Ginoni the goat is at the bottom of a series of 7 boulders, each higher than the last. She wants to reach the top, where there is a huge patch of grass that she’d like to graze. Being an athletic goat, she sometimes bounds up two boulders at a time; otherwise, she just jumps up one. Ginoni can use both one-boulder and two- boulder leaps within an ascent. Starting at the bottom, in how many ways could she reach the grass at the top?
Investigate what happens for different numbers of boulders and explain the pattern of how many different ways she can ascend.

Which graph represents the function g(x) = |x + 4| + 2?

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? )

What is fraction that is equivalent to 3/8