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a) Three bells ring at the intervals of 10, 15 and 20 minutes respectively. If they all ring at 10:00 a. m. at once, at what time will they ring together again ?

b) Three measuring tapes are of 24 m, 32 m and 48 m long. Find the shortest length that can be measured exactly by any one of these tapes.

c) A book, a pen and an exercise book cost Rs 50, Rs 25 and Rs 20 respectively. Find the smallest sum of money with which exact number of books, pens and exercise books can be purchase.

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? )

4. (10.03 mc) the equation of line cd is y = −2x − 2. write an equation of a line parallel to line cd in slope-intercept form that contains point (4, 5). (4 points) y = −2x + 13 y = negative 1 over 2 x + 7 y = negative 1 over 2 x + 3 − 2x − 3

The statements below can be used to prove that the triangles are similar. ? △abc ~ △xyz by the sss similarity theorem. which mathematical statement is missing? ∠b ≅ ∠y ∠b ≅ ∠z