Mathematics High School

Brown Law Firm collected data on the transportation choices of its employees for their morning commute. The table shows the percentages of the type of transportation of the male and female employees. A 5-column table has 3 rows. The first column has entries Male, female, total. The second column is labeled public with entries 12, 8, 20. The third column is labeled Own with entries 20, 10, 30. The fourth column is labeled other with entries 4, 6, 10. The fifth column is labeled total with entries 36, 24, 60. Consider the following events: A: The employee is male. B: The employee is female. C: The employee takes public transportation. D: The employee takes his/her own transportation. E: The employee takes some other method of transportation. Which two events are independent? A and C A and D B and D B and E.

Answers

Answer 1

The two events out of the listed events which are independent events are given by: Option A: A and C

What is chain rule in probability?

For two events A and B, by chain rule, we have:

[tex]P(A \cap B) = P(B)P(A|B) = P(A)P(A|B)[/tex]

What is law of total probability?

Suppose that the sample space is divided in n mutual exclusive and exhaustive events tagged as

[tex]B_i \: ; i \in \{1,2,3.., n\}[/tex]

Then, suppose there is event A in sample space.

Then probability of A's occurrence can be given as

[tex]P(A) = \sum_{i=1}^n P(A \cap B_i)[/tex]

Using the chain rule, we get

[tex]P(A) = \sum_{i=1}^n P(A \cap B_i) = \sum_{i=1}^n P(A)P(B_i|A) = \sum_{i=1}^nP(B_i)P(A|B_i)[/tex]

How to form two-way table?

Suppose two dimensions are there, viz X and Y. Some values of X are there as [tex]X_1, X_2, ... , X_n[/tex] values of Y are there as [tex]Y_1, Y_2, ..., Y_k[/tex]rows and left to the columns. There will be [tex]n \times k[/tex]values will be formed(excluding titles and totals), such that:

Value([tex]i^{th}[/tex] row, [tex]j^{th}[/tex] column) = Frequency for intersection of [tex]X_i[/tex] and [tex]Y_j[/tex]values are going in rows, and Y values are listed in columns).

Then totals for rows, columns, and whole table are written on bottom and right margin of the final table.

For n = 2, and k = 2, the table would look like:

[tex]\begin{array}{cccc}&Y_1&Y_2&\rm Total\\X_1&n(X_1 \cap Y_1)&n(X_1\cap Y_2)&n(X_1)\\X_2&n(X_2 \cap Y_1)&n(X_2 \cap Y_2)&n(X_2)\\\rm Total & n(Y_1) & n(Y_2) & S \end{array}[/tex]

where S denotes total of totals, also called total frequency.

n is showing the frequency of the bracketed quantity, and intersection sign in between is showing occurrence of both the categories together.

How to calculate the probability of an event?

Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.

Then, suppose we want to find the probability of an event E.

Then, its probability is given as:

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}[/tex]

where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.

How to find if two events are independent?

Suppose that two events are denoted by A and B.

They are said to be independent event if and only if:

[tex]P(A \cap B) = P(A)P(B)[/tex]

The given frequency table is:

[tex]\begin{array}{ccccc} &\text{Public}&\text{Own}&\text{Others}&\text{Total}\\\text{Male}&12&20&4&36\\\text{Female}&8&10&6&24\\\text{Total}&20&30&10&60\end{array}[/tex]

The probability table for the same labels would be:

[tex]\begin{array}{ccccc} &\text{Public}&\text{Own}&\text{Others}&\text{Total}\\\text{Male}&12/60&20/60&4/60&36/60\\\text{Female}&8/60&10/60&6/60&24/60\\\text{Total}&20/60&30/60&10/60&1\end{array}[/tex]

The events A, B,C,D and E are given as:

A: The employee is male. B: The employee is female. C: The employee takes public transportation. D: The employee takes his/her own transportation.E: The employee takes some other method of transportation.

Checking all the listed options one by one, for them being independent:

Case 1: A and C

P(A) = P(The employee is male. ) = 36/60

P(C) = P(The employee takes public transportation.) = 20/60[tex]P(A \cap C) = 12/60 \\\\ P(A)P(C) = \dfrac{36 \times 20}{60^2} = 12/60[/tex]

[tex]P(A \cap C) = P(A)P(C)[/tex]

Thus, A and C are independent events.

Case 2: A and D

P(A) = P(The employee is male. ) = 36/60

P(D) = P(The employee takes his/her own transportation.) = 30/60

[tex]P(A\cap D) = 20/60\\\\P(A)P(D) = \dfrac{30 \times 36}{60^2} = 12/60 \neq P(A \cap D)[/tex]

Thus, A and D are not independent events.

