Can I receive worked-out solutions for all the questions on this worksheet?

TRIPLE-Fs Bigfoot and Wolman are both proud members of the "Forest Fire Flyers", a determined group of pilots who use a special aircraft to drop water on seemingly uncontrollable forest fires in the Arrowhead Arbor Area (AAA). The 2 friends are quite competitive, but after many years it has become clear that Bigfoot is the more skilled flyer. A Bigfoot water-drop tends to cover 50% of a unit of forest fire per water- drop, while Wolfman has a 40% rate for a typical water-drop. Py Romania is the CFO (chief fire officer) of the Triple-Fs and Py often employs techniques, contests, and games to keep the pilots engaged and alert for their long shifts when fires do occur in the AAA. Py established a new contest where the 2 pilot-friends will each run a water-drop sortie on the same hot-spot in the forest. Bigfoot usually wins the contests since the rate of cover for Bigfoot is larger than the rate of cover for Wolfman. The random nature of the water-drops for the 2 friends will tend to overlap somewhat since water-drops tend to be independent of one another. Py "fixes" the 2 problems by awarding the water-drop "overlap" parts of the fire to Wolfman as a way to level the playing field. An abstraction of the situation is shown below where Bigfoot's drop is represented in blue, while Wolfman's drop is represented in white. The remaining red color is the proportion of fire that was untouched by either of the water-drops from the first sortie. overlap = 0.2 The mathematics behind the proportion for "overlap" is the fact that the water-drops are independent and thus: P(B and W) = P(B) . P(W), so the overlap area = 0.5 . 0.4 = 0.2. You can use the dimensions of the rectangles to also calculate the overlap. Since Bigfoot's rate of fire coverage is 50% the dimensions of the blue + overlap is I by 0.5. Wolfman's rectangle (white + overlap) is 0.4 by 1. The red rectangle represents the proportion of fire in this hot spot that was not touched by any water during the first sortie. You can calculate the area of the total water-drop coverage by using logic or you can also use this formula for the union of 2 sets: P(B or W) = P(B) + P(W) - P(B and W) = 0.5 +0.4 - 0.2 =0.7 Therefore, the area of the untouched red fire that remains is 30% or 0.3. After sortie #1 the status of the contest is as follows: Wolfman has been awarded 0.4 points and Bigfoot has been awarded 0.3 points. Now after sortie #2, Wolfman will be awarded 0.4 . 0.3 = 0.12 points and the remaining fire would be only 9% (0.09) of the original fire. The red rectangle below has an area of 0.09. Of course, the large rectangle below has dimensions 0.6 by 0.5. overlap After sortie #3, Wolfman will be awarded 0.4 . 0.09 points. (you can draw your own diagram for sortie #3). The 2 friends are making progress, but after 3 sorties there will be 2.7% (0.027) of the original fire remaining to be extinguished. Py will make the 2 friends run many more sorties. For the contest, Wolfman will be awarded: 0.4 + 0.12 + 0.036 + ... points. This sum happens to be an infinite geometric series. The formula for the infinite geometric series is: S.. = . If the contest had an infinite number of sorties, Wolfman would score exactly - points. 1. After an infinite number of sorties, Wolfman would win the contest with a total of points awarded. Calculate Bigfoot's awarded points after an infinite number of sorties. What if the original coverage rates were incorrect and instead of a 50% coverage rate, Bigfoot's rate was actually 40% and Wolfman's new coverage rate was actually 25% and not 40%. Recalculate Wolfman's score for the contest with the new rates of coverage. What if the original coverage rates were incorrect and instead of a 50% coverage rate, Bigfoot's rate was actually 40% and Wolfman's new coverage rate was actually 25% and not 40%. Recalculate Bigfoot's score for the contest with the new rates of coverage Let X = Wolfman's coverage rate and let Y = Bigfoot's coverage rate. Create a formula hat will calculate the Wolfman's score for the contest. Let X = Wolfman's coverage rate and let Y = Bigfoot's coverage rate. Create a formula hat will calculate the Bigfoot's score for the contest. 6. The graphs below show the relationship between Wolfman's coverage rate vs. Bigfoot's coverage rate when the contest will end in a tie. Use the graph to estimate Wolfman's coverage rate when Bigfoot's coverage rate is 0.3, that is, Find X if Y = 0.3 and the contest ends in a tie. -0:5 0!5 7. Use equations to find the exact fractional answer to #6