A marketing director for a beverage company conducted a study to investigate people’s soda preferences in two regions of the country. The director selected a random sample of 100 people from the east coast and a random sample of 100 people from the west coast to survey. The responses are summarized in the following table. East Coast West Coast
Regular soda 44 37
Diet soda 39 42
No preference 17 21
Total 100 100
Do the data provide convincing statistical evidence, at the level of α=0.05, that the preferences are different between the two regions of the country? Complete the appropriate inference procedure to support your answer.

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Answerprofit;

Answerbecause of prohibition keep bars shut down, the drink was popular with on-the-go people

You need to figure out at which x-value does the graph has a tangent line slope of -1.remember, the derivative is the slope of the tangent line. so find the derivative function and set it to equal -1 to find the x-value that will have a tangent line slope of 0.differentiate with the chain rule.    set the derivative to equal -1 and solve for x.      take log base 10 of both sides. also recall that  .    so the x-coord of the point of tangency is .the y-coordinate of this point of tangency can be calculated using the original function:     using point-slope form, the equation of the tangent line is      the x-intercept of this tangent line is when the graph is at y=0.    this rounds off to  .choice c.