Another way is to note that there are (104)(104) (“10 choose 4”) ways to select 4 balls from a collection of 10. If 4 of those 10 balls are “special” in some way (in this case, “special” = “red”), then the number of ways to choose 4 special balls is (44)(44). (The factor of (60)(60) is included to convey that, after choosing 4 special balls, we choose none of the 6 non-special balls.) This line of reasoning gives the second expression.

8 0

3 years ago

Which statement is the if/then conditional statement of the following? Vertical angles are congruent.

FinnZ [79.3K]

An if-then statement must hold under any condition. Let's take it case by case:

A. This one makes sense, and is perfect! If two angles are vertical, then they must be congruent. This holds no matter what. This is your answer.

B. This doesn't hold because Alternate Interior Angles can also be congruent (along with many others). Two angles don't have to be vertical to be congruent.

C. This one is also true because this is the contrapositive of Option A. (Read my reasoning on D to know what a contrapositive is). Therefore, this is correct.

D. This one is the contrapositive of B, which makes it the exact same as B. Thus, this is not the answer. Contrapositive, by the way, just means that it's the inverse and opposite of a given statement. Let's say P is the contrapositive of Q. If this is the case, then if Q is true, P must be true. In our case, Option D is the contrapositive of Option B and since Option B is not true, neither is D.

7 0

2 years ago