A and B are independent events. Which equation below must be true?A. P(A) = P(B)
B. P(A | B) = P(A)
C. P(A ∩ B) = P(A)
D. P(B) = P(A | B)

Answers

Answer 1

Answer: The correct answer for this question is B. P(A | B) = P(A). Another equation used for independent events is P(B | A) = P(B). When the multiplication rule is applied, this gives an alternative definition of independence which is:

P(A ∩ B) = P(A)*P(B)

Independent events are events that can occur without affecting or changing the probability of the other.

Answer 2

Answer:

Answer with Step-by-step explanation:

A and B are independent events.

Then, we have to find,which equation below must be true.

A. P(A) = P(B)

No, this is not true, example

A: Occurence of 1 in rolling a die P(A)=1/6

B: occurence of an even number on rolling a die P(B)=1/2

B. P(A | B) = P(A)

This is true

since, P(A|B)+P(A)/P(A∩B) and, P(A∩B)=P(A)P(B)

C. P(A ∩ B) = P(A)

This is not true

since, P(A∩B)=P(A)×P(B)

D. P(B) = P(A | B)

This is not true

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Factor completely and then place the factors in the proper location on the grid.a 2 - a - 20

Answers

Answer:

The correct answer is (a+4)(a-5)

Step-by-step explanation:

We have the polynomial $a^2-a-20$

For the polynomials of the form $ax^2+bx+c$ we have to rewrite the middle term as a sum of two terms whose product is, in this case, a.c=-20 and whose sum is b=(-1).

$a^2-a-20=\na^2+(-5+4)(a)-20=\n=a^2-5a+4a-20$

Because b=(-5)+4=(-1) and a.c=(-5).4=(-20)

Now we have to factor by grouping:

$a^2-5a+4a-20=\n(a^2+4a)-(5a+20)=\na(a+4)-5(a+4)=\n=(a-5)(a+4)$

Then, the correct answer is (a+4)(a-5)

The fully factored form of this expression would be
(A-5)(A+4).

How do you Solve 5(x+1)=3x+12?

Answers

Expand
5x+5=3x+12
Subtract 5 from both sides
5x=3x+12−5
Simplify 3x+12−5 to 3x+7
5x=3x+7
Subtract 3x from both sides
5x−3x=7
Simplify 5x−3x to 2x
2x=7
Divide both sides by 2
x=7/2

Expand
5x+5=3x+12x=7/2

An aluminum can is a right cylinder. Find the amount of paper needed for the can's label and the totalamount of aluminum needed to make the can. Round to the nearest tenth.
7 cm
12 cm
The amount of paper needed for the can's label is
1 cm?
The total amount of aluminum needed to make the can is
cm?
Please help put a bunch of points for this question do

Answers

Answer:

Label: About 527.9 square centimeters

Aluminum: About 835.7 square centimeters

Step-by-step explanation:

Amount of paper needed for the label:

You can imagine taking off the label and unrolling it, forming a rectangle. The height of this rectangle will be the height of the cylinder, while the length of the rectangle will be the circumference of the cylinder. Therefore, the area of that rectangle will be $2\pi r h= 2 \cdot \pi \cdot 7 \cdot 12\approx 527.9$ .

Amount of aluminum needed for the can:

This time, you need to add in the top and bottom of the can as well, which each have area $\pi r^2$ . Together, they have area $2\pi r^2=2\cdot \pi \cdot 7^2\approx 307.9$ . Adding this to the area of the sides, you get a total of about 835.7 square centimeters.