Suppose everyone in Los Angeles is either a UCLA fan (C) or a USC fan (S). USC fans convert to supporting UCLA at a per-capita rate of 5%. But every time a UCLA fan encounters a USC fan, there is a 1% chance that they become a USC fan. Finally, USC fans get fed up and move to Orange County at a rate proportional to the number of UCLA fans, with a proportionality constant of 0.08. Set up a system of differential equations to describe this situation.
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Suppose everyone in Los Angeles is either a UCLA fan (C) or a USC fan (S). USC fans convert to supporting UCLA at a per-capita rate of 5%. But every time a UCLA fan encounters a USC fan, there is a 1% chance that they become a USC fan. Finally, USC fans get fed up and move to Orange County at a rate proportional to the number of UCLA fans, with a proportionality constant of 0.08. Set up a system of differential equations to describe this situation.
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- Suppose that every year, only 10% of the fish in a lake have surviving offspring. If there were 100 fish in the lake last year, there would now be 110 fish. If there were 1000 fish in the lake last year, there would now be 1100 fish. Absent any inhibiting factors, populations of people and animals tend to grow by a percent of the existing population each year. Suppose our lake began with 1000 fish, and 10% of the fish have surviving offspring each year. Since we start with 1000 fish, Po 1000. How do we calculate P₁? The new population will be the old population, plus an additional 10%. Symbolically: = P1 = Po + 0.10Po Notice this could be condensed to a shorter form by factoring: P₁= Po+0.10Po = 1Po + 0.10Po= (1+0.10)Po= 1.10Po While 10% is the growth rate, 1.10 is the growth multiplier. Notice that 1.10 can be thought of as "the original 100% plus an additional 10%" For our fish population, P₁ = 1.10(1000) = 1100 We could then calculate the population in later years. Fill in the…You're a quality engineer at Norman's fouth largest cracker factory. where there are two production lines (A, which produces 20% of cracker boxes, and B which produces the rest). If a line produces more than one defective box in an eight -hour day, a maintenance check on the line is performed. Line A produces an average of 0.061 box defects PER Hour. Given that you're only looking at a line A, what is the probability that you will need a request a maitenance check.Opinions are split about a coffee company's pumpkin-flavored coffee (PFC). Yet every year over the last five years the consumption of pumpkin-flavored goods has increased. If we look at the numbers, it also becomes clear why a leading coffee company keeps offering the PFC earlier and earlier every year. According to a magazine, the amount spent by PFC buyers at the coffee company is about 17% higher than non-PFC buyers. The accompanying table shows a random sample of eight consumers, the amount they spend per week, and the number of PFCs purchased per week. PFC Spending 2 13.88 7 39.11 4 19.79 1 9.84 3 15.43 1 21.52 5 37.39 3 13.85 The slope is b1=4.465 The y-intercept is b0=6.840 Calculate the SST. SST= (Round to three decimal places as needed.)
- A computer manufacturer buys 30% of its chips from supplier A and the rest from supplier B. Two percent of the chips from supplier A are defective, as are 4% of the chips from supplier B. Approximately what percentage of the defective chips are from supplier B?Opinions are split about a coffee company's pumpkin-flavored coffee (PFC). Yet every year over the last five years the consumption of pumpkin-flavored goods has increased. If we look at the numbers, it also becomes clear why a leading coffee company keeps offering the PFC earlier and earlier every year. According to a magazine, the amount spent by PFC buyers at the coffee company is about 17% higher than non-PFC buyers. The accompanying table shows a random sample of eight consumers, the amount they spend per week, and the number of PFCs purchased per week. PFC Spending 2 13.88 7 39.11 4 19.79 1 9.84 3 15.43 1 21.52 5 37.39 3 13.85 The slope is b1=4.465 The y-intercept is b0=6.840 Because the slope is positive, it can be concluded that one extra PFC purchase per week will increase the average amount of spending per week by 4.46 dollars. Predict…Opinions are split about a coffee company's pumpkin-flavored coffee (PFC). Yet every year over the last five years the consumption of pumpkin-flavored goods has increased. If we look at the numbers, it also becomes clear why a leading coffee company keeps offering the PFC earlier and earlier every year. According to a magazine, the amount spent by PFC buyers at the coffee company is about 17% higher than non-PFC buyers. The accompanying table shows a random sample of eight consumers, the amount they spend per week, y, and the number of PFCs purchased, x, per week. PFC Spending 1 13.17 8 38.65 3 19.49 2 9.56 4 15.85 1 21.82 5 37.53 3 13.69 α=0.05 t= 3.07 p-value= 0.22 Construct a 95% confidence interval for the population slope. UCL = LCL = (Round to two decimal places as needed.)