Case 3: B and D

P(B) = P(The employee is female. ) = 24/60

P(D) = P(The employee takes his/her own transportation.) = 30/60

[tex]P(B \cap D) = 10/60 \neq P(B)P(D)=\dfrac{24 \times 30}{60^2} = 12/60[/tex]

Thus, B and D are not independent events.

Case 4: B and E

P(B) = P(The employee is female. ) = 24/60

P(E) = P(The employee takes some other method of transportation.) = 10/60

[tex]P(B \cap E) = 6/60 \neq P(B)P(E)= \dfrac{24 \times 10}{60^2} = 4/60[/tex]

Thus, B and E are not independent events.

Thus, the two events out of the listed events which are independent events are given by: Option A: A and C

Learn more about independent events here:

https://brainly.com/question/3898488

Answer 2

Answer:

First option!!

"A and C"

Step-by-step explanation:

Edge 2022

Related Questions

Two grains weighing 100kg 250 g and 150kg 250g are mixed and packed equally in 15 bags. Find the weight of each bag.
a.16.8 kg (b) 16.7 kg (c) 17 kg (d) 20 kg

Answers

Answer:

(B) 16.7 kg

Step-by-step explanation:

First, start by converting everything to kilograms (using unit converters):

[tex]250g(\frac{10^{-3}kg}{1g})=250*10^{-3}kg=0.25kg[/tex]

Then, add all the weights together:

[tex]100kg+0.25kg+150kg+0.25g=250kg+0.5kg=250.5kg[/tex]

Now, divide this number by 15 (since they are packed in 15 bags):

[tex]\frac{250.5kg}{15}=16.7 kg[/tex]

(B) 16.7 kg

© Find the perimeter of this sector.
Give your answer in simplest form in terms of T.
40°
12 m
The diagram is not drawn to scale.

Answers

Perimeter=40/360 *2*12m*3.14

Step-by-step explanation:

perimeter of a sector =r+r+angle/360×2πr

12+12+(40/360×2×22/7×12)

24+8.378

32.378cm

( 8 + 6 to the power of 2 divided 4

Answers

Answer:

35

Step-by-step explanation:

8 plus 6 equal 14 and power of 2 of 14 is 140 divided by 4 =35

Can anyone quickly help me solve tgese questions?​

Answers

m= 5x B= -6

M= -1/2 B= 5

M= 5x B= 2y

M= x B= y

please hurry -no links

For which equation is x = 3 a solution?​

Answers

Answer:

The answer is D.

Step-by-step explanation:

A could not be the answer beacuse 3 x 3 is 9. Add one more to that and you would get ten.

B could not be the answer because  4 x 3 is 12. Minus that by 2 ans you would get ten, not one.

C is not the answer either. 2 x 3 is 6. Minus that by one and you would get five, not three.

D is the right answer because 5 x 3 is 15. Add two to that and you would get 17.

As you can see, D is the right answer.

X+3=0
This is the answer
By the way I’m a 6th grader

Factor completely 625x8 − 1. (25x4 − 1)(25x4 1) (5x2 − 1)(5x2 1)(25x4 − 1) (5x2 − 1)(5x2 1)(5x2 1)(5x2 1) (5x2 − 1)(5x2 1)(25x4 1).

Answers

The complete factor of the polynomial  625x⁸ − 1 is (25x⁴ + 1)(25x⁴ − 1). Then the correct option is A.

What is polynomial?

Polynomial is an algebraic expression that consists of variables and coefficients. Variable are called unknown. We can apply arithmetic operations such as addition, subtraction, etc. But not divisible by variable.

Factor completely 625x⁸ − 1.

We know that

[tex]\rm a^2 - b^2 = (a+b)(a-b)[/tex]

(25x⁴)² − 1²

(25x⁴ + 1)(25x⁴ − 1)

The complete factor of the polynomial  625x⁸ − 1 is (25x⁴ + 1)(25x⁴ − 1). Then the correct option is A.

More about the polynomial link is given below.

https://brainly.com/question/17822016

Answer:I agree it is the. Verified one

Step-by-step explanation:

PLEASEEE HELPPPP!!!

CDE and FGH are shown below.
Which statement is true?

Answers

Answer:

NO enough information

Step-by-step explanation:

Tom makes ​$223.20 in 4days. How much does he make in 3​days?

Answers

Answer:

167.4$

Step-by-step explanation:

Because in 4 days he is making 223.20$ so he is makeig 55.8$ a day so instead of 4 days it's 3 what is 55.8 x 3=167.4

Hope this helps have a awesome afternoon:)

Find the volume in cubic feet. *
1 ft
Data
3ft
vo ft

Answers

I think the answer will be vo ft or it’ll be 3ft hopefully hahahahha

The minimum point on the graph y = f(x) is (2.-5). What is the minimum point on the graph of the
equation y = f(x) + 3?

