Consider two events such that P(A) = equals 3/5 , P(B) = 2/3 , and P(A ∩ B) = 1/5 . Are events A and B independent events?

Yes, they are independent because P(A) ⋅ P(B) = P(A ∩ B)
No, they are dependent because P(A) ⋅ P(B) ≠ P(A ∩ B)
Yes, they are independent because P(A) ⋅ P(B) ≠ P(A ∩ B)
No, they are dependent because P(A) ⋅ P(B) = P(A ∩ B)

Answers

Answer 1

Answer:

Option 2

Step-by-step explanation:

Checking whether P(A) × P(B) = P(A∩B) :

3/5 x 2/3 = 1/52/5 ≠ 1/5

Since this does not obey the Multiplication rule of probability, these events are not independent.

So, the answer is :

No, they are dependent because P(A) ⋅ P(B) ≠ P(A ∩ B)

Answer 2

Answer:

Option B

Step-by-step explanation:

Option A should be true if they are independent

P(A)P(B)3/5×2/32/5≠1/5

So

They are dependant


Related Questions

Please help the best answer will get brainliest

Answers

Answer:

164 cm^2

Step-by-step explanation:

Total surface area = 2 * area of triangle + areas of the 3 rectangles

= 2 * 1/2 * 5 * 4 + 5 * 9 + 5 * 9 + 6 * 9

=  20 + 45 + 45 + 54

= 164 cm^2

Which of these describes how the function is increasing and decreasing?

Answers

Answer:

increasing from -2 to +∞

Step-by-step explanation:

The graph starts at -2 and continues to the right which means it increases from -2.

Answer:

Increasing from -2 to positive infinity.

Step-by-step explanation: This is because this is the graph of the square root of x + 2. It will increase from -2 in the x range and eventually hit every single x value from -2 to positive infinity.

Percy solved the equation x2 7x 12 = 12. his work is shown below. is percy correct? explain. 1. (x 3)(x 4) = 12 2. x 3 = 12 or x 4 = 12 3. x = 9 or x = 8

Answers

Percy solved the equation by expanding the expression on the left-hand side, and this is incorrect

How to determine the true solution?

The equation is given as:

x^2 + 7x + 12 = 12

The first step in solving the equation is to equate the equation to 0.

i.e.

x^2 + 7x + 12 - 12 = 0

This given

x^2 + 7x = 0

From the question, Percy solved the equation by expanding the expression on the left-hand side

Hence, Percy's solution is incorrect

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Answer:

Percy is not correct because he applied the zero product property to a factored expression that was not equal to 0. He should have subtracted 12 from both sides to get x2 + 7x = 0 before factoring. The correct solutions are 0 and -7.

Roadstone Limited can resurface 7/8km of a road in a day. How many days will it take
to resurface a road of length 14 km?

Answers

Answer:

16 days

Step-by-step explanation:

Let x be the number of days that it will take.

7/8 km per 1 day

14 km    per x day

We have to solve the equation:

[tex]\frac{x}{1} =\frac{14}{\left( \frac{7}{8} \right) }[/tex]

[tex]\Longrightarrow x=14\times \frac{8}{7} =2\times 8=16[/tex]

Which is the best peer evaluation of the conclusion? the details and mechanics are good, but sentences 2 and 3 should be reorganized to include logical transitions. the word choice and style are good, but there are punctuation and organizational errors in sentences 1 and 2. the mechanics and organization are good, but sentences 1 and 3 should be edited to achieve a formal style and objective tone. the tone and style are good, but errors in grammar, spelling, and punctuation in sentences 1, 2, and 3 should be fixed.

Answers

The best peer evaluation is C. the mechanics and organization are good, but sentences 1 and 3 should be edited to achieve a formal style and objective tone.

What is the best peer evaluation?

The best peer evaluation is a critical review that critiques and provides feedback to other students on their academic work.

The purpose of a peer evaluation is to develop students' lifelong skills in assessing and providing feedback to others.

Peer evaluation also equips students with self-assessment skills to improve their own work.

Thus, the best peer evaluation is C. the mechanics and organization are good, but sentences 1 and 3 should be edited to achieve a formal style and objective tone.

