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Probability (6.5-6.6)
Contour Graphs & Cross-Sectional Models (7.1-7.2)
Partial Derivatives (7.3)
Compensating for Change (7.4)
Extreme Points & Optimization (8.1-8.2)
100
Weights of men are approximately normally distributed with a mean of 190 pounds and a standard deviation of 40 pounds. Federal requirements require FBI Police Officers to weigh between 117 and 238 pounds. What proportion of men fall in this interval?
0.8509
100
The function (0.4357p) / (0.00055724t^2) gives the amount of garbage (in tons) produced in one day by an amusement park when the admission price is p dollars and the daily high temperature is t ℉. Find the amount of garbage produced on a day when the high temperature is 95 degrees Fahrenheit and the admission price is $50.
4.332 tons
100
Find the first partial derivatives of f(x,y) = x^y
fx = yx^(y-1) fy = (ln x) x^y
100
The company’s October profit when they produce p thousand pirate eye patches and k thousand skeleton key chains can be modeled as: T(p,k) = 1000 - .35p^2 + 175p - .35pk - .525k^2 + 140k dollars Find the slope of the tangent line to the T = 18,000 contour curve at the point (300, 126.769)
0.809 thousand key chains / thousand eye patches
100
Consider the function T(x,y) = x^2 + 2y^2 - 8x + 4y Find & classify the critical point
The critical point is at T (4, -1) = -18 and is a minimum
200
The life span of a compact fluorescent brand of light bulb has the probability density function: f(t) = 24/t^3 What is the probability that a light bulb will have a life span less than 4.5 years?
0.7407
200
https://docs.google.com/document/d/1pMZomWQILQyuQ1mvAbQNk7qV0Un39mas00S6HLY1W7E/edit #1
f(p,4) = .893p^2 - 1.304p + 7.811 pounds gives the per capita consumption of peaches by people living in households with $40,000 yearly income where p+$1.50 dollars per pound is the price of peaches 7.7 pounds
200
Find the partial derivatives for Ga, Gb, and Gc: G(a,b,c) = ((1.2a^2 * b)/c) - 2b^2 + abc - c(ln a)
Ga = 2.4ab/c - ln(b)2b^2 + bc - c/a Gb = (1.2a^2)/c - 2ab^(a-1) + ac Gc = -1.2a^2b/c^2 + ab - lna
200
Given the equation f(m,n) = 3m^2 + 2mn + 5n^2 when m=2 and n=1, approximate the change in n if the change in m is .2
-.2
200
Locate & classify the critical point: R(k,m) = 3k^2 - 2km - 20k + 3m^2 - 4m + 60
(4,2,16) is a relative min
300
Delta Airlines quotes a flight time of 125 minutes for its flights from Cincinnati to Tampa. Assume actual flight times are uniformly distributed between 121 minutes and 139 minutes. What is the mean flight time for a flight from Cincinnati to Tampa?
130 minutes
300
https://docs.google.com/document/d/1pMZomWQILQyuQ1mvAbQNk7qV0Un39mas00S6HLY1W7E/edit #4
12; 12
300
Find both partial derivatives for the following equation: H(m,p) = me^-3p - 3.5m^5 + 5.1mp + m^p
Hm = e^-3p - 17.5m^4 + 5.1p + pm^(p-1) Hp = -3me^-3p + 5.1m + ln(m)(m^p)
300
A function giving the cost per T-shirt (the average cost) when c colors are used and n T-shirts are ordered is : A(c,n) = (-.02c^2 + .35c + .99)(.99897^n) + .46c + 2.57 dollars When 250 T-shirts are printed with 6 colors, how quickly is the average cost changing when more T-shirts are printed?
-$.002 per shirt
300
Find & classify the critical point: h(w,z) = .6w^2 + 1.3z^3 - 4.7wz
(0,0,0) is a saddle point (18.487, 4.720, -68.353) is a relative min
400
A medical research team has determined that for 28-year old females, the length of pregnancy from conception to birth varies according to a normal distribution with a mean of 262 days and a standard deviation of 18 days. According to the Empirical Rule, what percentage of 28-year old females will have a pregnancy that lasts more than 298 days?
.025 or 2.5%
400
https://docs.google.com/document/d/1mV-EH0qRDLlzJUZb4nGdBkP2i486jLeJw9hW-2u-guc/edit #1
As y decreases
400
Find the partials of the following equation: m(t,s) = s ln t + 3.75s + 14.96
mt = s/t ms = lnt + 3.75
400
For the following function, write the formula for dx/dy: f(x,y) = (15x^2)(y^3)
-3x/2y
400
A chain of candy stores models its profits from the sale of suckers & peppermint sticks as P(x,y) = -.002x^2 + 20x + 12.8y - .05y^2 thousand dollars where x thousand pounds of suckers are sold and y thousand pounds of peppermint sticks are sold Calculate the point of maximized profit:
(5000 pounds, 128 thousand pounds, 50,819.2 thousand dollars)
500
A pdf is normally distributed and has a mean of 5.3 and a standard deviation of 8.372 Estimate P(-11.444 < x <13.672) using the Empirical Rule and on your calculator
.815 or 81.5%
500
https://docs.google.com/document/d/1mV-EH0qRDLlzJUZb4nGdBkP2i486jLeJw9hW-2u-guc/edit #2
g(68,t) = -.000090t^3 + .003t^2 - .013t + 5.72 kg/day gives the average daily weight gain/loss of a pig weighing 68 kg when air temperature is t degrees Celsius
500
Find the first and second partials given the following equation: F(x,y) = 5x^3 - (2x^2)(y^5) + 4xy - 7y^3
Fx = 15x^2 - 4xy^5 + 4y Fy = (-10x^2)(y^4) + 4x - 21y^2 Fxx=30x-4y^5 Fxy = -20xy^4 + 4 Fyy = (-40x^2)(y^3) - 42y Fyx = -20xy^4 + 4
500
Find the change in s when the change in h= -.5 f(h,s) = .00091s[.103(2.5^h)+1] when h=3.5 and s=1148
377.57
500
Given the function: T(p,k) = 1000 - .35p^2 + 175p - .35pk - .525k^2 +140k Find the first partial derivatives & set up the system of equations needed to find the critical point
Tp = -.7p + 175 - .35k Tk = -.35p - 1.05k + 140 -.7p + 175 - .35k = 0 .35p - 1.05k + 140 = 0