Answers

Answer:

(2,-2)

Step-by-step explanation:

Adding 3 to the graph shifts everything towards the positive y direction by 3 unites. The new minimum will mantain the same x coordinate, and has its y raised by 3, thus is [tex](2; -5+3) = (2;-2)[/tex]

Why would you need to find the area of a shape?

Answers

Answer:

Calculating the area of a shape or surface can be useful in everyday life

Step-by-step explanation:

Answer:

Finding area of a shape helps you determine the space of an area. In the real world, you must learn area to be a house flipper.

Step-by-step explanation:

To find area...

l x w = area

A 5-card poker hand is dealt from a well shuffled regular 52-card playing card deck. Find the probability that the hand is a Flush (5 nonconsecutive cards each of the same suit).

Answers

Answer:

Step-by-step explanation:

There are 4 suits (clubs, diamonds, hearts, spades) Any one of them could contain the flush.

So the first part of your answer is

4 Then you must choose 5 cards from 13 or 13 C 5 - 9   see below.

Finally you must choose the total number of possible 5 card hands from 52 cards.

The remaining question is, how do you get rid of all the straights (cards that are in order?)

I think that is done by subtracting

1 number of straights that are royal straights

1 number of straights starting with the queen

1 number of straights starting with the  jack

1 number of straights starting with the 10

1 number of straights starting with the  9

1 number of straights starting with the  8

1 number of straights starting with the 7

1 number of straights starting with the6

1 number of straights starting with the 5

Total 9

4* 13 c 5 - 9 = 5139

52 C 5 = 2598960

Probabiity Flush = 5139/2598960 = 0.00197

help me please I beg.

Answers

Answer:

B

Step-by-step explanation:

2√12 = √4 x 3 = 4√3 = (4√3 x 3√5)

            √36 = 6 = (6 x √30)

4√3 x 3√5 = 12√15

6 x √30 =  6√30

12√15  x √30      180√2

÷                      =

6√30 x √30       180

-----------

180√2

÷

180

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

= √2 or 1.41

I hope this helps!

suppose the population of a town is growing exponentially. The population was 24,004 in 2008 and grew to 75,340 in 2010. What is the approximate growth rate of the population?

Answers

Answer:

Step-by-step explanation:

First thing you do is find the difference between the years recorded. So from 2008 to 2010 is two years. Second you find the difference between the populations which is 51,336 then divide it by two and you get the average growth in the population of 25,668

pls help me solve this

Answers

Answer:

s=24

Step-by-step explanation:

Can someone help me get the answer to this?

Answers

Answer:

ANSWER D).

.. [tex]\sqrt[3]{a^{2} }[/tex]

Step-by-step explanation:

[tex]x^{\frac{m}{n} } = \sqrt[n]{x^{m} }[/tex]

-

[tex]a^{\frac{2}{3} }[/tex] = [tex]\sqrt[3]{a^{2} }[/tex]

Answer:

D

Step-by-step explanation:

hopes this helps

PLSSSSSS answer quickly timed will award brainlest only if you tell me how to I'm a new brainly user. 7 8 9 10 don't answer already got those. nvm to late

Answers

here i create a question and give you your points back since no one answerd this queston sry that i didnt i didnt know the answer

Solve x2 8x = 33 by completing the square. Which is the solution set of the equation? {–11, 3} {–3, 11} {–4, 4} {–7, 7}.

Answers

The solution set of the given quadratic equation using factorization will be {-3,11}

Given equation is

[tex]x^{2} -8x-33 = 0[/tex]

What is a quadratic equation?

The polynomial equation whose highest degree is two is called a quadratic equation. The equation denoted by ax² + bx + c = 0, where a is non-zero.

Let us calculate the roots by factorization

[tex]x^{2} -11x+3x-33=0[/tex]

[tex]x(x-11)+3(x-11)=0[/tex]

[tex](x-11) (x+3)=0[/tex]

[tex]x-11=0\\x=11\\x+3=0\\x=-3[/tex]

Hence, the solution set of the given quadratic equation will be {-3,11}

To get more about quadratic equation visit:

https://brainly.com/question/1214333

Answer:

A

Step-by-step explanation:

Do you know how to do this??? Please help and give answers

Answers

Answer:

Answers below

Step-by-step explanation:

1) 31

2) 1

3) 7

4) 23

5) 21

6) 11

7) 5

Can the numbers 24,32,40 be the lengths of the three sides of a right triangle? Explain why or why not

Answers

Answer:

Yes .The Pythagorean equation is true.

