Somebody please assist me here

Somebody Please Assist Me Here

Answers

Answer 1

The base case of [tex]n=1[/tex] is trivially true, since

[tex]\displaystyle P\left(\bigcup_{i=1}^1 E_i\right) = P(E_1) = \sum_{i=1}^1 P(E_i)[/tex]

but I think the case of [tex]n=2[/tex] may be a bit more convincing in this role. We have by the inclusion/exclusion principle

[tex]\displaystyle P\left(\bigcup_{i=1}^2 E_i\right) = P(E_1 \cup E_2) \\\\ P\left(\bigcup_{i=1}^2 E_i\right) = P(E_1) + P(E_2) - P(E_1 \cap E_2) \\\\ P\left(\bigcup_{i=1}^2 E_i\right) \le P(E_1) + P(E_2) \\\\ P\left(\bigcup_{i=1}^2 E_i\right) \le \sum_{i=1}^2 P(E_i)[/tex]

with equality if [tex]E_1\cap E_2=\emptyset[/tex].

Now assume the case of [tex]n=k[/tex] is true, that

[tex]\displaystyle P\left(\bigcup_{i=1}^k E_i\right) \le \sum_{i=1}^k P(E_i)[/tex]

We want to use this to prove the claim for [tex]n=k+1[/tex], that

[tex]\displaystyle P\left(\bigcup_{i=1}^{k+1} E_i\right) \le \sum_{i=1}^{k+1} P(E_i)[/tex]

The I/EP tells us

[tex]\displaystyle P\left(\bigcup\limits_{i=1}^{k+1} E_i\right) = P\left(\left(\bigcup\limits_{i=1}^k E_i\right) \cup E_{k+1}\right) \\\\ P\left(\bigcup\limits_{i=1}^{k+1} E_i\right) = P\left(\bigcup\limits_{i=1}^k E_i\right) + P(E_{k+1}) - P\left(\left(\bigcup\limits_{i=1}^k E_i\right) \cap E_{k+1}\right)[/tex]

and by the same argument as in the [tex]n=2[/tex] case, this leads to

[tex]\displaystyle P\left(\bigcup\limits_{i=1}^{k+1} E_i\right) = P\left(\bigcup\limits_{i=1}^k E_i\right) + P(E_{k+1}) - P\left(\left(\bigcup\limits_{i=1}^k E_i\right) \cap E_{k+1}\right) \\\\ P\left(\bigcup\limits_{i=1}^{k+1} E_i\right) \le P\left(\bigcup\limits_{i=1}^k E_i\right) + P(E_{k+1})[/tex]

By the induction hypothesis, we have an upper bound for the probability of the union of the [tex]E_1[/tex] through [tex]E_k[/tex]. The result follows.

[tex]\displaystyle P\left(\bigcup\limits_{i=1}^{k+1} E_i\right) \le P\left(\bigcup\limits_{i=1}^k E_i\right) + P(E_{k+1}) \\\\ P\left(\bigcup\limits_{i=1}^{k+1} E_i\right) \le \sum_{i=1}^k P(E_i) + P(E_{k+1}) \\\\ P\left(\bigcup\limits_{i=1}^{k+1} E_i\right) \le \sum_{i=1}^{k+1} P(E_i)[/tex]


Related Questions

Use the five numbers 12, 11, 19, 16, and 12 to complete parts a) through e) below.
a) Compute the mean and standard deviation of the given set of data.
The mean is x = and the standard deviation is s =
(Round to two decimal places as needed.)

Answers

Answer:

mean = 14 and standard deviation = 3.03

Step-by-step explanation:

mean = sum of all numbers ÷ by the numbers available

= (11 + 12 + 12 + 16 + 19) ÷ 5

= 70 ÷ 5

= 14

FOR STANDARD DEVIATION * USE A SCIENTIFIC CALCULATOR THEY WON'T PENALIZE YOU*

follow these steps:

1. press mode then STAT

2. then press 1-VAR

3. put all the numbers on the table in ascending order

4 after press AC

5. press shift then 1

6. you will see many things but we are only interested in standard deviation, press *Var*

7. then select the standard deviation sign and press the equal sign

Let's say that the turkey sat on the counter for an additional hour (beyond the 390 minutes) and its temperature cooled to 80 degrees. Write that value in function notation

Answers

The value of the temperature in function notation is gotten as; f(x) = 91 - 11x

How to write a function Notation?

