A box contains red, blue, green, purple, and yellow crayons such that the probability of drawing a purple crayon is 3/7. An experiment consists of blindly choosing a crayon, replacing it, and choosing another crayon. The two draws are independent. A random variable assigns the number of purple crayons to each outcome. What is the range of the random variable?

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First we solve your equation step-by-step.4.5  (8  −  x)  +  36  =102  −  2.5  (3  x  +  24)step 1: 4.5  (8  −  x)  +  36  =  102  −  2.5  (3  x  +  24)simplify: (show   the  steps)−4.5  x  +72  =−7.5  x  +  42step 2: add 7.5  x to both sides.  −4.5  x  +  72  +  7.5  x  =−7.5  x+  42  +  7.5  x  3  x  +  72  =  42step 3: subtract 72 from both sides.  3  x  +  72  −  72  =  42  −  723  x  =  −30step 4: divide both sides by 3.3  x  3=  −303  x=  −10so x = -10