Answer the following question using the appropriate counting technique, which may be either arrangement with repetition, permutations, or combinations. be sure to explain why this counting technique applies to the problem.
how many possible birth orders with respect to gender are possible in a family with five children? (for example, bbbgg and bgbggbbbgg and bgbgg are different orders.)

a. permutations because the selections come from a single group of items, no item can be selected more than once and the order of the arrangement matters.
b. arrangements with repetitions because there are r selections from a group of n choices and choices can be repeated.
c. combinations because the selections come from a single group of items, no item can be selected more than once, and the order of the arrangement does not matter.
d. arrangements with repetitions because the selections come from a single group of items, and the order of the arrangement matters.

A. Permutations because the selections come from a single group of items, no item can be selected more than once and the order of the arrangement matters.

Step-by-step explanation:

To find the number of possible birth orders with respect to gender are possible in a family with five children we use Permutations because order of birth matter here.

Therefore , the correct answer is A. Permutations because the selections come from a single group of items, no item can be selected more than once and the order of the arrangement matters.

let f (x ) is a function and c be a positive real number,   the graph of the function g (x ) = f (cx ) is represented as follows.

when, c > 1,   the function compresses it in the x - direction.

when, 0 < c < 1, the function stretches it.

the function is g ( x ) = (9x )2.

the heighest power of x in g ( x ) = (9x )2 is 2, so the parent function is square function.

the equation of parent function is f ( x ) = x 2 .

the function is g ( x ) = (9x )2 and the parent function is f ( x ) = x 2 .

so, the functions f and g have the following relationship.

g ( x ) = f ( 9x ).

compare the function g ( x ) = f ( 9x ) with g (x ) = f (cx ).

c = 9 ( > 1 ).

so, the function g (x ) = (9x )2 compresses it in the x - direction.

step-by-step explanation:

add 8+12 to get a simplified answer of 12r-20