Let us first find the relationship between temperature and how long the turkey sits out.

The temperature after the normal 390 minutes  is equal to approximately 6.5 hours.

Let us create a ratio and solve for x, which represents the temperature change during that extra hour after the "normal time sitting out".

Thus;

(7.5/6.5) = (80/80+ x)

Solving for x gives x = -10.7.

This means that for every extra hour it sits out, the turkey cools approximately 11°. When we add that to 80°, we have 91° which is the expected temperature after 390 minutes (6.5 hours) of sitting out.

Thus, the motion as a function of time is;

f(x) = 91 - 11x

Read more about Function Notation at; https://brainly.com/question/27834526

#SPJ1

Quick please!
Will give brainliest
100 points
3(4j + 7 + 2j) or 3(6j +7) b. Use the distributive property to create an equivalent expression.

Answers

Answer:

3(4j + 7 + 2j)

12j + 21 + 6j

12j + 6j + 21

18j + 21 ----- (1)

3(6j +7)

18j + 21 --------(2)

eq 1 = eq. 2

both are equal

The function y=(x-4)2+3 is a transformation of the function y=x2. How is the functions vertex affected by the transformation?

Answers

It is shifted 4 units right and 3 units up.

use the point–slope formula to write an equation of the line that passes through(-5, -16 )and has a slope of m = 3 . Write the answer in slope–intercept form (if possible).

Answers

Answer:

y + 16 = 3(x + 5)

Step-by-step explanation:

When you write an equation in point-slope form, you only need two things: a point and a slope.

Given:

point: (-5, -16)slope (m): 3

The standard point-slope equation is

y - y₁ = m(x - x₁)

Plug in what you know.

y - (-16) = 3(x - (-5))

Simplify.

y + 16 = 3(x + 5)

This is your equation.

Learn with another example:

brainly.com/question/24436844

5, 3.1.24

f(x) = 3x² + 5; find f(x + 3) - [f(x) + 3]

Answers

Given that [tex]f(x) = 3x^2 + 5[/tex], we have

[tex]f(x + 3) = 3 (x + 3)^2 + 5 \\\\= 3 (x^2 + 6x + 9) + 5 \\\\= 3x^2 + 18x + 32[/tex]

so that

[tex]f(x+3) - (f(x) + 3) = (3x^2 + 18x + 32) - (3x^2 + 8) \\\\= \boxed{18x + 24}[/tex]

for what value of k will the relation not be a function
R={(k-8.3+2.4k,-5),(3/4k,4)}

Answers

Step-by-step explanation:

hope you can understand

It takes 70 pounds of seed to completely plant an 8-acre field. How many acres can be planted per pound of seed?

Answers

No. of pounds of seed it takes to plant an 8-acre field = 70 pounds.

No. of acres can be planted per pound of seed = 70/8

= 8.75.

thus, 8.75 acres can be planted per pound of seed.

Given the graph of the pre-image and image, identify the correct
coordinate transformation.

Answers

The preimage was shifted to the image by a translation 2 units right and 2 units up, so the answer is [tex](x,y) \longrightarrow (x+2, y+2)[/tex]

f(x)=7; find f(-3) and f(0.1)

Answers

Answer:

f(-3) = 7

f(0.1) = 7

Step-by-step explanation:

The function f(x)=7 gives an output of 7 for all inputs. In other words, no matter what we plug in for x, f(x) will equal 7.

When graphed, f(x)=7 produces a horizontal line at y=7. From there, you can also see that any value of x gives an output of 7.

why is smallest possible angle of a 36-gon 5 degrees instead of 4.72222222222?