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The following solid is a right pyramid with a square base. a) Calculate the length of AW b) Find the length of VW

Answers

Answer:

Step-by-step explanation:

what is 90% of $90,000,000​

Answers

Answer:

81000000

[tex]\frac{90}{100} *90000000\\ 90*900000\\ 9*9=81\\ then write all the zeros[/tex]

help meeeeee 1/2 X (6 X 4)+3 + 2

Answers

6x4=24

24x1/2=12

12+3=15

15+2=17

17 is the answer

Fill in the missing number. 50% of ????= 13

Answers

6.5 is the answer be great

Enrique is saving money to buy a graphing calculator. So far he has saved $30.
His math teacher told him he has saved 40% of what he will need. How much
does the calculator cost?

Answers

Answer: its free

Step-by-step explanation:

Tim, Ryan, and Joe are brothers. Their mom, Lisa gives them each a weekly allowance. Since Tim is older, she gives him 4 more dollars than Joe. Ryan is the youngest and receives 2 less dollars than Joe. Lisa gives a total of 20 dollars a week in allowance. With Joe receiving m dollars, which equation demonstrates the situation?

Answers

Answer:

m + (m+4) + (m-2) = 20 or 3m + 2 = 20

Step-by-step explanation:

(4a^3 - 36a^2 + 60a^2 + 72) \ (a - 6)

Answers

I think, if not sorry but I hope it helps !:)

Answer:

4a^2+48a+288+(fraction)1800/a-6

Step-by-step explanation:

Diego’s family car holds 14 gallons of fuel. Each day the car uses 0.6 gallons of fuel. A warning light comes on when the remaining fuel is 1.5 gallons or less.

Starting from a full tank, can Diego’s family drive the car for 25 days without the warning light coming on?

Select the correct choice.



A.) YES

B.) NO

Answers

No. The warning light will come on.

14/0.6 = 23.34 days only
Another method: 0.6 gallons • 25 days = 15 gallons needed for the journey of 25 days.

HELP FAST ITS EASY I JUST NEED TO MAKE SURE PLEASE SOMEONE WHO HAS REAL SKILL AND CAN FINSH THIS ANSWER IT PLEASE I BEG U GUYS I NEED TO FINISH (GIVING BRAINLIEST!!)

Answers

Answer: 71/28 or 2 15/28

Step-by-step explanation:

Turn both fractions into improper fractions.

5 1/4 = 21/4

2 5/7 = 19/7   multiply the denominator with the whole then add the     numerator, same denominator.

21/4 - 19/7 = ?  find common denominator to subtract

4 x 7 = 28  common denominator

Divide the new denominator by previous denominators then multiply by each respective numerator. 28 divided by 4 is 7 multiplied by 21 is 147, the same happens with 19/7.

147/28 - 76/28 = 71/28 or 2 15/28

#79 will give brainliest please help!​

Answers

Step-by-step explanation:

this means the factors of the various terms of x and the constant.

a = 4

b = 1

c = 9

and yes, if there would be negative factors, the signs wold be part of a, b and c too.

overall, this is then used to solve the quadratic equation.

the general solution is

x = (-b ± sqrt(b² - 4ac))/(2a)

2. A tent is cylindrical in shape with a conical top above it. The radius of the base of the tent is 7 m. The height of the cylindrical part is 10 m and the height of the conical part is 4 m. Find the volume of air in the tent and the area of canvas cloth needed to construct the tent.​

Answers

The answer should be 280 because it is an area and we multiply

Need help please answer ASAP!
(22-23)

Answers

Answer:

Question 22 is

[tex]x - 3[/tex]

Question 23 is

[tex]1.67 \times {10}^{ - 21} g[/tex]

Good evening! Can someone please answer this, ill give you brainliest and your earning 50 points. Would be very appreciated.

Answers

Answer:

Add 7 cubes to the big square and 1 cube to the three square strip on the bottom of the big square in Step 3

Sorry if the answer is unclear, I tried my hardest to explain it properly. Please tell me if it's right, and if it is, I would appreciate a Brainliest.

(I added an image of what the answer might be)

The pattern

For top

For beneath

x

Look

for 1 there is 1

for 2 there is 2²=4

for 3 there is 3²=9

So for 4

There will be 4²=16

What are the solutions of this quadratic equation? 6x2 6 = 12x 18 a. b. c. d.

Answers

The solution to the quadratic equation 6x² + 6 = 12x is x = 1

How to determine the solutions?

