Fantastique Bikes is a company that manufactures bikes in a monopolistically competitive market. The following graph shows Fantastique's demand curve, marginal revenue curve (MR), marginal cost curve (MC), and average total cost curve (ATC). Place the black point (plus symbol) on the graph to indicate the short-run profit-maximizing price and quantity for this monopolistically competitive company. Then, use the green rectangle (triangle symbols) to shade the area representing the company's profit or loss.

4) \( 2 x-2 x^{3} \) 10) \( 7 b^{2}-63 \)

You recently took a statistics exam in a large class. The instructor tells the class that the scores were Normally distributed, with a mean of 72 (out of 100 ) and a standard deviation of 12 . Your score was 96 . You would like to know what proportion of students did better than you did. Unfortunately, your calculator batteries are dead and you must now rely on Normal tables. You need to find which of the following? the area to the right of 2 the area to the right of 96 the area to the left of 96 the area to the left of 2

Bוо Fermenti lattici Una bustina da 5 g di fermenti lattici contiene 4 g di fibra solubile e 8 miliardi di cellule vive. a. Determina l'ordine di grandezza della massa di una singola cellula. b. Approssimando la cellula con una sferetta di diametro \( 1 \mu \mathrm{~m} \), calcola il volume, in \( \mathrm{mm}^{3} \), delle cellule contenute in una bustina di fermenti lattici. [a. \( \left.10^{-10} \mathrm{~g} ; \mathrm{b} .4 \mathrm{~mm}^{3}\right] \)

If a worker accidentally drops a bolt from the top of a 2304 foot tall tower, the height of the bolt after \( t \) seconds is given by the expression \( 2304-16 \mathrm{t}^{2} \). a. Find the height of the bolt after 2 seconds. b. Find the height of the bolt after 5 seconds. c. To the nearest whole second, estimate when the bolt hits the ground. d. Factor \( 2304-16 t^{2} \).

Solve: \( 17 x^{2}-33 x-2=0 \) \( x= \)