Suppose the names of the months of the year are placed in a hat and a name is drawn at random. (a) list the sample space for this experiment. (b) list the event consisting of the outcomes that the month drawn starts with the letter j. (c) what is the probability of drawing the name of a month that starts with j?

(a)

The sample space is a set whose elements are all the possible outcomes for the experiment. Since we will extract one of the months of the years, the sample space is the set composed by all the 12 months:

(b)

An event is a subset of the sample space. Events are often defined by their properties. In this example, the event E is the subset of the sample space defined as

So, we have

(c)

If all outcomes have equal probability, then the probability of an event is the ratio bewteen its cardinality, and the cardinality of the whole sample space:

In words, since there are three months beginning with J out of 12 months, we have a probability of 3 over 12 to pick a month starting with J, which simplifies to 1 over 4.

he used the algebra tiles correctly.

step-by-step explanation:

given : 3x(2x-1)

solution :

since he used algebra tiles .

armando's solution is the same in the solution shown in figure

as he distributed 2x into x and x and wrote them vertically

and also write   -1 vertically

and 3x into x and x and x and wrote it horizontally

performing the multiplication in the algebra tiles we get

and solving the given expression :

3x(2x-1)

since solving the expression using tiles   and solving the expression algebraically we get the same answer

thus   we can choose the first statement as the answer to this problem which is "he used the algebra tiles correctly".

ghjmutmum

step-by-step explanation: