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Mike Marquez purchased a lawn tractor for $9000.He made a down payment of $1000, and financed the rest at 7% in 24 months. He paid off the loan at the end of the fifteenth months. Find the amount of his refund using the rule of 78s?
Let x be a continuous random variable that follows a normal distribution with a mean of 185 and a standard deviation of 18. Find the value of x so that the area under the normal curve between μ and x is approximately 0.4812 and the value of x is greater than μ.
Find the value of x so that the area under the normal curve between μ and x is approximately 0.4800 and the value of x is greater than μ.
Find the value of x so that the area under the normal curve between µ and x is 0.4525 and the value of x is less than µ.
2. a) Find the derivatives of the following functions with respect to x.
X^3+Y^3=3
Y= (sin x) ^tan x
A metal bar with an initial temperature, 𝑇0, in the interval of 30°C ≤ 𝑇0 ≤ 35°C is dropped into a container of boiling water (100°C). The temperature of the metal bar, 𝑇 at any time, 𝑡 satisfies the following Newton’s Law of Cooling model 𝑑𝑇 𝑑𝑡 = −𝑘(𝑇 − 𝑇𝑚) where 𝑇𝑚 is the ambient temperature and 𝑘 is the constant. After 5 seconds, the temperature of the bar, 𝑇1 is in the interval of 40°C ≤ 𝑇1 ≤ 50°C. a. Find the equation that models the temperature of the metal bar, 𝑇 at any time, 𝑡 (choose a value of 𝑇0 and 𝑇1 from the given intervals, respectively). By using an appropriate analytical method, solve the derived model and explain the reason for the selection of the method. b. Compute the temperature of the metal bar after 100 seconds by using the derived model in Part 1(a) with THREE (3) different numerical methods with step size, ℎ = 10 seconds. Select the best numerical method to compute the temperature of the metal bar and justify your answer
3. Given a frustum of a right circular cone with a slant height of 9ft ., and the radii of bases are 5ft and 7ft. Find:
a. The lateral area
b. Altitude of the frustum
c. The altitude of the entire cone if the cone removed was replaced
Consider estimating the mean of a variable drawn from a population with mean u and standard deviation o, using the following formulae: Ĥ1 = x1. X + x2 2 X1 + 2x2 X +x2 3 is = %3D Assume that in all cases the individual estimates x, are independent of each other. Determine the bias, variance, and mean square error for each of the estimators. Which ones are biased?
Evaluate
lim 3nΣr=1 n^2/(4n+r)^3
n→∞
The drawing below shows a square with side a. A straight line intersects the square and encloses
an area A. The heights x and y on the left and right side (in a distance d from the square) of
the intersecting line can be varied. Assuming that x y and x; y a, nd an expression for
the enclosed area A(x; y) with respect to x and y.
