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A tree farmer estimates that if 80 apple trees are planted, the average yield will be 400 apples per tree. But because the size of the farm, for each additional tree planted the yield will decrease by 32 apples per tree. How many trees should be planted to maximize the total yield of apples? What is the maximum yield?
A car was purchased for $32,800. The value of the car decreases by $4,300 per year for each of the first seven years. Write a function that describes the value of the car, f(x), after x years where 0 ≤ x ≤ 7.
Consider a bivariate normal population with u1=0,u2=2,σ11=2,σ22=1,and p12=.5, write out the bivariate normal density.
a shipment of 150 television sets contains 3 defective units. Determine how many ways a vending company can buy three of these units and receive (a) no defective units, (b) all defective units and, (c) at least one good unit.
Let n be a natural number, and let f: R-->R be the function f(x) :=x^n. Show that f is differentiable on R and f '(x)=nx^n-1 for all x belonging to R
How many solution sets do systems of linear inequalities have? Must solutions to systems of linear inequalities satisfy both inequalities? In what case might they not? Use an example for discussion.
You select a random sample of n=14 families in your neighborhood and find the following family size (number of people in the family).
Determine if the given function can be extended to a continuous function at x=0. If so, approximate the extended function's value at x=0 (rounded to four decimal places if necessary).
Probability. Which pair has equally likely outcomes? List the letters of the two choices below which have equal probabilities of success, separated by a comma
Find the slope of the line that passes through the points (3, -5) and (-4, -6). Find the equation in slope-intercept form, of the line that passes through the points (3, 6) and (-7, -3); write equation in slope-intercept form.
Probability: Random Dart. A dartboard has 3 areas: the main board has a radius of 9 inches; there is a circle with a radius of 5 inches
Using life insurance tables, a retired man determines that the probability of living 5 more years is 0.91. He decides to take out a life insurance policy that will pay $31,000 in the event that he dies during the next 5 years. How much should he b..
A class of students opens several bags, counts the various colors of jelly beans, and calculates the proportion that are pink in each bag. Is it appropriate to use a Normal model to describe the distribution of the proportion of pink jelly beans?
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