In how many ways can you answer a 13-question true-false test if you answer each question with either a "true" or a "false"?

Step-by-step explanation:

There are two possibilities for each of 13 questions, true or false.  As a result, you have a chance of choosing either of the choices.  To find this, you would multiply the probability to the power of the number of cases, meaning .

so, converting firstly the mixed fractions to improper fractions and then "adding".

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.