Starting at 6 a.m. every morning, Matilda receives text messages on her cell phone from her mother, her best friend, and her brother according to three independent Poisson processes. Her mother texts Matilda on average once every hour. Her best friend sends a message once every 10 minutes, and she receives messages from her brother every 30 minutes.
A) Find the probability that by 7:30 a.m. Mary receives exactly four messages – two of her best friend and two of her mother.
B) With a chance of 75% a text message contains a typo independent of the sender. Find the probability that there are no typos in the text messages Matilda receives between 2 p.m. and 5 p.m.

Answers

Answer 1

Answer:

a) 0.0013 = 0.13% probability that by 7:30 a.m. Mary receives exactly four messages – two of her best friend and two of her mother.

b) [tex]1.6 \times 10^{-9}[/tex] probability that there are no typos in the text messages Matilda receives between 2 p.m. and 5 p.m.

Step-by-step explanation:

Poisson distribution:

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 interval.

A) Find the probability that by 7:30 a.m. Mary receives exactly four messages – two of her best friend and two of her mother.

Two from the best friend:

Her best friend sends a message once every 10 minutes.

From 6 to 7:30, there is an hour and a half, that is, 90 minutes, so the mean for her best friend is [tex]\mu = \frac{90}{10} = 9[/tex]

Two messages is P(X = 2). So

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 2) = \frac{e^{-9}*9^{2}}{(2)!} = 0.0050[/tex]

Two from the mother:

Message every hour = 60 minutes. So [tex]\mu = \frac{90}{60} = 1.5[/tex]. This is P(X = 2).

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 2) = \frac{e^{-1.5}*1.5^{2}}{(2)!} = 0.2510[/tex]

Two of her best friend and two of her mother:

Independent events, so the probability of both happening is the multiplication of their separate probabilities.

[tex]p = 0.005*0.251 = 0.0013[/tex]

0.0013 = 0.13% probability that by 7:30 a.m. Mary receives exactly four messages – two of her best friend and two of her mother.

B) With a chance of 75% a text message contains a typo independent of the sender. Find the probability that there are no typos in the text messages Matilda receives between 2 p.m. and 5 p.m.

In 3 hours, she is expected to receive:

3*60/10 = 18 messages from her best friend.

3*60/60 = 3 messages from her mother.

3*60/30 = 6 messages from her brother.

In total, 27 messages.

75% probability of a typo, so [tex]\mu = 0.75*27 = 20.25[/tex]

This is P(X = 0).

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-20.25}*20.25^{0}}{(0)!} = 1.6 \times 10^{-9}[/tex]

[tex]1.6 \times 10^{-9}[/tex] probability that there are no typos in the text messages Matilda receives between 2 p.m. and 5 p.m.


Related Questions

Which of the following best describes a triangle with one right angle and two congruent sides?
A right scalene triangle
B. acute scalene triangle
C. right isosceles triangle
D acute isosceles triangle

Answers

Answer:

C

Step-by-step explanation:

A is impossible. You cannot have both a right triangle and in the same triangle have an angle in it that is over 90 (that's the meaning of scalene)

B is sort of true, but only sort of. All scalene triangles have an angle over 90 and 2 acute angles.

C this is the answer to the question. It has 1 right angle and 2 equal sides. The two equal sides make it isosceles and the right angle is given.

D an acute triangle has three angles under 90 that add to 180. Not the right description.

A triangle with one right angle and two congruent sides is described as a "right isosceles triangle." (Option C)

Let's break down the terms:

1. Right Angle: A right angle is an angle that measures exactly 90 degrees.

2. Isosceles Triangle: An isosceles triangle is a triangle with at least two sides of equal length (congruent sides).

3. Right Isosceles Triangle: A right isosceles triangle is a special type of isosceles triangle where one of the angles is a right angle (90 degrees) and the other two angles are equal, each measuring 45 degrees.

In a right isosceles triangle, the two congruent sides are the legs of the right triangle, and the third side (opposite the right angle) is called the hypotenuse.

So, among the given options, the best description for a triangle with one right angle and two congruent sides is a "right isosceles triangle" (Option C).

