When we make inferences about the difference of two independent population proportions, what assumptions do we need to make? mark all that apply. a. random samples. b. normal distribution of the response variable. c. sample size must be greater than or equal to 30.d. counts of successes and failures at least 15 each for each group. e. the sum of the counts of successes and failures must be greater than 30.

(23*2)-12=x     x=34

step-by-step explanation:

i need a picture

step-by-step explanation:

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)