Amelia runs a catering business. Based on her records, her weekly profit can be modeled by P=-2x^2+152x-150P=−2x 2 +152x−150, where xx is the number of meals she caters and PP is her profit.

The least number of meals Amelia needs to cater in order to begin making profit = 38 meals.

Step-by-step explanation:

Given - Amelia runs a catering business. Based on her records, her weekly  

            profit can be modeled by P= -2x² + 152x - 150, where x is the  

            number of meals she caters and P is her profit. When P is negative,  

            Amelia losses money.

To find - What is the least number of meals Amelia needs to cater in order  

              to begin making profit.

Proof -

As given, P = -2x² + 152x - 150

Now,

Above the break-even point, she only get profit

The break -even point is a point where there is no profit, and no loss.

Now,

For break-even point,

⇒

⇒-4x + 152 = 0

⇒- 4x = - 152

⇒4x = 152

⇒x = = 38

∴ we get

If Amelia caters at least 38 meals , then she makes Profit.

an advantage of the standard deviation is that it increases as the dispersion of the data increases. e. the interquartile range is preferred when the data are not skewed or no have outliers. an advantage of the standard deviation is that it uses all the observations in its computation.