To know more about right isosceles triangle, refer here:

https://brainly.com/question/30966657

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A group decides to go white-water rafting on a river. The map they have of the river has the scale 3 inches:7 miles. On the map, the distance between the start point and the end point of their trip is 15 inches. What is the actual distance?

Answers

10 inches is a good size for the diametee

Choose the polynomial written in standard form and it’s in the picture

Answers

Answer:

C) x^7y²+4x³+10x³

Step-by-step explanation:

C) x^7y²+4x³+10x³

Which graph represents the solution 2x - 5y <3

Answers

Answer:

There is no picture... But here is a representation of the inequality on a graph

The graph 2x - 5y < 3 cut the x-axis at the point (3,0) and the y-axis at the point (0,-0.6).

What is inequality?

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relation between variables and the numbers.

Given inequality is 2x - 5y <3. A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

When the inequality 2x - 5y < 3 is plotted on the graph it covers the region which is less than the line 2x - 5y < 3. The graph cut the x-axis at the point (3,0) and the y-axis at the point (0,-0.6).

The graph of the given inequality is attached with the answer below.

To know more about inequality follow

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What is the estimate of the nearest integer of 38

Answers

Look down at the photos!

|

|

|

V

I’m kinda confused with the question but I think the answer is itself, or 38.

HELP PLEASE THIS IS 80% OF MY GRADE

Answers

Answer:

nice pfp also 2507.99

Step-by-step explanation:

you would find out 3/5ths of the amount of money she earned then multiply 20 by 2 then take that away from whatevers left from paying bills then subtract 12.99 from the 2520.98 you got after paying for the shirts leaving you with 2507.99

4283.30 divided by 5=856.66
856.66x3=2569.98
19.99+19.99+12.99=52.97
2569.98-52.97=2571.01

2/9 of the students in a school are in sixth grade.

a. How many sixth graders are there if the school has
90 students?

b. How many sixth graders are there if the school has
27 students?

c. if the school has x students write an expression for the number of students of sixth graders in terms of x

d. how many students are in the school of 42 of them are in 6th grade

Answers

Answer:

a) 20 sixth graders.

b) 6 sixth graders.

c) 2/9x sixth graders.

d) 189 students in the school.

Step-by-step explanation:

a) 2/9 of 90 = 2/9 * 90 = 20 students.

b) 2/9 of 27 = 2/9 * 27 = 6 students.

c) 2/9 of x = 2/9x

d) 42 = 2/9x so solve the equation: x = 189 students.

If we have 90 students in the school then we will have  20 sixth grade students.

a. From the details of the question, we have 2/9 of the students in the school in sixth grade. Hence;

Number of students in sixth grade = 2/9 × 90 = 20 sixth grade students

b. If the school has 27 students, number of sixth graders =  2/9 ×  27 = 6 sixth grade students

c. If we have x students in the school, the number of sixth graders =  2/9 × x = 2/9x students

d. If we have 42 students in sixth grade, the number of students in the school is;

2/9 × x = 42

x = 9/2 × 42 = 189 students

Learn more about fractions: https://brainly.com/question/1301963

What is the volume of the following rectangular prism? 3/20 2/3 units? 20 2

PLEASE HELP AND DONT GIVE SOME BS ANSWER ​

Answers

Answer: It's 1/10 square units^3

Step-by-step explanation: 3/20 * 2/3

multiply the 3 times the 2, then multiply the 20 times the 3 and you will get 6/60 which simplifies to 1/10. Hope this helps.

The cost of 5 squash and 2 zucchini is $132 Three squash and 1 zucchini cost $0.73. Write a system of
equations

Answers

Answer:

s=-130.54

z=392.35

if you were to run a business like this I belive you would be losing alot of money perhaps try and check if your missing a decimal

Step-by-step explanation:

Squash=s

Zucchini=z

5s+2z=132

3s+z=.73

Im not sure why your prices are so different, but I think you may have forgotten a decimal point.

set z by itself using the 2nd equation

z=-3s+.73

substitute the equation into the first one

5s+2(-3s+.73)=132

expand

5s-6s+1.46=132

move the 1.46 to the other side and simplify

-s=130.54

s=-130.54

now put this back into one of the equations to find z

3(-130.54)+z=.73

z=392.35

s is inversely proportional to t.
When s
0.4, t = 4
Work out s when t = 0.8​

Answers

s = 2

0.4x4 = 1.6
1.6/0.8 = 2

Answer:

0.2

Step-by-step explanation:

Sorry i dk how to explain it

What is the right answer

Answers

Answer:

B) y = 1/3x - 2

Step-by-step explanation:

i plotted the points on a graph and found the rise and the run

..........................................................................

