According to a survey, 49% of U. S. adults have purchased a state lottery ticket in the past 12 months. Of these 49%, about 27.5% have annual incomes less than $36,000. (Adapted from Gallup) (a) Find the probability that a randomly selected U. S. adult purchased a state lottery ticket in the past 12 months and has an annual income less than $36,000. (b) Find the probability that a randomly selected U. S. adult who purchased a state lottery ticket in the past 12 months has an annual income greater than or equal to $36,000. (c) Would it be unusual for a randomly selected U. S. adult to have purchased a state lottery ticket in the past 12 months and to have an annual income less than $36,000? Explain.

a. P = 0.13475

b. P = 0.725

c. No. About 13% of the U.S. adults have purchased a lottery ticket in the last 12 months and have an income below $36,000.

Step-by-step explanation:

Probability of selecting a person that has  purchased a lottery ticket: P("L")=0.49

Probability of having an income less than $36,000, given that has purchased a lottery ticket in the last 12 months P("I<36" | "L")=0.275.

a. Probability that a randomly selected U.S. adult purchased a state lottery ticket in the past 12 months and has an annual income less than $36,000

P("L"&"I<36") = P("I<36" | "L") * P("L") = 0.275 * 0.49 = 0.13475

b. Probability that a randomly selected U.S. adult who purchased a state lottery ticket in the past 12 months has an annual income greater than or equal to $36,000.

P("I>36" | "L") = 1 - P("I<36" | "L") = 1 - 0.275 = 0.725

c. Would it be unusual for a randomly selected U.S. adult to have purchased a state lottery ticket in the past 12 months and to have an annual income less than $36,000

No. About 13% of the U.S. adults have purchased a lottery ticket in the last 12 months and have an income below $36,000.

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204

180-142=38 for the acute angle next to the entry

90+38=128

180-128=52

a=52

step-by-step explanation: