A gas station sells two grades of gasoline: regular and super. These are priced at $2.00 and $3.00 per gallon, respectively. Let X₁ and X₂ denote the amounts of these grades purchased (gallons) on a particular day. Suppose X₁ and X₂ are independent Normal random variables with E(X₁) = 1000, sd(X₁) = 90, E(X₂) = 800, and sd(X₂) = 45. The revenue from sales is Y = 2X₁ + 3X₂. (a) Find the mean and standard deviation of Y, i. e., E(Y) and sd(Y). (b) Find the probability that the revenue Y does not exceed 4500. Hint: Y is Normally distributed. (c) Find the probability that the gas station sells regular gasoline more, i. e., pr (X₁ > X₂). Attach the R codes or write out the formula(s) you used for full credit.

Which expression is equal to (21)(7)(3x) using the associative property? (21 · 7 · 3)x (7)(21)(3x) 32(7 + 3x) (3x)(7)(21)

An annual marathon covers a route that has a distance of approximately 26 miles. winning times for this marathon are all over 2 hours. the following data are the minutes over 2 hours for the winning male runners over two periods of 20 years each. earlier period 14 12 15 22 13 10 19 13 9 14 20 18 16 20 23 12 18 17 6 13 recent period 7 11 7 14 8 9 11 14 8 7 9 8 7 9 9 9 9 8 10 8 (a) make a stem-and-leaf display for the minutes over 2 hours of the winning times for the earlier period. use two lines per stem. (use the tens digit as the stem and the ones digit as the leaf. enter none in any unused answer blanks. for more details, view how to split a stem.) minutes beyond 2 hours earlier period 0 1 2 (b) make a stem-and-leaf display for the minutes over 2 hours of the winning times for the recent period. use two lines per stem. (use the tens digit as the stem and the ones digit as the leaf. enter none in any unused answer blanks.) minutes beyond 2 hours recent period (c) compare the two distributions. how many times under 15 minutes are in each distribution

The curved part of the figure is the semicircle what is the best approximation for the area of this figure