Find the exact coordinates of the point on the curve y =x /1 + ln(x) at which the gradient of the tangent is equal to 1/4.

Use the four functions below for this question. compare and contrast these four functions using complete sentences focus on the slope and y- intercept first, and then on any additional properties of each function

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.

Alex took his brother to a birthday party. the party was scheduled to last for 1 and 3/4 hours but they stayed for 4/5 of an hour more. how long did she stay at the party?