Step-by-step explanation:

yes, they can, because of the equation below :

a² = b² + c²

40² = 32² + 24²

1600 = 1024 + 576

1600 = 1600 ✓

how much are 8 figures

Answers

~Shoto Todoroki here~

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

8-Figures represents eight digits and a 8-figure salary will fall between $10,000,000 – $99,999,999. People who are earning this amount of income are typically multi-millionaires and would be considered quite wealthy.

its some one make 8 million dollars a year i think or more

Julia decides to make 5 batches of salad dressing. How much sugar should she use?

A)4/5 cup
B)1 1/5
C)5 1/4
D)1 1/4

Answers

D) 1 1/4

She needs 1/4 to make 1 batch so multiply that by 5 (or add 1/4, 5 times) 5 * 1/4 = 5/4 = 1 1/4

You just received your final exam score from your teacher. At the top of an exam, it says you missed five questions and got 33 out of 38 questions correct, for a score of 78%. You think your teacher may have made an error when calculating your percentage. Which sentence best describes the test score you received?

Answers

Answer:

hope this helps you◉‿◉◉‿◉

Refer to the figure. Justify your answer. Each side length is doubled. Describe the change in the PERIMETER. *

Answers

Answer:

  perimeter is doubled to 30.8 cm

Step-by-step explanation:

The perimeter is the sum of side lengths. The perimeter of this figure is the sum ...

  4 cm + 5 cm + 6.4 cm = 15.4 cm

__

When the side lengths are doubled, the perimeter is doubled:

  2(4 cm) +2(5 cm) +2(6.4 cm) = 2(4 cm +5 cm +6.4 cm) = 2(15.4 cm)

  = 30.8 cm

The perimeter is doubled.

__

Additional comment

Any scale factor that applies to all of the side lengths also applies to the perimeter.

How do we get energy frome the food we eat

Answers

This energy comes from the food we eat. Our bodies digest the food we eat by mixing it with fluids (acids and enzymes) in the stomach. When the stomach digests food, the carbohydrate (sugars and starches) in the food breaks down into another type of sugar, called glucose.

Step-by-step explanation:

The food we eat is taken inside the body.

The body or the organ system starts breaking down the food into small soluble parts.

The digestive system digests food and its by products is energy and thats how we get energy from food

HELP ASAP The mass of a radioactive substance follows a continuous exponential decay model. A sample of this radioactive substance has an initial mass of 4366 kg and decreases continuously at a relative rate of 4% per day. Find the mass of the sample after six days

Answers

Answer:

3318.2

Step-by-step explanation:

Since you first have to find out 4% of 4366 (174.64), then what you do is write an equation that states 4366-(174.64*6), then you get your answer :)

Mr. White tutors one of his students after school.
The job pays $250 for ten hours of work.
He needs to make $750.
How many hours of tutoring would Mr. White need to work?

Answers

Answer:

30 hours of work

Step-by-step explanation:

Ok if Mr. White  works 10 hours he gets 250$
250+250=500$
10 + ㅤ10 = 20 hours
500+250=750
20ㅤ+ 10 = 30

so this means he will have to work 30 to get 750$

Answer:

30 hours

Step-by-step explanation:

If 10 hours = $250

Than you can divide 750/250 and you’ll get 3. Multiply 3 by 10 ( 3 • 10 ) and you’ll get 30 hours.


I hope it helps! Have a great day!

Muffin ^^

Johnny measured the wading pool at the Belleville Community Center and calculated that it has a circumference of 6.28 meters. What is the pool's diameter?

Answers

Answer: 1 Meter

Step-by-step explanation: The circumference is 6.28 meters. Replace C with 6.28 in the formula.

C  = 2 × ​ × r

6.28 ≈ 2 × 3.14 × r

6.28 ≈ 6.28 × r

6.28 ÷ 6.28  ≈ r

1 ≈ r

The radius is about 1 meter.

SHOW WORK

The rectangular floor of a classroom is 35 feet in length and 30 feet in width. A scale drawing of the floor has a length of 7 inches. What is the area, in square inches of the floor in the scale drawing?

Answers

Divide the lengths to find the scale :

35/7 = 5

Now divide the width by the scale to get the scaled width:

30/5 = 6 inches


the scaled drawing is 7 x 6


area of scaled drawing = 7 x 6 = 42 square inches

Use the given graph to determine the limit, if it exists. (4 points)

Answers

Check the picture below.

now, when it comes to limits, we're not concerned if the value of the function is the same as the limit at that location, we're only concerned on to where is the function approaching, now it may not get there, but that is where it's approaching or seem to be approaching.

in this case, the piece-wise function has a hole when x = 3, meaning f(x) ≠ 3 when x = 3, however if we look at the progress from say 6, 5.9, 5.5, 5.1, 4.9, 4.8, 4.1, 3.7, 3.000001, it seems to be approaching 3, thus that is its limit.

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