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Ron has 900 meters of fence and wants to enclose a rectangular region that contain four congruent rectangular pens within it. Ron will use all 900 meters of fence to create one large rectangle and four congruent rectangular pens within the larger rectangle. What will be the largest dimensions of the rectangle so as to enclose the largest possible area?
a) Include appropriate labels and identify themb) Indicate the meaning of any variables in 'a', include domain restrictions if any.c) create a one-variable function, A, for the area of the entire region.d) apply knowledge to determine the dimensions of the region and the maximum area can enclose under these restrictions. Show all steps and justification
Each week the company has 1200 pounds of peat, 800 pounds of perlite, and 600 pounds of organic material available. How many 20-pound bags of each mix should be packaged in order to maximize weekly profit?
If f is continuous on [0,1] and if (integral from zero to one of (f(x) x^n)dx)) =0 for n in the Naturals, prove that f(x)=0 on [0,1]/ Hint: The integral of the product of f with any polynomial is zero. Use the Weierstrass approximation theorem to ..
A linear regression model has a slope of -2.5 and an intercept of 10. The sample coefficient of determination is 0.50. What is the value of the sample correlation coefficient?
A salesperson's weekly paycheck is 15% more than her coworker's paycheck. The two paychecks total $1475. Find the amount of each paycheck. (Round your answer to the nearest cent).
Find the first and third quartiles of the data set.
The recording devices record the time the sound reaches each one. How far directly north of site B should a second explosion be done so that the measured time difference recorded by the devices is the same as that for the first detonation?
Information from the American Institute of Insurance indicates the mean amount of life insurance per household in the United States is $110,000. This distribution follows the normal distribution with a standard deviation of $40,000.
A function f is given by the following table: Approximate the area between the x-axis and y=f (x) from x=0 to x=4 using Simpson's Rule.
Define f(x) = x if x is rational and f(x)=0 if x is irrational. Compute the integration 1top0bottom f dx and integration 1top0bottom f dx. is f integrable on [0,1]?
Characterize the set of all real numbers with the discrete metric as to whether it is compact, complete, or totally bounded. Use definitions only!
a sky diver jumping from a plane at a height of 5,000 feet. He will fall 16 feet in the first second. Thereafter, until the parachute opens, the distance fallen during each second will be 32 feet more than the distance fallen during the previous s..
Find the domain and range of these functions
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