At a dinner party, two desserts are being served. Six of the guests choose cheesecake, and eight of the guests choose apple pie. Modify your diagram from #1 to show that the ratio 6:8 is equivalent to 3:4. Upload your modified diagram AND use complete sentences to explain why it shows that 6:8 and 3:4 are equivalent ratios.

Which transformations could have occurred to map △abc to △a"b"c"? a rotation and a reflection a translation and a dilation a reflection and a dilation a dilation and a rotation

An automobile assembly line operation has a scheduled mean completion time, μ, of 12 minutes. the standard deviation of completion times is 1.6 minutes. it is claimed that, under new management, the mean completion time has decreased. to test this claim, a random sample of 33 completion times under new management was taken. the sample had a mean of 11.2 minutes. assume that the population is normally distributed. can we support, at the 0.05 level of significance, the claim that the mean completion time has decreased under new management? assume that the standard deviation of completion times has not changed.

Given: ae ≅ ce ; de ≅ be prove: abcd is a parallelogram. we have that ab || dc. by a similar argument used to prove that △aeb ≅ △ced, we can show that △ ≅ △ceb by. so, ∠cad ≅ ∠ by cpctc. therefore, ad || bc by the converse of the theorem. since both pair of opposite sides are parallel, quadrilateral abcd is a parallelogram.