The two co-captains and three coaches take Izzy out for lunch. The restaurant automatically charges a gratuity on the subtotal (before tax) for parties of six or more. Fill in the bill to show the amounts for the subtotal, tax, and total. Explain below. Gratuity (18% of Subtotal)$8.64 Sales Tax (6.5% of Subtotal) Total Amount ​

Suppose that the price p, in dollars, and the number of sales, x, of a certain item follow the equation 4 p plus 4 x plus 2 pxequals56. suppose also that p and x are both functions of time, measured in days. find the rate at which x is changing when xequals2, pequals6, and startfraction dp over dt endfraction equals1.5.

Carla was trying to decide what to do saturday evening. she has $100 available to spend for the evening. she has narrowed her choices down to these events: braves game, a concert of an artist she likes, or the georgia aquarium. admission to the braves game is $25, hot dogs cost $10, sodas cost $5. the concert costs $25 for admission, $20 for a souvernir t-shirt, and $10 for a soda. the georgia aquarium has the show of a lifetime with an all you can eat and drink that costs $100. carla does not want to take any driving chances, so in addition to the cost of the aquarium, she will also need to pay for her uber/lyft, which is $15 each way. which option should carla choose if she wants to spend the least? based on that choice, what then is carla's oppotunity cost? fully explain your answer in at least one paragraph.

Use the given degree of confidence and sample data to construct a confidence interval for the population mean mu . assume that the population has a normal distribution. a laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 185 milligrams with sequals 17.6 milligrams. a confidence interval of 173.8 mgless than muless than 196.2 mg is constructed for the true mean cholesterol content of all such eggs. it was assumed that the population has a normal distribution. what confidence level does this interval represent?