A company manufactures rope, and the total cost of producing r r feet of rope is C ( r ) C(r) dollars. What does it mean to say that C ( 2000 ) = 800 ? C(2000)=800? What are the units of C ′ ( r ) ? C′(r)? Suppose that C ( 2000 ) = 800 C(2000)=800 and C ′ ( 2000 ) = 0.35 . C′(2000)=0.35. Estimate C ( 2100 ) , C(2100), and justify your estimate by writing at least one sentence that explains your thinking. Do you think C ′ ( 2000 ) C′(2000) is less than, equal to, or greater than C ′ ( 3000 ) ? C′(3000)? Why? Suppose someone claims that C ′ ( 5000 ) = − 0.1 . C′(5000)=−0.1. What would the practical meaning of this derivative value tell you about the approximate cost of the next foot of rope? Is this possible? Why or why not?

Tom and carol are resident aliens, married, and want to file a joint return. they have two children. sydney is 5 years old and a resident alien. benjamin is 2 years old and a u.s. citizen. both children lived with the parents in the united states all year. tom, carol, and sydney have individual taxpayer identification numbers (itins). benjamin has a social security number. tom earned $30,000 in wages. carol had $8,000 in wage income. they had no other income. tom and carol provided all the support for sydney and benjamin. sydney and benjamin attended daycare while tom and carol were at work. tom and carol did not receive dependent care benefits from a dependent care benefits plan or flexible spending account. the daycare center provided the baker's with a statement indicating the amount of $3,250 paid for 2018, their name, address and valid employer identification number. 6. who can tom and carol claim as a qualifying child for the child tax credit? a. sydney b. benjamin c. both sydney and benjamin d. neither sydney or benjamin