Answers

The smallest interior angle of the given regular polygon with 36 sides is; 170°

How to find the sum of interior angles of a polygon?

The formula for calculating the sum of interior angles of a regular polygon is; S = (n − 2) × 180°

where n is number of sides of the polygon

We are told that number of sides of ploygon is 36. Thus;

S = (36 - 2) × 180°

S = 6120°

Thus;

Smallest possible angle of polygon = 6120/36 = 170°

Sum of external angles of a regular polygon is;

S = 360/n

S = 360/36

S = 10°

Read more about Polygon Angles at; https://brainly.com/question/1592456

#SPJ1

Find the area of the shaded portion of the
figure. All angles are right angles.
Dimensions are in inches.
3
8
5

Answers

Answer:  22 square inches

======================================================

Explanation:

The white rectangle is 3 by 6 with area of 3*6 = 18 square inches.

The larger rectangle is 8 by 5 with area of 8*5 = 40 square inches.

The difference of these will get us the shaded area:

40 - 18 = 22 square inches


Given the function f(x) = 8x^2-3x+2 Calculate the following values

Answers

[tex]1) \text{ } f(-2)=8(-2)^{2}-3(-2)+2=\boxed{40}\\\\2) \text{ } f(-1)=8(-1)^{2}-3(-1)+2=\boxed{13}\\\\3) \text{ } f(0)=8(0)^{2}-3(0)+2=\boxed{2}\\\\4) \text{ } f(1)=8(1)^{2}-3(1)+2=\boxed{7}\\\\5) \text{ } f(2)=8(2)^{2}-3(2)+2=\boxed{28}[/tex]

Isabella is making a scrapbook each page of the scrapbook is a square with a length of 11 in if each page holds three pictures that each have an area of 15 in squared what is the remaining area on each page and square inches that can be used for decoration

Answers

The remaining area of the page will be 80 square inches.


What is an area?

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the square in a two-dimensional plane is called the area of the square.

The area of the remaining part will be calculated as;-

Area of the square page will be = 11 x 11 = 121 square inches.

Area of three pictures will be = 15 x 3 = 45 square inches.

So the remaining area will be = 121 - 45 = 80 square inches.

Therefore the remaining area of the page will be 80 square inches.

To know more about an area follow

https://brainly.com/question/25292087

#SPJ1

algebra 2 help needed image below urgent !!!

Answers

Answer:

Domain = x ≥ 0

Range = y ≥ 20

Step-by-step explanation:

The equation in slope-intercept form would look like this:

y = 4x + 20

The slope is $4 because that is the money that can be made depending on the week. Because he received a random $20 at the beginning, this is just an additional income.

                     ---------------------------------------------------------------------------

In this scenario, the domain (x-values) represent the number of weeks. The range (y-values) represent the total money made.

So the domain is asking, what is the lowest/highest amount of weeks he can save for? We know the number of weeks cannot be negative because he can't save for negative weeks. However, he could save for zero weeks. He can be saving for theoretically infinite weeks. Therefore, the domain is x ≥ 0.

The range is asking, how much money can he save? Since he starts out with a baseline of $20, this is the lowest amount of money he can have. If he were to save for an infinite amount of weeks, he could make an infinite amount of money. Therefore the range is y ≥ 20.

A bag of 20 marbles consists of 5 blue marbles, 4 red marbles and 9 yellow marbles. You draw a marble out of the bag, put it back then draw out another marble. Calculate the probability you will draw a blue marble on your first draw and then draw a blue marble on your second draw? Write your answer a percentage to the nearest hundredth.

Answers

The probability you will draw a blue marble on your first draw and then draw a blue marble on your second draw is 0.063.

What is probability?

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

Total marbles = 20

Number of blue marbles = 5

P(blue) = 5/20

P(blue∩blue) = P(blue)×P(blue)

= (5/20)(5/20)

= 25/400

= 1/16

= 0.0625 ≈ 0.063

Thus, the probability you will draw a blue marble on your first draw and then draw a blue marble on your second draw is 0.063.

