Hannahs favorite toy character is sold wearing one of many outfits. an outfit consists of one shirt, one pair of pants, and one cap. the shirt can be striped, plain, or polka dotted. the pants may be denim or plaid . the cap may be a cowboy hat or a baseball cap. if hannah picks a to y at random from the shelf and there are an equal number of toys wearing each outfit, what is the probability that the toy is dressed in a polka dotted shirt and a cowboy hat?

Total number of shirt types available = 3

probability that the toy is dressed in a polka dotted shirt , = 1/3

Total number of cap varities = 2

probabiity that the toy is wearing a cowboy hat = 1/2

Probability that the toy is dressed in a polka dotted shirt and a cowboy hat =

Since, the type of pant is not mentioned. The probability that the toy is wearing any pant is 1. Therefore it need not be taken into consideration.

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!