Ariane borrows $500 on a 3−year loan. She is charged 5% simple interest per year. How much interest is she charged for 3 years? What is the total amount she has to pay back? After 3 years, Ariane is charged $ in interest. She pays a total amount of $ .

Muscles, a membership-only gym is hoping to open a new branch in a small city in pennsylvania that currently has no fitness centers. according to their research approximately 12,600 residents live within driving distance of the gym. muscles sends out surveys to a sample of 300 randomly selected residents in this area (all of who respond) and finds that 40 residents say they would visit a gym if one was located in their area. based on the past survey research, muscles estimates that approximately 30% of these respondents would actually join the gym if they opened one in the area. based on this information and the results of the sample survey, about how many residents should muscles expect to join its new branch? a) 134 b) 504 c) 1,680 d) 3,780

Write each of the following numerals in base 10. for base twelve, t and e represent the face values ten and eleven, respectively. 114 base 5 89t base 12

Parabolas y=−2x^2 and y=2x^2 +k intersect at points a and b that are in the third and the fourth quadrants respectively. find k if length of the segment ab is 5.