Learn more about the probability here:

brainly.com/question/11234923

#SPJ1

Tim has 9 pencils in his book bag. Jaime has 3 more pencils than Tim. Which of the following equations would describe n, the number of pencils that Jaime has in her book bag?

Answers

The equation is 9+3=12

Need help with this geometric question

Answers

Answer: QN=19

Step-by-step explanation:

Diagonals of an isosceles trapezoid are congruent, so NQ=PM.

By the segment addition postulate, NQ=QR+RN=3x+7.

So,

[tex]6x-5=3x+7\\\\3x-5=7\\3x=12\\\\x=4[/tex]

So, [tex]QN=3(4)+7=\boxed{19}[/tex]

5m³ into cm³
Show the answer step by step ​

Answers

Answer: So you want to convert 5 cubic meters into cubic centimeters? If you're in a rush and just need the answer, the calculator below is all you need. The answer is 5000000 cubic centimeters.

Step-by-step explanation:

what is the general term for sequence -6;3;15;30?​

Answers

Answer:

[tex] \frac{3}{2} n {}^{2} + \frac{9}{2} n - 12[/tex]

Step-by-step explanation:

This sequence is a quadratic sequence meaning that we should find the difference and the constant second difference.

The difference between the 4 terms is in the sequence:

9;12;15

The constant second difference is 3.

Use your method of finding the general term:

2a=3 3a+b=9 a+b+c=-6

a=3/2 3(3/2)+b=9 3/2+9/2+c=-6

b=9/2 c=-12

Standard form for quadratic sequence:

[tex] {an}^{2} + bn + c[/tex]

Therefore your general term is the one stated above in the answer.

Hope that helps!

In parallelogram ABCD, diagonals AC and BD intersect at point E, AE = x^2 - 12, and CE = 4x What is AC?

Answers

The length of the AC is x^2  + 4x  - 12.

What is a parallelogram?

That quadrilateral in which opposite sides are parallel is called a parallelogram.

Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.

Given :

In Parallelogram ABCD, diagonals AC and BD intersect at point E.

such that

AE = x^2 - 12,

CE = 4x

We know that the diagonal of a parallelogram bisect each other.

x^2 - 12 = 4x

x^2  - 4x  - 12= 0

(x-6)(x-2) = 0

Hence, the value of x = 6, 2.

AC = AE + CE = x^2  + 4x  - 12.

The length of the AC is x^2  + 4x  - 12.

Learn more about Parallelogram ;

https://brainly.com/question/12871564

#SPJ1

Ratio of men to women working for a company is 7to5 there are 75 women working for the company what is total number of employees

Answers

Answer:

There is a total of 180 employees.

Step-by-step explanation:

men : women

  7    :       5

5 units = 75

   1 unit = 15

12 units = 180

what is it asap please​

Answers

There is a 70% probability that a pupil who uses the swimming pool and gym will be selected. How do I know this? Well, since 30 pupils use neither, this means at least 50/80 pupils use both. This reduces to 5/8, so 5/8 pupils use both the gym and swimming pool. 5/8 as a decimal is equal to 70%, because 80% would be 6/8, 90% would be 7/8, and 100% would be 8/8.

That’s one way to do it.


Another way to solve this is as follows:

Since 22 pupils use the swimming pool and 34 use the gym, that means 56 pupils use both total. 56/80 reduces to 7/10, which as a decimal is 70% or 0.7.

Your final answer: Probability = 70%

If you need more help, let me know and I will gladly assist you!

A survey of 600 randomly selected high school students determined that 290 play organized sports. what is the probability that a randomly selected high school student plays sports

Answers

Answer:

29/60

Step-by-step explanation:

probability of playing is 290/600 which when simplified is29/60

Discriminat step by step of x^2+4x+5=0

Answers

Answer:

-4

Step-by-step explanation:

x^2+4x+5=0

a=1,b=4^1 C=5

4^2-4×1×5

-4

The vehicle preference of police officers and firefighters is given in the table.
Police Officers Firefighters
Cars 12
Trucks 9
SUVS 15
3
4
2
Based on the information in the table, which of the following is an example of independent events.