- Opinions are split about a coffee company's pumpkin-flavored coffee (PFC). Yet every year over the last five years the consumption of pumpkin-flavored goods has increased. If we look at the numbers, it also becomes clear why a leading coffee company keeps offering the PFC earlier and earlier every year. According to a magazine, the amount spent by PFC buyers at the coffee company is about 17% higher than non-PFC buyers. The accompanying table shows a random sample of eight consumers, the amount they spend per week, and the number of PFCs purchased per week. PFC Spending 2 13.88 7 39.11 4 19.79 1 9.84 3 15.43 1 21.52 5 37.39 3 13.85 The slope is b1=4.465 The y-intercept is b0=6.840 SST= 854.740 Partition the SST into the SSR and the SSE. SSE= SSR= (Round to three decimal places as needed.) Opinions are split about a coffee company's pumpkin-flavored coffee (PFC). Yet every year over the last five years the consumption of pumpkin-flavored goods has increased. If we look at the numbers, it also becomes clear why a leading coffee company keeps offering the PFC earlier and earlier every year. According to a magazine, the amount spent by PFC buyers at the coffee company is about 17% higher than non-PFC buyers. The accompanying table shows a random sample of eight consumers, the amount they spend per week, and the number of PFCs purchased per week. PFC Spending 2 13.88 7 39.11 4 19.79 1 9.84 3 15.43 1 21.52 5 37.39 3 13.85 Calculate the slope and y-intercept for the regression formula. The slope is b1=4.465 The y-intercept is b0=6.840 Provide an interpretation for the value of the slope. Because the slope is positive, it can be…Opinions are split about a coffee company's pumpkin-flavored coffee (PFC). Yet every year over the last five years the consumption of pumpkin-flavored goods has increased. If we look at the numbers, it also becomes clear why a leading coffee company keeps offering the PFC earlier and earlier every year. According to a magazine, the amount spent by PFC buyers at the coffee company is about 17% higher than non-PFC buyers. The accompanying table shows a random sample of eight consumers, the amount they spend per week, and the number of PFCs purchased per week. PFC Spending 2 13.88 7 39.11 4 19.79 1 9.84 3 15.43 1 21.52 5 37.39 3 13.85 Calculate the slope and y-intercept for the regression formula. The slope is b1=(Round to three decimal places as needed.)
- Opinions are split about a coffee company's pumpkin-flavored coffee (PFC). Yet every year over the last five years the consumption of pumpkin-flavored goods has increased. If we look at the numbers, it also becomes clear why a leading coffee company keeps offering the PFC earlier and earlier every year. According to a magazine, the amount spent by PFC buyers at the coffee company is about 17% higher than non-PFC buyers. The accompanying table shows a random sample of eight consumers, the amount they spend per week, and the number of PFCs purchased per week. PFC Spending 2 13.88 7 39.11 4 19.79 1 9.84 3 15.43 1 21.52 5 37.39 3 13.85 The slope is b1=4.465 The y-intercept is b0=(Round to three decimal places as needed.)Opinions are split about a coffee company's pumpkin-flavored coffee (PFC). Yet every year over the last five years the consumption of pumpkin-flavored goods has increased. If we look at the numbers, it also becomes clear why a leading coffee company keeps offering the PFC earlier and earlier every year. According to a magazine, the amount spent by PFC buyers at the coffee company is about 17% higher than non-PFC buyers. The accompanying table shows a random sample of eight consumers, the amount they spend per week, y, and the number of PFCs purchased, x, per week. PFC Spending 1 13.17 8 38.65 3 19.49 2 9.56 4 15.85 1 21.82 5 37.53 3 13.69 t= 3.07 Identify the p-value p-value= (Round to three decimal places as needed.)Opinions are split about a coffee company's pumpkin-flavored coffee (PFC). Yet every year over the last five years the consumption of pumpkin-flavored goods has increased. If we look at the numbers, it also becomes clear why a leading coffee company keeps offering the PFC earlier and earlier every year. According to a magazine, the amount spent by PFC buyers at the coffee company is about 17% higher than non-PFC buyers. The accompanying table shows a random sample of eight consumers, the amount they spend per week, y, and the number of PFCs purchased, x, per week. PFC Spending 1 13.17 8 38.65 3 19.49 2 9.56 4 15.85 1 21.82 5 37.53 3 13.69 α=0.05 t= 3.07 p-value= 0.022 Construct a 95% confidence interval for the population slope. UCL = 6.69 LCL = 0.75 What conclusions about PFC purchases and spending can be drawn from these…