The quadratic equation is given as:

6x² + 6 = 12x

Equate the equation to 0

6x²  - 12x + 6 = 0

Expand the equation

6x²  - 6x - 6x + 6 = 0

Factorize the expression

6x(x  - 1) - 6(x - 1) = 0

Factor out x - 1

(6x - 6)(x  - 1) = 0

Split

6x - 6 = 0 or x - 1 = 0

Solve for x in both instance

x = 1 or x = 1

Hence, the solution to the quadratic equation 6x² + 6 = 12x is x = 1

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Can somebody help me with this? Please and Thank you

Answers

[tex]\text{Given that,}~ p(x) = x^2 +3 ~ \text{and}~ h(x) = \sqrt{x-3} \\\\(p \circ h)(x)\\\\=p(h(x))\\\\=p\left(\sqrt{x-3}\right)\\\\=\left(\sqrt{x-3} \right)^2 +3\\\\=x-3 +3\\\\=x[/tex]

PLEASE HELP
a41= 5 7 2

Answers

The answer is a= 572/41

At what point does the line given by the following equation cross the y-axis?
y = 6/9x+3

a. (0,3)

b. (3,0)

c. (0,-)

d. (-9/2,0)

Answers

Answer:

A

Step-by-step explanation:

In a slope-intercept equation, the format goes like this:

y = mx + b

M = Slope

B = Y-intercept

In the equation, y = 6/9x + 3:

The slope is 6/9

The y-intercept is 3.

So what the question means by "cross the y-axis" is when the line on the graph is going through the y-intercept point.

Because the y-intercept is 3, the ordered pair would look like this:

(0, 3)

Note: The y-intercept is when the x-intercept has a value of 0 and the y-intercept is only on the y-axis, never the x-axis.

Therefore, the answer would be Option A. (0, 3)

Learn with an example
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Watch a tutorial
When Abigail had one cat, she needed to serve 2 cans of cat food each day. Now that Abigail
has adopted a second cat, she needs to serve a total of 3 1/2 cans each day. How much extra
food is needed to feed the second cat?
Write your answer as a fraction or as a whole or mixed number.
cans

Answers

Based on the information provided, to feed the second cat it is necessary 1 1/2 extra cans or 1.5 cans.

How much extra food is needed to feed the second cat?

This difference can be found by substracting the total cans fed with only one cat to the total fed with two cats:

3 1/2 cans - 2 cans = 1 1/2 cans, which can also be expressed as 1.5 cans.

Based on this, to have a second cat implies 1.5 extra cans.

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Carl is covering the rectangular prism-shaped
box with cloth.
5 in.
2 in.
-
12 in.
what is the minimum amount of cloth carl
needs to cover the entire box?

Answers

The minimum amount of cloth carl needs to cover the entire box will be 188 square inches.

What is a surface area?

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

Given that:-

The length width and the height of the prism are 5 , 2 , and 12 inches respectively.

The minimum amount of cloth carl needs to cover the entire box will be the surface area of the prism

Surface area = 2 [ (5 x 2)+ (12 x 5) + (12 x 2)]  

Surface area= 188 square inches

Therefore the minimum amount of cloth carl needs to cover the entire box will be 188 square inches.

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(URGENT) Maurice and Rhonda a are traveling in the same direction along the same road. Maurice is traveling at 55 mph and is exactly 15 miles ahead of Rhonda, who is traveling at 65 mph. How many hours will it take Rhonda to catch Maurice?

Answers

Answer:

Step-by-step explanation:

Givens

Maurice

55 miles an hour

15 miles ahead of Rhonda

d1

Rhonda

65 miles per hour

d2

The distance has to be the same for both in order to meet.

Formula

d1 = d2

d = r * t                                   where r is the speed.

65*t = 55t + 15                       Subtract 55t from both sides

Solution

65t - 55t = 55t - 55t + 15       Combine

10t = 15                                    Divide both sides by 10

10t/10 = 15t/10            

t = 1.5 hours

Answer

They will meet in 1.5 hours.

A person can read 24 pages of a book in 1/3 of an hour. What is this person's reading rate in pages per hour?

48

12

72

8

Answers

Answer:

72

Step-by-step explanation:

If he reads 24 pages in 1/3 of an hour, he reads 3 times as many pages in 1 hour.

3 × 24 pages = 72 pages

Answer: 72

19. A soccer field is a rectangle 90 meters wide and 120 meters long. If you were
asked to run from one corner to the other corner diagonally across, what is the
distance?
a. 150 meters
b. 1500 meters
c. 15 meters
d. 200 meters

Answers

It would be 150 meters if we are talking of terms of diagonal.
120x120=14400
90x90=8100
14400+8100=22500
Square root of 22500=150
Hope this helps!

