The vertices of a quadrilateral in the coordinate plane are known. How can the perimeter of the figure be found?

Correct question:

An urn holds 3 red and 7 black balls. Players A and B take turns withdrawing balls until a red one is chosen. Calculate the probability that A picks the red ball. (A goes first, followed by B, with no replacement of drawn balls).

Answer:

The likelihood that A picks the red ball is 58.33 %

Step-by-step explanation:

A will select the red ball if it is drawn 1st, 3rd, 5th, or 7th.

1st draw: 9C2

3rd draw: 7C2

5th draw: 5C2

7th draw: 3C2

Calculating for all possible scenarios gives us:

9C2 = (9!) / (7!2!) = 36

7C2 = (7!) / (5!2!) = 21

5C2 = (5!) / (3!2!) = 10

3C2 = (3!) / (2!) = 3

Adding these possibilities results in 36 + 21 + 10 + 3 = 70.

The total outcomes for selecting a red ball = 10C3

10C3 = (10!) / (7!3!)

= 120.

The probability that A selects the red ball is determined by dividing the sum of possible events by the overall outcomes.

P( A selects the red ball) = 70 / 120

= 0.5833

= 58.33 %

Answer:

1. Addition Property of Equality

2. Segment addition

3. Substitution Property of Equality.

4. Transitive Property of Equality.

Step-by-step explanation:

Given: CD = EF and AB = CE

To Show: AB = DF

Following the steps outlined:

1. CD + DE = EF + DE by the (addition) Property of Equality.

This shows that the same value has been added to both sides of the equation.

2. CE = CD + DE and DF = EF + DE through (segment addition).

This indicates that CE and DF are segments, and the length of any segment equals the total of its parts.

3. CE = DF according to the (Addition, subtraction, substitution, transitive) Property of Equality. Recognizing that CE = CD + DE and using the fact that CD = EF allows us to replace CD with EF.

So, CE = EF + ED = FD (via substitution) Property of Equality.

4. Since AB = CE and CE = DF, we can conclude AB = DF by the (transitive) Property of Equality.

This follows the rule that if x = y and y = z, then x = z.