a. Find the profit function P/) where represent the number of doughnuts sold. b. If 100 doughnuts were soid, what is the total profit? How many doughnuts must be made aálid sold to break even? d. How many dougimuts should be sold to gain a profit of C. PO00.00?

A. By how much does the machine decrease in value (in dollars) in 1 year? B. Predict when (in years) the value of the copy machine will be zero.

Run the following lines in R:   x <- c(8.23, 8.97, 2.72, 1.09, 2.03, 8.07, 8.92, 2.14, 5.6, 2.43, 0.49, 5.8, 5.38, 5.89, 2.31, 5.05, 6.57, 9.21, 9.99, 2.81, 8.86, 9.68, 6.41, 9.36)y <- c(6.7, 6.3, 2, 2.5, 3.4, 2.7, 6.6, 5.3, 7.3, 2.5, 1.9, -0.3, -1, 4, 6.5, 2.5, 0.6, 5.5, 3.6, 1.8, 2.4, 3.2, 6.1, 5.6)   Using the varials x and y that you just created, fit a linear model using y as the dependent variable and x as the independent variable and provide the following:   What is the equation of the regression line?y^ =  +  x   How many degrees of freedom would need to be used when obtaining a ?p-value associated with the test statistic for the slope parameter?Degrees of Freedom =    What is the value of the coefficient of determination?R2 =    What is the value of the correlation coefficient?Correlation =    Is there a statistically significant relationship between x and y at the α=0.07 significance level? (answer “Yes” or “No” without quotes)YesNo

b. The amount that a spring stretches is directly proportional to the weight of the object attached to it. If a spring is stretched 10 cm by a weight of 8 kg, how much will it be stretched by a weight of 3 kg? as of: Wednesday, April 14, 2021 pag N3CS21 Practice Set 20

Your friend makes up a game to play over Zoom during the shelter in place, and asks if you would like to play.  The rules are: You win $8 if you roll a 6. You win $4 if you roll a 4 or 5 Otherwise, you have to pay $10. a. Complete the PDF Table. List the X values, where X is the profit, from smallest to largest. The first value is filled in for you.  Round to 4 decimal places where appropriate.  Probability Distribution Table X P(X) -10           b. Find the expected profit. $ (Round to the nearest cent)c. Interpret the expected value. You will win this much if you play a game. This is the most likely amount of money you will win. If you play many games, on average, you will likely win, or lose if negative, close to this amount.