/5 * 180/pi
3/5 * 180/1
3/1 * 36
3*36
108 degrees
5/3pi * pi/180
5/3 * 1/180
1/3 * 1/36
1/108
Write the equation in standard form and then find the center (h, k) and
x^2+8x+ y2 + 4y - 5= 0
Answer:
Center is at (-4, -2) and the radius = 5.
Step-by-step explanation:
Convert to Standard form:
x^2 + 8x + y2 + 4y - 5= 0
Completing the square:
(x + 4)^2 - 16 + (y + 2)^2 - 4 = 5
(x + 4)^2 + (y + 2)^2 = 5 + 16 + 4
(x + 4)^2 + (y + 2)^2 = 25
(x - h)^2 + (y - k)^2 = r^2 Comparing:-
The center is at (-4, -2) and the radius = 5.
200 students, which was 40% of the 7th graders said that the dress code was an important issue at school. How many students are in the 7th grade?
Answer:
there are 80 students
Step-by-step explanation:
In how many different ways can a person select one book from 3 novels, one book from 5 biographies and one book from 7 self-help books?
a). 15
b). 105
c). 3
d). 22
Answer:
[tex] Ways = 3*5*7= 105[/tex]
And that's equivalent to:
[tex] Ways= (3C1) (5C1) (7C1) =3*5*7=105[/tex]
Where C represent the term combinatory defined as:
[tex] nCx = \frac{n!}{x! (n-x)!}[/tex]
And then the number of ways to select the three books are 105, and the best option would be:
b). 105
Step-by-step explanation:
For this case we can use the multplication principle of counting or sometimes called the product rule.
We have a total of 3 novels, 5 biographies and 7 self-help books. And we can find the number of ways that a person can select the three books with theis product:
[tex] Ways = 3*5*7= 105[/tex]
And that's equivalent to:
[tex] Ways= (3C1) (5C1) (7C1) =3*5*7=105[/tex]
Where C represent the term combinatory defined as:
[tex] nCx = \frac{n!}{x! (n-x)!}[/tex]
And then the number of ways to select the three books are 105, and the best option would be:
b). 105
We want to see in how many different ways a person can select one book from 3 novels, one book from 5 biographies and one book from 7 self-help books, the correct option is b: 105.
To get the numbe of different ways, the first thing we need to do is find the selections.
Here we have 3 selections:
Novel selection.Biography selectionSelf-help selection.Now we need to find the number of options for each of these selections, and just multiply the numbers of options.
we have:
Novel selection: 3 optionsBiography selection: 5 optionsSelf-help selection: 7 optionsNumber of different ways of selecting = 3*5*7 = 105
So the correct option is b.
If you want to learn more, you can read:
https://brainly.com/question/3349431
Find an equation of the circle that has center (1, -1) and passes through (5, -6).
Answer:
Step-by-step explanation:
(x-1)²+(y+1)²=41
Please help me!!!!!
Answer: is answer b
Step-by-step explanation:
Answer: The answer is B
Step-by-step explanation:I did the quiz
Please solve this !!! ASAP !!!
Answer the picture below.Please ignore the blue dot that was a miss click.
the answer is
48 2/9 ft.
I did the equation for it
Ty’s experimental probability of winning a certain game is 1/3. Jana’s expiremental probability of winning the same game is 3/4. If Ty and Jana each played the game 120 times, how many more games would Jana expect to win over Ty?
Answer:
Jana is expected to win 40 more games over Ty.
Step-by-step explanation:
If Ty plays the game 120 times, he is expected to win in 1/3 part of 120 games, which is ( 1/3 * 120 =) 40 games.
If Jana plays the game 120 times, she is expected to win in 2/3 part of 120 games, which is ( 2/3 * 120 =) 80 games.
If Jana is expected to win 80 times an Ty is expected to 40 times, then Jana is expected to win ( 80 - 40 =) 40 more games over Ty.
What’s the correct answer for this?
Answer:
2 is the answer according to me
Negative numbers have positive square roots.
O A. True
B. False
Answer:
false
Step-by-step explanation:
Answer:
false
Step-by-step explanation:
negative numbers can't have square roots
Question 2(Multiple Choice Worth 5 points)
(03.09 LC)
What is the default view in a Word document?
O Copy View
O Editing View
O Paste View
O Reading View
Answer:
EDITING VIEW
Step-by-step explanation:
What is the volume of the pyramid?
A solid oblique pyramid has an equilateral triangle as a base
with an edge length of 4/3 cm and an area of 12/3 cm.
O 12/3 cm3
16/3 cm
24/3 cm3
32/3 cm3
Answer:
16/9 cm³Step-by-step explanation:
Volume of a triangular pyramid = 1/3 * Base area * height
Given the Base area = area of the equilateral triangle = 12/3 cm
Height of the pyramid = length of its edge = 4/3 cm
Substituting this values in the formula we have;
V = 1/3 * 12/3 * 4/3
V = 48/27
V = 16/9 cm³
The volume of the given triangular pyramid is; B: 16/3 cm²
What is the Volume of the Pyramid?
Formula for volume of a triangular pyramid is;
V = ¹/₃ * Base area * height
We are given;
Base area = area of the equilateral triangle = 12 cm²
Height of the pyramid = length of its edge = 4/3 cm
Thus;
V = ¹/₃ * 12 * (4/3)
V = 16/3 cm³
Read more about Volume of Pyramid at; https://brainly.com/question/16203922
which list orders the anglesof trangle abc smallest to largest...ab=130 and ac=120 and bc=180
Answer:
I think goes 130 and then 180 then 120 it's need to be to have an angle i think.
Step-by-step explanation:
Because it's a-c so abc is 120
a-b is 130 and b-c it's gona be 180
I might be wrong but i have 2 answer 120 130 180 or
130 180 120.