(Prove that):
1-2sin A. cos A
= sin^2(45-A)​

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The ratio of rock songs to dance songs on jonathan’s mp3 player is 5: 6. the total number of rock and dance songs jonathan has is between 101 120. how many rock songs does he have?

The management of a supermarket wants to adopt a new promotional policy of giving a free gift to every customer who spends more than a certain amount per visit at this supermarket. the expectation of the management is that after this promotional policy is advertised, the expenditures for all customers at this supermarket will be normally distributed with a mean of $95 and a standard deviation of $20. if the management wants to give free gifts to at most 10% of the customers, what should the amount be above which a customer would receive a free gift?