Select all the compositions of rigid motions that can be described as a single translation, rotation, or reflection.
a. rm ⚬ rn
b. t⟨a, b⟩ ⚬ rm
c. t⟨c, d⟩ ⚬ t⟨a, b⟩
d. rm ⚬ t⟨a, b⟩
e. rm ⚬ rn ⚬ rp

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

Find the volume of the solid generated when the region bounded by y= x and y= 4√x is revolved about the x-axis the volume of the solid is: (type an exact answer cubic units)

Prove the divisibility of the following numbers: 25^9 + 5^7 is divisible by 30.also, read as (25 to the power of 9) + (5 to the power of 7) is divisible by 30. blank x 30what is the blank? ( it should be expressed in exponent form)