a) Find P(at least 7)= b)Find P(at most 5)= ENTER YOUR ANSWER TO 2 DECIMAL PLACES
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a) Find P(at least 7)=
b)Find P(at most 5)=
ENTER YOUR ANSWER TO 2 DECIMAL PLACES
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- Decay of Litter Litter such as leaves falls to the forest floor, where the action of insects and bacteria initiates the decay process. Let A be the amount of litter present, in grams per square meter, as a function of time t in years. If the litter falls at a constant rate of L grams per square meter per year, and if it decays at a constant proportional rate of k per year, then the limiting value of A is R=L/k. For this exercise and the next, we suppose that at time t=0, the forest floor is clear of litter. a. If D is the difference between the limiting value and A, so that D=RA, then D is an exponential function of time. Find the initial value of D in terms of R. b. The yearly decay factor for D is ek. Find a formula for D in term of R and k. Reminder:(ab)c=abc. c. Explain why A=RRekt.A Troublesome Snowball One winter afternoon, unbeknownst to his mom, a child bring a snowball into the house, lays it on the floor, and then goes to watch T.V. Let W=W(t) be the volume of dirty water that has soaked into the carpet t minutes after the snowball was deposited on the floor. Explain in practical terms what the limiting value of W represents, and tell what has happened physically when this limiting value is reached.A prominent university conducted a survey on the effect of part-time work on student grade point average (GPA). Let x be the hours worked per week and y the GPA for the year. A summary of the results is below. What can the university conclude with α = 0.05? n=31 Σ y= 56 , Σ x=515 Σ y^2= 128 , Σ x^2= 11022 Σ yx= 827 , Σ (y- ŷ)² = 23 A) Compute the quantities below. b̂0= & b̂= What GPA is predicted when a students works 18 hours a week? B) Obtain/compute the appropriate values for H1: β > 0. critical value = test statistic= C) Compute the corresponding effect size(s) and indicate magnitude(s).If not appropriate, input and/or select "na" below.
- Q9: Assume that a researcher wants to estimate the proportion of “A” grade scorers in STAT101 course for the population of SEU students in 2020. Assume also that the proportion of “A” grade scorers in 2020 is not known. How many SEU students must be surveyed from STAT101 course in order to be 90% confident and the margin of error should not exceed two percentage points? (Given zα/2 = 1.64). 1- 1821 2- 1781 3- 1618 4- 1681An investor has his savings invested in various investments. The amount at the end of each month, in the first semester, is shown in the table. a. Assuming that the rate of change of the amount can be represented by: y ′ (x) = (0.06y (x)) / x, obtain an approximation for the amount in the month of August, using the Improved Euler method, using h = 1 and initial condition given by the data for the month of June.b. What is the relative percentage error knowing that the particular solution of the PVI is y (x) = e ^ (0.06 lnx + 4.46).A tank contains 200 liters of fluid in which 30 grams of saltis dissolved. Brine containing 1 gram of salt per liter is thenpumped into the tank at a rate of 4 L/min; the well-mixedsolution is pumped out at the same rate. Find the number A(t)of grams of salt in the tank at time t.Solve with assuming that pure water is pumped intothe tank.
- A.) An average young male in the United States gains weight at the rate of 18(x − 10)−1/2 pounds per year, where x is his age (11 ≤ x ≤ 20). † Find the total weight gain from age 14 to 19. B.) Runners and other athletes know that their ability to absorb water when exercising varies over time as their electrolyte levels change. Under certain circumstances, the absorption rate of water through the gastrointestinal tract will be f(t) = 2te−t/2 liters per hour, where t is the number of hours of exercise.† Find the number of liters of water absorbed during the first 7 hours of exercise. (Round your answer to one decimal place.)Overtaking City A has a current population of 500,000 people and grows at a rate of 3%/yr. City B has a current population of 300,000 and grows at a rate of 5%/yr.a. When will the cities have the same population?b. Suppose City C has a current population of y0 < 500,000 and a growth rate of p > 3%/yr. What is the relationship between y0 and p such that Cities A and C have the same population in 10 years?The population, P, of the city of Hazelton has grown according to the mathematical model P = 65,000(1.075)*, where t is the number of years since 2005. a) At what percentage is the population growing? b) If this trend continues, during which year will the population reach approx. 100,000?
- Certain pieces of antique furniture increased very rapidly in price in the 1970s and 1980s. For example, the value of a particular rocking chair is well approximated by V=70(1.2)^t, where VV is in dollars and tt is the number of years since 1975. At time t, what is the rate at which the price is increasing? rate =Suppose you own a restaurant and have a cook whose ability and attitude you are suspicious of. One ofthe dishes on the menu is duck cassoulet, which uses duck legs that have been slow fried over a couple of hoursin oil that does not exceed a temperature of 175 degrees. This is a time consuming and monotonous process,but one that results in excellent meat that you sell for a large mark-up. You suspect your cook is lazy anddoesnít properly monitor and maintain the oil temperature. You take a random sample of 12 duck legs andtake them to a forensics lab where you are able to discover the maximum temperature the meat has reached.Within your sample the mean maximum temperature of the duck legs is 182 degrees with a standard deviationof 5 degrees. Meat cooked precisely to 175 degrees is what your cook is supposed to do. Test the claim thatyour employee is capable (meaning he doesnít over-fry the meat) at the 90% conÖdence level.The population P (in millions) of Italy from 2003 through 2015 can be approximated by the model P = 57.59e0.0051t, where t represents the year, with t = 3 corresponding to 2003. (a) According to the model, is the population of Italy increasing or decreasing? Explain. Because the coefficient of the model is ---Select--- positive negative , the population is ---Select--- increasing decreasing . (c) Use the model to predict the populations of the country in 2021 and 2026. (Round your answers to three decimal places.) 2021 million 2026 million