Answers

Answer:

1. 17.8 cm

2. 32.0 cm

3. 15.9 m

Step-by-step explanation:

1. Determination of the length of the arc.

Radius (r) = 6 cm

Angle at the centre (θ) = 170°

Pi (π) = 3.14

Length of arc (L) = ?

L = θ/360 × 2πr

L = 170/360 × 2 × 3.14 × 6

L = 17/36 × 37.68

L = 17.8 cm

2. Determination of the length of the arc.

Diameter (d) = 13 cm

Angle at the centre (θ) = 282°

Pi (π) = 3.14

Length of arc (L) = ?

Next, we shall determine the radius. This can be obtained as follow:

Diameter (d) = 13 cm

Radius (r) =?

r = d/2

r = 13/2

r = 6.5 cm

Finally, we shall determine the length of the arc. This can be obtained as follow:

Radius (r) = 6.5 cm

Angle at the centre (θ) = 282°

Pi (π) = 3.14

Length of arc (L) = ?

L = θ/360 × 2πr

L = 282/360 × 2 × 3.14 × 6.5

L = 282/360 × 40.82

L = 32.0 cm

3. Determination of the length of the arc.

Radius (r) = 11 m

Angle at the centre (θ) = 83°

Pi (π) = 3.14

Length of arc (L) = ?

L = θ/360 × 2πr

L = 83/360 × 2 × 3.14 × 11

L = 83/360 × 69.08

L = 15.9 m

solve for X
(4x+7)
(2x+5)​

Answers

Answer:

x= 28

Step-by-step explanation:

combine the equations and set equal to 180, since a striaght line is 180 degrees. When combined you get, 6x + 12=180. Subtract, 180-12=168, then divide by 6 to get 28

these are fractions. Help plz will give brainly

Answers

Step-by-step explanation:

hakssmsjxxajxnskjznzmzKsjx

2m+3(m-8)=1 I need this answer pls

Answers

Answer:

m=5

Step-by-step explanation:

Which is the better buy?
4-pack of light bulbs for $6.84
Or
9-pack of light bulbs for $15.66

Answers

Answer:

The 9 pack is cheaper.

Step-by-step explanation:

A pack of 9 for $15.66 would cost 57 cents per bulb.

A pack of 6 for $6.84 would cost 87 cents per bulb.

The 9 pack would be cheaper to buy.

Hope this helps!

PLZ HURRY IT'S URGENT!!!
What is the vertex of the following quadratic?

y=a(x−h)2+k
options:

(h, k)


(k, -h)


(k, h)


(-h, k)

Question 2
What is the vertex of the following quadratic?

y=2(x+3)2−5
options:

(-3, 5)


(3, -5)


(-3, -5)


(3, 5)

Question 3
What is the vertex of the following quadratic?

y=23(x−1)2+7
options:

(-1, 7)


(-1, -7)


(1, -7)


(1, 7)

Question 4
What is the vertex of the following quadratic?

y=−3(x−9)2−2
options:

(-2, -9)


(9, -2)


(-9, -2)


(-2, 9)

Question 5
What is the vertex of the following quadratic?

y=(x+4)2−6
options:

(4, -6)


(-6, 4)


(-6, -4)


(-4, -6)

Answers

Answer:

1. h,k

2. -3, -5

3. 1, 7

4. 9, -2

5. -4, -6

Step-by-step explanation:

Please help!!!!! So lost

Answers

It’s open circle and a line pointed left so less than of equal to 75?

A 2.5-kg bag of grass seed covers an area of 1200 m2. How much seed is needed to cover a square park with side length 500 m?