8.
A circular plate has a diameter of 11 inches. An ant walking along the edge makes 1.5 revolutions in 4
minutes. Approximately how many inches does the ant travel in one minute? Round your answer to the
nearest tenth of an inch.

Answers

Answer:

[tex]12.95 \: inches[/tex]

Step-by-step explanation:

We were told that the diameter of the circular plate is 11 inches. In order to find the distance the ants travel to make one revolution we have to first find the circumference of the circular plate. Circumference is:

[tex]2\pi \: r[/tex]

The radius would be half of the diameter (11). Therefore the radius is 5.5.

[tex]r = 5.5 \: \: \: \: \: \pi = 3.14 \\ cir = 2(3.14) \: (5.5) \\ cir = 6.28 \times 5.5 \\ cir = 34.54[/tex]

Since we found the circumference of the circular plate that means that we know how much one revolution made by the ants would be (34.54). Since the ant made 1.5 revolutions we have to multiply 34.54 by 1.5.

[tex]34.54 \times 1.5 = 51.81[/tex]

So we now know that the ant walked 51.81 inches in 4 minutes, now we have to find the distance he would walk in 1 minute.

Let x be the unknown value*

[tex] 51.81 \:inches = 4 \:minutes \\ x \:inches = 1 \: minutes\\ \\ 51.81=4x \\ \\\frac{51.81}{4} = x \\ \\ 12.95 = x[/tex]

Drag the tiles to the correct boxes to complete the pairs.
Simplify the inequalities and match them with the graphs that represent them.

Answers

Answer:

1) 1, 2) 3, 3) 2, 4) 4

Step-by-step explanation:

Solve the inequalities and match with the graphs

1) 7x < 42 ⇒ x < 42/7 ⇒ x < 6 ⇔ matching the graph 12) 3x > 15 ⇒ x > 15/3 ⇒ x > 5 ⇔ matching the graph 33) x + 1 < 8 ⇒ x < 8 - 1 ⇒ x < 7 ⇔ matching the graph 24) 2x > 12 ⇒ x > 12/2 ⇒ x > 6 ⇔ matching the graph 4

Answer:

7x < 42

x + 1 < 8

3x > 15

2x > 12

Step-by-step explanation:

> means "more than" (shading to the right)

< means "less than" (shading to the left)

Solve the given inequalities

    7x < 42  

⇒ 7x ÷ 7 < 42 ÷ 7

⇒  x < 6

An open circle on 6, shading to the left

   3x > 15  

⇒ 3x ÷ 3 > 15 ÷ 3

⇒ x > 5

An open circle on 5, shading to the right

   x + 1 < 8  

⇒ x + 1 - 1 < 8 - 1

⇒ x < 7

An open circle on 7, shading to the left

   2x > 12  

⇒ 2x ÷ 2 > 12 ÷ 2

⇒ x > 6

An open circle on 6, shading to the right

5. For the past 10 days, a city planner has counted the number of
northbound cars that pass through a particular intersection During
that time, 200 or more cars were counted 9 out of 10 days.

a. What is the experimental probability that there will be 200 or more
northbound cars passing through the intersection on the eleventh day?

b. What is the experimental probability that there will not be 200 or
more northbound cars passing through the intersection on the
eleventh day?


Can someone please help I’m stuck ( and please show the work) thank you.

Answers

Event=200 or more cars

The number of cars was counted on 10 days and thus there were 10 trials.

# of trials=10

200 or more cars were counted on 9 of the 10 days and thus the event occurs 9 times.

# of times the event occurs= 9

The probability is the number of times the event occurs divided by the number of trials:

P ( 200 or more cars)= # of times the event occurs / # of trials

=9/10
0.9
90%

We know that the sum Of the probabilities Of an event And it’s Complement needs to be equal to 1.

P( event ) + P ( complement)= 1

What is it is “200 or more cars”

P( 200 or more cars) + P (not 200 or more cars) = 1

Since P ( 200 or more cars) = 9/10 we can replace P ( 200 or more cars) in the equation by 9/10

9/10 +P ( not 200 or more cars) =1

Subtract 9/10 from each side

-9/10= 1-9/10

Combine like terms

P( not 200 or more cars) = 1/10= 0.1 = 10%

A: 9/10 = 0.9 = 90%
B: 1/10= 0.1= 10%
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