Determine the equations of any vertical asymptotes and the values of x for an holes in the graph of the ration funcion 1. asymptotes: x=4; hole: x=7
2. asymptotes: x=−4; hole: x=8
3. asymptotes: x=−8, x=−4; no holes
4. asymptotes: x=8, x=4; no holes

An electronics manufacturer wants to know if customers would be interested in a detachable keyboard for their tables and if so, what the most important features would be. the manufacturer partners with an electronics store to include copies of the survey with every purchase at that store for one week. which of the following best explains why this random sample is unlikely to be a good representative sample of tablet owners' preferences for a detachable keyboard? a) one week is likely not enough time to get a large enough sample. b) most people won't bother to send in the survey, which is likely to skew the results c) there is no way to verify whether the responders to the survey actually own a tablet d) the survey is biased because it was conducted through an electronics store, not the general population

Using the information in the customer order, determine the length and width of the garden. enter the dimensions. length: feet width: feet

Find the volume of the solid obtained by rotating the region enclosed by the curves y=1x and y=7^-x about the x-axis. (use symbolic notation and fractions where needed.) volume =