Aspinner is separated into equal sections numbered 1 through 8. the spinner is spun, and 2 coins are flipped. using the fundamental counting principle, how many total possible outcomes are there?

Using the fundamental counting principle, the total possible outcomes are:

                                 32

The spinner is spun, and 2 coins are flipped.

Now when a spinner is spin then total 8 outcomes are possible.

Since any of the 8 numbers could be obtained on the spin( 1 to 8)

and when a coin is flipped then there are only two possible outcome i.e.

either Head or Tail.

Hence, the total number of possible outcomes are:

                                8×2×2=32

( since the first possibility 8 is possible from spinner and the  '2' outcomes are possible from each of the flip of a coin  )

              Hence, the answer is:

                          32

The fundamental counting principle states that the total number of outcomes for any compound event is found my multiplying the total number of possible outcomes for each event. The spinner has 8 possible outcomes which are the  integers from 1 to 8, each of the two coins has two possible outcomes, a head and a tail.

By the fundamental counting principle, there total number of outcome is calculated as shown below,

There are 32 possible outcomes.

the polynomial is a perfect square trinomial of the form a^2-2ab+b^2:

option a. true

step-by-step explanation:

9x^2-12x+4

comparing with the form a^2-2ab+b^2

1.) a^2=9x^2

solving for a: square root both sides of the equation:

sqrt(a^2)=sqrt(9x^2)

a=sqrt(9) sqrt(x^2)

a=3x

2.) b^2=4

solving for b: square root both sides of the equation:

sqrt(b^2)=sqrt(4)

b=2

to be a perfet square trinomial 2ab must be equal to 12x. let's check:

2ab = 2 (3x) (2)

2ab = 12x

correct

yes.. it's proven to be 36.