Answers

An example of independent events is P(Police Officers and choose cars).

Which pair of events are called independent events?

When one event's occurrence or non-occurrence doesn't affect the occurrence or non-occurrence of another event, then such events are called independent events.

Symbolically, we have:

Two events A and B are said to be independent if we have:

P(A ∩ B) = P(A)P(B)

                    Police Officers         Firefighters

Cars               12                             3

Trucks            9                              4

SUVs              15                             2

Let  P(A) = Firefighters choose cars

P(B) = Firefighters choose Trucks

P(A ∩ B)  =  Police Officers choose cars

Thus,

P(A ∩ B) = P(A)P(B)

12 = (4) ( 3)

Hence,  an example of independent events is P(Police Officers and choose cars).

Learn more about independent events;

https://brainly.com/question/12619550

#SPJ1

Samantha is 9 years younger than her brother Maurice. In 10
years, Maurice will be 1.5 times older than his sister. Find their
present ages.

Answers

Step-by-step explanation:

hope you can understand

Answer:

Samantha is 8 years and Maurice is 17 years

Step-by-step explanation:

First represent Samantha's brother's age with a variable, x.

Secondly, find Samantha's age. since shes 9 years younger, then it will be her brother's age which is x minus 9

Thirdly, in ten years, they will all age hence 10 will be added to all their ages.

Fourthly, once 10 has been added to their after 10 years, rhen we realise Maurice age will be 1.5 timess Samantha's age... Then you solve the resulting equation.

is y=6x-3 a function

Answers

Yes it is

Step-by-step explanation:

it is a linear function as it is written in the standard form Y=MX+C

Yes!
Slope-intercept form, y=mx+b, of linear equations, emphasizes the slope and the y-intercept of the line.
y=6x-3 is a simple function in slope intercept form.

The velocity of a car over five hours is given by v(t)=60ln(t+1),0≤t≤5 in kilometers per hour. What is the total distance traveled from t=0 to t=5? Round your answer to the nearest whole number and do not include units.

Answers

Step-by-step explanation:

as the velocity is not constant over time, we actually have to integrate v(t) over the interval 0<=t<=5 to get the distance.

v(t) = 60×ln(t + 1)

V(t) = 60 × integral(ln(t + 1)) between 0 and 5.

integral(ln(t + 1)) = (t + 1)ln(t + 1) - t + C

V(t) = 60 × ((t + 1)ln(t + 1) - t + C)

the distance traveled between t = 0 and t = 5 is then

60 × ((5 + 1)ln(5 + 1) - 5 + C) - 60 × ((0 + 1)ln(0 + 1) - 0 + C) =

= 60×(6ln(6) - 5 + C) - 60×(1ln(1) + C) =

= 60×(5.750556815... + C) - 60×C =

= 60×5.750556815... = 345.0334089... ≈ 345 km

The functions f(x) = x2 – 2 and g(x) = –x2 + 5 are shown on the graph.

The graph shows f of x equals x squared minus 2, which is an upward opening parabola with a vertex at 0 comma negative 2 and a point at negative 1 comma negative 1 and a point at 1 comma negative 1. The graph also shows g of x, which is a downward opening parabola with a vertex at 0 comma 5 and a point at negative 1 comma 4 and a point at 1 comma 4.

Explain how to modify the graphs of f(x) and g(x) to graph the solution set to the following system of inequalities. How can the solution set be identified?

y > x2 – 2
y ≥ –x2 + 5

Answers

We will need to shade the region above f(x) and the region below the function g(x)…

How to transform the graph into the solution set?

We have:

f(x) = x² - 1

g(x) = -x² + 4

Both of these are already graphed, and we want to transform it into:

y > f(x)

y ≤ g(x)

The first inequality means that we need to graph f(x) with a dashed line, because f(x) is not part of the solution, and then we shade all the region above f(x)…

For the other inequality, we use a solid line (because the points on the line are solutions) and then we shade the part below the curve…

If you want to learn more about inequalities, you can read:

brainly.com/question/18881247

Other Questions
Which is true of dependent events? a.) the probability of all dependent events can be calculated using the or formula b.) you can use a two-way frequency table to calculate the conditional probability of events that are dependent. c.) the outcome of one event has no effect on the outcome of a second event. d.) you can find the and probability of dependent events using the formula branliest to correct answer please no guessing Which one of the followingmolecules would be mostlikely to travel by facilitateddiffusion?A. Uncharged oxygen molecule (02)B. a large organic moleculeC. Uncharged neon atoms (Ne) Although these days many people have self-cleaning ovens, if your oven gets really dirty you may have to resort to one of the spray-on oven cleaner preparations sold in supermarkets. What evidence is there that such oven cleaners work by a chemical reaction? help fast pleasei have no idea what to do in math so i need help in a 2017 national study, what percentage of u.s. high school seniors reported having had sexual activity? Brainstorming is part of the..Somebody help me 7. In the end, does Santiago win or lose? Doeshis pride ultimately lead him to defeat ortriumph? Use the rational zeroes theorem to state all the possible zeroes of the following polynomial:f (x) = 3x^(6) + 4x^(3) - 2x^(2) + 4 How many calories were in the chicken meatballs, with steamed vegetables and brown rice?320 calories400 calories500 calories700 calories Sometimes, a data set has two values that have the highest and equal frequencies. In this case, the distribution of the data can best be described as Which network lets its users send and receive data as if their devices were connected to the private network even if they are not? An open tank contain oil of specific gravity 0.75 on top ofwater. If the depth of oil is 2m and the depth of water is 3m.calculate the gauge and absolute pressures at the bottom of thetank when the atmospheric pressure is 1bar Navigating your way home through an unfamiliar route due to road construction would draw upon your ________ intelligence. Which of the following statements best describes the impact noise pollution has on wildlife?It can improve the echolocation abilities of marine mammals.It improves communication between species.It reduces reproductive rates.All of these choices are correct. Which option below has the correct order of steps to complete a stoichiometric calculation to determine percent yield?A. Write a balanced equation, determine the limiting reactant, calculate the theoretical yield, calculate the percent yieldB. Write a balanced equation, determine the excess reactant, calculate the theoretical yield, calculate the percent yieldC. Determine the excess reactant, write a balanced equation, calculate the theoretical yield, calculate the percent yieldD. Calculate the percent yield, determine the limiting reactant, write a balanced equation, calculate the theoretical yield 1. active listening a strategy for showing other people you are interested in what they are saying and that you understand what they are saying and how they feel about it 2. barrier a strategy for giving feedback when you give constructive feedback by placing a suggestion for improvement with positive feedback before and after the suggestion for improvement 3. body paragraphs to state only the main points of something that that has been said or written 4. communication a personal belief that one should work hard and do a good job 5. conclusion anything that interferes with a message being sent or received 6. constructive feedback the person who receives a message 7. introduction a summarization of a piece of writing's main points 8. netiquette the person who creates or composes a message and delivers it either orally or in writing 9. paraphrase detailed information about a performance, including specific information about what was done well and how the performance could be improved 10. receiver an interesting and compelling paragraph that gets a reader interested in what they will be reading 11. sandwich technique an exchange of information 12. sender words or phrases that help a reader move through and make sense of the sequence of information 13. summarize paragraphs that present details to support the main idea of a piece of writing 14. transitions guidelines for courteous electronic communication 15. work ethic to restate information using other words A student spilled a bottle of ammonia in one corner of the laboratory. Soon the whole laboratory was felled with pungent irritating small. The students immediately opened the windows and doors and switched on the exhaust fans. After sometime, students got relief. Explain what did actually happen? What is the vertex of the function f(x)=|x-9|+2 what is the binomial system of nomenclature como se prepara un informe de lectura