Answers

Answer:

520.83 k g  of seed

Step-by-step explanation:

Answer:

A #2.5#-#kg# bag of grass seed covers an area of #1200# #m^2#. How much seed is needed to cover a square park with side length #500# #m#?

Step-by-step explanation:

Match each slope and y-intercept with the appropriate linear equation.

Answers

Answer:

see below

Step-by-step explanation:

(1,4)

(2,1)

(3,2)

(4,3)

i listed them in the order shown, like if i wrote 4 then it's 4th on the list lol

Answer:

I'm gonna say the order from left to right so for example, if I say 1 1 to 4, i mean the first one on the left, leads to the last one on the right. Answers are below:

Step-by-step explanation:

1 to 4

2 to 1

3 to 3

4 to 2.

And before you say i copied the person above me, I didn't. Their answers are wrong, all i did was copy the idea because i don't have enough time to write out the actual answers. Hope this helped.

Help me out with this question please mathematic ✏️

Answers

Answer:

the second bubble is the answer

Step-by-step explanation:

What is the perimeter of the shaded figure?

Answers

the perimeter is 5 units

What is an equation of the line that passes through the points (4, 3) and (-6, 3)?

Answers

Answer:

Step-by-step explanation:

(4,3)(-6,3)

3-3/-6-4

m=0

y=3

Answer:

y=3

Step-by-step explanation:

Something that I notice about this is that the 2 y coordinates are the same

This means that the line isn't increasing nor decreasing, it's constant

if we look at the y=mx+b

we have, so far,

y=0x+b

we just need be

we know that when x=4 y=3 so we have

3=(0)(4)+b

b=3

so the answer is just y=3

Express g(x) = x4 + 2x3 − x2 + 4x + 12 as the product of linear and irreducible quadratic terms.

Answers

If your asking for the answer it’d be
x= -1

find the perimeter n area pls !

Answers

Answer:

6yx

Step-by-step explanation:

x is divided by -2 less than 5

Answers

Answer:

X/-2>5

Step-by-step explanation:

This is an Inequality

Refer to the Exhibit Teacher's Salary. Find the probability that a randomly selected teacher receives a salary of $45,000 or more. (Do not round your answer)

Answers

Answer:

[tex]P(x \ge 45000) = 0.77935[/tex]

Step-by-step explanation:

Given [Missing from the question]

Exhibit Teacher's Salary:

[tex]\bar x=50000[/tex]

[tex]s = 6500[/tex]

Required

Calculate [tex]P(x\ge 45000)[/tex]

First, we calculate the z score

[tex]z = \frac{x - \bar x}{s}[/tex]

[tex]z = \frac{45000 - 50000}{6500}[/tex]

[tex]z = \frac{-5000}{6500}[/tex]

[tex]z = -0.77[/tex]

[tex]P(x \ge 45000) = P(z \ge -0.77)[/tex]

[tex]P(x \ge 45000) = 1 - P(z \le -0.77)[/tex]

From the table:

[tex]P(z \le -0.77) = 0.22065[/tex]

So, we have:

[tex]P(x \ge 45000) = 1 - 0.22065[/tex]

[tex]P(x \ge 45000) = 0.77935[/tex]

Determine whether each relation is a function. If so, provide the domain and range.

Answers

Answer:

Not a function

Step-by-step explanation:

A relation is considered a function if and only if every input value has exactly one output value.

The relation given does not satisfy the condition of a function. The input value, height = 160 cm, is related to different output values (age).

Therefore, the relation is not a function.

Which of the following inequalities is equivalent to ​

Answers

Answer: the last one

Step-by-step explanation:

please help! i fell asleep and only have until 2:45!! i have other questions that i couldn’t get a pic of.

27.2 is 68% of what number?

what number is 162.2% of 55?

12 is what percent of 20?

15 is 25% of what number?

Find 17% of 655.

Answers

Answer:

For the one in the picture, it is 121. A.

Step-by-step explanation:

This is because 45% of 220 is 99. But, the question is asking for how many coins are NOT, so you do 220 - 99 to get 121.

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