Alexa has finished her culinary training program and is now working full-time as a chef in a hotel resort restaurant. she has tripled her salary from when she was working part-time to pay her expenses through school. how should this increased income affect her budget? make comparisons with her previous budget and her current budget. the answer is c.

If tana tanb=k, show that(1+k)cos(a+b)=(1-k)cos(a-b)

Martha has a deck of cards. she has lost some of the cards, and now the deck only contains nine spades, eleven diamonds, eight clubs, and twelve hearts. martha predicts that whenever she draws a card from the deck without looking, she will draw a club one-fifth of the time. which activity would best allow martha to test her prediction? a. randomly draw a card from the box and see if it is a club. b. randomly draw a card. then, continue to draw another card until all eight clubs are drawn. c. randomly draw and replace a card 120 times. then, observe how close to 30 times a club is drawn. d. randomly draw and replace a card 100 times. then, observe how close to 20 times a club is drawn.

If 7x=9y, y/z = 7/5 , then x/z = (a) 2/7 (b) 7/9 (c) 9/5 (d) 9/7 (e) 5/9