Joanie believes that you cannot use cross products to solve the proportion StartFraction 50 over 3 EndFraction = StartFraction 75 over x EndFraction for x. She says that if you multiply both sides of the equation by x, you get StartFraction 50 x over 3 EndFraction = 75. Then, if you multiply both sides of the equation by 3, you get 50 x = 75, which is a different equation than you would get if you cross multiplied. What mistake did Joanie make in her reasoning?

Questions 9-10. use the table of educational expenditures to answer the questions. k-12 education expenditures population indiana $9.97 billion 6.6 million illinois $28.54 billion 12.9 million kentucky $6.58 billion 4.4 million michigan $16.85 billion 9.9 million ohio $20.23 billion 11.6million 9. if the amount of k-12 education expenses in indiana were proportional to those in ohio, what would have been the expected value of k-12 expenditures in indiana? (give the answer in billions rounded to the nearest hundredth) 10. use the value of k-12 education expenditures in michigan as a proportion of the population in michigan to estimate what the value of k-12 education expenses would be in illinois. a) find the expected value of k-12 expenditures in illinois if illinois were proportional to michigan. (give the answer in billions rounded to the nearest hundredth) b) how does this compare to the actual value for k-12 expenditures in illinois? (lower, higher, same? )

Which equation is equivalent to the given expression? -(1/2y+1/4) a. -1/4(1+2y) b. 1/4(2y-1) c. -2(1/4y-1/8) d. 2(1/8-1/4y)

What are the measures of angles a, b, and c? show your work and explain your answers. 25 points